Applicability of weight-shift microlight aircraft for measuring the turbulent exchange above complex terrain
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APPLICABILITY OF WEIGHT-SHIFT MICROLIGHT AIRCRAFT FOR MEASURING THE TURBULENT EXCHANGE ABOVE COMPLEX TERRAIN A dissertation submitted to the FACULTY OF BIOLOGY, CHEMISTRY AND GEOSCIENCES OF THE UNIVERSITY OF BAYREUTH, GERMANY to attain the academic degree of DR. RER. NAT. presented by STEFAN METZGER Diplom Geoökologe born September 13, 1980 in Schweinfurt, Bavaria, Germany Bayreuth, 2013-04-15
I APPLICABILITY OF WEIGHT-SHIFT MICROLIGHT AIRCRAFT FOR MEASURING THE TURBULENT EXCHANGE ABOVE COMPLEX TERRAIN Supervisors Prof. Dr. Thomas Foken Prof. Dr. Klaus Butterbach-Bahl
II Die vorliegende Arbeit wurde in der Zeit von September 2007 bis Oktober 2012 an der Universität Bayreuth am Lehrstuhl für Hydrologie, Abteilung Mikrometeorologie, unter Betreuung von Prof. Dr. Thomas Foken und Prof. Dr. Klaus Butterbach-Bahl angefertigt. Vollständiger Abdruck der von der Fakultät für Biologie, Chemie und Geowissenschaften der Universität Bayreuth genehmigten Dissertation zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.). Promotionsgesuch eingereicht am: 2012-10-08 Wissenschaftliches Kolloquium am: 2013-04-15 Prüfungsausschuss: Prof. Dr. Thomas Foken (Erstgutachter) Prof. Dr. Jens Bange (Zweitgutachter) Prof. Dr. Bernd Huwe (Vorsitzender) Prof. Dr. Michael Hauhs Prof. Dr. Andreas Held Dekan: Prof. Dr. Beate Lohnert
III The present dissertation was conducted from September 2007 to October 2012, as external doctoral candidate of the University of Bayreuth, Department of Micrometeorology, Bayreuth, Germany. The research aircraft and the majority of the infrastructure were provided by the Karlsruhe Institute of Technology, Institute of Meteorology and Climate Research, Atmospheric Environmental Research, Garmisch-Partenkirchen, Germany. The bulk of preparation, implementation and analysis of the experiments were performed at the Chinese Academy of Sciences, Institute of Atmospheric Physics, State Key Laboratory of Atmospheric Boundary Layer Physics and Atmospheric Chemistry, Beijing, China. The doctoral thesis was completed while employed at the National Ecological Observatory Network, Fundamental Instrument Unit, Boulder, CO, U.S.A. This doctoral thesis was performed under stipend funding by the German Academic Exchange Service, Helmholtz Association of German Research Centers, China Scholarship Council and the European Union under the Science and Technology Fellowship China. The flight in Inner Mongolia was funded by the German Research Foundation, research group 536 “Matter fluxes in grasslands of Inner Mongolia as influenced by stocking rate”, and the National Natural Science Foundation of China (grant number 41021004). The publications were funded by the German Research Foundation and Open Access Publishing Fund of the Karlsruhe Institute of Technology / Helmholtz Association. This material is based upon work supported by the National Science Foundation under the grant DBI0752017. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.
IV Contents CONTENTS ......................................................................................................................................... IV ACKNOWLEDGEMENTS ................................................................................................................... V LIST OF MANUSCRIPTS .................................................................................................................. VI SUMMARY ....................................................................................................................................... VIII ZUSAMMENFASSUNG ...................................................................................................................... X 1INTRODUCTION ......................................................................................................................... 1 1.1The eddy-covariance method ................................................................................................. 1 1.2Effects of complex terrain ...................................................................................................... 2 1.3Motivation .............................................................................................................................. 3 1.4Objectives of this thesis ......................................................................................................... 4 2EXPERIMENTS AND DATA ...................................................................................................... 6 2.1The weight-shift microlight aircraft ....................................................................................... 6 2.2Bavaria, Germany .................................................................................................................. 8 2.3Brandenburg, Germany .......................................................................................................... 8 2.4Inner Mongolia, P.R. China ................................................................................................... 9 3RESULTS .................................................................................................................................... 11 3.1Wind measurement .............................................................................................................. 11 3.2Turbulent flux measurement ................................................................................................ 16 3.3Spatial resolution and extrapolation of turbulent fluxes ...................................................... 22 4CONCLUSIONS .......................................................................................................................... 29 NOTATION ......................................................................................................................................... 32 REFERENCES .................................................................................................................................... 35 LIST OF APPENDICES ...................................................................................................................... 43 APPENDIX A: INDIVIDUAL CONTRIBUTIONS TO THE JOINT PUBLICATIONS .................. 44 APPENDIX B: METZGER ET AL. (2011) ........................................................................................ 48 APPENDIX C: SUPPLEMENT TO METZGER ET AL. (2011) ....................................................... 73 APPENDIX D: METZGER ET AL. (2012) ........................................................................................ 87 APPENDIX E: METZGER ET AL. (2013) ....................................................................................... 106 ERKLÄRUNG ................................................................................................................................... 131
V Acknowledgements In 2007 I set out on a journey to combine my curiosity about the orient, family, and enthusiasm for atmospheric science… Now, about five years later I feel equally at home in Germany, China and the U.S., we are speaking Chinese at home, and I might soon be a doctor… I want to use this opportunity to thank the wonderful persons who have made possible this development. From the very start Benjamin Wolf pointed me to Garmisch-Partenkirchen, and you always had a sympathetic ear – thank you! I am much obliged to my supervisors Thomas Foken and Klaus Butterbach-Bahl, for your trust in my abilities, your scientific and personal guidance, and the flexibility you provided me on this path. Special recognition goes to Wolfgang Junkermann, for your unfailing patience when introducing the aircraft to me, and your outstanding performance of the hairrising flight patterns. My gratefulness to Xunhua Zheng for hosting me and providing indispensable infrastructure and negotiation skills. Further I am thankful to my co-authors, Frank Beyrich, Matthias Mauder, Frank Neidl, Klaus Schäfer, Hans-Peter Schmid, Baltasar Trancon y Widemann, and Sebastian Wieneke, for your pivotal stimuli and your contributions to the manuscripts. My appreciation to many other individuals who found innumerable ways to inspire and support this journey, including; Wolfgang Babel, Jens Bange, Frauke Barthold, Tobias Biermann, Benjamin Blank, Timothy Brown, Josef-Michael Burger, Yimin Cao, Dao Charuchittipan, Lifang Chen, Yong Chen, Michael Dannemann, Jia Deng, Francesco di Maio, Sofia Dos Santos Mendes, Elias, Leyla and Roland Felgenträger, Edwin Haas, Shenghui Han, Jordan Hixson, Natascha Kljun, Alexandra Lehmann, Jens-Peter Leps, Chunyan Liu, Ronghua Liu, Henry Loescher, Tiina Markkanen, Alan Page, Raül Ramos, Matthias Reiche, Jakob Reitberger, Charlotte Roehm, David Schaffrath, HansEckhart Scheel, Andreas Schmidtler, Clemens Smolders, Christian Sperber, Rainer Steinbrecher, Jeffrey Taylor, Aline van den Kroonenberg, Ulrich Weisensee, Georg Wichmann, Hongkai Zhang, Yuandi Zhu, Rose Zuurbier. My heartfelt thanks to my wife Liang Sun and to our families. Your steady support and unswerving faith were the building blocks on which I could develop my potential.
VI List of manuscripts The dissertation is presented in cumulative form. It consists of three individual manuscripts. Two manuscripts have been published in the peer-reviewed journal Atmospheric Measurement Techniques, of which the first one also includes a 14 page supplement. A third manuscript has been published in the peer-reviewed journal Biogeosciences. Published manuscripts Metzger, S., Junkermann, W., Butterbach-Bahl, K., Schmid, H. P., and Foken, T.: Corrigendum to "Measuring the 3-D wind vector with a weight-shift microlight aircraft" published in Atmos. Meas. Tech., 4, 1421–1444, 2011, Atmos. Meas. Tech., 4, 1515-1539, doi:10.5194/amt-4-1515-2011, 2011. Includes one supplement. Publisher’s Note: Due to mistakes on the publisher’s side it was necessary to revise the original article Atmos. Meas. Tech., 4, 1421–1444, 2011 in this Corrigendum. Please use this Corrigendum as the main document. Metzger, S., Junkermann, W., Mauder, M., Beyrich, F., Butterbach-Bahl, K., Schmid, H. P., and Foken, T.: Eddy-covariance flux measurements with a weight-shift microlight aircraft, Atmos. Meas. Tech., 5, 1699-1717, doi:10.5194/amt-5-1699-2012, 2012. Metzger, S., Junkermann, W., Mauder, M., Butterbach-Bahl, K., Trancón y Widemann, B., Neidl, F., Schäfer, K., Wieneke, S., Zheng, X. H., Schmid, H. P., and Foken, T.: Spatially explicit regionalization of airborne flux measurements using environmental response functions, Biogeosciences, 10, 2193-2217, doi:10.5194/bg-10-2193-2013, 2013. Publications not included in this thesis Peer-reviewed Sun, F., Ma, Y., Li, M., Ma, W., Tian, H., and Metzger, S.: Boundary layer effects above a Himalayan valley near Mount Everest, Geophys. Res. Lett., 34, L08808, doi:10.1029/2007gl029484, 2007. Eigenmann, R., Metzger, S., and Foken, T.: Generation of free convection due to changes of the local circulation system, Atmos. Chem. Phys., 9, 8587-8600, doi:10.5194/acp-9-8587-2009, 2009.
VII Not peer-reviewed Metzger, S., Ma, Y. M., Markkanen, T., Göckede, M., Li, M. S., and Foken, T.: Quality assessment of Tibetan Plateau eddy-covariance measurements utilizing footprint modeling, Advances in Earth Sciences, 21, 1260-1267, 2006. Metzger, S., and Foken, T.: COPS experiment – Convective and orographically induced precipitation study, 1 June 2007 – 31 August 2007 – Documentation, Universität Bayreuth, Abteilung Mikrometeorologie, Bayreuth, Germany, 72 pp. ISSN:1614-8924, 2007. Eigenmann, R., Metzger, S., and Foken, T.: Generation of free convection due to changes of the local circulation system, Atmos. Chem. Phys. Discuss., 9, 11367-11411, doi:10.5194/acpd-9-11367-2009, 2009. Metzger, S., Junkermann, W., Butterbach-Bahl, K., Schmid, H. P., and Foken, T.: Measuring the 3-D wind vector with a weight-shift microlight aircraft, Atmos. Meas. Tech. Discuss., 4, 1303-1370, doi:10.5194/amtd-4-1303-2011, 2011. Broadwell, I., Jenkins, G., and Metzger, S.: Three perspectives: careers in China, Phys. World, 24, 42-43, 2011. Metzger, S., Junkermann, W., Mauder, M., Beyrich, F., Butterbach-Bahl, K., Schmid, H. P., and Foken, T.: Eddy-covariance flux measurements with a weight-shift microlight aircraft, Atmos. Meas. Tech. Discuss., 5, 2591-2643, doi:10.5194/amtd-5-2591-2012, 2012.
2 INTRODUCTION are along-, cross-, and vertical wind speeds with respect to the Cartesian coordinates x, y, and z; t is time, and z is the measurement height. Term I in Eq. (1) represents the tendency of s in the vertical column below the sensor, i.e. storage. Terms II–IV represent the turbulent flux divergence, and terms V–VII represent advection through the layer between the surface and sensor. For low or sparse canopies it is assumed that this layer is well-mixed, and that steady state conditions prevail during the averaging period (/0), which cancels term I from Eq. (1). Assuming horizontal homogeneity (/0, /0) implies equal horizontal inflow and outflow at opposite faces of a control volume (e.g., Finnigan et al., 2003), and cancels horizontal flux divergence (terms II–III) and advection (terms V–VI) from Eq. (1). Furthermore, neglecting large-scale subsidence or convection (≡0) cancels term VII from Eq. (1), and hence only term IV remains. Using dimensional analysis and similarity numbers it can be shown that the eddy covariance ′ is constant with height in the atmospheric surface layer to within approximately 10% (e.g., Foken, 2008a). When all above conditions hold true, the total flux is then equal to the EC measurement; ′ . (2) 1.2 Effects of complex terrain As long as the one-dimensional transport Eq. (2) is valid, a single ground-based EC measurement can represent the spatially averaged flux to or from an underlying ecosystem. In reality however, every ecosystem is inhomogeneous to some extent, and a graduation from less to more complex surfaces is much more applicable. Here and in the following, complex refers not only to the structure, function and spatio-temporal distribution of the surface sources and sinks, but also to surface topography. Consequently, real-world measurement conditions principally invalidate the assumption of onedimensional transport in various forms and degrees (e.g., Finnigan, 2008; Foken et al., 2011; Leuning et al., 2012; Mahrt, 2010; Mauder et al., 2007b). Aside from sensor limitations (e.g., Dellwik et al., 2010; Kochendorfer et al., 2012), it is this oversimplification that is held responsible for the systematic energy imbalance that is frequently observed across EC sensor networks (e.g., Foken et al., 2011; Leuning et al., 2012; Wilson et al., 2002). The lack of agreement between the sum of the turbulent heat fluxes and the available energy also challenges the validity of EC flux measurements of climate effective trace gases (Ruppert et al., 2006). Kaminski et al. (2012) find that EC flux measurements efficiently constrain modeling approaches for relatively homogeneous situations, but are not robust against unknown complexity. Failure to explicitly consider spatial representativeness increases the uncertainty in the observed spatio-temporal flux structure of EC sensor networks. This effect is also known as location bias (Schmid and Lloyd, 1999). Such bias can be introduced by preferential measurement locations, e.g., on hill tops rather than in valleys (Finnigan, 2008), or in dryer rather than in moister areas (Desjardins et al., 1997). Also, the source area of an EC flux measurement varies in space and time, as a function of atmospheric stability and the wind field. Over complex terrain, the spatial representativeness of an EC measurement thus varies from diurnal over seasonal to inter-annual time scales (Göckede et al.,
INTRODUCTION 3 2008). Biases are introduced when the source area changes systematically over surfaces with distinctly different biophysical properties and source/sink behavior (e.g., Chen et al., 2012). 1.3 Motivation Data from EC sensor networks are being used to parameterize, constrain and evaluate land surface schemes in climate models (e.g., Williams et al., 2009). In this way biases in EC flux observations propagate directly into the resultant data products (Leuning et al., 2012). Improved characterization of the uncertainties in the EC observations would significantly foster our ability to understand, model, forecast and eventually mitigate environmental change (Jung et al., 2011). The motivation of this dissertation is to provide an airborne measurement platform which enables studying some of the mechanisms that lead to systematically biased flux estimates from EC sensor networks. Despite most EC flux observations are performed at ground-based sites in the time domain, much of turbulence theory is conceptually formulated in the spatial domain (e.g., Kaimal and Finnigan, 1994; Lenschow et al., 1980; Mahrt, 2010; Panofsky and Dutton, 1984). As compared to time domain measurements, EC flux measurements in the spatial domain do not rely on the passive transport of atmospheric eddies with the mean wind (Taylor, 1915). E.g., the speed of a research aircraft is typically much faster than the wind speed. Through active propulsion in space, fast response airborne measurements more completely capture the true spatial variation of the turbulent exchange over heterogeneous surfaces (e.g., Kustas et al., 2006). Thus, airborne soundings cover a comparatively larger range in the state space of environmental drivers and responses. If sufficient measurement accuracy is warranted, this results in a high signal to noise ratio in the airborne observations (Lenschow and Sun, 2007). However, spatial sampling does not per se obsolete the assumptions in the one-dimensional transport Eq. (2). Yet, compared to their ground-based pendants, aircraft EC measurements tend to better fulfill some of the assumptions that justify cancellation of the respective terms from Eq. (1). Because of their short duration, change in the storage term I is likely small (steady state conditions). It is hypothesized that, during unstable stratification, surface heterogeneity induces non-propagating eddies (NPE, term VII), which in turn cause horizontal compensatory flows (terms II–III, V–VI, e.g., Foken et al., 2011; Mahrt, 2010). These NPEs are explicitly resolved in a spatial sample, but not in a temporal one. Moreover, each of terms II–III, V–VII is more likely approaching zero for an instantaneous spatial average than for a stationary temporal average (Steinfeld et al., 2007). Lastly, the effect of vertical flux divergence (term IV) on the airborne EC measurement is negligible, as long as the soundings are performed close to the surface (e.g., Isaac et al., 2004). If higher flight altitudes are required, term IV can also be approximated from convective boundary layer (CBL) scaling (e.g., Deardorff, 1974), stacked flight patterns (e.g., Betts et al., 1990), or from a conservation approach (Bange et al., 2006). Above properties make airborne flux data particularly valuable for the analysis of atmospheric transport mechanisms (e.g., Hiyama et al., 2007; Mauder et al., 2007a; Strunin et al., 2004), and facilitates the derivation of scaling laws (e.g., Lenschow and Stankov, 1986; Mahrt, 2000). This motivates using aircraft observations of the surface-atmosphere exchange also for separating uncertainties in EC flux measurements due to;
4 INTRODUCTION (i) sampling errors; (ii) direct effects of surface heterogeneity, such as location bias through variable source/sink behavior and surface roughness, and; (iii) indirect effects of surface heterogeneity, such as transport by NPEs. However, to date manned platforms, such as fixed wing aircraft and helicopters, are expensive to operate or not applicable in settings such as remote areas beyond the range of an airfield. Unmanned aerial vehicles on the other hand provide mobility, yet do not allow a comprehensive sensor package due to payload restrictions (e.g., overview in Dias et al., 2012; Egger et al., 2002; Hobbs et al., 2002; Martin et al., 2011; Thomas et al., 2012). In order to enable the relation of airborne EC flux measurements to surface properties, aircraft are bound to fly at low and constant altitude above ground. To follow topographically structured terrain, an aircraft must therefore possess a high ratio of climb rate to airspeed, which only few airborne platforms provide. This dissertation intends to make accessible an alternative airborne measurement platform which combines comprehensive, terrainfollowing observations over complex terrain with a minimal demand in cost, transport and infrastructure. After successfully applying a weight-shift microlight aircraft (WSMA) to aerosol and radiation transfer studies (e.g., Junkermann, 2001; Junkermann, 2005), it was hypothesized that WSMA can also fulfill above requirements. The possibility of low-level, terrain-following EC flux measurements with WSMA is explored in this dissertation, which can provide a viable addition to existing airborne measurement platforms. Such development could aid overcoming the lack of applicable measurement platforms and techniques to study thus far poorly understood CBL processes over complex terrain. 1.4 Objectives of this thesis The overarching goal of this dissertation is to evaluate the suitability of WSMA for gaining new insights in the spatial variability of heat and moisture exchange above complex terrestrial surfaces. Three concrete objectives are assigned to this goal; (i) assessing the suitability of WSMA based 3D wind vector measurement for EC applications; (ii) quantifying the uncertainty in WSMA based measurements of turbulence statistics and EC flux, and; (iii) demonstrating the usefulness of WSMA based EC flux measurements to spatially resolve the land-atmosphere exchange above complex and not readily accessible terrain. These objectives are addressed by three individual publications as well as supplementary materials presented in Appendices B–E of this thesis. Metzger et al. (2011, Appendix B) address objective (i) by developing, establishing and evaluating a generalized calibration strategy for the wind measurement from airborne platforms. This strategy consists of an expanded algorithmic description of the wind measurement (Supplement to Metzger et al., 2011, Appendix C), in combination with a specific sequence of flight patterns used for calibration. The principal aim of this paper is to enable accurate wind measurements even during low-level, terrain-following flight, such as required for EC soundings over complex terrain. Hence, the
INTRODUCTION 5 possibility to dynamically offset the effect of pilot input on the wind measurement is sought. It is shown that this can be realized through consideration of the lift coefficient, i.e. the ratio of aircraft gravitational to propulsion forces, in the wind computation. All sources of uncertainty are quantitatively propagated through the algorithmic description, and the WSMA wind measurement is evaluated against independent reference measurements. The findings emphasize that WSMA are capable of accurately measuring the 3D wind vector. Hence the necessary basis is provided for the study of precision and spectral quality of the wind measurement, which is prerequisite for reliable EC flux measurements. Metzger et al. (2012, Appendix D) address objective (ii) by, first of all, quantifying the precision of the wind measurement from WSMA, the lynchpin of flux calculations from aircraft. From here, the smallest resolvable changes in friction velocity, and sensible- (H) and latent (LE) heat flux are estimated. Secondly, measurements of wind, temperature, humidity and respective fluxes are compared between independent ground-based reference installations and the WSMA. Some differences are observed, which could be related to inconsistencies in the ground-based installations, and to their different abilities to capture flux contributions from NPEs. These findings encourage the use of WSMA as a low cost and highly versatile flux measurement platform. In combination with its high transportability and unique flight characteristics, the WSMA is thus well suited to study landatmosphere interactions above complex terrain. The objective (iii) is addressed in Metzger et al. (2013, Appendix E). In this paper, low-level EC measurements from WSMA are used to characterize the exchange of heat and moisture over a complex landscape in Inner Mongolia, P.R. China. From CBL scaling it is found that the vertical flux gradients below the terrain-following flights satisfy the surface layer definition. Consequently the WSMA based EC measurements can be interpreted as surface fluxes. Wavelet decomposition of the WSMA turbulence data is then combined with footprint modeling and a machine learning technique to infer environmental response functions. From these response functions high resolution maps of the heat and moisture exchange over the entire Xilin River Catchment are extrapolated. These maps are then summarized for each land cover type, providing information on the individual source strength and spatial variability. This study emphasizes the potential of WSMA based EC flux measurements above complex terrain to (a) provide high-resolution inventories of the land-atmosphere exchange, (b) advancing the location bias treatment of ground-based flux measurements from diagnostic assessment (e.g., Chen et al., 2011) to prognostic transfer functions, and consequently (c) separating the effects of sampling errors and surface heterogeneity in long-term sensor networks. The algorithms developed in the course of this thesis are intended for future use beyond the data collected and analyzed here. For this purpose all algorithms are implemented in a software package in the R programming language (R Development Core Team, 2012). This software package is currently available upon request, and will be released to The Comprehensive R Archive Network (http://cran.rproject.org/) in the near future.
6 EXPERIMENTS AND DATA 2 Experiments and data The results presented in this thesis are based on three extensive flight campaigns with the WSMA. In Sect. 2.1 the WSMA and its scientific equipment are briefly introduced. The publications presented in Appendices B and C are based on data that were collected during two flight campaigns in Germany (Sects. 2.1, 2.3). These campaigns were conducted with the sole purpose to explore the possibility of wind and EC flux measurements with the WSMA. The dataset used for the publication in Appendix D was collected during a third flight campaign in China (Sect. 2.4). This campaign was performed as integral part of the Sino-German research collaboration MAGIM (DFG research group 536). All flight campaigns were initiated by K. Butterbach-Bahl, I developed the measurement strategies, and W. Junkermann performed the majority of the research flights. 2.1 The weight-shift microlight aircraft According to the safety and regulatory standards of the European Civil Aviation Conference, microlight aircraft are defined as aircraft with a maximum stall speed of 65 km h−1 and a take-off mass of no more than 450 kg. Figure 1 shows the weight-shift microlight research aircraft D–MIFU. It consists of two distinct parts, the wing and the trike (the unit hung below the wing, containing pilot, engine and the majority of the scientific equipment). The weight-shift control system is enabled by the pilot’s direct application of pitching or rolling moments to the wing via the basebar. Counterbalance is provided by the mass of the trike unit suspended below the wing. Simple procedures for certification of installations on an open aircraft allow a wide spectrum of applications as well as the flexible installation of scientific equipment. At an operational airspeed of ≈100 km h−1, D–MIFU can carry a maximum of 80 kg scientific payload from 15 m a.g.l. (above ground level) to 4000 m a.s.l. (above sea level). The full performance characteristics can be found in Junkermann (2001), and additional technical detail is provided in Metzger et al. (2011, Appendix B). The structure of a WSMA differs from common fixed-wing aircraft, which provides exceptional transportability and climb rate, and qualifies it for applications in complex and inaccessible terrain. However, these structural features might also expose the trike-based wind measurement to variable distortion in the flow field around the wing. Firstly, the trike, i.e. the turbulence measurement platform, is free to rotate in pitch and roll against the wing. Secondly, the wing deforms aeroelastically with aircraft trim, which changes its aerodynamic properties. These characteristics complicate the accurate and precise measurement of the true 3D wind vector, and consequently the dependable measurement of EC fluxes.
EXPERIMENTS AND DATA 7 Fig. 1. Weight-shift microlight research aircraft D-MIFU, aircraft structural features are highlighted by dash-dotted lines. Sensor locations of wind-measuring five hole probe (5HP), inertial measurement and global positioning system (IGS, inside aircraft nose) and universal laser altitude sensor (ULS, below pilot seat) are indicated. Figure modified after Metzger et al. (2011, Appendix B). The WSMA is equipped with fast response instruments that enable capturing the turbulent scales of atmospheric motion. A detailed description of the installation points, models and characteristics of the deployed sensors and data acquisition is given in Metzger et al. (2011, Appendix B). In short, most variables are sampled at 100 Hz and are block-averaged and stored at 10 Hz, yielding a horizontal resolution of approximately 2.5 m. To conduct fast wind measurements, the WSMA is outfitted with a combination of inertial measurement and global positioning system (IGS, RT3102, Oxford Technical Solutions, Upper Heyford, England), and a five-hole pressure probe (5HP, in-house development). The principle is to resolve the meteorological wind vector from the vector difference of the aircraft’s inertial velocity (captured by the IGS) and the wind vector relative to the aircraft (captured by the 5HP, Supplement to Metzger et al., 2011, Appendix C). Additional acceleration measurements (ADXL330, Analog Devices, Inc., Norwood, U.S.A.) were installed in the hang point of trike and wing, and in the 5HP. These enable investigating potential influences on the wind measurement from WSMA engine or propeller resonance, or from the natural frequencies of the trike and the wing. On the underside of the 5HP, air temperature is measured with a 50 μm thermocouple (CHAL-002, OMEGA Engineering, Inc. Stamford, U.S.A.). An open path infrared gas analyzer (IRGA, OP2, ADC Bioscientific, Great Amwell, UK) to the port side of the 5HP is used to measure
8 EXPERIMENTS AND DATA the concentration of water vapor. The instrument response of both the thermocouple and the IRGA is 50 Hz. In addition, a slow (2 Hz instrument response) humidity reference from a TP3 dew point mirror (Meteolabor AG, Wetzikon, Switzerland) is stored at ≤0.1 Hz. A third-order Savitzky-Golay complementary filter (Chen et al., 2004) is used to correct drift of the IRGA due to pressure changes with altitude. This filter bases the humidity fluctuations measured by the IRGA on the slow dew point mirror reference. A filter window size of 13.9 s or ≈350 m maximizes the integral over the humidity power spectrum, and is used to correct the measurements. Additional slow measurements (≤0.1 Hz) of surface temperature (CT infrared thermometer, Optris GmbH, Berlin, Germany) and downwelling short wave radiation (LI–200 SZ, LI–COR Inc., Lincoln, Nebraska) are used in this thesis. 2.2 Bavaria, Germany The first flight campaign took place from 19 June to 11 July 2008 over Lake Starnberg, Germany (47.9°N, 11.3°E). The lake is located in the foreland of the German Alps, which is a slightly rolling landscape (600–800m a.s.l.) and mainly consists of grassland with patches of forest. The campaign was designed to acquire the necessary datasets for developing and calibrating a WSMA wind computation algorithm which enables to dynamically offset the effects of pilot input. For this purpose 31 flights of 8 specific patterns were performed in the free atmosphere above Lake Starnberg. Of these, 10 ideal realizations of these patterns are used in Metzger et al. (2011, Appendix B). Aside from the WSMA, no additional scientific equipment was deployed. This campaign was funded and implemented solely under the Karlsruhe Institute of Technology. 2.3 Brandenburg, Germany An evaluation of the WSMA wind and EC flux measurements against ground-based reference measurements was carried out during the second flight campaign between 14 and 21 October 2008. This experiment was performed around the boundary layer field site Falkenberg (52.2°N, 14.1°E) of the German Meteorological Service (DWD), Richard-Aßmann Observatory, Lindenberg, Germany. This field site lies in the basically flat North German Plain, and the terrain height varies between 40 m and 130 m a.s.l. within an area of 20×20 km2. The land cover is dominated by agriculture and forests, interspersed by equal amounts of lakes, meadows and settlements. This campaign was funded by the Karlsruhe Institute of Technology, and implemented in close collaboration with the DWD. To evaluate the accuracy of the WSMA wind measurement, Metzger et al. (2011, Appendix B) use data from an instrumented 99 m tower and from sonic detection and ranging (SODAR, PCS-2000/64, Metek GmbH, Elmshorn, Germany). The 99 m tower provided cup measurements of wind speed at four levels (40, 60, 80, and 98 m a.g.l., Wind Sensor Classic, Adolf Thies GmbH, Göttingen, Germany). The wind direction was measured with vanes at heights of 40 and 98 m a.g.l. (Wind Direction Sensor Classic, Adolf Thies GmbH, Göttingen, Germany), and a static pressure reference was provided at 1 m a.g.l. (PTB220A, Vaisala Oy, Helsinki, Finland, 10 min averages). Tower profile and pressure data were averaged and stored in 10 min intervals. Sonic anemometers (USA-1, Metek GmbH, Elmshorn, Germany) provided wind vector measurements at a rate of 20 Hz at 50 and 90 m a.g.l. The SODAR wind vector profiles (15 min averages) reached, at increments of 20 m, from 40 to 240 m a.g.l. 17 cross-shaped flight patterns with legs of 3 km length were performed with their center
EXPERIMENTS AND DATA 9 between the 99 m tower and the SODAR. The flights were carried out at the approximate sounding levels of the 99 m tower and the SODAR (50, 100, 150, 200 and 250 m a.g.l.). This enables the direct comparison of the wind components between the WSMA and the ground-based measurements. Moreover, Metzger et al. (2012, Appendix D) compare turbulence statistics, EC fluxes and power spectra between the WSMA and ground-based measurements. For this purpose additional data from installations on the 99 m tower, an EC surface flux measurement, a large-aperture scintillometer (LAS), a wind profiler, and from radio soundings are used. In combination with the sonic anemometers, open path IRGAs (LI-7500, LI-COR Biosciences, Lincoln, U.S.A.) at 50 m and 90 m a.g.l. enable the comparison of turbulence statistics, EC fluxes and power spectra between WSMA and tower. The 99 m tower was further equipped with profile measurements of temperature (HMP-45, Vaisala Oy, Helsinki, Finland) and humidity (Frankenberger Psychrometer, Theodor Friedrichs GmbH, Hamburg, Germany) at 40, 60, 80, and 98 m a.g.l (10 min averages). The profiles are interpolated to the heights of the EC installations and are used to compare average temperature and humidity measurements between WSMA and tower. The two lowest levels of the cross-shaped flight patterns were performed at the approximate height of the tower EC installations, and provided 36 individual flight legs for this comparison. Identical instrumentation as on the tower was used for an additional EC surface flux measurement upwind (south) of the tower base, at 2.4 m a.g.l. Also 10 min area-averaged surface sensible heat fluxes were derived from the LAS. Furthermore, hourly estimates of the CBL depth were derived from SODAR and wind profiler data, and from six-hourly routine radio soundings performed by the DWD. The surface sensible heat fluxes measured at the 2.4 m EC and the LAS are used in conjunction with the CBL depths to approximate vertical flux profiles. On two days, simultaneous tower and WSMA measurements of the sensible heat flux are compared to these flux profiles. 2.4 Inner Mongolia, P.R. China The third flight campaign was performed from 23 June to 4 August 2009 over the remote steppe of the Mongolian Plateau. The hilly investigation area south of the provincial capital Xilinhot, Inner Mongolia, China (43.6°N, 116.7°E, 1000–1400 m a.s.l.) is covered by semi-arid grassland, intersected by a dune belt. The land cover in the investigation area varies distinctly in space and time (Ketzer et al., 2008; Schaffrath et al., 2011). On the small scale landscape position effects soil moisture availability. On larger scales management practices such as haymaking, grazing or irrigated agriculture are suspected to cause a vast heterogeneity in the heat and moisture fluxes between surface and atmosphere. As integral part of the Sino-German research collaboration MAGIM (Matter fluxes in grasslands of Inner Mongolia as influenced by stocking rate), the goal of this flight campaign was to support long-term ground-based measurements through gaining new insights in the spatial distribution of fluxes on the regional scale. In addition to the WSMA measurements, Metzger et al. (2013, Appendix E) deployed a ceilometer (LD40 – Vaisala Oy, Helsinki, Finland) for this purpose. The ceilometer provided 10 min vertical profiles of the atmospheric laser radiation backscatter intensity. The depth of the convective boundary layer (CBL) was inferred from this data using the maximum gradient method (Emeis et al., 2008) in combination with semi-daily radiosonde ascends in nearby Xilin Hot (World Meteorological Organization station 54102, http://weather.uwyo.edu/upperair/sounding.html). The CBL depth is used to characterize the
10 EXPERIMENTS AND DATA horizontal mixing between surface and flight level and to determine the source area of the WSMA based EC flux measurements. EC measurements with the WSMA were performed along 14 individual straight line flight patterns, which followed the terrain at ≈50 m a.g.l. Two flight lines perpendicular to the prevailing wind direction were chosen on a daily basis, and repeated until a minimum of 40 km of data was acquired. This resulted in a total of 35 WSMA soundings during the flight campaign, of which Metzger et al. (2013, Appendix E) selected 12 flights for analysis with stationarity of the solar irradiance being the selection criteria. This flight campaign was funded by the German Research Foundation, and was implemented in collaboration between the Karlsruhe Institute of Technology and the Chinese Academy of Sciences.
RESULTS 11 3 Results In the following, the results of the development and application of WSMA based EC flux measurement are outlined and related to the corresponding publications in Appendices B–E. This development process starts with the wind measurement (Sect. 3.1), continues to the turbulent flux measurement (Sect. 3.2) and concludes with a sample application of the WSMA based EC flux measurement over complex and previously inaccessible terrain (Sect. 3.3). 3.1 Wind measurement The EC technique relies upon the precise measurement of fluctuations of atmospheric quantities, based on negligible sensor drift throughout an averaging period. Measured from aircraft, the determination of the wind vector requires a sequence of thermodynamic and trigonometric equations (Supplement to Metzger et al., 2011, Appendix C). These equations propagate various sources of error, and are consequently the lynchpin for EC flux measurements from aircraft. An abundance of methods exists for calibrating these algorithms to the individual aerodynamic properties of a wide range of fixed-wing aircraft (e.g., Tjernström and Friehe, 1991; van den Kroonenberg et al., 2008; Williams and Marcotte, 2000). However, none of the existing methods is capable of treating WSMA specific effects on the wind measurement, originating from trike rotation and wing deformation. Hence, Metzger et al. (2011, Appendix B) advance the existing wind calibration procedures with focus on (i) creating a formal calibration framework, (ii) retaining applicability to fixed-wing aircraft, and (iii) offsetting WSMA specific effects on the wind measurement. The result is a bottom-up calibration procedure in three stages; (i) basic calibration of temperature and pressure sensors; (ii) general in-flight calibration of flow angle measurements, and; (iii) WSMA specific in-flight calibration of flow angle measurements. These three stages are composed of a sequence of seven calibration steps A–G, which is shown in Fig. 2. Each step targets one or more variables in the wind vector computation, utilizes experimental data under defined environmental conditions, and results in incrementally refined system performance. Additional information on the flight maneuvers used for this purpose as well as variable definitions is provided in Metzger et al. (2011, Appendix B).
18 RESULTS because it is the axis of plugand socket connection between IGS and 5HP, i.e. the axis with the least margin for resonance. No remnants of this scale discrepancy are evident in the wind measurements, in particular between 1‒5 Hz (Metzger et al., 2012, Fig. 3, Appendix D). This leads to the conclusions that (i) the wind vector computation correctly accounts for the displacement of 5HP and IGS, and (ii) the cause of enhanced 5HP acceleration measurements (especially longitudinal to the body) lies in the fixture of the acceleration sensor in the 5HP, rather than in the mounting of the 5HP against the IGS. The spectral behavior of the wing acceleration measurements is different to those of the trike. It displays a distinct peak around 0.7 Hz, which is only present in the transverse component of the trike measurements. It can be understood as the wing's natural frequency, i.e. its inertia. Fig. 5. Smoothed power spectra of acceleration measurements in the WSMA trike coordinate system. The dashed vertical line indicates the −3 dB frequency (20 Hz) of the Butterworth low-pass filter in the wind vector data acquisition system. Figure modified after Metzger et al. (2012, Appendix D). Subsequently, Metzger et al. (2012, Appendix D) quantify the impact of WSMA spectral properties on the windand EC flux measurement. For this purpose a fast Fourier transformation is applied to the 36 tower and WSMA fast response data series during the comparison flights. Each individual transform is normalized to a sum of unity. To reduce scatter, the normalized transforms of all tower and WSMA measurements, respectively, are then binned into frequency bands and ensemble-
RESULTS 19 averaged. Here, only the results for the cospectra are discussed. In Fig. 6 ensemble cospectra (Co) are presented as function of the normalized frequency n=f·z/U¯, with f being the sampling frequency, z being the measurement height, and U¯ being the horizontal wind speed for the tower and the true airspeed for the WSMA, respectively. Also shown is the reference cospectrum of Massman and Clement (2004), with the spectral maximum at n=0.1 for unstable stratification (Kaimal and Finnigan, 1994, 24 out of 36 flights). The momentum flux at the tower exhibits large scatter in the individual cospectra at both installation heights, and the ensemble cospectrum is not calculated. The scatter might result from the wind direction dependent correlation of the horizontaland vertical wind components at the USA‒1 sonic anemometers (e.g., Mauder et al., 2007c). All analyzed ensemble cospectra approximately follow the reference cospectrum, and for the heat fluxes the peak of the tower cospectra coincide with n=0.1 of the reference cospectrum. The cospectral peaks of the WSMA measurements are marginally shifted towards higher frequencies around n=0.2. Metzger et al. (2012, Sect. 3.3.3, Appendix D) associate increased variance in the WSMA wind components with spectral artifacts resulting from the treatment of the net flow distortion in the time-, but not in the frequency domain (Metzger et al., 2011, Appendix B). In order to quantify the impact on the WSMA flux measurement, all individual cospectra are compared between the WSMA and the reference cospectrum in the range of the wing’s natural frequency (0.4≤f≤2 Hz). To account for the influence of stratification, the peaks of the reference cospectra are calculated using the forms of Kaimal et al. (1972). Relative to the entire frequency range the spectral artifacts lead to a systematic deviation in the fluxes of momentum, sensibleand latent heat of 3±6%, −1±6% and 1±3% (median differences), respectively. Fig. 6. Average cospectra of all measurements between tower and WSMA. Also shown is the reference cospectrum of Massman and Clement (2004, dashed line). Figure from Metzger et al. (2012, Appendix D). The WSMA wind and flux measurements are corrected for this spectral inconsistency before comparing them to ground based measurements. The appropriate correction factors are estimated from the comparison of measured spectra and cospectra to modeled ones (Metzger et al., 2012, Sects. 3.3.3, 3.3.4, Appendix D). A maximum likelihood functional relationship (MLFR, Ripley and
20 RESULTS Thompson, 1987), which considers the random error in the data, is used to compare tower and WSMA measurements. For this purpose the statistical random error ran is calculated after Lenschow and Stankov (1986) and Lenschow et al. (1994), and consolidated after Mahrt (1998) for the ensemble of all measurements ( ens). Averages of along-wind component u, temperature T and absolute humidity a agree very well between tower and WSMA (Table 1). The MLFRs for standard deviations (2‒34%) and fluxes (17‒21%) indicate higher estimates of the airborne measurements compared to the tower. Considering the 99.5% confidence intervals the observed differences are not significant, with exception of the temperature standard deviations. It must be noted that the magnitude of the flow distortion correction for the USA‒1 sonic anemometers at the tower alone is in the order of the observed differences between the tower and the WSMA. Moreover, the amplitude resolution test by Vickers and Mahrt (1997) would reject 28 out of 36 tower sonic temperature data sets. The problem is related to the insufficient sonic temperature resolution (0.01 K) of the USA‒1, which appears as additional spectral energy in the form of high frequency white noise. Consequently the USA‒1 measurements cannot be regarded as reliable reference for the temperature standard deviations, and the applied spectral correction factors and resulting MLFRs must be interpreted with caution. The Table 1. Results of the maximum likelihood functional relationships between tower and WSMA measurements. Shown are the MLFR slope and its standard error Slope± , weighted coefficient of determination R2, residual standard error res, the average statistical random error ran and the ensemble random error ens. Table from Metzger et al. (2012, Appendix D). Variable Slope± R2 res ran ens Averages u 0.99±0.02 1.00 9% 15% 3% T 1.00±0.00 1.00 0% 0% 0% a 0.99±0.00 1.00 1% 2% 0% Standard deviations u 1.15±0.05 0.99 21% 9% 2% v 1.02±0.05 0.98 20% 8% 1% w 1.10±0.03 0.99 9% 5% 1% T 1.34±0.07 0.98 17% 7% 1% a 1.17±0.08 0.98 23% 9% 1% Fluxes u* 1.21±0.07 0.98 13% 25% 5% H 1.17±0.08 0.98 10% 29% 8% LE 1.17±0.10 0.96 25% 34% 7%
RESULTS 21 problem is less pronounced for the sensible heat flux. The white noise in the USA‒1 sonic temperature measurement does not affect the measurement of, or the correlation with, the vertical wind measurement. The result is a modest underestimation of −3% of the tower sensible heat flux due to reduced coherence of sonic temperature and vertical wind at high frequencies. (iii) Subsequently Metzger et al. (2012, Appendix D) investigate whether the differences between WSMA and tower measurements can be related to their different spatial representativeness. For this purpose a cross-wind distributed footprint parameterization is used together with Corine Land Cover 2006 data (Version 13, European Environment Agency, 2010, 100 m horizontal resolution). The spatial context of the platforms agrees well when considering the average footprint contributions over all tower-WSMA comparison measurements. For both platforms most of the footprint covers arable land (95‒97%). Contributions from the remaining land covers are sub-percent except for forest (2‒ 3%), and meadows do not contribute at all. Taking a closer look at the individual, simultaneous measurements the source areas can however differ considerably. Over all simultaneous measurements the actual overlap ranges from 12‒68% of the footprint weights, with a median of 35±17%. However varying overlap did not systematically alter the differences in the flux measurements between tower and WSMA (R2≤0.07). Hence, spatial representativeness cannot explain the remaining differences between WSMA and tower measurements. (iv) Lastly, Metzger et al. (2012, Appendix D) assess the potential impact of principal differences of spatial averaging (LAS, WSMA) and temporal averaging (tower EC) on the measured fluxes. For this purpose simultaneous measurements of the sensible heat flux on two days are inter-compared between the measurement platforms using boundary layer scaling. Any H measured by tower EC and extrapolated to flight altitude is lower by 25‒40% compared to the LAS. At the same time H measured by the WSMA is ≤25% lower compared to the LAS, but 15‒25% higher compared to the tower EC. The footprints of all measurements is dominated by >90% contributions from arable land. Consequently differing source areas of the measurements do not qualify as potential reason for the observed differences. Foken (2008b) and Mahrt (2010) suggest that the energy balance non-closure frequently observed from tower EC measurements is connected to the interaction of terrain heterogeneity and turbulent scales. Following their hypothesis, the tower EC cannot adequately capture flux contributions from NPEs due to its inability of spatial sampling. On the other hand a LAS captures NPEs up to the dimension of its path length, with increasing sensitivity towards the center of its optical path (Foken et al., 2010). Also airborne EC is capable of spatial sampling and captures some of the associated flux, depending on the horizontal extent of the NPEs and the flight path. The presence of NPEs in the study area has been shown (Steinfeld et al., 2007; Uhlenbrock et al., 2004), and can thus be considered a potential explanation for the deviation of the tower EC results from the WSMA, and even more so from the LAS results. Metzger et al. (2012, Appendix D) show that turbulence measurements from WSMA can be achieved with sufficient precision and accuracy to enable EC flux calculation. Differences in the order of 15‒ 25% remain between the fluxes measured by the ground based instruments and the WSMA. However, the 99.5% confidence intervals in the comparison between tower and WSMA indicate that the differences are insignificant and the WSMA flux measurement is unbiased. The precision of the WSMA flux measurement can be quantified to ≤10% (1 MLFR slope error).
22 RESULTS 3.3 Spatial resolution and extrapolation of turbulent fluxes The overarching goal of airborne eddy-covariance flux measurements is to bridge the gap between observations and data assimilation approaches on different spatial scales. Metzger et al. (2013, Appendix E) develop a procedure that aids this purpose by ‘mining‘ the information content of EC flux observations. Through accomplishment of four subsequent steps this LTFM procedure extracts quantitative response functions with environmental drivers; (i) low level EC flux flights; (ii) time-frequency analysis of the flux observations; (iii) composition of continuous biophysical surface properties in the flux footprint, and; (iv) environmental response function from non-parametric machine learning techniques. In developing the LTFM procedure, the objective of Metzger et al. (2013, Appendix E) is to spatially explicitly characterize the exchange of sensibleand latent heat over the heterogeneous steppe landscape of the Xilin River Catchment (XRC), Inner Mongolia, P.R. China (Sect. 2.4). (i) The LTFM procedure requires the relation of the airborne measured fluxes to land cover properties. To enable this requirement an aircraft is bound to measure close to the surface, where characteristic fluxes from different land covers are not yet fully homogenized (or blended, Mason, 1988; Wood and Mason, 1991). Moreover the flux must be measured at a constant altitude above ground, so as to avoid artificial flux contributions through altitude fluctuations along vertical gradients (Vickers and Mahrt, 1997). However investigation areas are seldom ideally flat, and topography can vary significantly across a domain. To safely follow terrain contours at a low and constant altitude above ground, the aircraft must possess a low ratio of true airspeed to climb rate. The WSMA fulfills this requirement, and terrain-following EC flux measurements with the WSMA were conducted at 50 m a.g.l. in the XRC. From boundary layer scaling it is found that the vertical flux gradients below the flight level satisfy the surface layer definition (constant within |5–10%|). Hence measured H and E can be interpreted as surface fluxes. (ii) Metzger et al. (2013, Appendix E) use the wavelet cross-scalogram technique to enable a high spatial discretization of turbulent flux measurements, without neglecting flux contributions from long wavelengths. For each individual 10 Hz observation the wavelet cross-scalogram represents the measured turbulent flux as contributions from different atmospheric transport scales. Theoretically, this enables a spatial resolution of ≈2.5 m of the WSMA flux measurement. However, for an individual sample the random error is excessively large, but decreases inversely proportional to the square root of the sample size (e.g., Lenschow and Stankov, 1986). In search of a suitable sample size, a compromise must be found between random error (high resolution) and smearing (low resolution) of the resulting flux estimates. Metzger et al. (2013, Appendix E) find that the typical length scale of surface heterogeneity is in the order of 1000 m. Thus, a flight path length of 1000 m is a physically meaningful window for the computation of turbulence statistics and fluxes. Hence, while retaining a spatial discretization of 90 m, the wavelet cross-scalogram is integrated over centered subintervals of 1000 m length. Compared to an integration length of 90 m this results in a decrease of the ensemble random error (Mahrt, 1998) of ≈70% for a flight line of 20 km length. This procedure
RESULTS 23 yields a high number of flux observations along a flight line, which provides previously unachievable resolution and coverage of the environmental state space. The downside of the low-frequency support of wavelets is that edge effects due to the finite overall data set increase with scale. Torrence and Compo (1998) define the cone of influence as the boundary where the power of edge-related artifacts is damped by a factor of e-2. In general, more certain flux contributions below the cone of influence include transport scales up to ≈⅓ of the flight length. For the flights in the XRC the less certain flux contributions above the cone of influence are small (−15% to −4% median differences for all flights). These contributions are included in the analysis, to ensure inclusion of identical transport scales close to the start or end, and at the center of a dataset, and to preserve the global covariance. (iii) The spatial variation of temperature and precipitation in the XRC follows altitudinal and latitudinal trends (Auerswald et al., 2009; Wittmer et al., 2010). To resolve the effective state of biophysical surface properties over time, Metzger et al. (2013, Appendix E) use Moderate Resolution Imaging Spectroradiometer (MODIS) data. Here, 8-day composites of the land surface temperature (LST, MOD11A2.5, 1 km resolution), and 16-day composites of the enhanced vegetation index (EVI, MOD13Q1, MYD13Q1, 250 m resolution) are used. The LST and EVI datasets are bi-linearly interpolated to the 90 m resolution of an existing land cover classification, and linearly interpolated in time to yield an individual map for each flight day. Turbulence statistics for each 1000 m subinterval over a wavelet scalogram is used to evaluate the 2D footprint model described in Metzger et al. (2012, Appendix D). An individual evaluation is carried out for each overflown cell of the land cover, LST and EVI grids (i.e., every 90 m along the flight path). With the overflown grid cell as base point, and the footprint weights wxy 1 xy w for each grid cell with position x, y, relative to the base point, the footprint composition is calculated; , xy xyxy LSTwLST (5) , xy xyxy EVIwEVI (6) with the land surface temperature and enhanced vegetation index for each grid cell, LSTxy and EVIxy, respectively. For graphical representation the footprint weights of all evaluations along a flight line are superimposed and normalized to a sum of unity. In Fig. 7 LST and EVI generally follow the land cover patterns, e.g. lower temperature and higher greenness for irrigated agriculture and marshland. However, it is also evident that the static land cover classification cannot reflect the current surface conditions. E.g., the marshland in the north-western quadrant appears dried-out (high LST and low EVI), while the steppe area in the north-eastern quadrant shows large variations in LST. I.e., the land cover classification represents the long-term effects of vegetation, climate, soil and topography. However, biophysical surface properties also vary significantly within land cover classes. This is likely as a function of geomorphological properties such as aspect, slope and soil type, but also due to the large variability of convective rainfall events across the study area (e.g., Schaffrath et al., 2011).
24 RESULTS Fig. 7. Flight along pattern O12 on 8 July 2009, 12:16–12:24 Chinese standard time (UTC+8 h, white dashed line). The composite flux footprint along the flight line (30%, 60%, 90% contour lines) is superimposed over maps of land cover (upper left panel), land surface temperature (LST, upper right panel), and enhanced vegetation index (EVI, lower left panel). The land cover color codes are abbreviated for bare soil (Bare), marshland (Marsh), generic steppe (Steppe), irrigated agriculture (Irrigated), and rainfed agriculture (Arable). Figure from Metzger et al. (2013, Appendix E). (iv) Environmental response functions (ERF, Desjardins et al., 1994) are an approach to utilize quantitative information about the EC measurement’s spatial context. The general idea is to establish a functional relationship between spatially or temporally resolved flux observations (responses) and
RESULTS 25 corresponding environmental drivers. Metzger et al. (2013, Appendix E) base the development of a catchment-specific ERF on the works of Chen et al. (1999), Hutjes et al. (2010) and Ogunjemiyo et al. (2003). The LTFM procedure advances these approaches; (a) Thus far, a suitable number of flux observations was obtained by either shortening the timedomain EC averaging interval (Chen et al., 1999; Ogunjemiyo et al., 2003), or by stratifying repeated observations along the same flight line on different days (Hutjes et al., 2010). The inherent drawbacks are the neglect of either long wavelength contributions to the flux measurement, or inter-day variability of ecosystem drivers. Both are overcome using the wavelet cross-scalogram technique; (b) Previously, the development of ERFs has solely focused on drivers in the footprint of the flux observations, namely discrete land cover classifications. This procedure ignores within-class variability across a catchment, e.g. along climatic or altitudinal gradients, which is overcome by using continuous variables such as LST and EVI instead. Also, substituting discrete with continuous variables enables the use of more advanced scaling algorithms. In addition, the present approach considers meteorological drivers such as downwelling shortwave radiation (S↓), mixing ratio (MR), and potential temperature (θ). This avoids the need to stratify or preselect data, and enables constructing a single ERF that is valid for the observation period and, within in range of the measured variables, across a catchment of interest. (c) Hitherto, ERFs were determined as the inverse of a linear mixing matrix, using either numerical (Chen et al., 1999) or regression methods (Hutjes et al., 2010; Ogunjemiyo et al., 2003). Such procedure assumes a linear relationship between drivers and responses, which is subject of on-going discussion and research (e.g., Raupach and Finnigan, 1995). Instead, the present approach uses boosted regression trees (BRT), a non-parametric machine learning technique, to establish an ERF between drivers and responses. In contrast to parametric approaches, BRT does not assume a predetermined form of the response, but constructs an ERF according to information in the data. BRT can fit complex nonlinear relationships, automatically handle interactions between drivers, and provide predictive performance that is superior to most traditional modeling methods (e.g., Hu et al., 2010). Metzger et al. (2013, Appendix E) apply BRTs to N=8446 observations during 35 flights in the XRC (Sect. 2.4). The purpose is to extract the relationships between H, LE and land cover (LST, EVI) and meteorological (S↓, MR, and θ) variables. In Fig. 8 the BRTs for H are summarized as partial dependence plots. These show the effect of each individual variable on the response after subtraction of the offset (161 W m−2), and after accounting for the average effects of all other variables in the model. The partial dependence plots in Fig. 8 are sorted in order of the relative importance of the response variables (Friedman, 2001). The most important responses of H are non-linear (LST, θ), followed by linear responses (S↓, MR, and EVI). With the exception of MR and EVI the individual responses are positive in sign.
26 RESULTS Fig. 8. Boosted regression tree partial response plots of H for all five state variables in order of their relative importance (in braces). The fitted function (black) shows the variable response of the BRT over the range of one individual state variable, while the remaining state variables are held at an average, constant value. The red dashed line is a smoothed representation of the fitted function (locally weighted polynomial regression). Figure from Metzger et al. (2013, Appendix E). To evaluate the performance of the BRT models, MLFRs are established between BRT fitted values for H and LE and the observed fluxes. For both, H and LE the agreement between the BRT fitted values and the observed fluxes is excellent, with approximately unity slope and ≤1% median absolute deviation in the residuals. For the duration of each flight pattern, the trained BRT models are used to extrapolate H and LE across the XRC. For this purpose the median meteorological state variables during each flight pattern as well as topical grids of MODIS LST and EVI data are used. Grid cells that exceed the state space of the BRT training data set are excluded from extrapolation. Fig. 9 shows the resulting flux grids for three different days, with a spatial coverage of ≥92%. Despite the land cover classification was never used during the extrapolation process, several landscape units are clearly recognizable in the flux maps. For instance both, the Xilin river valley to the west, as well as the mountainous headwater area to the east display low sensibleand high latent heat fluxes. On the contrary, the non-vegetated basin on the northern tip shows consistently low evapotranspiration.
RESULTS 27 Fig. 9. Maps of LTFM predicted fluxes of sensible heat (H, top) and latent heat (LE, bottom) on 13, 17 and 26 July 2009 (left to right). Percentages in braces after the flight identifier (O8, O7, C2) indicate the spatial coverage of the prediction throughout the catchment. Meteorological state variables from the superimposed flight lines are used in the respective LTFM prediction. Figure taken from Metzger et al. (2013, Appendix E). To assess the reliability of the LTFM method for spatially resolving and extrapolating turbulent fluxes, Metzger et al. (2013, Appendix E) establish an uncertainty budget (Table 2); (a) Metzger et al. (2012, Appendix D) have shown that turbulent flux measurements with the WSMA platform and instrumentation are unbiased, and precise to ≤10%; (b) For a single flux measurement the systematic and random components of the uncertainty due to the limited sampling size of turbulent eddies are <1±57% for H and <1±121% for LE, respectively; (c) Small median residuals of 0±5% for H and 0±6% for LE between fitted and observed values emphasize that the BRT fitting technique is unbiased; (d) However, potential biases in the LTFM procedure can result from using non-linear BRT response functions for prediction. E.g., deviations from the true value of LST of similar magnitude but opposite sign do not cancel out in the predictions. Metzger et al. (2013, Appendix E) quantify the resulting bias for three different test cases (Table 2: Spatiotemporal analysis, BRT response function, BRT state variables). The systematic differences
34 NOTATION Parameters and variables α Attack an g le [rad] β Sidesli p an g le [rad] ρ Air densit y [k g m −3] θ Potential tem p erature [K] a Absolute humidit y [ g m −3] CL Lift coefficien t [-] e Euler’s number ( ≈2.71828 ) [-] E V I Enhanced ve g etation index [-] f Measurement fre q uenc y [Hz] H Sensible heat flux [W m −2] L Lif t [N] LE Latent heat flux [W m −2] LS T Land surface tem p erature [K] M R Mixin g ratio [ g k g −1] n Normalized fre q uenc y [-] N Sam p le size [-] R 2 Wei g hted coefficient of determination [-] s Scalar q uantit y ( wildcard ) [-] S Surface area of win g [ m 2] S ↓ Downwellin g shortwave radiation [W m −2] u* Friction velocit y [ m s−1] t Time [s] T Air tem p erature [K] u Alon g -wind s p eed [ m s−1] U ¯ Horizontal wind s p eed for the tower and the true airs p eed for the WSMA [ m s−1] v Cross-wind s p eed [ m s−1] vtas True airs p eed [ m s−1] wu p w U p wash velocit y [ m s−1] w Foot p rint wei g h t [-] w Vertical wind s p eed [ m s−1] x , y , z Cartesian coordinates [-] z Measurement hei g h t [m]
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LIST OF APPENDICES 43 List of Appendices LIST OF APPENDICES ...................................................................................................................... 43 APPENDIX A: INDIVIDUAL CONTRIBUTIONS TO THE JOINT PUBLICATIONS ................... 44 APPENDIX B: METZGER ET AL. (2011) ......................................................................................... 48 APPENDIX C: SUPPLEMENT TO METZGER ET AL. (2011) ........................................................ 73 APPENDIX D: METZGER ET AL. (2012) ......................................................................................... 87 APPENDIX E: METZGER ET AL. (2013) ....................................................................................... 106
50 APPENDIX B: METZGER ET AL. (2011) Fig. 1. Weight-shift microlight research aircraft D-MIFU, aircraft structural features are highlighted by dash-dotted lines. Sensor locations of the five hole probe (5HP), inertial navigation system (INS, inside aircraft nose) and universal laser sensor (ULS, below pilot seat) are indicated. For details on the respective installations see Sect. 2.2 and Table 2. Figure 3 details the layout of the five hole probe. The full performance characteristics can be found in Junkermann (2001). D-MIFU consists of a KISS 450 cambered wing by Air Creation, France, and the ENDURO-1150 trike manufactured by Ultraleichtflug Schmidtler, Germany. Owing to its aeroelasticity, the tailless delta wing is termed a flex-wing, contributing ≈15 % to the aircraft weight. The primary parts of the wing structure are the leading edges joined at the nose to the keel tube, which runs the root length of the wing (Fig. 1). Stretched over upper and lower surface is a high strength polyester sail. At a span of 9.8 m and keel length of 2.1 m, the wing provides a surface (S) of 15.1 m2. It is put under considerable internal loads during rigging, it’s form and rigidity being ensured by cross-tubes, rods and a wiring system. The basebar in front of the pilot seat is linked to the keel via two uprights and tensioned flying wires. It provides transmission of pitch and roll forces and is the primary flight control (Gratton, 2001). In the hangpoint on the wing keel the trike is attached to the wing. Since the trike is free to rotate in pitch and roll without hindrance, there is no pendular stability. In this regard the relationship of trike to wing is similar to the relationship of a trailing bomb to its carrier (e.g. HELIPOD, Bange and Roth, 1999). However trike and wing are fixed in their longitudinal axis, i.e. in the heading direction. The trike does not contribute significantly to the WSMA’s lift, but represents a large portion of weight (≈85 %), drag, and provides all thrust through a 73 kW pusher engine-propeller combination. Flight stability in three axes is based on the offset of torques appearing at different locations on the wing (Cook, 1994). Torques result from wing aerodynamical effects, which sum nearest to neutral (slight nose-down torque for cambered wings) in one point along the wing’s chord line, termed the wing’s centre of pressure (Fig. 2). The centre of gravity, as far as the wing is concerned, is located in the hangpoint. The net aerodynamical torque is offset by a longitudinal lever arm between the centres of pressure and by a longitudinal -gravity, determining the aircraft’s trim speed (the airspeed at which the aircraft will fly steadily without pilot input). Moreover increasing airspeed will result in an aeroelastical flattening of the wing, which is in contrast to FWA. This in turn can alter the balance of torsional loads and with it the circulation about the wing (Cook and Spottiswoode, 2006). 2.1 Physical properties The need to adapt wind calibration procedures designed for fixed-wing aircraft is mainly caused by two structural features of the WSMA. The trike, i.e. the turbulence measurement platform, is mobile for pitching and rolling movements below the wing. Therefore the trike-based flowand attitude angles must be measured with high resolution, precision and accuracy. Moreover, wing aerodynamics depends on its aeroelasticity with airspeed, and varying flow distortion in front of the wing must be considered. The effects of these WSMA features are not necessarily independent of each other, and may have a different impact on the wind measurement depending on the aircraft dynamics at a particular time. Therefore the WSMA was equipped with motion sensors. On the trike these were placed in the fuselage (Inertial
APPENDIX B: METZGER ET AL. (2011) 51 Fig. 2. Geometrical features of the weight-shift microlight aircraft and coordinate systems with axes X, Y, and Z used to compute the wind vector. The superscripts a, b, g, m and w represent, respectively, the aerodynamic-, body-, geodetic-, meteorological and wing coordinate systems (Supplement A). (A) Starboard view: Angle of attack (α), pitch angle (), normalized radius (n), wing upwash direction (ξ), centre of gravity and centre of pressure. (B) Rear view: Roll angle (); (C) Top view: Sideslip angle (β) and true heading (). Navigation System, INS) and the wind measuring pressure probe (3-D acceleration), extending ≈0.7 m and ≈3.5 m forward from fuselage and aft-mounted propeller, respectively (Figs. 1 and 2). Further, the wing was equipped with motion sensors in the hangpoint (3-D acceleration) and atop the wing (3-D attitude). The INS is the most reliable motion sensor (Table 2), since it integrates the complementary characteristics of global positioning system (unbiased) and inertial measurement (precise). Position and velocity are calculated from inertial measurements of 3-D acceleration and 3-D angular rate, and matched with data from two global positioning units using a Kalman filter. The INS outputs 3-D vectors of position, attitude, velocity, angular rates and acceleration. Airborne wind measurements are susceptible to distortion, since the aircraft itself is (a) a flow barrier and (b) must produce lift to remain airborne (Wyngaard, 1981; Cooper and Rogers, 1991). The aircraft’s propeller, trike, and wing can be sources of flow distortion. Only little distortion from trike structural features is expected transverse to the pressure probe: the trike body is symmetric on its port and starboard side, and the pressure probe, propeller and pilot are centred on its longitudinal axis (Figs. 1 and 2). In contrast the body is asymmetric on its upside and underside, and the propeller location is 0.8 m higher than the pressure probe. This suggests symmetric flows in transverse, and asymmetric flows in longitudinal and vertical directions. All of which are expected to carry continuously through the pressure probe location, since the probe is rigidly fixed to the trike. This however is not the case for distortion from the WSMA wing. While the wind measurement encounters lift-induced upwash from the wing (Crawford et al., 1996; Garman et al., 2008), the trike, and with it the pressure probe, has rotational freedom in pitch and roll towards the WSMA wing. In the following we will outline the dependences of upwash generation from the wing. The amount of lift (L) generated by the wing equals the aircraft’s sum of forces perpendicular to the airstream: L=ma g,z,(1) with the aircraft mass (m) and the vertical acceleration (ag,z) in the geodetic coordinate system (GCS, superscript g, positive northward, eastward and downward) at the wing’s centre of gravity (measured at, or dislocated to the hangpoint). For simplicity the acceleration perpendicular to the airstream was approximated by the vertical acceleration in the GCS. The maximum deviation during severe vertical manoeuvring (only used for evaluation) does not exceed ±1%. Also the aircraft control forces applied by the pilot meet in the hangpoint. During ABL measurements these are primarily changes in power setting and wing pitch to adjust the aircraft altitude. For level, unaccelerated flight, lift essentially equals the aircraft’s weight force, but is opposite in sign. The loading factor (LF) during vertically accelerated flight is then LF = L mg , the ratio of liftto weight force with g= 9.81 m s−2. Normalizing Lfor the airstream’s dynamic pressure (pq)and
52 APPENDIX B: METZGER ET AL. (2011) Fig. 3. Layout of the five hole probe, with letters indicating sensor locations. (A) The half sphere tip of the five hole probe, with ports for totaland differential pressure measurements. (B) Ports for static pressure measurement downstream of the half sphere. (C) Thermocouple and port for the capacitive humidity measurement. (D) Location of five hole probe 3-D acceleration sensor. Additional information is given in Sect. 2.2. the wing’s surface area (S) yields the unit-free lift coefficient (CL): CL =1 pq L S =2 ρv2 tas L S,(2) with wing loading (L S). Moreover pqin Eq. (2) can be substituted by air density (ρ) and true airspeed (vtas). In CL the wing’s ability to generate lift is determined to be approximately linear with wing pitch. As a consequence of lift generation air rises in front of the wing, which is defined as upwash. Crawford et al. (1996) provide the following parametrization to calculate the upwash velocity (vw up) for FWA: vw up =1 π2nvtas CL =1 π2n vtas pq L S,with δv tas p q δvtas ≈−0.3hPa −1.(3) Here vw up is defined as the tangent on a circle with normalized radius n. Thereby nis the separation distance from the wing’s centre of pressure to the position of the pressure probe, normalized by the effective wing chord (Fig. 2). The wing upwash direction ξis then enclosed by nand the trike body axis Xb. Since the wing is free to rotate in pitch and roll, vw up carries the orientation of the wing coordinate system (WCS, superscript w, positive forward, starboard, and downward). In Eq. (3) vw up varies inversely with n. Furthermore vw up can be expressed either directly proportional to vtas and CL, or directly proportional to relative airspeed (v tas p q ) and L S. Based on the functional relation between lift and upwash generation a treatment for the wind measurement from WSMA is derived in Sect. 4.1. 2.2 Instrumentation and data processing Wind measurement by airborne systems is challenging. High resolution sensors are needed to determine the attitude, position, and velocity of the aircraft relative to the earth, as well as the airflow in front of the fuselage. The instrumentation involved in the wind measurement and data acquisition, including the respective manufacturers, is summarized in Table 1. A more detailed description of sensor characteristics and uncertainties is provided in Table 2, while respective locations are displayed in Figs. 1 and 3. The principle is to resolve the meteorological wind vector from the vector difference of the aircraft’s inertial velocity (recorded by the inertial navigation system) and the wind vector relative to the aircraft. To determine the latter, the aircraft was outfitted with a specially designed lightweight five hole half sphere pressure probe (5HP, e.g. Crawford and Dobosy, 1992; Leise and Masters, 1993). Figure 3a shows the half sphere tip of the 5HP, with a total pressure (pt) port at its centre. Two additional pressure ports on each, the vertical (p1,p3) and the horizontal axis (p2,p4), surround the central port at an angle of τ=45 ◦. These differential
APPENDIX B: METZGER ET AL. (2011) 53 Table 1. Overview of sensors and electronic instrumentation used for the wind measurement. Component Model Manufacturer Address Butterworth low pass filter AF40-4BU TP E.S.F. electronic G¨ ottingen, Germany Electronic compass module TCM2-20 PNI Sensor Corporation Santa Rosa, USA Humidity sensor SHT75 Sensirion AG Staefa, Switzerland Industrial computer PR-Z32-EA-ST Diamond Systems Corporation Newark, USA Inertial navigation system RT3102 Oxford Technical Solutions Upper Heyford, England Differential pressure sensor PCLA12X5D Sensortechnics GmbH Puchheim, Germany Statistic pressure sensor SP82AL Capto As. Horten, Norway Thermocouple CHAL-002 OMEGA Engineering, Inc. Stamford, USA Three-axis accelerometer ADXL330 Analog Devices, Inc. Norwood, USA Universal laser sensor ULS (Second edition) Laser Technology, Inc. Centennial, USA Operating system Minix 2.0 Andrew Stuart Tanenbaum Amsterdam, Netherlands pressure readings are used to determine attack angle (α)and sideslip angle (β), respectively, arrows indicate the direction of positive angular measurement. Polyetherketone tubings of ≤80 mm length and 1 mm inner diameter are used to connect these ports of 1.5 mm diameter to their respective pressure transducers. Additional (unnumbered) pressure ports at 45◦increments are not used in this study. Six pressure ports are located downstream of the half sphere (Fig. 3b). These are ring-compensated around the circumference of the five hole probe for flow angle independent static pressure (ps) measurement. Figure 3c shows the freely suspended 50 μm type K thermocouple for fast temperature (Ts) measurement and the 10 mm port for a capacitive humidity measurement (e). Time constants of thermocouple and humidity sensor are <0.02 s and <5s at vtas =27ms −1, respectively. Humidity readings are solely used to provide the air density correction (Eq. A10) for the vtas computation. At a typical true airspeed of 28 m s−1only about 30 % and 15 % of the dynamicand differential pressure transducers’ range is exploited, respectively.Thishoweverenablesthe5HPtobeusedalsoonfaster aircraft such as motorized gliders, e.g. for inter-comparison measurements. Plugand-socket connectors with locating pins insure a repeatable location of the 5HP with respect to the INS within <0.1◦. The whole installation weights in at 350 g. 100 Hz temperature and pressure signals pass through hardware (analogue) four-pole Butterworth filters with 20 Hz cut-off frequency to filter high-frequency noise. Filter slope and frequency were chosen to allow miniaturization and comply with the system’s 15 Hz bottleneck filter frequency of the infra-red gas analyser for EC flux calculation (not used in this study). The filter leads to a phase shift in the signal of ≈20 ms, and the amplitude of a 10 Hz sine signal is reduced by <1 %. The INS data are stored in a standalone system at a rate of 100 s−1. Remaining data streams for the wind computation are stored centrally at a rate of 10 s−1by an in-house developed data acquisition system (embedded Institute for Meteorology and Climate Research data acquisition system, EIDAS). EIDAS is based on a ruggedized industrial computer and a real-time UNIX-like operating system. 5 V analogue signals at ≥10 Hz pass through a multiplexer and A/D converter at a resolution of 16 bits. For oversampled variables (100 Hz) the resulting signal is block averaged. The INS has a latency time for internal calculations of ≈4 ms. Yet INS and EIDAS data streams have to be merged to calculate the ambient wind, and later turbulent fluxes. Therefore the resulting time lag between INS and 5HP of ≈16 ms has to be considered. The appropriate time shift of one to two 100 Hz increments is determined via lagged correlation. During post-processing the 100 Hz INS data set is then shifted by this increment before block averaging to 10 Hz. A spike test revealed ≈7 % missing values in the wing attitude data, which were filled via linear interpolation. To enable angular averaging or interpolation, heading angles were transformed from polar to Cartesian coordinates. 3 Wind vector Approaches to compute the wind vector from fixed-wing aircraft are often similar in principle, though differ considerably in detail (e.g., Tjernstr¨ om and Friehe, 1991; Williams and Marcotte, 2000; van den Kroonenberg et al., 2008). Therefore we provide a supplement to this study at http://www.bayceer.uni-bayreuth.de. Supplement A details the specific implementation that was found suitable for the wind measurement with our weight-shift microlight aircraft. A model to propagate uncertainty through the wind vector equations is provided in Supplement B. Relevant notation and abbreviations are listed in Supplement C. The system’s calibration was arranged bottom-up, i.e. from single instrument to collective application. The procedure starts with the laboratory calibration of the individual sensors, continues with the characterization of flow around the 5HP, and concludes with the treatment of WSMA specific effects on the wind measurement. Finally three
54 APPENDIX B: METZGER ET AL. (2011) Table 2. List of measured variables, sensor characteristics, signal processing and data acquisition. Individual sensor locations are described in Sect. 2.2 and displayed in Figs. 1 and 3. Resolution refers to the smallest change registered by the data acquisition (DAQ) units. σis the overall sensor uncertainty provided by the manufacturer in form of one standard deviation. Signal rates are displayed for sampling, filtering and storing (Signal SFS). Data acquisition takes place in two forms, standalone (SA) and on the central DAQ unit EIDAS. For non SA devices signal forwarding via A/D converter, recommended standard 232 (RS232) or serial peripheral interface (SPI) is indicated (Interface DAQ). Quantity Variable Sensor Range Resolution σSignal SFS [s−1]Interface DAQ Airframe motion Latitude/longitude RT3102 ±89.9◦/±180◦6×10−15◦1.1 m 100 100 SA Altitude sea level RT3102 <18 000 m 0.001 m 2.7 m 100 100 SA Altitude ground level ULS 0.15–500 m 0.001 m 0.04 m 10 10 RS232 EIDAS Heading, body bRT3102 0–360◦0.00006◦0.1◦100 100 SA Heading, wing wTCM2-20 0–360◦0.1◦0.5◦16 10 RS232 EIDAS Pitch/roll, body b/bRT3102 ±90◦/±180◦0.00006◦0.06◦100 100 SA Pitch/roll, wing w/wTCM2-20 ±20◦0.1◦0.2◦16 10 RS232 EIDAS 3-D velocity, body vm gs RT3102 0–515 m s−10.0001 m s−10.02 m s−1100 100 SA 3-D ang. rat., body bRT3102 ±100◦s−10.0006◦s−10.01◦s−1100 100 SA 3-D accel., body abRT3102 ±10 g 0.00001 g 0.001 g 100 100 SA 3-D accel., wing ADXL330 ±3 g 0.0003 g 0.01 g 100 100 A/D EIDAS 3-D accel., 5HP ADXL330 ±3 g 0.0003 g 0.01 g 100 100 A/D EIDAS Relative air motion Static pressure ps,ASP82AL 0–1000 hPa 0.02 hPa 0.1 hPa 100 20 10 A/D EIDAS Dynamic pressure pq,APCLA12X5D ±12.5 hPa 0.0005 hPa 0.06 hPa 100 20 10 A/D EIDAS Attack pressure pαPCLA12X5D ±12.5 hPa 0.0005 hPa 0.06 hPa 100 20 10 A/D EIDAS Sideslip pressure pβPCLA12X5D ±12.5 hPa 0.0005 hPa 0.06 hPa 100 20 10 A/D EIDAS Fast temp. TsCHAL-002 −20–60 ◦C 0.0015 K 0.5 K 100 20 10 A/D EIDAS Humidity, 5HP eSHT75 0–70 hPa 0.07 hPa 0.3 hPa 10 10 SPI EIDAS independent lines of analysis are used to quantify the overall system uncertainty: (a) uncertainty propagation through respective equations, (b) in-flight testing and (c) comparison of the measured wind vector with ground based measurements. 3.1 Wind tunnel study Priortoin-flight use, the five hole probe was tested in an open wind tunnel at the Technical University of Munich, Germany, Institute for Fluid Mechanics. Objectives were to (a) confirm the applicability of transformation Eqs. (A5)–(A7) and (b) determine the 5HP’s uncertainty in the operational range of the WSMA. The 5HP was mounted on D-MIFU’s nosecap and measuring occurred at airflow velocities ranging from 20 to 32 m s−1(equivalent to 2–6 hPa wind tunnel dynamic pressure). The dynamic pressure at the design stagnation point (i.e. the wind tunnel angles of attack ˜α=0 ◦and sideslip ˜ β=0 ◦) was measured at airflow velocity increments of 1 m s−1. At increments of 2 m s−1a total of 570 permutations of 10 predefined angles ˜αand ˜ β, each ranging from 0◦to +20◦, were measured. In addition one-dimensional symmetry tests were performed for six predefined angles ˜α and ˜ βranging from −20◦to +20◦at an airflow velocity of 30 m s−1. For the WSMA operational true airspeed of 28 m s−1(or 4.5 hPa dynamic pressure during flight) the uncertainty of the wind tunnel airflow velocity was 0.7 % or σ= 0.03 hPa dynamic pressure. The airflow angles were varied by a calibration robot, the uncertainty in the wind tunnel angles was σ˜α, ˜ β<0.1◦(equal to the alignment repeatability between 5HP and INS). The wind tunnel angles ˜α,˜ βare related to the airflow angles αand βused for the wind calculation (Boiffier, 1998): α=˜α, β=arctan tan ˜ β cos ˜α.(4) The wind vector calculated from airborne measurements is very sensitive to uncertainties in its input variables. Calibration in laboratory and assessment in wind tunnel yield the basic sensor setup. However the effect of sensor and alignment uncertainties on the wind vector is not straightforward, and involves numerous trigonometric functions (Supplement A). To make the influence of individual measured quantities on the wind vector transparent, linear uncertainty propagation models were used (Supplement B). The intention is to investigate the wind measurement’s uncertainty constraint by sensor setup and wind model description under controlled
APPENDIX B: METZGER ET AL. (2011) 55 Table 3. Flight campaign summary for locations Lake Starnberg (ST), Lindenberg (LI), and Xilinhot (XI). Anticyclonic and cyclonic conditions are indicated by a and c, respectively. For the flight patterns racetrack (RACE), wind square (SQUA), variance optimization (VARI), vertical wind specificflights (VW1–VW3) and the comparison to ground based measurements (COMP) the number of available datasets for each date is given together with respective track length (km) in parenthesis. Additional information is given in Sect. 3.2. Date 19 Jun 24 Jun 25 Jun 11 Jul 15 Oct 16 Oct 18 Oct 20 Oct 21 Oct 31 Jul 2008 2008 2008 2008 2008 2008 2008 2008 2008 2009 Location STSTSTSTLILILILILIXI CYC 950 hPa a a c c a c a a c a CYC 500 hPa a a a a a c a a a a p[hPa] 1019 1021 1020 1015 1017 1008 1020 1018 1012 1010 Tmax [◦C]22.4 21.6 27.7 27.8 14.8 14.3 13.1 16.5 21.7 31.1 Cloud cover 5/8 4/8 4/8 4/8 8/8 8/8 5/8 4/8 4/8 7/8 RACE 2 (10) 4 (10) 4 (10) 4 (10) SQUA 5 (12) 1 (12) VAR I 6 (20) 4 (20) 2 (80) VW1 1 (4) VW2 1 (11) 1 (11) VW3 1 (9) COMP 6 (12) 5 (12) 6 (12) boundary conditions. Because of flow distortion effects (Sect. 2.1) the boundary conditions during flight however are less well known and might be significantly different from the laboratory. Therefore a methodology for in-flight calibration and evaluation was derived. It consists of a WSMA specific calibration model and -flight patterns. 3.2 Flight campaigns These patterns were carried out during three flight campaigns at different sites, each with its characteristic landscape and meteorological forcing: 3.2.1 Lake Starnberg, Germany The first flight campaign took place from 19 June to 11 July 2008 over Lake Starnberg (47.9◦N, 11.3◦E). The lake is located in the foreland of the German Alps, that is a slightly rolling landscape (600–800 m a.s.l.) and mainly consists of grassland with patches of forest. The campaign focused on early morning soundings in the free atmosphere above Lake Starnberg. 3.2.2 Lindenberg, Germany In a second campaign from 14–21 October 2008 comparison flights were carried out at the boundary layer measurement field of the German Meteorological Service, Richard-Aßmann-Observatory, near Lindenberg (52.2◦N, 14.1◦E). The area lies in the flat North German Plain (40– 100 m a.s.l.), where land-use in the vicinity is dominated by an equal amount of agriculture and forests, interspersed by lakes. Flights in the atmospheric boundary layer were conducted under near-neutral stratification (stability parameter |z L|≤0.2). 3.2.3 Xilinhot, China To extend the operational range, an additional dataset under conditions approaching free convection ( z L−0.2) was included in this study: From 23 June to 4 August 2009 an Eddy-Covariance flux campaign was performed over the steppe of the Mongolian Plateau. The hilly investigation area south of the provincial capital Xilinhot, Inner Mongolia, China (43.6◦N, 116.7◦E, 1000–1400 m a.s.l.) is covered by semi-arid grassland, intersected by a dune belt. A summary of all flights as well as an overview of the synoptic weather conditions is provided in Table 3. Synoptic wind direction and cyclonality (CYC) were retrieved from the objective weather type data base of the German Meteorological Service (Bissolli and Dittmann, 2001). The XI flight on 31 July 2009 was supplemented with publicly available data from the US National Centre for Environmental Prediction. Prevailing wind direction throughout all flight days was south-west. Sea level pressure (p), 2 m a.g.l. maximum temperature (Tmax) and cloud coverage are 24 h observations of the closest national meteorological service station on the respective day. 3.3 Flight patterns In the following, the strategies of the individual flight patterns at these three sites are categorized in five classes and briefly outlined. The first four of them serve to isolate independent parameters for the flow distortion correction,
56 APPENDIX B: METZGER ET AL. (2011) while the last one is used to compare aircraft to ground based measurements. The patterns are used for the actual calibration and evaluation of the wind measurement in Sect. 4. 3.3.1 Racetrack pattern The first type of flight pattern consists of two legs parallel to the mean wind direction at constant altitude (one pair), one upstream leg (subscript +) and one downstream leg (subscript −). The legs are suitably aligned with the mean wind when having opposite tracks for identical aircraft settings. For any racetrack pair flown at constant true airspeed (vtas), the (assumed homogeneous and stationary) mean wind (vm) cancels out (Leise and Masters, 1993; Williams and Marcotte, 2000): |vm gs|=1 2(|vm gs,+|+|vm gs,−|) =1 2(vtas,++ |vm|)+(vtas,−− |vm|) =vtas.(5) In this way the INS measured ground speed (|vm gs|) can be used to minimize the difference ||vm gs|−vtas|by iteratively adjusting dynamic pressure in Eq. (A8). This yields an inverse reference for dynamic pressure, which is solely based on INS data. Since the temperature and static pressure sensitivities of Eq. (A8) are two orders of magnitude lower than that of the dynamic pressure (Table 5), the inverse reference can now be used to adjust the 5HP measured dynamic pressure to in-flight conditions. A total of 14 racetrack pairs at airspeeds ranging from 21 to 32 m s−1were conducted in the calm and steady atmosphere above the ABL (Table 3). 3.3.2 Wind square pattern The second type of flight pattern consists of four legs flown at constant altitude and constant vtas in the cardinal directions (north (N), east (E), south (S), west (W)). Assuming that the flights were carried out in a homogeneous and stationary wind field, the measured horizontal wind components (vm u,vm v) should be independent of aircraft heading, i.e. constant at each side of the wind square. With it a potential offset in βcan be determined: The offset in βis changed iteratively, until the standard deviation of vm uand vm vthroughout a wind square is minimized. For flights above the ABL, in addition the vertical wind component can be expected to be negligible. A potential offset in αcan be determined in a similar fashion to β, however, under the constraint of minimizing the absolute value of the vertical wind component (vm w). The wind square pattern further allows to estimate the uncertainties of vtas and β: Since the flight legs are aligned in the cardinal directions, along-track wind components (vm u(N, S), vm v(E, W)) are predominantly sensitive to errors in vtas. Cross-track wind components (vm v(N, S), vm u(E, W)) are predominantly sensitive to errors in β. Thus, errors in vtas and βcan be estimated as: σ uv,tas =1 2v m u (N)−v m u (S) 2 +v m v (E)−v m v (W) 2 σ uv,β =1 2v m v (N)−v m v (S) 2 +v m u (E)−v m u (W) 2 .(6) Six wind squares were flown above the ABL at airspeeds from 23 to 29 m s−1(Table 3). 3.3.3 Variance optimization pattern The third type of flight pattern is a straight and level ABL sounding, intended for EC flux measurement. The assumption made here is that errors in the flow angles increase the wind variance. In contrast to the previous two patterns, this method does not imply homogeneity or stationarity. It can therefore be applied even in the presence of thermal turbulence, i.e. in the convective ABL (Tjernstr¨ om and Friehe, 1991; Khelif et al., 1999; Kalogiros and Wang, 2002a). Offsets and slopes for αand βwere computed to minimize (a) the sum of the wind components variances plus (b) the absolute value of the mean vertical wind. Here it is expected that vm wapproaches zero for a sufficiently high number of datasets above approximately level terrain. Twelve straight and level ABL soundings (or 360 km of flight data, Table 3) at airspeeds from 24 to 28 m s−1between 50 and 160 m above ground were used for this variance optimization. 3.3.4 Vertical wind specific patterns The fourth type of flight pattern specifically addresses errors in vm w, the wind component crucial for EC flux applications. Based on Lenschow (1986) straight-flight calibration patterns were performed above the ABL. These are intended to assess and minimize the possible influence of aircraft (in our case WSMA) lift and trim on vm w. At airspeeds ranging from 21 to 32 m s−1five vertical wind (VW) specificflights, divided into three sub-patterns, were utilized in this study (Table 3): –VW1 – (Level acceleration – deceleration): whilst the engine’s power setting was gradually varied, the wing pitch (and with it lift coefficient) was adjusted to maintain flight altitude. With this pattern the influence of aircraft trim on vm wcan be determined. –VW2 – (Smooth oscillation): starting from level flight the power setting was slowly varied, while the wing pitch was adjusted to maintain constant vtas. In consequence, the aircraft ascended and descended about the mean height, while CL remained approximately unchanged. VW2 was used to assess the influence of wing pitch and aircraft vertical velocity on vm w.
APPENDIX B: METZGER ET AL. (2011) 57 –VW3 – (Forced oscillation): starting from level flight the wing pitch was forcibly alternated. The aircraft ascended and descended around the mean height, while power setting remained unchanged. In response aircraft accelerations and velocities, and with it the airflow around the aircraft, changed. VW3 was used to assess the integral influence of vertically accelerated flight on vm w, as e.g. during terrain following flights in the ABL (see Sect. 4.1, Step G6). 3.3.5 Comparison to ground based reference measurements The fifth and last type of flight pattern is a series of comparison measurements between WSMA and ground based measurements. These were carried out at the boundary layer measurement field of the German Meteorological Service, Richard-Aßmann-Observatory, near Lindenberg. The lower part of the ABL was probed by a 99-m tower and a SODAR with their base at 73 m a.s.l. The 99-m tower provided cup measurements (10 min averages) of wind speed at four levels (40, 60, 80, and 98 m a.g.l.), the wind direction was measured with vanes at heights of 40 and 98 m a.g.l. (10 min averages). Sonic anemometers mounted at the tower provided turbulent wind vector measurements at 50 and 90 m a.g.l. The SODAR wind vector profiles (15 min averages) reached, at increments of 20 m, from 40 to 240 m a.g.l. In addition a reference for static pressure was provided at 1 m a.g.l. 17 cross-shaped patterns (van den Kroonenberg et al., 2008), with flight legs of 3 km centred between tower and SODAR, were performed at 24 and 27 m s−1airspeed (Table 3). The flights were carried out at the approximate sounding levels of tower and SODAR (50, 100, 150, 200 and 250 m a.g.l.). This allows a direct comparison of WSMA and ground based measured wind components. Aircraft and sonic wind measurements were filtered using the stationarity test for wind measurements by Foken and Wichura (1996). SODAR, cup and vane data were stratified for the best quality rating assigned by the German Meteorological Service. Simultaneous wind data of WSMA and ground based measurements were accepted for comparison only if they agreed to within ±20 m height above ground (which equals ≈2σof variations in WSMA altitude). This data screening resulted in a total of 20 data couples (between WSMA and cups/vanes, sonics and SODAR) for vm uv, and 19 data couples for vm w. Compared to cups/vanes, sonics and SODAR, the WSMA soundings were on average higher above ground by 0.1 ±5.5, 8.7 ±5.6, and 0.5 ±5.3 m, respectively. 4 Application to weight-shift microlight aircraft To understand operational requirements for setup and calibration of the wind vector measurement, aircraft attitude and dynamics were assessed for a straight and level boundary layer flight (Table 3, variance optimization flight on 31 July 2009). Histograms of aircraft properties were calculated from ≈3×104data points sampled ≈50 m a.g.l. (Fig. 4). Variations in true airspeed and aircraft vertical movement were resulting from aircraft manoeuvres to follow the terrain contours as well as thermal turbulence (labile stratification, stability parameter z L≈−0.9). Attitude angles (b,b) indicate constant upward pitching and anticlockwise roll of the trike, respectively. Pitching as well as rolling increase in magnitude with vtas, i.e. power setting of the engine. The pitching moment can be understood as the dynamic balance with vtas between propeller thrust and the drag difference between the trike (low) and the wing (high). This is confirmed by an estimate of the attack angle (α), which shows fewer variation due to alignment with the streamlines, though alike bincreases with vtas (≈0.4◦per ms −1). The rolling moment can be understood as counterbalance of the clockwise rotating propeller torque. In addition side-slipping of the trike over its port side was detected from an estimate of the sideslip angle (β), increasing at a rate of ≈−0.6◦per m s−1with vtas. The operational range in αand βestimates were found ≈|15◦|, averaging to 6.0 ±1.8◦and −5.5 ±3.2◦, respectively (Fig. 4). Following the lift Eq. (2), wing pitch decreases with vtas. That is, with increasing vtas the noses of wing and trike approach each other. Wing roll does not display dependence on vtas, i.e. no counter reaction on propeller torque or trike roll. The wing loading factor (LF) was found to vary within a range of σ≈0.1 g (Fig. 4), from which the upwash variation in front of the wing can be assessed. Using five hole probe measured vtas in Eq. (3) the upwash velocity (vw up) at 5HP location was determined to 1.52 ±0.19 m s−1. D-MIFU is travelling at low airspeed and has a small relative separation (n) between wing and 5HP. Both factors lead to an increase in vw up. Various research aircraft have been assessed with regard to upwash generation (Crawford et al., 1996), compared to which D-MIFU ranges mid-table. This can be ascribed to the low wing loading, whichisafractionofthoseoffixed-wing aircraft, and decreases vw up. Wing loading, and with it vw up, are directly proportional to vertical acceleration and aircraft mass in Eq. (1). Hence σ≈10 % variation in LF (Fig. 4) accounts for most of the variance in vw up. In addition aircraft mass can vary during the flight due to fuel consumption (±4 %) and among measurements due to weight differences of pilots (±2 %). Due to the trike’s rotational freedom, upwash about the wing’s centre of pressure can partially translate into alongand sidewash (longitudinal and transverse to the trike body, respectively) at the 5HP location in the trike body coordinate system (BCS). Mean aerodynamic chord theory yields the centre of pressure’s position of the wing within 0.2 m or <10 % chord length of the centre of gravity. Assuming the centres of pressure and gravity to coincide, the pitch difference between wing and trike can be neglected, and vw up is easily transformed
58 APPENDIX B: METZGER ET AL. (2011) Fig. 4. Histograms of aircraft properties derived for the flight on 31 July 2009 (Table 3). Component density is scaled so that the histograms have a total area of one. Red vertical lines indicate distribution average (solid) and standard deviation (dashed). The black dashed bell curve displays a reference normal distribution: True airspeed (vtas), attack angle (αA), sideslip angle (βA), aircraft vertical velocity (vm,z gs ), trike pitch- (b) and roll (b) angles, loading factor (LF, the ratio of liftto weight force), as well as wing pitch- (w) and roll (w) angles. into the BCS: the transformation Eq. (A13) was carried out about zero heading difference, the wing upwash direction (ξ=−41.9 ±0.3◦), and the roll difference between wing and trike. Wing upwash net effect at the 5HP location was then directed forward, right and upward with 1.01 ±0.13 m s−1, 0.12 ±0.13 m s−1,and−1.12 ±0.14 m s−1in trike body coordinates (Fig. 5). 4.1 Wind measurement calibration The sensitivity of the wind model description was analysed by linear uncertainty propagation models (Supplement B). The first model in Eq. (B1) permits to express the sensitivity of the wind computation as a function of attitude angles, flow angles and true airspeed. It was carried out for two reference flight states at vtas =27ms −1. In State 1 attitude and flow angles were assumed small (1◦), as it would be typical for calm atmospheric conditions. This allows for the small-angle approximation in Eq. (B1), resulting in uncertainties for the wind components (vm uvw) as a function of the heading angle (). In State 2 attitude (10◦)andflow angles (−15◦) were approximately increased to their 95 % confidence intervals during soundings in the convective ABL (Fig. 4). Consequently the full form of Eq. (B1) must be used for State 2. It allows to calculate the maximum uncertainty in the wind components (|vm uvw|) over all ,as well as to compare these between both flight states. Both states were inferred uncertainties of 1◦and 0.5 m s−1for
APPENDIX B: METZGER ET AL. (2011) 59 Table 4. Input uncertainty (IU) from the linear uncertainty propagation model Eq. (B1). For the sensitivity analysis the model was forced with two different reference states, State 1 with small and State 2 with enhanced flow (α,β) and attitude (b,b,b,) angles. Both states were inferred similar uncertainty quantities fiin α,β,b,b,b, and true airspeed (vtas). After calibration Step B the reference State 2 was used for the uncertainty propagation: the actual uncertainties in (a) the flow computation (α,βand vtas, Table 5), and (b) the sensor alignment (b,b,b) were inferred. Additional information is given in Sect. 4.1. Variable αβ bbbvtas IU Model forcing State 1 1◦1◦1◦1◦0...360◦27 m s−1 State 2 −15◦−15◦10◦10◦0...360◦27 m s−1 fi,sensitivity 1◦1◦1◦1◦1◦0.5 m s−1 fi,propagation 0.76◦0.76◦0.1◦0.1◦0.1◦0.34 m s−1 Results State 1 – sensitivity vm u[ms −1]<0.01 0.47cos<0.01 <0.01 0.47cos0.50 1.08 vm v[ms −1]<0.01 −0.47sin<0.01 <0.01 −0.47sin0.50 1.08 vm w[ms −1]0.47 <0.01 −0.47 <0.01 <0.01 <0.01 0.95 |vm uv|[ms −1]0.01 0.47 <0.01 0.01 0.47 0.5 1.08 |vm w|[ms −1]0.47 0.01 0.48 0.01 0.00 <0.01 0.97 Results State 2 – sensitivity |vm uv|[ms −1]0.21 0.47 0.21 0.14 0.42 0.45 1.34 |vm w|[ms −1]0.41 0.05 0.32 0.14 0.00 0.22 1.14 Results State 2 – propagation |vm v|[ms −1]0.16 0.36 0.02 0.01 0.04 0.30 0.64 |vm w|[ms −1]0.31 0.04 0.03 0.01 0.00 0.15 0.55 Fig. 5. Histograms of wing-generated alongwash, sidewash and upwash at the five hole probe location. Results are calculated from wing properties in Eqs. (1)–(3) and then rotated from winginto trike body coordinates (Fig. 2) using Eq. (A13). Presented is the same dataset and in the same manner as in Fig. 4. angularand vtas measurements, respectively. From State 1 it can be seen that the major uncertainty in the horizontal wind components (vm uv) originates from vtas, sideslip angle (β) and heading angle (), where βand carry similar sign and sensitivity (Table 4). On the contrary, the vertical wind component (vm w) is similarly sensitive to attack angle (α) and pitch angle (), yet with reversed sign. As compared to State 1, in State 2 the absolute uncertainties in the horizontal (|vm uv|) and vertical (|vm w|) wind components are increased by 24 % and 18 %, respectively. The increase however does not originate from the most sensitive terms, but from formerly negligible terms such as trike roll (b).
66 APPENDIX B: METZGER ET AL. (2011) Fig. 10. Smooth oscillation flights (VW2) on 24 June 2008 (left) and 25 June 2008 (right). In addition to the variables explained in Fig. 8 the vertical aircraft velocity (vm,z gs ) is shown. Additional information is given in Sect. 4.1 Step G3. independence of vm wfrom vtas, the detected BIAS depends on αup,off in Eq. (7). Both, αup,off and αupw,slo were determined using the VW1 flight on 25 June 2008 during ambiguous cyclonality atop and below measurement altitude (Table 3). In Fig. 9 the determination of αupw,slo depends on the change of CL, while the offset αup,off depends on the ambient vertical wind. During the inverse reference procedure vm wwas forced to zero while, e.g. in an anticyclone, subsidence occurs. In such a situation αup,off would be underestimated. During the VW flights on 24 and 25 June 2008, cyclonality and BIAS in vm wboth changed. While αupw,slo is insensitive, no constant αup,off could be determined from the VW flights. At this point the variance optimization flights in the ABL are of importance. Assuming constant ABL height (approximately fulfilled for noontime EC soundings) the second optimality criteria states that due to mass conservation vm wapproaches zero for a sufficiently high number of datasets. With it αup,off was determined directly from ABL flights. Using the first variance optimization optimality criteria, i.e. the minimization of the wind variance, also αand βslopes were tested. Step G5 – Iterative treatment of cross dependences An approach similar to Eq. (7), the explanation of upwash in α, was used to explain sidewash in β: β∞=βA−βupw,off +βupw,sloCL,(8) using the calibration criteria of the wind square flights for parametrization. According to Eq. (A11) cross dependence occurs between the parametrizations in αand β. This problem was solved by iterating the optimality criteria for wind square, vertical wind, and variance optimization flights in sequence. The order of this sequence, i.e. first optimizing for the horizontal wind components (vm uv), then for the vertical wind component (vm w), was chosen due to their different order of magnitude and importance for EC application. Spurious contamination with vm wwould change vm uv only by a fraction. The other way around however would result in considerably higher contamination in vm w.Thefinal calibration coefficients are summarized in Table 6. Compared to the upwash parametrization, sidewash was found to be modest (βupw,off =−0.004 rad) and less sensitive regarding CL (βupw,slo =−0.010 rad, Table 6). This is in line with the initial attempt to resolve the circulation around the wing and the trike movement explicitly (Fig. 5). The findings also confirm our initial hypothesis that flow transverse to the pressure probe requires less correction than in the vertical direction (Sect. 2.1): leaving dynamic considerations aside (i.e. lift coefficient is zero), the magnitude of the sideslip angle correction is one order of magnitude lower than the attack angle correction (0.039 rad, offsets in Table 6). For a true airspeed of 30 m s−1this affects the wind measurement to approximately −0.1 m s−1and 1.2 m s−1, respectively. The transverse distortions increase and the vertical distortions decrease at a ratio of ≈1:3, when considering interactions with propeller and wing (i.e. non-zero lift coefficient, slopes in Table 6). Step G6 – Application to terrain following flight The uncertainty of the correction during terrain following flight can be assessed from the regression errors, e.g. in the upwash attack angle for the vertical wind. In Step G3 the level acceleration-deceleration flight was used to calibrate the regression slope. This slope did not differ significantly compared to the forced oscillation flight, with −0.027 ±0.002 and −0.024 ±0.002, respectively. In Step G4 we used 12 ABL flights or 360 km of flight data to
APPENDIX B: METZGER ET AL. (2011) 67 parametrize the regression offset (0.039 ±0.003). The combined errors in slope and intercept were applied to the terrain following flight on 31 July 2009. The resulting uncertainty in the vertical wind measurement is within 0.1 m s−1(RMSE) for the mean and 1 % for the variance. This compares to the magnitude of the correction, which is in the order of 0.5 m s−1for the mean and 3 % for the variance, respectively. Many variables in the ABL scale with distance from the exchange surface (e.g. Mahrt, 2000; Mahrt et al., 2001). Interpretable results can be achieved by flying at approximately constant altitude above ground (e.g. Betts et al., 1990; Vickers and Mahrt, 1997). Yet many terrestrial surfaces are not ideally flat. During terrain following measurements we focus on mostly horizontal flight tracks between 40 and 80 km extend. Typical altitude gradients during such flight patterns are 100 m vertical on 10 km horizontal, and rarely reach ±5◦ climb angle. In order to adjust aircraft altitude, the pilot anticipates the terrain contours at a scale of kilometres. At typical airspeeds this corresponds to an adjustment of power setting and wing pitch through the pilot at frequencies <0.1 Hz. In addition to the low frequency control forces, also external forces due to atmospheric turbulence and mesoscale motions meet in the hangpoint. An increase in the vertical wind variance in the order of 1 % would result when applying the correction for low frequency pilot actions to the entire frequency spectrum. Consequently the correction is only applied to frequencies <0.1 Hz. This is achieved by calculating Eqs. (7), (8) through a third order Savitzky-Golay complementary filter (e.g. Chen et al., 2004). The treatment leads to a decrease in the vertical wind variance in the order of −3 %. This is expected since the impact of the low frequency pilot actions on the wind measurement is removed. Low frequency atmospheric motions, such as turbulent organized structures, overlap with pilot actions in frequency space. The effect of low frequency atmospheric motions on the correction can be estimated with a simple example. In a large-scale downdraft of velocity wdan aircraft of mass mand airspeed vtas has to produce the total lift L=mag,z(1+wd/vtas), see Eq. (1). As compared to zero vertical wind conditions the lift, and with it the lift coefficient in Eq. (2), is changed by the ratio of wd/vtas.For the flight on 31 July 2009 a ratio of ±1 % is equivalent to wd=±0.27 m s−1, a typical value for turbulent organized structures in the ABL (e.g., Steinfeld et al., 2007). To test the influence on the correction a sinusoidal signal with amplitude 1 % and frequency 0.01 Hz was added to the measured lift coefficient. The maximum deviation from the undisturbed measurement is within ±3 %, or sub centimetre. The variance of the vertical wind is changed by <0.01 %. We conclude that the correction can be applied to the entire frequency range ≤0.1 Hz without introducing significant uncertainty to the wind measurement. 4.2 Wind measurement evaluation After completing all calibration steps, the wind measurement with the WSMA was evaluated. The evaluation was carried out in three lines of analysis, (a) uncertainty propagation, (b) wind square flights, and (c) comparison to ground based wind measurements. For a true airspeed of 27 m s−1 the propagation of uncertainties in sensors (flow angle differential pressures, dynamicand static pressures, static temperature, and water vapour pressure), their basic calibration and wind model description yield an uncertainty (σ) of 0.76◦, 0.76◦, and 0.34 m s−1in attack angle (α), sideslip angle (β) and true airspeed, respectively (Table 5). Feeding the input uncertainty Eq. (B1) with these quantities extends the uncertainty propagation to the wind components (Table 4). The input error is formulated worst case, and parametrized for the 95 % confidence intervals of the attitude and flow angles. In addition the uncertainty of the inertial navigation system (0.02 m s−1) was considered in the wind vector Eq. (A1). This allows to estimate the maximum potential uncertainty by sensor setup and wind model description. The results for the maximum overall uncertainty bounds are 0.66 and 0.57 m s−1for the horizontal (vm uv) and vertical (vm w)wind components, respectively. Figure 11 shows the results of all wind square flights. For wind velocities >2ms −1vm uv determined for individual legs deviate less than 10 % from the average for the entire square. The residuals did not scale with the average wind velocity, to a greater degree they are likely to result from an incomplete removal of wind field inhomogeneities over the 12 km long flight paths. Therefore a horizontal wind velocity of 2 m s−1 can not be considered as a detection limit for wind measurements from WSMA. Also no systematic deviation for aircraft orientation could be detected. However vm wshows a slight sensitivity of −0.05 on vtas (R2= 0.46). Using the cardinal direction evaluation criteria Eq. (6), RMSE in α∞,β∞and |vm tas|were computed to 0.31, 0.33 and 0.26 m s−1, respectively. These compare well to the results from the uncertainty propagation (Tables 4 and 5), which amount to 0.31, 0.36 and 0.34 m s−1for αA,βAand vtas, respectively. Figure 12 shows a qualitative comparison of WSMA and ground based wind measurements for the flight on 15 October 2008. The vertical profile shows an equal number of flights at 24 and 27 m s−1true airspeed. Despite one outlier in vm vand vm wat 120 m a.g.l., no distinct differences in average wind velocities between ground based measurements and WSMA are apparent. The comparability of WSMA and ground based wind measurement was further quantified by calculating RMSE and BIAS for all measurements accepted for the comparison (Table 3). The impact of calibration Steps C–G on these measures is displayed in Fig. 13. The measurement of the horizontal wind components (vm uv)was mainly improved (14 %, relative to the initial uncertainty) by means of the in-flight dynamic pressure correction (Step D). After the wind square analysis (Step E) the measurement
68 APPENDIX B: METZGER ET AL. (2011) Fig. 11. Results from the wind square flights. For the horizontal wind components (vm uv) the x-axis displays the residuals (leg average–square average), while the y-axis shows the wind magnitude. In contrast the vertical wind component (vm w) is plotted against the true airspeed. Flight legs are depicted with different symbols according to their position in the square pattern. Dashed lines indicate a 10 % criteria for vm uv, and the zero line for vm w. was not further improved nor deteriorated. Yet the vertical wind measurement (vm w) receives its greatest improvement (31 %) during Steps F–G, i.e. variance optimization and vertical wind specific patterns: During these steps BIAS and dBIAS, i.e. its dependence on vtas, were reduced. In contrast to the findings from the wind square analysis, with a sensitivity of ≈+0.05 a slight positive dependence of all wind components on vtas remained. Considering all data couples between WSMA and ground based measurements, RMSE and BIAS amount to 0.50 and −0.07 m s−1for vm uv and 0.37 and −0.10 m s−1for vm w, respectively. In addition to the above mentioned outlier, two more suspects were identified for the flight on 18 October 2008, again concurrent for vm vand vm w. A possible explanation is the increased land surface heterogeneity sensed by the aircraft while travelling through the wind field. On the northern and western limbs of the aircraft cross pattern, forest patches of ≥200 m edge length interrupt the flat arable land immediately upwind. Therefore WSMA measurements can include turbulence and wake effects generated at the forest edges. In contrast tower measurements are not subject to comparable roughness changes until ≈2km in upwind direction. Omitting the three outliers from the statistics, RMSE and BIAS between WSMA and ground based measurements improve to 0.39 and −0.11 m s−1for vm uv and 0.27 and −0.10 m s−1for vm w, respectively. 4.3 Discussion Distortions of the wind measurement originating from the interactions of the aeroelastic wing, propeller and trike structural features were successfully corrected for conditions approximating straight, terrain following flight. Yet the treatments integral to Eqs. (A7), (7) and (8) leave room for improvement: Compared to ground based measurements the aircraft underestimated the wind components ≈−0.1 m s−1. A possible reason could be the discarded offset during the dynamic pressure (pq)in-flight calibration (Sect. 4.1, Step D). Rather forcing the linear fit to zero would slightly enhance the slope of pqand with it compliance to the aircraft’s inertial speed. During the wind square and comparison flights contradictory sensitivities (regression slope −0.05 versus +0.05) of the wind components on the true airspeed were found. For the variability in vtas during a thermally turbulent flight in the atmospheric boundary layer (σ= 1.24 m s−1, Fig. 4) this corresponds to ±0.06 m s−1deviation in the wind components. Since this deviation is one order of magnitude lower than the system’s input uncertainty, it was not further treated. The lift coefficient is used as sole explanatory variable for the observed net upwash in the linear calibration models Eqs. (7) and (8). This treats the influence of aircraft trim (i.e. dynamic pressure) and lift (i.e. loading factor) on
APPENDIX B: METZGER ET AL. (2011) 69 Fig. 12. Vertical profiles for horizontal (vm uv) and vertical (vm w) wind components of simultaneous ground based and weight-shift microlight aircraft measurements on 15 October 2008, 14:50–16:00 CET. Different symbols indicate the different wind sensors. Black circles represent aircraft measurements at 24 m s−1true airspeed, while grey circles represent measurements at 27 m s−1true airspeed. Vertical error bars indicate one standard deviation of the aircraft altitude. the wind measurement with similar sensitivity. The study by Visbal and Shang (1989) however shows that the flow field response of airfoils to pitch oscillations depends on the excitation frequency. With the Fourier method proposed by Kalogiros and Wang (2002b) the frequency dependence of the wing induced upwash can be modelled for FWA. The distinct difference from time domain methods is an amplified (≈20 %) upwash correction in the inertial subrange of atmospheric turbulence compared to lower frequencies. Due to little contributions of the inertial subrange, the effect on the eddy flux measurement at flight altitude (≤4%) ishowever relatively small. At the same time a transformation from the wing to the trike coordinate system would be required, carrying a potentially variable phase difference. Moreover the interactions with propeller and trike, resulting in the net flow distortion, remain untreated. Isolating these interactions would require considerably more in-flight data and analytical effort. In return such procedure could address forenamed dependence of the wind components on vtas and additionally allow for superior wind measurements during turning manoeuvres. 5 Conclusions We have shown that carefully computed wind vector measurements using a weight-shift microlight aircraft are not inferior to those from other airborne platforms. A 10 % limit of contamination of the wind components by the aircraft movement, as used by the US National Centre for Atmospheric Research, was fulfilled even during severe vertical manoeuvring. For flights including rising and sinking of the aircraft, such as during terrain following Eddy-Covariance applications, three independent lines of analysis yield comparable uncertainty. This convergence is remarkable and emphasizes the integrity of sensing elements and wind model description. The procedure further enables to quantify the overall operational uncertainty (root mean square error) to 0.4 m s−1for the horizontal and 0.3 m s−1for the vertical wind components. Independent consideration of trike movement and wing circulation according to the fixed-wing aircraft theory was not successful. Instead flow distortion of fuselage, propeller and wing were minimized by an approach integrated in the dynamic pressure and flow angle computations. The magnitude of distortion was treated as slope correction in the dynamic pressure computation. The distortion’s distribution in components longitudinal, transverse and vertical to the wind measurement was subsequently parametrized in the attackand sideslip angle computations. The lift coefficient
70 APPENDIX B: METZGER ET AL. (2011) Fig. 13. Influence of the calibration Steps C–G on root mean square error (RMSE) and bias (BIAS) between weight-shift microlight aircraft and all simultaneous ground based measurements of the horizontal (vm uv) and the vertical (vm w) wind components. dBIAS indicates the difference in BIAS between measurements at 27 and 24 m s−1true airspeed. was successfully used as sole variable explaining the upwash distribution, containing in it the effects of aircraft trim and lift. After the treatment an inconclusive dependence of the vertical wind measurement on the aircraft’s true airspeed remained. In-flight tests relate this dependence to an uncertainty of 0.06 m s−1in the vertical wind measurement. As compared to ground based measurements the final wind components were marginally underestimated by the aircraft (≈−0.1 m s−1). Our findings emphasize that the 3-D wind vector can be measured reliably from a highly transportable and low-cost weight-shift microlight aircraft. Hence the necessary basis is provided for the study of precision and spectral quality of the wind measurement, which is prerequisite for reliable EddyCovariance flux measurements. This brings the weight-shift microlight aircraft platform an important step closer towards a fullfeatured environmental research aircraft. Supplementary material related to this article is available online at: http://www.atmos-meas-tech.net/4/1515/2011/ amt-4-1515-2011-supplement.pdf. Acknowledgements. Special recognition has to be given to Josef-Michael Burger, Matthias Mauder, Frank Neidl, Rainer Steinbrecher and Rose Zuurbier at the Karlsruhe Institute of Technology, Institute for Meteorology and Climate Research. Burger and Zuurbier carried out the bulk of the wind-tunnel measurements, whereas Mauder contributed his micrometeorological advise. Neidl programmed and continuously maintained the data acquisition system, while Steinbrecher initiated windand flux measurements with the weight-shift microlight aircraft in the first place. Our gratefulness to Xunhua Zheng and her work-group at the Chinese Academy of Sciences, Institute of Atmospheric Physics, who was hosting our project and providing indispensable infrastructure. We are much obliged to Frank Beyrich of the German Meteorological Service, Richard-Aßmann-Observatory, who permitted us to carry out the evaluation flights and provided us with the corresponding SODARand tower data for this study. Our thanks to Jens Bange and Aline van den Kroonenberg of the Technical University of Braunschweig, Institute of Aerospace Systems (now Eberhard Karls University of T¨ ubingen, Institute for Geoscience), for their tireless advise. Stipend funding by the German Academic Exchange Service, Helmholtz Association of German Research Centrers, China Scholarship Council and the European Union under the Science and Technology Fellowship China is acknowledged. The flight in Inner Mongolia was funded by the German Research Foundation, research group 536 “Matter fluxes in grasslands of Inner Mongolia as influenced by stocking rate”. The publication was funded by the German Research Foundation and Open Access Publishing Fund of the Karlsruhe Institute of Technology. We thank John Kalogiros and an anonymous reviewer for their valuable comments and detailed feedback. Edited by: J.-P. Pommereau References Baldocchi, D., Falge, E., Gu, L., Olson, R., Hollinger, D., Running, S., Anthoni, P., Bernhofer, C., Davis, K., Evans, R., Fuentes, J., Goldstein, A., Katul, G., Law, B., Lee, X., Malhi, Y., Meyers, T., Munger, W., Oechel, W. U. K., Pilegaard, K., Schmid, H., Valentini, R., Verma, S., Vesala, T., Wilson, K., and Wofsy, S.: FLUXNET: A new tool to study the temporal and spatial variability of ecosystem-scale carbon dioxide, water vapour, and energy flux densities, B. Am. Meteorol. Soc., 82, 2415–2434, 2001. Bange, J. and Roth, R.: Helicopter-borne flux measurements in the nocturnal boundary layer over land – a case study, Bound.-Lay. Meteorol., 92, 295–325, 1999. Betts, A. K., Desjardins, R. L., Macpherson, J. I., and Kelly, R. D.: Boundary-layer heat and moisture budgets from FIFE, Bound.- Lay. Meteorol., 50, 109–138, 1990. Beyrich, F., Leps, J. P., Mauder, M., Bange, J., Foken, T., Huneke, S., Lohse, H., Ludi, A., Meijninger, W. M. L., Mironov, D., Weisensee, U., and Zittel, P.: Area-averaged surface fluxes over the LITFASS region based on Eddy-Covariance measurements, Bound.-Lay. Meteorol., 121, 33–65, 2006. Bissolli, P. and Dittmann, E.: The objective weather type classification of the German Weather Service and its possibilities of application to environmental and meteorological investigations, Meteorol. Z., 10, 253–260, 2001.
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APPENDIX C: SUPPLEMENT TO METZGER ET AL. (2011) 73 Appendix C: Supplement to Metzger et al. (2011) Supplement to Metzger, S., Junkermann, W., Butterbach-Bahl, K., Schmid, H. P., and Foken, T.: Measuring the 3-D wind vector with a weight-shift microlight aircraft It is the intention of this supplement to make transparent the procedures in the main article, and to guide the reader through the relevant calculations. Supplement A provides the formulary necessary to compute the wind vector from a weight-shift microlight aircraft. A model to propagate uncertainty through the wind vector equations is provided in Supplement B1. Relevant notation and abbreviations are listed in Supplement C. References to literature are given at the end of the document. Supplement A Wind measurement transformation equations The wind measurement from aircraft requires several coordinate systems, as well as angles to transform between them (Fig. 2). We define the wind vector vm=(vm u,vm v,vm w) in the standard meteorological coordinate system (MCS, superscript m, positive eastward, northward, and upward). Then vmcan be calculated from navigation, flow and attitude measurements: In the MCS vmis expressed as the vector difference between the aircraft’s ground speed vector (vm gs), directly measured by the inertial navigation system (INS), and the true airspeed vector (vtas m ), essentially measured by the five hole probe (5HP, Williams and Marcotte, 2000): vm=vm gs −vm tas =vm gs −Mbm ×Mab(−vtas)+vb lev.(A1) Yet the quantity directly measured by the 5HP is the true airspeed scalar vtas. The second, decomposed form of the wind vector Eq. (A1) indicates that several calculation steps are necessary to arrive at the desired vector quantity vm tas.
74 APPENDIX C: SUPPLEMENT TO METZGER ET AL. (2011) In the following we will walk through these successive steps, starting with the 5HP measurements. From the ports of the 5HP (Fig. 3) three differential pressures were measured: pq,A=pt−ps,(A2) pα=p3−p1,and (A3) pβ=p4−p2.(A4) Measured dynamic pressure pq,A(subscript upper-case letters A–G indicate calibration stage), and attackand sideslip differential pressures pα,pβwere used to calculate the airflow angles (Williams and Marcotte, 2000): αA=2 9sin(2τ) pα pq,A ,and (A5) βA=2 9sin(2τ) pβ pq,A .(A6) Here τ=45 ◦is the angle between the central port ptand the other ports p1through p4on the 5HP half sphere. Defining the normalization factor D=1+tan2αA+tan2βAthe measured dynamic pressure pq,Acan be corrected for the pressure drop occurring at elevated airflow angles: pq,B=pq,A9−5D2 4D2−1 .(A7) Now we can derive vtas from the thermodynamic measurements of the 5HP: Due to stagnation at the tip of the 5HP ambient air is heated from its intrinsic temperature (Ts) to total temperature (Tt). Assuming adiabatic heating, Bernoulli’s equation v2 tas =2cp,h(Tt−Ts) =2cp,hTsps ps+pq−κ −1,(A8)
APPENDIX C: SUPPLEMENT TO METZGER ET AL. (2011) 75 gives vtas as a function of the temperature difference (Leise and Masters, 1993). Since Ttcan not be measured directly, it is substituted in Eq. (A8) by the adiabatic process (ram rise) Tt=Tsps ps+pq−κ ,(A9) with the Poisson number κ=1−c v,h c p,h . Furthermore the wind measurement should be independent of air humidity (subscript h). Therefore the specific heats under constant pressure (subscript p) cp,hor constant volume (subscript v) cv,hof moist air have to be derived from the specific heat constants for dry air (subscript d) and water vapour (subscript w), cp,d= 1005 Jkg −1K−1,cp,w= 1846 Jkg −1K−1,cv,d= 718 Jkg −1K−1, and cv,w= 1384 Jkg −1K−1 (Khelif et al., 1999): cp,h=cp,d1+qcp,w cp,d −1, cv,h=cv,d1+qcv,w cv,d −1,with specific humidity being q=εe ps+e(ε−1),(A10) where ε=0.622 is the ratio of molecular weight of water vapour to that of dry air, and eis the 5HP measured water vapour pressure. Once derived, the scalar quantity vtas has to be transformed into a vector quantity. This can be achieved by defining the aerodynamic coordinate system (ACS, superscript a, positive forward, starboard, and downward), which has its origin at the 5HP tip. In this coordinate system the true airspeed vector has the components va tas =(−vtas,0,0). Since the ACS is aligned with the streamlines its orientation however varies in time. Therefore va tas is transformed into a fixed coordinate system, that is the trike body coordinate system (BCS, superscript b, positive forward, starboard, and downward) with its origin in the INS. This is accomplished by successive rotations about the vertical axis Zaand the transverse axis Ya. Following Lenschow (1986) the
82 APPENDIX C: SUPPLEMENT TO METZGER ET AL. (2011) qSpecific humidity RReference measurement RMSE Root mean square error SWing surface area TTemperature vVelocity scalar or vector component vVelocity vector x, y, z Distances on respective coordinate axes z LStability parameter αAngle of attack βAngle of sideslip εRatio of molecular masses ΘPitch κPoisson number ΦRoll ξWing upwash direction πPerimeter constant ρAir density σStandard deviation, RMSE τAngle between central and surrounding ports on half-sphere ΨHeading ΩBody rate C3 Subscripts – superscripts 1–4 Pressure ports ∞Free airstream +,−Into wind, with wind ˜Wind tunnel
APPENDIX C: SUPPLEMENT TO METZGER ET AL. (2011) 83 a Aerodynamic coordinate system, positive forward, starboard, and downward A–G Calibration steps b Body coordinate system, positive forward, starboard and downward d Dry air g Geodetic coordinate system, positive northward, eastward and downward gau Gaussian uncertainty propagation gs Ground speed h Humid air lev Lever arm m Meteorological coordinate system, positive eastward, northward and upward off Offset q Dynamicr Inverse reference s Staticslo Slope t Totaltas True airspeed u, v, w Wind components in x, y, z directions up Upwash w Water vapour; Wing coordinate system, positive forward, starboard and downward x, y, z Standard Cartesian coordinate axes αAngle of attack βAngle of sideslip
84 APPENDIX C: SUPPLEMENT TO METZGER ET AL. (2011) C4 Abbreviations 5HP Five hole probe ABL Atmospheric boundary layer ACS Aerodynamic coordinate system, positive forward, starboard, and downward a.g.l. Above ground level a.s.l. Above sea level BCS Body coordinate system, positive forward, starboard and downward D-MIFU Name of aircraft DAQ Data acquisition E East EC Eddy covariance EIDAS Embedded Institute for Meteorology and Climate Research data acquisition system FWA Fixed-wing aircraft GCS Geodetic coordinate system, positive northward, eastward and downward INS Inertial navigation system IU Input uncertainty LI Lindenberg MCS Meteorological coordinate system, positive eastward, northward and upward N North S South ST Lake Starnberg ULS Universal laser sensor VW1–VW3 Vertical wind specific flight patterns W West
APPENDIX C: SUPPLEMENT TO METZGER ET AL. (2011) 85 WCS Wing coordinate system, positive forward, starboard and downward WSMA Weight-shift microlight aircraft XI Xilinhot
86 APPENDIX C: SUPPLEMENT TO METZGER ET AL. (2011) References ISO: Statistics – vocabulary and symbols – Part 1: Probability and general statistical terms, vol. ISO 3534-1, International Organization for Standardization, Geneva, Switzerland, 1993. Khelif, D., Burns, S. P., and Friehe, C. A.: Improved wind measurements on research aircraft, J. Atmos. Ocean. Tech., 16, 860–875, 1999. Leise, J. A. and Masters, J. M.: Wind measurement from aircraft, Tech. rep., United States Department of Commerce, National Oceanic and Atmospheric Administration, Aircraft Operations Center, MacDill Air Force Base, 1993. Lenschow, D. H.: Aircraft measurements in the boundary layer, in: Probing the Atmospheric Boundary Layer, American Meteorological Society, Boston, Massachusetts, USA, 39–55, 1986. Mauder, M., Liebethal, C., G¨ ockede, M., Leps, J. P., Beyrich, F., and Foken, T.: Processing and quality control of flux data during LITFASS-2003, Bound.-Lay. Meteorol., 121, 67–88, 2006. Taylor, J. R.: An Introduction to Error Analysis: the Study of Uncertainties in Physical Measurements, University Science Books, Mill Valley, California, USA, 2nd edn., 1997. Vogt, S. and Thomas, P.: Sodar – a useful remote sounder to measure wind and turbulence, J. Wind Eng. Ind. Aerod., 54, 163–172, 1995. V¨ orsmann, P.: Ein Beitrag zur Bordautonomen Windmessung, Ph.D. thesis, Technische Universit¨ at Braunschweig, 1985. Williams, A. and Marcotte, D.: Wind measurements on a maneuvering twin-engine turboprop aircraft accounting for flow distortion, J. Atmos. Ocean. Tech., 17, 795–810, 2000.
APPENDIX D: METZGER ET AL. (2012) 87 Appendix D: Metzger et al. (2012) Atmos. Meas. Tech., 5, 1699–1717, 2012 www.atmos-meas-tech.net/5/1699/2012/ doi:10.5194/amt-5-1699-2012 © Author(s) 2012. CC Attribution 3.0 License. Atmospheric Measurement Techniques Eddy-covariance flux measurements with a weight-shift microlight aircraft S. Metzger1,2,3,W.Junkermann 1,M.Mauder 1, F. Beyrich4, K. Butterbach-Bahl1,H.P.Schmid 1,andT.Foken 5 1Karlsruhe Institute of Technology, Institute for Meteorology and Climate Research, Atmospheric Environmental Research, Garmisch-Partenkirchen, Germany 2Chinese Academy of Sciences, Institute of Atmospheric Physics, State Key Laboratory of Atmospheric Boundary Layer Physics and Atmospheric Chemistry, Beijing, China 3National Ecological Observatory Network, Fundamental Instrument Unit, Boulder, USA 4German Meteorological Service, Richard-Aßmann-Observatory, Lindenberg, Germany 5University of Bayreuth, Department of Micrometeorology, Bayreuth, Germany Correspondence to: W. Junkermann (w[email protected]) Received: 18 February 2012 – Published in Atmos. Meas. Tech. Discuss.: 30 March 2012 Revised: 17 June 2012 – Accepted: 18 June 2012 – Published: 19 July 2012 Abstract. The objective of this study is to assess the feasibility and quality of eddy-covariance flux measurements from a weight-shift microlight aircraft (WSMA). Firstly, we investigate the precision of the wind measurement (σu,v ≤0.09 m s−1,σw=0.04 ms−1), the lynchpin of flux calculations from aircraft. From here, the smallest resolvable changes in friction velocity (0.02 m s−1), and sensible- (5 W m−2) and latent (3 W m−2) heat flux are estimated. Secondly, a seven-day flight campaign was performed near Lindenberg (Germany). Here we compare measurements of wind, temperature, humidity and respective fluxes between a tall tower and the WSMA. The maximum likelihood functional relationship (MLFR) between tower and WSMA measurements considers the random error in the data, and shows very good agreement of the scalar averages. The MLFRs for standard deviations (SDs, 2–34 %) and fluxes (17–21 %) indicate higher estimates of the airborne measurements compared to the tower. Considering the 99.5 % confidence intervals, the observed differences are not significant, with exception of the temperature SD. The comparison with a largeaperture scintillometer reveals lower sensible heat flux estimates at both tower (−40 to −25 %) and WSMA (−25– 0 %). We relate the observed differences to (i) inconsistencies in the temperature and wind measurement at the tower and (ii) the measurement platforms’ differing abilities to capture contributions from non-propagating eddies. These findings encourage the use of WSMA as a low cost and highly versatile flux measurement platform. 1 Introduction Energy and matter fluxes between the Earth’s surface and the atmosphere can be determined using the eddy-covariance (EC) method. This method is based on the Reynolds decomposition of the Navier-Stokes equation, and it assumes steady state conditions and horizontal homogeneity (e.g. Kaimal and Finnigan, 1994). Nevertheless, the EC method is frequently used in complex terrain, for which applicability is subject of on-going research (e.g. Foken et al., 2010; G¨ ockede et al., 2008). In particular, it is assumed that the mean vertical wind approaches zero for a sufficiently long averaging interval. This requirement is more likely fulfilled by spatial than by temporal measurements, because spatial measurements enable registering atmospheric motions on larger scales (e.g. Mahrt, 2010). Under conditions of negligible advection and horizontal flux divergence, the total vertical flux is then inferred from the covariance between the vertical wind and the scalar of interest (e.g. temperature, humidity). Ground-based measurements of turbulent fluxes are of local character and are therefore not necessarily representative of their greater surroundings, especially in complex terrain (e.g. Desjardins et al., 1997; Isaac et al., 2004b; Mahrt, 2010). The spatial gap between in-situ observations, satellite observations and modelled data needs to be considered as one plausible explanation for their frequently observed mismatch (e.g. Kanda et al., 2004; Lu et al., 2005). Here
88 APPENDIX D: METZGER ET AL. (2012) process studies with airborne platforms provide a valuable link to understand and bridge scale discrepancies (e.g. Bange et al., 2002; Davis et al., 1992; Hiyama et al., 2007; Isaac et al., 2004a). At the same time, fixed-wing aircraft and helicopters are expensive to operate or not applicable in settings such as remote areas beyond the range of an airfield. Unmanned aerial vehicles on the other hand provide mobility, yet do not allow a comprehensive sensor package due to payload restrictions (e.g. Egger et al., 2002; Hobbs et al., 2002; Martin et al., 2011; Thomas et al., 2012). Here the weightshift microlight aircraft (WSMA) can provide an alternative at low cost-, transportand infrastructural demand. After successfully applying a WSMA to aerosol and radiation transfer studies (Junkermann, 2001, 2005), Metzger et al. (2011) showed that carefully computed wind measurements from WSMA are not inferior to those from other airborne platforms. On this basis, the feasibility of EC flux measurements from WSMA in the atmospheric boundary layer (ABL) is explored in this study. The overarching perspective is to work towards an airborne platform that allows characterising complex terrain in remote areas, including the measurement of regional turbulent fluxes. Contributions to the EC flux measurement originate from turbulent atmospheric motions on a variety of wavelengths and amplitudes. In order to reliably estimate the total flux, the fluctuations of the vertical wind and the scalars must be measured with high accuracy and precision. Furthermore, the instrumentation and data acquisition must possess a suitable frequency response and sampling rate. In the case of airborne measurements, the carrier can additionally influence the spectral quality of the measurement. Therefore, the present study commences with (i) an assessment of the measurement errors. To evaluate the system performance, we (ii) compare spectral properties, averages, deviations and fluxes between WSMA and tower-based EC measurements. The analysis continues with (iii) a study of the measurements’ spatial context, which is inferred from footprint modelling. The (iv) comparison to a large-aperture scintillometer (LAS) brings to attention the effect of larger-scale atmospheric motions on the results and completes the study. 2 Materials and methods 2.1 The weight-shift microlight aircraft The structure of a WSMA differs from common fixed-wing aircraft: it consists of two distinct parts, the wing and the trike, which hangs below the wing and contains the pilot, engine and the majority of the scientific equipment. This particular structure provides the WSMA with exceptional transportability and climb rate, which qualifies it for applications in complex and inaccessible terrain. A detailed description of the physical properties of the WSMA used in this study as well as characteristics and manufacturers of sensors and data acquisition is given in Metzger et al. (2011). In short, most variables are sampled at 100 Hz and are block-averaged and stored at 10 Hz, yielding a horizontal resolution of approximately 2.5 m. To conduct fast wind measurements, the WSMA is outfitted with a combination of global positioning system and inertial measurement unit (GPS/IMU), and a five-hole pressure probe (5HP). The principle is to resolve the meteorological wind vector from the vector difference of the aircraft’s inertial velocity (captured by the GPS/IMU) and the wind vector relative to the aircraft (captured by the 5HP). The structural features of the WSMA also influence the wind measurement: (i) the wing deforms aeroelastically with aircraft trim, and (ii) the trike is free to rotate in pitch and roll against the wing. Metzger et al. (2011) present a time domain procedure which treats the impact of the WSMA’s structural features as well as pilot input on the wind measurement. The remaining maximum deviation of the vertical wind component is 0.15 m s −1 during severe vertical manoeuvres. At typical airspeeds between 23–30 m s −1 , simultaneous wind measurements from WSMA and ground-based instrumentation agree within 0.3 m s −1 for the vertical and within 0.4 m s −1 for the horizontal components (root mean square error). The present study investigates the potential influence of resonance from the WSMA’s engine or propeller, or from the natural frequencies of trike and wing, on the wind measurement. For this purpose, acceleration measurements in the hang point of trike and wing, in the global positioning system/inertial measurement unit and in the five-hole probe, are used. The acceleration measurement in the hang point is transformed to the trike coordinate system. A 100 Hz dataset consisting of ≈3×10 5 data points sampled during a level long-distance flight on 31 July 2009 (Metzger et al., 2011, Table 3) is used for the assessment. Air temperature is measured with a 50 μm thermocouple. The temperature error introduced by intermittent solar radiation at the unshielded thermocouple is <0.05 K at nominal true airspeed (Metzger et al., 2011). An OP2 infrared gas analyser (IRGA, ADC Bioscientific, Great Amwell, UK) is used to measure the concentration of water vapour. The instrument response of both the thermocouple and the IRGA is 50 Hz. In addition, a slow (2 Hz instrument response) humidity reference from a TP3 dew point mirror (Meteolabor AG, Wetzikon, Switzerland) is stored at ≥0.1 Hz. Vertical profile flights revealed a dependence of the IRGA measurements on flight altitude. This dependence was related to a malfunctioning temperature compensation of the light source as well as air permeability of the light chamber. From measurements of calibration gases in a climate chamber, the temperature compensation is updated in post-processing. Similar measurements were conducted in a pressure chamber to determine the time constant of the light chamber permeability (≈60 s or 1500 m of horizontal flight). In order to correct the permeability effect, a third-order Savitzky-Golay complementary filter (Chen et al., 2004) is used. The complementary filter corrects for the IRGA’s drift by basing the humidity
APPENDIX D: METZGER ET AL. (2012) 89 fluctuations measured by the IRGA on the slow dew point mirror reference. A window size of 13.9 s or ≈350 m maximises the integral over the humidity power spectrum, and is used to correct the measurements. In the present study, also the influence of measurement precision on the eddy-covariance flux results is investigated. For this purpose, we follow Garman et al. (2006) and define measurement precision as 1 σrepeatability. The precision of all variables entering the EC flux calculation is presented in Table 1. In the case of the GPS/IMU, precision originates from Kalman filter outputs, and in the case of the 5HP, it is calculated from laboratory and wind tunnel measurements (Metzger et al., 2011). 2.2 Field campaign A comparison between the airborne WSMA and groundbased measurements was carried out during a flight campaign between 14 and 21 October 2008. This experiment was performed around the boundary layer field site Falkenberg (52.2 ◦ N, 14.1 ◦ E) of the German Meteorological Service (DWD), Richard-Aßmann Observatory, Lindenberg, Germany. This field site lies in the basically flat North German Plain, and the terrain height varies between 40 m and 130 m above sea level (a.s.l.) within an area of 20 ×20 km 2 . To characterize surface heterogeneity, we use the Corine Land Cover 2006 data with a horizontal resolution of 100 m (Version 13, European Environment Agency, 2010). The arable land was harvested before the study period, and, consequently, the surface properties differed mainly between but not within landscape units. We thus regrouped the 28 Corine Land Cover fractions in the study area into five landscape units, thereby reducing unnecessary scatter (Figs. 7 and 9). The resulting representation of the landscape around the Falkenberg site (20 ×20 km 2 ) is dominated by agriculture (47 %) and forests (38 %), interspersed by equal amounts (5 %) of lakes, meadows and settlements. A full characterisation of the Falkenberg site and its instrumentation is presented by Beyrich and Adam (2007). Data from an instrumented 99 m tower are used for the comparison of the WSMA measurements. Sonic anemometers (USA-1 – Metek GmbH, Elmshorn, Germany) as well as open path IRGAs (LI-7500 – LI-COR Biosciences, Lincoln, USA) were installed at 50 m and 90 m above ground level (a.g.l.). These instruments sampled the wind vector, sonic temperature and humidity at a rate of 20 Hz, enabling EC flux computation. For the USA-1, the manufacturer’s 2-D flow distortion correction was operationally applied to the wind vector measurement. These data are used for the comparison of the average wind as well as variances, covariances and power spectra between the WSMA and the tower. The tower was further equipped with profile measurements of temperature (HMP-45 – Vaisala Oy, Helsinki, Finland) and humidity (Frankenberger Psychrometer – Theodor Friedrichs GmbH, Hamburg, Germany) at 40, 60, 80, and 98 m a.g.l. Table 1. Measurement precision of global positioning system/inertial measurement unit (GPS/IMU), five-hole probe (5HP), thermocouple, and infrared gas analyzer (IRGA). Quantity Precision Heading (GPS/IMU) 0.1 ◦ Pitch, Roll (GPS/IMU) 0.04 ◦ 3-D velocity (GPS/IMU) 0.02 m s −1 3-D angular rate (GPS/IMU) 0.01 ◦ s −1 3-D acceleration (GPS/IMU) 0.01 m s −2 Attack angle (5HP) 0.08 ◦ Sideslip angle (5HP) 0.18 ◦ True airspeed (5HP) 0.05 m s −1 Temperature (thermocouple) 0.04 K Humidity (IRGA) 0.005 g m −3 The profiles are interpolated to the heights of the EC installations and are used to compare average temperature and humidity between tower and WSMA. A static pressure measurement (PTB220A – Vaisala Oy, Helsinki, Finland) at 74 m a.s.l. is extrapolated to the heights of the tower EC installations using the hypsometric equation. It is used for the conversion of the tower EC fluxes from kinematic units to units of energy. Tower profile and pressure data were averaged and stored in 10 min intervals. Identical instrumentation as on the tower was used for an additional EC surface flux measurement upwind (south) of the tower base, at 2.4 m a.g.l. The half-hourly sensible heat flux was determined from this measurement as an operational product of the DWD. Global radiation was measured at 2 m using a CM24 pyranometer/albedometer (Kipp and Zonen, Delft, The Netherlands) and stored as 10 min averages. Also 10 min area-averaged surface sensible heat fluxes were derived from a large-aperture scintillometer. At an effective beam height of 43 m a.g.l., the near-infrared LAS runs along a path length of 4.7 km (Fig. 9). The LAS was developed and built by the Meteorology and Air Quality Group of the Wageningen University; technical details are presented in Meijninger et al. (2006). Furthermore, hourly estimates of the ABL depth were derived from sonic detection and ranging and wind profiler data, and from six-hourly routine radio soundings performed by the DWD. The surface sensible heat fluxes measured at the 2.4 m EC and the LAS are used in conjunction with the ABL depths to approximate vertical flux profiles. Simultaneous WSMA measurements of the sensible heat flux are compared to these flux profiles. In the course of the flight campaign, the atmospheric conditions changed from very weak to strong turbulent mixing. The cloud cover (09:00 to 15:00 UTC) decreased from 8/8 to 4/8, and the maximum available global radiation increased from 280 W m −2 at the beginning to 460 W m −2 at the end of the campaign. Also the wind speed increased from 2 m s −1 to 10 m s −1 at the 50 m tower level, with the wind direction
90 APPENDIX D: METZGER ET AL. (2012) changing from west to south. The ranges of the surface sensible and the latent heat fluxes were 0–100 W m −2 and 0–200 W m −2 , respectively. The sensible heat flux slightly increased in the course of the campaign, while the latent heat flux remained approximately comparable throughout the flight days. Also the maximum ABL depth increased from 250 m to 1150 m in the course of the campaign. The atmospheric stratification was neutral to unstable, with the median of the stability parameter z/L =−0.18 ±0.21 from WSMA and −0.14 ±0.29 from tower measurements. 2.3 Data processing Eddy-covariance data were post-processed analogously for the 99 m tower and for the WSMA turbulence measurements. The software package TK3 (Mauder and Foken, 2011) was used to process the tower EC data, applying the raw data treatments and flux corrections as put forward in Foken et al. (2012). (i) The raw data were screened for spikes using the algorithm of Hojstrup (1993). Visual inspection revealed that neighbouring spikes in the IRGA data were not detected by the algorithm. The original algorithm uses average and standard deviation criteria with low break down points for small sample sizes (Rousseeuw and Verboven, 2002). After substituting the criteria with the median and the median absolute deviation, the spikes were efficiently removed. (ii) The time delay due to separation between the vertical wind measurement and adjacent sensors was determined and corrected by maximizing their lagged correlation. (iii) To correct for potential misalignment, the USA-1 wind measurement was rotated into the streamline coordinate system using the planar-fit method by Wilczak et al. (2001). (iv) The temperature variance as well as the sensible heat flux was calculated using the crosswind correction by Liu et al. (2001). (v) The formulations by Webb et al. (1980) were used to correct the latent heat flux for density fluctuations. To handle the WSMA data, an analysis package with similar processing steps was developed in GNU R version 2.13 (R Development Core Team, 2011), which is available upon request. Several forenamed corrections are not applicable to the WSMA measurement and were omitted: (iii) the aircraft vertical wind is already defined in geodetic normal, which is perpendicular to the spatial average of the streamlines, and (iv) the air temperature is directly measured by the thermocouple. The sensitivity of the WSMA measured fluxes on the remaining corrections was tested for a flight in the convective boundary layer (z/L =−0.8) at 50 m a.g.l. No spikes were present in this dataset, and consequently the spike elimination (i) had no influence on the results. The corrections for time delay (ii), high frequency spectral loss (Moore, 1986) and density fluctuations (v) only affected the latent heat flux. The median differences between applying and neglecting these corrections were in the order of 5 %, 1 % and 20 %, respectively, which is in agreement with the findings of Mauder and Foken (2006). In the following, the correction for high frequency loss due to sensor separation is not applied because its influence is negligible at measuring heights ≥50 m. The fluxes computed from both software packages were compared using regression analysis and showed perfect agreement with unity slope. Consequently, comparability is ensured when calculating fluxes from tower and WSMA platforms with their respective software packages. 2.4 Evaluation strategy 2.4.1 Propagation of sensor errors The eddy-covariance technique relies upon the precise measurement of fluctuations of atmospheric quantities, based on negligible sensor drift throughout an averaging period. Our intention is to evaluate whether sensor precision and drift facilitate the use of the weight-shift microlight aircraft as turbulence measurement platform. Measured from aircraft, the determination of the wind vector requires a sequence of thermodynamic and trigonometric equations (e.g. Metzger et al., 2011). These equations propagate various sources of error, and are consequently the lynchpin for EC flux measurements from aircraft. Here we propagate known sensor precisions to atmospheric quantities, which yields the minimum resolvable change in the associated fluxes. Thereafter, the maximum achievable averaging period for the flux calculation is determined as a function of sensor drift. 2.4.2 Spectral properties of the aircraft As opposed to ground-based measurements, the weight-shift microlight aircraft is subject to several simultaneous motions, such as locomotion, engine and propeller rotation. Our intention is to assess if and to what extent the WSMA’s motions influence the wind measurement. For this purpose, a spectral analysis was carried out by fast Fourier transformation of acceleration measurements in the hang point of trike and wing, in the global positioning system/inertial measurement unit and in the five-hole probe. We present power spectra representative for these structural parts of the WSMA and interpret the spectral behaviour in the context of the wind measurement. 2.4.3 Comparison between tower and aircraft measurements Measurements with the weight-shift microlight aircraft were conducted along a cross-shaped pattern within 1.5 km horizontal distance of the tall tower from 15 to 18 October 2008 (Fig. 7). A total of 36 flights of 3 km length or ≈120 s duration are compared to simultaneous tower measurements. The WSMA was travelling at two different airspeeds, 24 m s −1 and 27 m s −1 , and was flying within 0.5±5.3 m altitude of the corresponding installations on the tower. The WSMA temperature and densities were transformed to potential quantities at the respective tower height. The objective of the
APPENDIX D: METZGER ET AL. (2012) 91 comparison is to assess the quality of the WSMA measurement, with focus on the EC flux. The objective is not to quantify the actual exchange between surface and atmosphere. The comparatively short flight legs are therefore a compromiseofsamplesize(≈1200 data points from WSMA) and vicinity of the measurement platforms. Differing spectral contributions can lead to a systematic bias in the flux estimates between the platforms. To ensure equal contributions from the long wave part of the spectrum, we constrain the averaging periods to the same normalized frequency. The tower averaging period τ tow =τ air ·v tas /|uvw| then results from the flight duration for one leg τ air and the ratio of airspeed v tas to the module of the wind vector |uvw|. For τ air ≈120 s and the ratio v tas /|uvw|≈5, the appropriate tower averaging period is τ tow ≈600 s or 10 min. Using this averaging period, the tower results were calculated at increments of 1 min. The WSMA was more frequently travelling upwind (180 ±720 m median difference) than downwind of thetower.Inawindowof±10 increments, the tower result was chosen that minimized the scatter (root mean square error) between all flux measurements of both platforms. This allows taking into account advection between the platforms, as well as potential timing differences of the data acquisition systems. Best agreement was reached for a shift of 2±6 increments, corresponding to an upwind distance of 600 ±1800 m for an air mass travelling at 5 m s −1 . In order to detect systematic differences between tower and WSMA measurements, a regression-like analysis was applied to all 36 flights. Simple least-squares regression is strictly applicable only when one measurement is without error (Lindley, 1947). This however is not the case for the measurements in our study, which are subject to uncertainties such as random statistical error. Instead, we use maximumlikelihood fitting of a functional relationship (MLFR, Ripley and Thompson, 1987). This method assigns a weight to each data couple in the relationship, which is inversely proportional to its error variances. In our case, the squared random statistical errors in the tower and WSMA measurements are used, which appreciates reliable data and depreciates uncertain data couples. These errors are inferred from the integral length scales of the WSMA measurements (Appendix A), and define an inner and an outer scale of confidence in the comparison. The errors in the MLFR coefficients are determined from a jackknife estimator (Quenouille, 1956; Tukey, 1958). Since the regression intercepts were not significant, the relationships were forced through the origin, and confidence intervals were determined from the slope error. The coefficient of determination R 2 was calculated in analogy to weighted least-squares regression (Kvalseth, 1985; Willett and Singer, 1988). It is the proportion of variation in weighted Ythat can be accounted for by weighted X. Finally, the residual standard error is determined using Eq. (A4). 2.4.4 Spatial analysis We use footprint modelling in order to assess the spatial context of measurements. For this purpose, the along-wind footprint parameterization of Kljun et al. (2004) was combined with a suitable crosswind distribution (Appendix B). The resulting model is computationally fast, considers 3-D dispersion and is applicable beyond the atmospheric surface layer. We compare the overlap of the tower and WSMA footprints as well as the contribution of different land covers to the measurements. 2.4.5 Comparison with large-aperture scintillometer In addition to towerand aircraft-based eddy-covariance measurements, we also include sensible heat flux estimates from the large-aperture scintillometer in the comparison. On seasonal average, LAS measures 10–20 % higher values of the sensible heat flux compared to tower EC measurements (e.g. Liu et al., 2011; Meijninger et al., 2006). In particular above heterogeneous terrain, the capture of elevated, nonpropagating eddies (NPE) by the LAS, but not by the tower EC, is discussed as a potential reason for the observed differences (Foken et al., 2010). In this respect, the spatially averaged EC measurement from WSMA is similar to the LAS. Consequently, the objective of the comparison with LAS is to aid the interpretation of systematic differences between the spatially (aircraft) and temporally (tower) averaged EC measurements. On 20 and 21 October 2008, two flights of 4.7 km length or ≈150 s duration were conducted ≈1km to the east of, and parallel to the LAS measuring path (Fig. 9). The duration of the WSMA flight translates to ≈750 s or 12.5 min averaging interval at the 50 m and 90 m levels of the tower. Nevertheless, the tower flux measurements are averaged over 10 min, identical to Sect. 2.4.3. For longer averaging intervals, the time series became increasingly instationaryon21October2008,andtheflux magnitude decreased. WSMA temperature and density measurements were transformed to potential quantities at the mean flight altitude, i.e. 108 m and 119 m a.g.l. on 20 and 21 October 2008, respectively. Using boundary layer scaling, the results from LAS and WSMA are compared to simultaneous tower EC measurements at 2.4 m, 50 m and 90 m a.g.l., which are located at the LAS transmitter site. 3Results 3.1 Propagation of sensor errors In the first part of this section, we assess the WSMA’s measurement precision and its impact on EC flux measurements over short flight legs. In the second part, we evaluate the maximum flux averaging period facilitated by the drift (accuracy) of the sensors.
98 APPENDIX D: METZGER ET AL. (2012) Fig. 8. Vertical profile of the sensible heat flux during two flights: 20 October 2008, 10:53–10:55 UTC (red) and 21 October 2008, 09:56–09:59 UTC (blue). Heat fluxes are compared between largeaperture scintillometer (LAS), tower eddy covariance at 2.4 m, 50 m and 90 m (TOW02, TOW50, TOW90) and the weight-shift microlight aircraft (WSMA). Where available, error bars show the random statistical error and the altitude standard deviation. Additional information is given in the text. 4 Discussion The propagation of sensor errors enables defining the minimum change in an atmospheric quantity that can be reliably resolved by the WSMA measurements of respective variables. For the wind measurement, this coincides with the lower margin of the standard deviations observed at both tower and WSMA (Fig. 4). We thus conclude that the precision of the wind measurement warrants eddy-covariance flux measurements under unstable to slightly stable stratifications. The precision of the vertical wind is better by a factor of two compared to the horizontal wind components. This can be traced back to the better precision of the attackand pitch (≤0.08 ◦ ) angles compared to the sideslipand heading (≤0.18 ◦ ) angles. From the assessment of sensor accuracies, we found that the wind and scalar measurements facilitate the signal levels required for the resolution of mesoscale ABL structures. This enables extending averaging intervals and spectral analyses up to a scale of tens of kilometres. The focus of this study is on the comparison of turbulence statistics between weight-shift microlight aircraft and tower measurements. A potential source of uncertainty is the flow distortion correction of the USA-1 sonic anemometers used at the tall tower. Two different corrections are provided by the manufacturer, of which the “milder” 2-D version was used in the operational setup of the DWD. A post processing comparison for the presented tower data shows that the 3-D version would lead to a systematic increase in the wind SDs by ≈35 %, and in the fluxes by ≈15 %. From instrument comparison, the 2-D correction seems to be more Fig. 9. Footprint effect levels of the measurements from Fig. 8 on 20 October 2008 (A) and 21 October 2008 (B), presented similarly to Fig. 7. In addition, the weighted footprint along the LAS path is shown (red), and the footprints from the tower measurements at 50 m (black) and 90 m (yellow) are distinguished. appropriate. However, it must be noted that the magnitude of this correction alone is in the order of the differences in the wind SDs and the fluxes observed between the tower and the WSMA. Longer averaging intervals at the tower or detrending of the WSMA data did not change the general behaviour, but increased the scatter in the comparison. Moreover, vertical flux divergence can be ruled out as potential error source, since the measurements were conducted at approximately the same altitude above ground. Also, altitude fluctuations by the WSMA were accounted for by using potential quantities of temperature and densities at the tower pressure level. In the following, we consequently focus on the effects of spectral artifacts and surface heterogeneity. During the investigation of the WSMA spectral properties, a scale discrepancy was detected between accelerations acting at the five-hole probe and their accounting in the global positioning system/inertial measurement unit, i.e. the wind computation (Fig. 1). No remnants of this scale discrepancy are evident in the wind measurements, in particular between 1–5 Hz. This leads to the conclusions that (i) the wind vector computation correctly accounts for the displacement of 5HP and GPS/IMU, and (ii) the cause of enhanced 5HP acceleration measurements (especially longitudinal to the body) lies in the fixture of the acceleration sensor in the 5HP, rather than in the mounting of the 5HP against the GPS/IMU. The spectral peak in the WSMA vertical and streamwise wind components (Fig. 3) coincides with the wing’s natural frequency around 0.7 Hz (Sect. 3.2). A less pronounced peak between 0.15–0.4 Hz in the transverse wind component coincides only with a peak in vertical accelerations (Fig. 1). Both spectral features can potentially be associated with the treatment of wing upwash in the time domain, but not in the frequency domain (Metzger et al., 2011). The WSMA wind and flux measurements were corrected for this spectral inconsistency before comparing them to ground-based measurements. The appropriate correction factors were estimated
APPENDIX D: METZGER ET AL. (2012) 99 from the comparison of measured spectra and cospectra to modelled ones. Because of large scatter in the momentum flux cospectra at the tower, no ensemble was calculated. We speculate that the scatter originates from the wind direction-dependent correlation of the horizontal and vertical wind components at the USA-1 sonic anemometers (e.g. Mauder et al., 2007b). The erroneous sonic temperature spectrum indicates problems with the measurement of the temperature SD and the sensible heat flux at the tower. The amplitude resolution test by Vickers and Mahrt (1997) would reject 28 out of 36 tower sonic temperature data sets. The problem was related to the insufficient sonic temperature resolution (0.01 K) of the USA-1, which appears as superficial spectral energy in the form of high-frequency white noise. Spectral correction factors analogous to the WSMA measurements were used in an attempt to correct the systematic overestimation of the temperature SD. Such a procedure changes the maximum likelihood functional relationship between tower and aircraft temperature SD from −9 % underestimation to 34 % overestimation of the WSMA measurement. At the same time, the residual standard error in the MLFR increases from 9 % to 17 %. The scattering can be suppressed by rejecting data points with weak temperature SD (<0.05 K), resulting in a reduced overestimation of 15 % of the WSMA measurement. Consequently, the USA-1 measurements cannot be regarded as reliable reference for the temperature SD, and the spectral correction factors must be interpreted with caution. The problem is less pronounced for the sensible heat flux. The white noise in the USA-1 sonic temperature measurement does not affect the measurement of, or the correlation with, the vertical wind measurement. The result is a modest underestimation of −3 % of the tower sensible heat flux due to reduced coherence of sonic temperature and vertical wind at high frequencies. The humidity measurements agree well between the platforms in the time and in the frequency domain. Several outliers in the WSMA latent heat flux measurement coincide with WSMA flights west of the tall tower, which are closer to a forest edge. Increased mechanical turbulence downwind of the forest edge is a potential explanation for increased turbulent fluxes. This finding however does not hold for the sensible heat flux and the friction velocity, which is in contradiction to scalar similarity. As a potential source for the observed differences, we assess the spatial context of the tower and aircraft measurements. The footprint results illustrate that the land cover contributions are very similar for both platforms. Provided the land cover data are a suitable proxy for the land-atmosphere exchange, differences between tower and WSMA measurements cannot be attributed to different land cover contributions alone. However, the footprint analysis also reveals that the source areas only share a fractional overlap. Consequently, the observed differences can potentially originate from the platforms’ principally different sampling strategies. Foken (2008) and Mahrt (2010) conclude that the energy balance non-closure frequently observed from tower EC measurements is connected to the interaction of terrain heterogeneity and turbulent scales. For this purpose, the transfer of heat between surface and atmosphere is considered separately for smaller, random eddies and for larger, nonpropagating eddies. Thereof, the transfer by the small, random eddies is measured by the tower EC. However, an additional transfer component is suspected to occur at significant surface heterogeneities, leading to the generation of non-uniformly distributed NPEs. Based on intensive measurement campaigns and modelling efforts, the presence of NPEs in the study area has been shown (Uhlenbrock et al., 2004). At 100 m measuring height, the resulting average horizontal imbalance of the sensible heat flux is in the order of 4–19 % (Steinfeld et al., 2007). In the same study area, Beyrich et al. (2006) found comparable differences between surface flux estimates from aircraft and tower of 11 % for the sensible heat and 23 % for the latent heat. Furthermore, a tendency was shown to close the energy balance on the regional scale with spatially averaging methods (Mauder et al., 2007a). This suggests that the tower EC cannot adequately capture all flux contributions due to its inability of spatial sampling. On the other hand, a large-aperture scintillometer captures NPEs up to the dimension of its path length, with increasing sensitivity towards the centre of the path (Foken et al., 2010). Also airborne EC is capable of spatial sampling and captures some of the associated flux, depending on the horizontal extent of the NPEs and the flight path. Therefore, the presence of NPEs in the study area can be considered a potential explanation for the deviation of the tower EC results from the WSMA, and even more so from the LAS results. In order to further adjust results from tower and airborne EC measurements, the raw data could be high-pass filtered, which restricts low-frequency flux contribution to an identical threshold (e.g. Thomas et al., 2012). This study combines several principles and methods for the purpose of quantifying: (i) the suitability of airborne instrumentation for EC measurements, (ii) the complex feedback of WSMA motions on the EC measurement, and (iii) the direct intercomparison of measurement platforms with differing spatial representativeness. The applied techniques are not restricted to use with the WSMA, but are general enough to be used for the development and assessment of other airborne platforms. 5 Conclusions We have shown that turbulence measurements from a weight-shift microlight aircraft can be achieved with sufficient precision to enable eddy-covariance flux calculation. Furthermore, a coordinated setup of tall tower, large-aperture scintillometer and weight-shift microlight aircraft measurements avoids typical errors due to averaging intervals and vertical flux divergence (e.g. Betts et al., 1990). Differences
100 APPENDIX D: METZGER ET AL. (2012) on the order of 15–25 % remain between the fluxes measured by the ground-based instruments and the WSMA. At that, the LAS generally measured the highest flux magnitude, followed by the WSMA and the tower. However, the 99.5 % confidence intervals of the maximum likelihood functional relationships between tower and WSMA include unity slope. Consequently, the observed differences can be considered insignificant, and the accuracy of the WSMA flux measurement is quantified to ≤10 % (1 σslope error). Nevertheless, several potential reasons for the disagreement of the results between the measurement platforms are investigated. (i) The WSMA wind and flux measurement is subject to spectral artifacts originating from its wing, and the results are corrected prior to the comparison. (ii) The flow distortion correction and the temperature resolution at the tower sonic anemometer measurement alone can explain the full magnitude of the disagreement. (iii) A footprint analysis allows excluding differences in the surface areas as the primary reason for the disagreement. (iv) Principal differences between spatially and temporally averaging flux measurements may also explain the observed differences. In particular, energy transfer by non-propagating eddies above heterogeneous terrain is discussed as a potential reason. We conclude that the WSMA is a suitable tool to promote the on-going research of surface-atmosphere interactions in heterogeneous landscapes. The flux measurement is sufficiently accurate to cover the required flight transect length (10–100 km). Moreover, the WSMA’s low ratio of true airspeed to climb rate is well suited for terrain-following flight over complex terrain. Using e.g. wavelet analysis, the regional turbulent exchange measured from the aircraft can be located in space and in spectral scale (Mauder et al., 2007a; Strunin and Hiyama, 2004). All of the above features are beneficial for the study of yet poorly understood exchange mechanisms between the Earth’s surface and the atmosphere. This further substantiates the versatility of the WSMA as a low cost and widely applicable environmental research aircraft. Appendix A Integral length scales and statistical error The integral length scale λcan be interpreted as the typical size of the most energy-transporting eddies. It is calculated by integration of the autocorrelation function from zero lag to the first crossing with zero at lag r 0 (Bange et al., 2002; Lenschow and Stankov, 1986): λ= r0 0 f (x)f (x +r) f (x) 2 dr. (A1) Here frepresents a turbulent quantity c(scalars or wind components), but also combinations of these with the vertical wind f(x)=w (x) ·c (x) (Bange, 2007). Hence, the integral scales of the turbulent fluxes were directly calculated from the data of the weight-shift microlight aircraft. The transformation into the integral time scale τof simultaneous tower measurements is carried out by division of λwith the mean horizontal wind speed at the tower. This assumes that Taylor’s hypothesis of frozen turbulence is valid (Taylor, 1915). The random statistical error of the sample average ¯ fis simply the square root of its variance (f ) 2 . However, the errors in the variance Vof f, or the covariance Fof its combinations, are functions of the integral scales λ,τ. The random statistical errors σ V and σ F were determined after Lenschow and Stankov (1986); Lenschow et al. (1994): σ 2 V =2·V 2 ·λ L,(A2) σ 2 F =2·F 2 ·λ L·1+r 2 wc r 2 wc ,(A3) with the averaging length Land the correlation coefficient between vertical wind and the turbulent quantity r wc .Itisassumed that λL,andthatwand care Gaussian distributed. The momentum flux consists of two orthogonal components, u w and v w , with the wind components u,vand w.The calculation of its random error is obtained from Gaussian error reproduction of the errors in its components (Bange et al., 2002). The individual random errors of the WSMA and the tower measurement, σ air and σ tow , respectively, were summarized for each variable over all flight legs: σ ran = n air σ air + n tow σ tow 2n−1,(A4) resulting in the average random error in the data couples σ ran with the sample size n. The ensemble random error σ ens considers the reduction of the random error with the sample size (Mahrt, 1998): σ ens =σ ran √n,(A5) with zero expected value σ ens and the standard deviation σ ran of the population. While σ ran is a measure for the average dispersion of the data couples, σ ens quantifies the level of confidence we can expect from comparing the entire dataset between the two platforms. To use Eqs. (A4)–(A5) for data obtained during different flight days, we use normalized error estimates. Yet, the normalized errors are excessively large when the denominator, i.e. the measurement quantity, approaches zero. For turbulent fluxes, this is usually the case under stable conditions, where e.g. intermittent turbulence can violate the assumptions in the integral length scales. Consequently, we constrain the calculation of σ ran and σ ens for the fluxes to values of u ∗ >0.2ms −1 and H,E>20 W m −2 , resulting in N=28, 15 and 24 samples, respectively.
APPENDIX D: METZGER ET AL. (2012) 101 Fig. B1. Cross-wind and along-wind integrated distributions of the footprints for case 2, z=100 m from Markkanen et al. (2009). Upper and lower panels display longitudinal and cross-sections, respectively. The footprint weight distributions are shown on the left side, and the cumulative distributions are shown on the right side. Appendix B Footprint modelling The footprintor source weight function quantifies the spatial contributions to each measurement (Schmid, 2002; Vesala et al., 2008). Analytical footprint models are often limited, e.g. regarding stability regimes or measurement heights (e.g. Kormann and Meixner, 2001, subsequently referred to with KM01). Lagrangian footprint models overcome these limitations and additionally consider 3-D dispersion, but are computationally expensive. The footprint model of Kljun et al. (2004, KL04) is a parameterization of the backward Lagrangian model of Kljun et al. (2002, KL02) in the range −200 ≤z/L ≤1, u ∗ ≥0.2ms −1 ,and1m≤z≤z i , with the boundary layer depth z i . Thus, it combines little computational effort with broad applicability. The parameterization depends upon friction velocity u ∗ , measurement height z, standard deviation of the vertical wind σ w and the aerodynamic roughness length z 0 ,ofwhichu ∗ ,zand σ w are measured directly. The roughness length is inferred using the logarithmic wind profile with the integrated universal function for momentum exchange after Businger et al. (1971) in the form of H¨ ogstr¨ om (1988). The KL04 is a cross-wind integrated footprint model, i.e. it does not resolve the distribution perpendicular to the main wind direction. In order to account for cross-wind dispersion, the KL04 was combined with Table B1. Median performance of the footprint parameterizations KL04+ and KM01 compared to the reference Lagrangian model of Kljun et al. (2002). Uncertainty measures NMSE, MAD and rare explained in the text. Direction Along-wind Cross-wind Model KL04+ KM01 KL04+ KM01 NMSE 0.34 ±0.05 0.95 ±0.48 0.34 ±0.05 0.33 ±0.36 MAD [%] 0.43 ±0.10 0.63 ±0.28 0.08 ±0.05 0.12 ±0.14 r0.91 ±0.00 0.66 ±0.12 0.99 ±0.01 0.99 ±0.01 a Gaussian cross-wind distribution function (Kljun et al., 2012). The combination of KL04 with this cross-wind distribution results in a computationally fast footprint parameterization which considers 3-D dispersion and is not constrained to applications in the surface layer. In the following, we refer to this model as KL04+. To evaluate model performance, KM01 and KL04+ were compared to the reference Lagrangian model KL02. For this purpose, four existing realizations of the KL02 model were used from Markkanen et al. (2009, Table 1, case 1 (L= −32 m, u ∗ =0.27 m s −1 ) and case 2 (L=−76.6m, u ∗ = 0.295 m s −1 ), z=50 m and 100 m). Markkanen et al. (2009) adopted case 1 from Leclerc et al. (1997), and referenced the results to large eddy simulations (Raasch and Schr¨ oter, 2001). The above parameter sets do not include σ v and σ w , which were derived using the integral turbulence characteristics proposed by Lumley and Panofsky (1964) and Panofsky et al. (1977), respectively. The computed footprint weights were summarized for each cell of a grid with 100 m horizontal spacing and subsequently integrated over cross-wind and along-wind direction, respectively (Fig. B1). In both directions, KL04+ assigns more weight to the close range compared to KM01 (Fig. B1 left panels). This is consistent throughout the range of the tested atmospheric conditions (not shown). In along-wind direction, KL04+ reproduces KL02 very well until the cumulative distribution accounts for approximately 80 % of the footprint (Fig. B1 upper right panel). Contributions from below the measurement location due to along-wind dispersion are slightly pronounced by KL04+, and neglected by KM01. The cross-wind distributions of both KL04+ and KM01 agree reasonably well with KL02. To quantify the model comparison, normalized mean square error (NMSE, Hanna and Paine, 1989), median absolute deviation (MAD, Rousseeuw and Verboven, 2002) and Pearson’s coefficient of correlation (r) are used. The NMSE is based on variance statistics and is thus sensitive to the few largest deviations in the dataset. In contrast, the MAD is the middle value of the error distribution, and is more sensitive to the error frequency. We use NMSE and MAD to assess the model performance around the peak and the tail of the footprint, respectively. The correlation coefficient provides information on the degree of similarity between the models’ distributions. Table B1 summarizes the results of the model
102 APPENDIX D: METZGER ET AL. (2012) comparison. In both along-wind and cross-wind directions, the similarity between KL04+ and KL02 is as good or better than between KM01 and KL02 (r). In along-wind direction, KL04+ is considerably closer to KL02 in the close range (NMSE) and the far range (MAD) compared to KM01. A similar deviation between KM01 and KL02 has been reported by Kljun et al. (2003). In cross-wind direction, both KL04+ and KM01 agree equally well with KL02. For all metrics, the standard errors over the four parameter sets are smaller for the KL04+ model, pointing out its reliability. Acknowledgements. Recognition has to be given to Frank Neidl and Rainer Steinbrecher at the Karlsruhe Institute of Technology, Institute for Meteorology and Climate Research. Neidl programmed and continuously maintained the data acquisition system, while Steinbrecher initiated windand flux measurements with the weight-shift microlight aircraft in the first place. Thanks go to Ulrich Weisensee and Jens-Peter Leps at the German Meteorological Service, Richard-Aßmann-Observatory Lindenberg for performing the tower turbulence measurements. We are obliged to Xunhua Zheng and her workgroup at the Chinese Academy of Sciences, Institute of Atmospheric Physics, which was hosting our project and providing indispensable infrastructure. Our thanks to Jens Bange at the Eberhard Karls University of T¨ ubingen, Institute for Geoscience, for his advice regarding the flight campaign design. The authors wish to thank Henry Loescher at the National Ecological Observatory Network, Fundamental Instrument Unit for his continued support. Stipend funding by the German Academic Exchange Service, Helmholtz Association of German Research Centres, China Scholarship Council and the European Union under the Science and Technology Fellowship China is acknowledged. 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106 APPENDIX E: METZGER ET AL. (2013) Appendix E: Metzger et al. (2013)
APPENDIX E: METZGER ET AL. (2013) 107 2194 S. Metzger et al.: Spatially explicit regionalization of airborne flux measurements Fig. 1. Location of the Xilin River catchment in the Inner Mongolia Autonomous Region, China (modified after Steffens et al., 2008). small areas around the immediate measurement locations (e.g. Kaharabata et al., 1997; Schuepp et al., 1992). On the other hand aircraft-based measurements can provide flux information at regional scales (e.g. Desjardins et al., 1995) but are restricted to short periods of time. Thus the temporal and spatial characteristics of ground-based and airborne measurements complement each other (Gioli et al., 2004; Mauder et al., 2007). It is desirable to integrate both approaches in an effort to provide suitable datasets for the design, constraint, and evaluation of mass and energy exchange models at site as well as at regional scales (Chen et al., 1999; Desjardins et al., 1997). In the following we briefly review the requirements for spatial scaling of airborne EC measurements, and the applicability of airborne EC measurements over complex terrain. Aggregation approaches enable estimating the exchange over entire landscapes, provided fluxes for characteristic land cover features or domains are known (Beyrich et al., 2006). Flight path segmentation can be a useful tool to directly relate airborne EC measurements to landscape units (e.g. Desjardins et al., 1994; Vellinga et al., 2010). It is also possible to functionally relate these measurements to land cover properties, which then reflect the effects of vegetation, climate, soil and topography on the flux strength. For example, Kirby et al. (2008) propose a method for discerning individual fluxes in a heterogeneous landscape based on subsets of “pure” flux fragments. Another approach is to utilize quantitative information about the EC measurement’s spatial context, on which basis environmental response functions (ERFs, Desjardins et al., 1994) can be derived. The general idea of ERFs is to establish a relationship between spatially or temporally resolved flux observations (responses) and corresponding environmental drivers. Hence ERFs are a quantitative mechanism to extract relationships from, and to condense the information content in a dataset. If sufficiently accurate, the extracted relationships can then be used, e.g. to bridge observational scales or to adjust the spatial representativeness of ground-based flux measurements. In addition, current methods to spatially resolve surface fluxes are mainly focused on remote sensing algorithms (e.g. Fan et al., 2007) and process-based land surface models (e.g. Vetter et al., 2012). These procedures often demand far-reaching assumptions, such as the closure of the energy and water balances (e.g. Anderson et al., 2012), or are challenging with respect to the required data basis (e.g. Kaminski et al., 2012; Ziehn et al., 2011). In contrast, accurate ERFs enable inferring high-resolution surface flux maps directly from observational data with minimal, quantifiable assumptions. However, ERFs cannot provide insights, e.g. into ecosystem pools. Consequently, ERFs might be suitable for complementing data assimilation and remote sensing approaches, e.g. through contributing to the design, constraint and evaluation of flux algorithms. The forenamed applications require the relation of the airborne measured fluxes to land cover properties. To enable this requirement an aircraft is bound to measure close to the surface, where characteristic fluxes from different land covers are not yet fully homogenized (or blended, Mason, 1988; Wood and Mason, 1991). Moreover, the flux must be measured at a constant altitude above ground, so as to avoid artificial flux contributions through altitude fluctuations along vertical gradients (Vickers and Mahrt, 1997). However investigation areas are seldom ideally flat, and topography can vary significantly throughout a domain. To safely follow terrain contours at a low and constant altitude above ground, the aircraft must possess a low ratio of true airspeed to climb rate. Only a few airborne platforms fulfil this requirement (e.g. Bange et al., 2006; Gioli et al., 2004; Thomas et al., 2012), with the weight-shift microlight aircraft (WSMA) being one of them (Metzger et al., 2011, 2012). In forenamed studies we describe a WSMA that enables airborne EC flux measurements in remote settings at reasonable cost and minimal infrastructural demand. The objectives of the present study are to investigate the possibilities of (i) deriving meaningful EC fluxes from WSMA measurements over complex terrain, and (ii) scaling the results to a domain of interest. We applied the WSMA over the undulating steppe of the Xilin River catchment (XRC), Inner Mongolia, China (Fig. 1). On 21 days in the summer of 2009, flights along line transects were conducted at 50–100 m a.g.l. From boundary layer scaling it is found that the vertical flux gradients below the flight level satisfy the surface layer definition (constant within 5–10%). Hence measured sensible (H) and latent heat flux (LE) can be interpreted as surface fluxes (Sect. 3.1). Because of its climate and management practices typical for semiarid grasslands of China (Butterbach-Bahl et al., 2011), intensive ecological research commenced in the XRC in the late 1970s (Jiang, 1985). Besides Tibet, Inner Mongolia is Biogeosciences, 10, 2193–2217, 2013 www.biogeosciences.net/10/2193/2013/
114 APPENDIX E: METZGER ET AL. (2013) S. Metzger et al.: Spatially explicit regionalization of airborne flux measurements 2201 Fig. 5. Flow chart showing how input and reported data streams are processed along the four principal steps of the LTFM method. Additional detail is provided in Sects. 2.4.4 and 4, and a summary of all notation can be found in Appendix A. 2.4.4 Environmental response function We base the development of a catchment-specific ERF on the works of Chen et al. (1999), Hutjes et al. (2010) and Ogunjemiyo et al. (2003). The general idea is to establish a functional relationship between spatially or temporally resolved flux observations (responses) and corresponding environmental drivers. Figure 5 provides an overview of the novel approach to ERF presented in the following. Thus far, a suitable number of flux observations was obtained by either shortening the time-domain EC averaging interval (Chen et al., 1999; Ogunjemiyo et al., 2003), or by stratifying repeated observation along the same flight line on different days (Hutjes et al., 2010). The inherent drawbacks are the neglect of either long wavelength contributions to the flux measurement, or inter-day variability of ecosystem drivers. Both are overcome using the wavelet crossscalogram technique (Sect. 2.4.2). Previously, the development of ERFs has solely focused on drivers in the footprint of the flux observations, namely discrete land cover classifications. This procedure ignores within-class variability across a catchment, e.g. along climatic or altitudinal gradients, which can be overcome by using continuous variables such as LST and EVI instead. In addition, the present approach considers the meteorological drivers S↓, mixing ratio (MR), and potential temperature (θ). This avoids the need for stratifying or pre-selecting data, and enables constructing a single ERF that is valid for the entire observation period and, within the range of the measured variables, throughout a catchment of interest. Hitherto, ERFs were determined as the inverse of a linear mixing matrix, using either numerical (Chen et al., 1999) or regression methods (Hutjes et al., 2010; Ogunjemiyo et al., 2003). Such a procedure assumes a linear relationship between drivers and responses, which is subject of on-going discussion and research (e.g. Raupach and Finnigan, 1995). Instead, the present approach uses boosted regression trees (BRTs), a non-parametric machine learning technique, to establish an ERF between drivers and responses. In contrast to parametric approaches, BRTs do not assume a predetermined form of the response, but construct an ERF according to the information in the data. It is for this reason that not the absolute values of the land surface and meteorological drivers are important, but rather their spatial variability and coherence. In case of the land surface drivers for example, the only assumption made here is that the spatial patterns of LST and EVI approximate the spatial patterns of source strength in Hand LE (e.g. Holmes, 1970; Oke, 1987). This is a much weaker assumption than a mechanistic link, and adds power to the method. BRTs can fit complex nonlinear relationships, automatically handle interactions between drivers, and provide predictive performance that is superior to most traditional modelling methods (e.g. Hu et al., 2010). Here we use the BRT work package by Elith et al. (2008), which builds upon the GBM library by Ridgeway (2012). To identify the optimal choice of parameters and variables for the BRTs, a sensitivity analysis was conducted www.biogeosciences.net/10/2193/2013/ Biogeosciences, 10, 2193–2217, 2013
APPENDIX E: METZGER ET AL. (2013) 115 2202 S. Metzger et al.: Spatially explicit regionalization of airborne flux measurements Fig. 6. Flight along pattern O12 on 8 July 2009, 12:16–12:24 CST (white dashed line). The composite flux footprint along the flight line (30 %, 60 %, 90 % contour lines) is superimposed over maps of land cover (left panel), land surface temperature (LST, centre panel), and enhanced vegetation index (EVI, right panel). The land cover colour code and corresponding abbreviations are identical with Fig. 2. using the cross-validation (CV) procedure described in Elith et al. (2008). During cross validation all available data are divided into 10 random combinations of training (90 %) and evaluation (10 %) fractions, which allows assessing and optimising model performance. The parameter settings that minimized predictive deviance for the present dataset were found to be: absolute (Laplace) error structure, bag fraction (0.7), tree complexity (5), learning rate (0.1), and number of trees (104). The initial set of variables also included time of the day, MODIS albedo, atmospheric pressure, land cover, z, zi,u,u∗,z0, virtual potential temperature, as well as elevation, topographic wetness index, aspect, and slope of the footprint modelled source area. We use the variable dropping algorithm by Elith et al. (2008) to reach a compromise between predictive deviance and model parsimony. This algorithm (i) fits a BRT model, (ii) performs a 10-fold CV, (iii) drops the least important predictor (determined from the improvement to the model and the number of splits, Friedman, 2001), and (iv) repeats this sequence until a stopping criterion is reached. The mean CV deviance can be used to decide how many variables can be removed without significantly affecting predictive performance. Here, we set an upper threshold of 30 W m−2for the mean CV deviance, which equals ≤1/2 the random sampling error in the flux observations (Table 4). The dropping of variables first stopped for LE at 29.2 W m−2mean CV deviance, yielding a set of the five most important predictors (LST, EVI, S↓, MR, and θ). For Hthe same predictor set yields a mean CV deviance of only 22.6 W m−2. Remarkably, atmospheric pressure, z,and ziwere no significant predictors for the observed fluxes. This indicates that the chosen flight/analysis strategy effectively minimizes cross-contamination of the flux observations by vertical flux/pressure gradients. Analogously the algorithm dropped elevation, aspect, and slope of the footprint modelled source area as predictors. This shows that slope-induced effects on radiative transfer or turbulence generation do not significantly impact the flux observations. Consequently, the final BRT model is fitting an ERF to Hand LE as function of only the five most important predictors. This ERF is then used to predict Hand LE throughout the XRC, as a function of LST and EVI for each grid cell, and the median S↓,MR, and θfor the duration of a flight. In the following we will use the term LTFM to refer to the overall procedure consisting of Low level flights, Time–frequency-, Footprint-, and Machine learning analyses (Fig. 5). 2.5 Uncertainty Throughout the present study, we use the median and the median absolute deviation as preferred measure of location and scale, respectively (Croux and Rousseeuw, 1992; Rousseeuw and Verboven, 2002). All resulting uncertainty estimates are representative of one standard deviation. For the purpose of detecting systematic differences between observations and predictions, we use the maximum-likelihood fitting of a functional relationship (MLFR, Ripley and Thompson, 1987). This method assigns a weight to each data couple in the relationship, which is inversely proportional to its error variances. In our case, the squared random flux errors in the observations, and the residuals in the BRT cross-validation ensemble are used. This appreciates reliable data and depreciates uncertain data couples. The errors in the MLFR coefficients are determined from a jackknife estimator (Quenouille, 1956; Tukey, 1958). If the regression intercepts were not significant, the relationships were forced through the origin, and confidence intervals were determined from the slope error. The coefficient of determination R2was calculated in analogy to weighted least-squares regression (Kvalseth, 1985; Willett and Singer, 1988). It is the proportion of variation in the weighted dependent variable that can be accounted for by the weighted independent variable. Biogeosciences, 10, 2193–2217, 2013 www.biogeosciences.net/10/2193/2013/
116 APPENDIX E: METZGER ET AL. (2013) S. Metzger et al.: Spatially explicit regionalization of airborne flux measurements 2203 Uncertainty in the LTFM up-scaling procedure originates from different sources during measurement and data analysis. Part of these uncertainty terms exhibit random characteristics; i.e. they tend to cease with sample size. Another part however will systematically bias the results, independent of sample size. An uncertainty budget for the random and systematic uncertainties in the LTFM procedure will consist of uncertainty terms for (i) instrumentation and hardware, (ii) turbulence sampling, (iii) spatio-temporal analysis, (iv) BRT residuals, (v) BRT response function, and (vi) BRT state variables. While uncertainty terms (i), (ii), and (iv) can be quantified with readily available procedures (Sects. 2.4, 3.3), in teh following we describe several techniques to assess terms (iii), (v) and (vi). 2.5.1 Spatio-temporal analysis in heterogeneous terrain Under the umbrella of spatio-temporal analysis, we quantify in the following the uncertainty contribution from wavelet analysis, footprint modelling, and the assumption of linear mixing. The fluxes derived from the wavelet cross-scalogram were adjusted to match the leg-averaged fluxes from timeseries EC, which avoids bias between both techniques. Also areas above the wavelet cross-scalogram COI were used in the flux calculation to ensure including all scales of turbulent transport along the entire transect. However, values above the COI are potentially distorted due to edge effects, in particular close to the beginning and the end of each transect. These artefacts propagate in the resulting variances and fluxes, and consequently into the footprint estimates. Additional spatial uncertainty terms result from the use of an “offline” footprint model that does not consider the actual flow field, as well as from the MODIS EVI and LST data. The use of BRTs does not expect a linear response between the state variables and the flux signal. However, LTFM still assumes the linear mixing of the flux signal with respect to the contributing surface patches with different biophysical properties and source strengths. To quantify the error inherent in the above analysis steps, we compare maps of LTFM predicted fluxes to airborne flux observations. (i) The BRT is trained with all available observations (N=8466). (ii) Using the median state variables along each flight leg (N=42), the BRTs response function is used to predict a similar number of flux maps (Fig. 11). (iii) The LTFM footprints are superimposed over these flux maps. (iv) For each flux observation, a predicted flux is calculated as the footprint-weighted average of all contributing cells, and (v) predictions and observations are compared. 2.5.2 Response function BRTs are a non-parametric machine learning technique in which a response function is constructed according to the coherencies in the training data. As a direct consequence the predictive performance of BRTs depends on how complete the combinations of state variables in the evaluation data are represented in the training data. Here we assess the susceptibility of the BRT response function and predictive performance to missing state variable combinations in the training data. For this purpose, 12 incomplete training datasets are created, each of which omitting a different flight out of the total of 12 flights in Table 1. For each incomplete training dataset, (i) the BRT is trained, (ii) the resulting response function is used with the state variables along the omitted flight for prediction, and (iii) predictions and observations are compared. 2.5.3 State variables Here, we consider the uncertainty resulting from disregarding part of the natural variability in the state variables that are used for spatially and temporally explicit BRT predictions. For this purpose we quantify the disregarded parts of the natural variability in each state variable and propagate it through the full BRT model. While explicit in time, the meteorological variables measured by the aircraft do not cover the entire catchment. We estimate a measure of spatial variability from all subsequent pairs of flights that are located in different areas of the catchment (Table 1, Fig. 2). The median differences throughout the catchment for S↓(−6±12 W m−2), θ(−1.1±1.1K),andMR(−0.5±0.3gkg −1) are not significant (Wilcoxon rank-sum test, p≥0.18). On the contrary, MODIS EVI and LST are explicit in space, but not continuous in time. The 8-day trends from one scene to the next are accounted for in the BRT procedure through temporal interpolation between the MODIS scenes (Sect. 2.2). However, processes of shorter duration, such as frequent events of small-scale convective precipitation, go unaccounted. Hence we estimate a measure of the natural variability between two MODIS scenes. For this purpose we calculate the median change of all grid cells between all subsequent MODIS scenes, amounting to 0.01 ±0.05 for EVI and −0.5±6.2K for LST. The random part of EVI and LST natural variability by far exceeds the MODIS data product uncertainty of ≈0.015 (Xiang et al., 2003) and ≈1 K (Wan and Li, 2008), respectively. Hence MODIS data product uncertainty was not considered separately. The correlation matrix between the state variables was calculated using all 8446 aircraft observations. A variancecovariance matrix was calculated from this correlation matrix and the random part of the state variables’ natural variability. Preserving the variance-covariance relationship, 1000 samples were drawn from a multivariate normal distribution with zero mean. These represent 1000 combinations of co-existing natural variability in the state space of the BRT model. The propagation through the BRT model was performed individually for each combination by (i) superimposing the estimated natural variability over the measured state variables of all 8446 observations, (ii) performing a BRT prediction, and (iii) comparing the results to the undisturbed predictions. www.biogeosciences.net/10/2193/2013/ Biogeosciences, 10, 2193–2217, 2013
APPENDIX E: METZGER ET AL. (2013) 117 2204 S. Metzger et al.: Spatially explicit regionalization of airborne flux measurements 3 Results and discussion In the first part of this section, we assess the surface– atmosphere mixing regimes. From there wavelet analysis, footprint modelling and BRTs are used to infer ERFs between land surface properties and the flux measurements. Lastly, uncertainties in the LTFM up-scaling procedure are analysed and discussed. 3.1 Horizontal mixing between surface and flight level On spatial average energy conservation requires that the vertical profiles of Hand LE approach their respective entrainment flux at the top of the CBL (e.g. Deardorff, 1974; Sorbjan, 2006). The linear vertical flux gradient of Hthroughout the CBL was calculated (−0.21 W m−2m−1 –−0.06 W m−2m−1), assuming that Hceases at the statically stable entrainment zone around 0.8 CBL. However, the entrainment flux of Eis unknown. Hence we cannot estimate the vertical flux gradient of E, but assume a comparable order of magnitude as for H. The resulting effect of the vertical flux gradient below the flight level is −5±2% of H, which falls well within the surface layer definition (e.g. Raupach and Finnigan, 1995; Stull, 1988, flux constant within 5−10%). Thus, it is feasible to assume that Hand Emeasured at flight level are representative of surface fluxes. The characteristic length scale of surface heterogeneity is on the order of several hundred to thousand meters, with an average of LH=1012 ±715 m (Table 2). Along identical flight paths LHis comparable between days with different meteorological settings (e.g. 15 and 17 July 2009, 26 and 30 July 2009). This confirms the usefulness of the surface temperature measurement as a proxy for surface heterogeneity. Only the longer flight paths C1 and C2 cross the dune belt in the centre of the catchment (Fig. 2). The dune belt is the largest continuous land cover after steppe, and consequently the autocorrelation function of Tsestimates large values of LH(1458–2615 m). During all flights, LHwas small compared to the Raupach length (LR=1532–5214 m), and thus the influence of the surface heterogeneity is confined within the CBL (zi=1100–2500 m). Here we use the thermal blending height (zTB1 =40 ±29 m) as an estimate for the vertical level where quasi-equilibrium of the turbulent exchange between land surface and atmosphere is reached. At all times the flight level (z=48–102 m) is above zTB1 and below ≈10 % of the CBL depth, a common estimate for the depth of the atmospheric surface layer (e.g. Raupach and Finnigan, 1995; Stull, 1988). Hence it is feasible to assume that the turbulence measurement at flight level is representative for the land surface in the flux footprint. The interpretation of the flux observations might be more complicated for measurement heights below the thermal blending height (limited spatial representativeness) or above the surface layer (vertical flux gradient). The blending length formulations LTB1 (1660±723) and LTB2 (957±441) are used to assess the minimum size of surface heterogeneity that significantly influences the flow at flight level. Here we use 255 m <L TB2 <1852 m as a guideline, because LTB2 is also representative of the magnitude of surface heterogeneity. The native resolution of the EVI data (230 m) and the land cover data (90 m) is equal to or better than LTB2, and thus sufficient to reproduce the variability of the land cover. In comparison, the native resolution of the LST data (1000 m) is coarse, potentially leading to an attenuation of the ERFs. Using the wavelet cross-scalogram, long wavelength contributions to the flux do not constrain the spatial resolution of the flux computation along the flight path. Nevertheless, the random flux error is inversely proportional to the square root of the averaging length (e.g. Lenschow and Stankov, 1986), and propagates directly into the computation of the ERFs. Hence, we consider a trade-off between random error (high resolution) and smearing (low resolution) of the resulting flux estimates. The upwind distance (perpendicular to the WSMA flight path) where 80 % of the flux contributions are included in the footprint, L80% =1171±314 m, is comparable in magnitude to LH. Thus, a flight path length of similar extent (1000 m) is a physically meaningful window for the computation of turbulence statistics and fluxes, because (i) changes in the turbulent flux (response) are resolved at the same spatial scale as the characteristic surface heterogeneity (driver); (ii) the turbulence statistics used for footprint calculations are representative on the same spatial scale as the upwind extent; and (iii) the random error for each flux estimate decreases by ≈70 % compared to a window length of 90 m. The (aerodynamic) roughness length is usually below 1 m, with exception of the low wind speed situation on 17 July 2009, pattern O11, and the higher flight levels (z≥ 97 m) on 26 July 2009 (Table 2). 3.2 Flux un-mixing The presentation of the flux un-mixing results follows the sequence of the LTFM analysis steps. In Sect. 3.2.1 the spatially resolved flux observations from the wavelet cross-scalogram are illustrated. Subsequently, footprint modelling is used to infer the biophysical surface properties in the source area of each flux observation (Sect. 3.2.2). In Sect. 3.2.3 the ERFs between flux observations and meteorological and land surface drivers are established. These ERFs are then used to predict the surface fluxes throughout the XRC, which are finally summarized for different land covers (Sect. 3.2.4). 3.2.1 Spatially resolved flux measurement Here and in the following we use a flight along pattern O12 for illustration, which follows a shallow elevation gradient (Fig. 4 bottom panel). This flight pattern is particularly suitable for this purpose because of its marked land cover changes over a relatively short distance. The wavelet Biogeosciences, 10, 2193–2217, 2013 www.biogeosciences.net/10/2193/2013/
118 APPENDIX E: METZGER ET AL. (2013) S. Metzger et al.: Spatially explicit regionalization of airborne flux measurements 2205 Table 2. Mean length scales ±SD between repetitions during the WSMA flights selected for analysis. Shown are CBL depth zi, aerodynamic roughness length z0,flight altitude z, thermal blending height zTB1, length scale of surface heterogeneity LH, Raupach length LR, the thermal blending lengths LTB1 and LTB2, and the upwind distance from the WSMA L80%, where 80 % of the flux contributions are included in the flux footprint. Date Time (CST) ID z i (m) z 0 (m) z(m) z TB1 (m) L H (m) L R (m) L TB1 (m) L TB2 (m) L 80% (m) 8 Jul 2009 10:20–10:50 O10 1100 0.21 ±0.13 59 ±445±7 802 ±192 1532 ±105 1046 ±171 255 ±5931±52 12:00–12:50 O12 1800 0.07 ±0.05 72 ±624±2 700 ±58 4093 ±164 2160 ±263 628 ±39 1574 ±147 13 Jul 2009 11:30–12:10 O8 1900 0.04 ±0.05 51 ±041±4 1055 ±5 4770 ±3 1330 ±122 999 ±12 1440 ±127 12:40–13:10 O3 2100 0.05 ±0.07 51 ±238±5 858 ±95 4292 ±236 1134 ±45 1108 ±220 1305 ±64 15 Jul 2009 11:30–12:20 O11 2200 0.06 ±0.04 55 ±411±2 370 ±54 5214 ±508 1950 ±223 1368 ±304 1470 ±168 12:30–13:00 O7 2100 0.26 ±0.19 57 ±717±6 298 ±76 3507 ±82 984 ±117 1207 ±132 1081 ±128 17 Jul 2009 11:00–11:30 O11 1400 1.13 ±0.81 48 ±122±0 366 ±37 1589 ±65 788 ±74 440 ±28 720 ±74 12:20–13:00 O7 1400 0.05 ±0.06 52 ±219±8 507 ±219 3136 ±169 1381 ±54 950 ±159 1296 ±150 26 Jul 2009 12:50–15:30 C1 2500 1.75 ±1.91 97 ±485±68 1458 ±913 2626 ±284 1974 ±562 752 ±196 991 ±331 13:10–15:10 C2 2500 2.30 ±2.12 102 ±583±51 1459 ±632 2430 ±382 1921 ±325 916 ±310 945 ±191 30 Jul 2009 11:00–13:30 C1 1600 0.48 ±0.34 56 ±346±21 1653 ±161 3097 ±340 2403 ±1438 1015 ±22 1042 ±100 11:10–13:20 C2 1600 0.11 ±0.01 54 ±051±13 2615 ±84 3798 ±735 2853 ±601 1852 ±51 1206 ±0 cross-scalogram allows a high spatial discretization of turbulent flux measurements. At the same time it includes flux contributions from wavelength that are significantly longer than the 1000 m subinterval for each flux observation (Fig. 4). The resulting high number of flux observations along a flight line leads to previously unachievable resolution and coverage of the state space. Spatially coherent flux contributions are detected on transport scales (eddy sizes) of 500–2000 m, that is of similar size as the extent of homogeneous surface patches LH. Strong local flux contributions are confined to scales <500 m, and approximately decay within the lower threshold of the observed blending lengths LTB1 and LTB2. This confirms a close coupling between atmospheric turbulence structures with surface patchiness, and consolidates the interpretation of the length-scale approach. The less certain flux contributions above the wavelet COI are small (−15 to −4 % median differences for all flights). In the present example the COI is confined to relatively small scales (≤4 km), which is a direct result of the comparatively short flight. In general, more certain flux contributions below the COI include transport scales up to ≈1/3oftheflight length, and can reach ≈16 km for flight patterns C1 and C2. However, this also implies that the maximum considered transport scale differs between the flight patterns, just as it would be the case for the time-domain EC method. The wavelet crossscalogram reveals strong turbulent transport in the second and fourth quarter of the flight for H, and in the first and third quarter for LE (Fig. 4). When integrated over all transport scales for each overflown 90 m cell of the land cover grid, these patterns correspond to strong upward fluxes. 3.2.2 Land cover In Sect. 3.2.1, turbulence statistics and fluxes were integrated for each overflown 90 m cell of the land cover grid. In the following we expand the integration window to overlapping subintervals of 1000 m length, while retaining a spatial discretization of 90 m. Such a procedure significantly reduces the random sampling error (Sect. 3.1), though at the cost of decreasing the number of resulting observations by one window size (dN≈10). The resulting turbulence statistics are used to calculate the source area of each individual flux observation along the flight line, which are superimposed over the land cover grids. Figure 6 shows that in general LST and EVI follow the land cover patterns, e.g. lower temperature and higher greenness for irrigated agriculture and marshland. However, it is also evident that the static land cover classification cannot reflect the current surface conditions. For example, the marshland in the north-western quadrant appears dried-out (high LST and low EVI), while the steppe area in the north-eastern quadrant shows large variations in LST. Hence, biophysical surface properties also vary significantly within the land cover classes. This is likely a function of geomorphological properties such as aspect, slope and soil type, but also due to the large variability of convective rainfall events across the study area (e.g. Schaffrath et al., 2011). Following superimposition of the footprints over the land cover data, the spatial contributions of different surface properties to each flux observation can be quantified (Fig. 7). It is evident that measured Bo changes in correspondence with the dominating land cover, i.e. low Bo for marshland and irrigated agriculture, and high Bo for bare soil and steppe. LST and EVI are stratified between the land covers, although in different sequence compared to the regional average (Fig. 3). The variability of LST and EVI within the land cover classes is equal to or larger than the between-class variability, in particular for marshland, irrigated and rainfed agriculture. While LST and EVI behave inversely for all natural land covers (−0.78 <r<−0.10), the contrary is true for irrigated (r=0.92) and rainfed (r=0.30) agriculture. www.biogeosciences.net/10/2193/2013/ Biogeosciences, 10, 2193–2217, 2013
APPENDIX E: METZGER ET AL. (2013) 119 2206 S. Metzger et al.: Spatially explicit regionalization of airborne flux measurements The latter finding appears counter-intuitive, but can be explained by tillage farming in the low-level plains with crops that are not adapted to the semiarid climate, such as potatoes. The albedo of these densely vegetated crops can be lower compared to the sparsely vegetated steppe land cover (α≈0.2, Ketzer et al., 2008), resulting in higher foliage temperatures. Only two natural land covers, marshland and mountain meadow, exhibit similarly high EVI values as the field crops (Figs. 2, 3). Nevertheless, the LST of these land covers is comparatively low. In case of the marshland this can be explained by water-saturated soils with high heat capacity. Conversely, lower temperatures in accordance with the adiabatic temperature gradient are expected for the mountain meadows at higher altitudes. In Fig. 8 Hand LE observations along the flight line are shown together with the LST and EVI in the respective source area. Because of the 1000 m integration window over the wavelet cross-scalogram, the results appear smoother compared to Fig. 4, where a 90 m integration window is used. It is apparent that Hand LE both systematically change with LST (rH=0.64, rLE =−0.84) and EVI (rH=−0.62, rLE =0.73). However, peaks in H(3 km and 9 km in Fig. 8) and in LE (0 km and 7 km) do not manifest when their respective land surface drivers in the footprint are maximal. Instead they seem to follow a trade-off function between LST and EVI. 3.2.3 Environmental response functions Thus far our findings indicate that the interactions between land surface and atmosphere are multi-facetted and potentially non-linear. Hence we use LST and EVI as topical, spatio-temporal proxies for the source strength of Hand LE, rather than using the land cover classification directly. In comparison to earlier flux un-mixing studies (Chen et al., 1999; Hutjes et al., 2010; Ogunjemiyo et al., 2003), this has the benefit of (i) providing individual source strength representations for the effects of surface moisture and temperature, and (ii) representing the land surface by continuous (LST, EVI) rather than discrete variables (land cover classes), thus enabling the use of more advanced scaling algorithms. Here, we use BRTs to extract the relationships between all (N=8446) flux observations and land cover (LST, EVI) and meteorological (S↓, MR, and θ) variables. While BRTs are capable of reproducing complex interactions through multilayered branching, the fitted function can be summarized, e.g. as partial dependence plots (Fig. 9). These show the effect of each individual variable on the response after (i) subtraction of the offset (H0=161 W m−2,LE 0=176 W m−2), and (ii) accounting for the average effects of all other variables in the model. The partial dependence plots in Fig. 9 are sorted in order of the relative importance of the response variables (Friedman, 2001). The most important responses of Hare non-linear (LST, θ), followed by linear responses (S↓, MR, and EVI). With the exception of MR and EVI, the individual responses are positive in sign. The order of the responses for LE is partially different (MR, LST, θ,S↓,and EVI), and only the responses on S↓and EVI are approximately linear (not shown). With exception of MR (concave, maximal response around 10 g kg−1) and LST (convex, minimal response around ≈310 K), the signs of the responses for LE are positive. It appears surprising that Hand LE are only weakly related to S↓. This can be explained by using only noontime flights in the present study, where S↓mainly fulfils the purpose of accounting for varying cloud/radiation conditions between different measurement days. In addition, during individual flights S↓was usually constant to within ≤10 % (Table B1). However, when using ERFs to reproduce a diurnal cycle, a much larger dependence of Hand LE on S↓would be expected. In Fig. 10 MLFRs are established between BRT fitted values for Hand LE and the observed fluxes (N=8446). Here we use the BRT cross-validation residuals and the random sampling errors in the observations to determine the MLFR weights of each data point. Uncertainty terms (i), (iii), (v) and (vi) (Sect. 2.5) cannot be quantified individually for each observation. Hence these terms are not considered here, but in the final uncertainty budget (Tables 3 and 4). For both Hand LE the agreement between the BRT fitted values and the observed fluxes is excellent. Contrary to our initial anticipation, the ERFs are not attenuated by the relatively coarse MODIS LST resolution, as indicated by approximately zero MLFR offset and unity slope. The median absolute deviation in the residuals is small (≤1 %). However, several outliers are found for moderate to high fluxes of H(N=41) and LE (N=133), for which the BRTs underestimate the observed value by −150 Wm−2or more. The majority of these cases occur during the flights O8 on 13 July 2009 and C1 on 26 July 2009, respectively. On both dates the outliers concur with highly intermittent solar irradiance (200 <S↓<1200 W m−2) along a short section of the flight paths. For instance an intermittent cloud cover can disrupt the functional relation between the irradiance (driver) and the flux (response) observations, because, (i) at a flight level of 50–100 m a.g.l., the aircraft irradiance measurement does not represent S↓in the source areas of Hand LE, and (ii) the plant physiological response can vary substantially on spatio-temporal scales that are small compared to atmospheric transport processes between the land surface and the aircraft. Our choice of land surface and meteorological drivers appears to work well for describing the noontime surface– atmosphere exchange of heat and water vapour over a moisture-limited landscape. However, it is important to note that appropriately describing exchange processes over longer periods of time, for different landscapes or scalars might require finding an entirely different set of predictors. Biogeosciences, 10, 2193–2217, 2013 www.biogeosciences.net/10/2193/2013/
120 APPENDIX E: METZGER ET AL. (2013) S. Metzger et al.: Spatially explicit regionalization of airborne flux measurements 2207 Fig. 7. Biophysical surface properties in the footprint of each observation (N=124) along the flight pattern O12 on 8 July 2009, 12:16– 12:24 CST, summarized by land cover. Shown are (clockwise from top right panel) land surface temperature, enhanced vegetation index, Bowen ratio, and the land cover fraction in the footprint. The dashed lines are land cover averages for LST and EVI, and the spatial trend for Bo. The land cover colour code and corresponding abbreviations are identical with Fig. 2. Fig. 8. Sensible heat flux (left panels) and latent heat flux (right panels) along the flight pattern O12 on 8 July 2009, 12:16–12:24 CST. Also shown is the random sampling error (error bars) for each observation (N=124), and the spatial trend (dashed line). The top and bottom panels show the land surface temperature and the enhanced vegetation index in the footprint of each observation, respectively. 3.2.4 Extrapolation and summarization For the duration of each flight pattern, the trained BRT models are used to extrapolate Hand LE throughout the XRC. For this purpose the median meteorological state variables during each flight pattern as well as topical grids of MODIS LST and EVI data are used. Grid cells that exceed the state space of the BRT training dataset (N=8446) are excluded from extrapolation. Fig. 11 shows the resulting flux grids for three different days, with a spatial coverage of ≥92 %. Because of the identical state space ranges for BRT training and prediction, also the ranges of the extrapolated turbulent fluxes are within limits of the observations. Despite that the land cover classification was never used during the extrapolation process, several landscape units are clearly recognizable in the flux maps. For instance bot, the Xilin River valley and the mountainous headwater area to the east display low Hand LE. On the contrary, the non-vegetated basin on the northern tip shows consistently low evapotranspiration. For a given meteorological boundary condition (MR, θ, S↓), the heat fluxes within several hours of solar zenith can be expressed as a function of LST and EVI (Fig. 9). In turn, these biophysical surface properties are characteristic within a land cover class (Fig. 3). Here, we aggregate all grid cells of the flux maps according to land cover class, resulting in sample distributions of Hand LE. This allows www.biogeosciences.net/10/2193/2013/ Biogeosciences, 10, 2193–2217, 2013
APPENDIX E: METZGER ET AL. (2013) 121 2208 S. Metzger et al.: Spatially explicit regionalization of airborne flux measurements Table 3. Median land cover specificflux estimates of Hand LE from the LTFM procedure over all flight patterns ±median spatial variability within the respective land cover. Also shown are the corresponding median ensemble random uncertainties σens(H), σens(LE) and land cover specificsamplesizeN. Land cover H(Wm−2)LE(Wm −2)σens(H) σens(LE) N Bare soil 193 ±32 136 ±38 1 % 1 % 22049 Sand dunes 188 ±37 144 ±55 1 % 1 % 43424 Marshland 125 ±55 230 ±59 1 % 1 % 20722 Steppe 202 ±40 138 ±46 <1% <1 % 321956 Mountain meadow 114 ±47 260 ±69 1 % 1 % 25175 Settlements 172 ±40 155 ±46 3 % 5 % 1404 Rainfed agriculture 183 ±35 147 ±40 1 % 1 % 17024 Irrigated agriculture 116 ±32 224 ±41 5 % 5 % 1068 Table 4. Median systematicand random uncertainty terms (in parentheses) for a single flux observation or grid cell throughout the LTFM procedure. Source HLE Instrumentation and hardware 0 % (8 %) 0 % (7 %) Turbulence sampling 0 % (57 %) 0 % (121 %) Spatio-temporal analysis 2 % (40 %) 4 % (47 %) BRT residuals 0 % (5 %) 0 % (6 %) BRT response function 11 % (69 %) 18 % (77 %) BRT state variables 13 % (77 %) 14 % (75 %) a formal transition from a mosaicto a tile representation of Hand LE over the XRC for the duration of each flight pattern (Mengelkamp et al., 2006). These sample distributions then enable the analysis of land cover specific source strengths (36 W m−2<H <364 W m−2,46Wm −2<LE < 425 W m−2), as well as the spatial variability within a land cover (11 W m−2<σ H<169 W m−2,14Wm −2<σ LE < 152 W m−2). Table 3 gives an overview of the median land cover specificHandLEoverallflight patterns, and their median spatial variability. These results fall well within the range of summertime ensemble average fluxes during solar noon observed by ground-based EC measurements over different land covers in this region (100 Wm−2<H< 310 W m−2and 100 Wm−2<LE <480 W m−2; Gao et al., 2009; Hao et al., 2007; Hao et al., 2008; Shao et al., 2008). In comparison, the flight-line average heat fluxes are in the range of 71 Wm−2<H<310 W m−2and 46 Wm−2< LE <300 W m−2(Table B2). However, the magnitudes of Hand LE are not only functions of land cover, but also proportional to the available energy. The available energy changes within, but in particular between flight days. To alleviate this effect and to enable the comparison between different flights, we calculate the Bowen ratio Bo =H/LE between the sample distributions. Despite differences in the meteorological drivers (MR, θ, S↓), the median land cover specific Bo agrees well between subsequent flight patterns on all measurement days (Fig. 12). Fig. 9. Boosted regression tree partial response plots of Hfor all five state variables in order of their relative importance (in braces). The fitted function (black) shows the variable response of the BRT over the range of one individual state variable, while the remaining state variables are held at an average, constant value. The red dashed line is a smoothed representation of the fitted function (locally weighted polynomial regression). During the afternoon flights, 12 ±9 % higher Bo values are observed compared to the morning flights, as expected from a land surface that desiccates in the course of the day. Nevertheless, the 99.9 % confidence interval includes unity slope. Hence, for several hours within solar zenith Bo does not change significantly, and can be interpreted as a characteristic land surface property. On this basis we summarize the regional flux estimates for the duration of the flight campaign as time series of land cover specific Bo ratios (Fig. 12). The order of Bo between the land covers follows the order of the land cover specific EVI approximately inversely, while the temporal pattern follows the pattern of the land cover specific LST (Fig. 3). High Bo values until mid-campaign indicate that the land surface dries out. This trend is reversed toward the end of the campaign, when the approach of humid air masses leads to considerable precipitation. The median daily Biogeosciences, 10, 2193–2217, 2013 www.biogeosciences.net/10/2193/2013/
122 APPENDIX E: METZGER ET AL. (2013) S. Metzger et al.: Spatially explicit regionalization of airborne flux measurements 2209 Fig. 10. Maximum likelihood functional relationships between N=8446 aircraft observation and LTFM predictions of sensible heat flux (left) and latent heat flux (right). The weight of each data point in the relationship is represented by the size of the circles. The error bars show the cross-validation residuals for the LTFM predictions, and the ensemble random sampling error for the aircraft measurement. The 99.9 % confidence intervals are too narrow to be displayed properly. Fig. 11. Maps of the LTFM predicted fluxes of sensible heat (H, top) and latent heat (LE, bottom) on 13, 17 and 26 July 2009 (left to right). The colour gradient from blue over grey to red represents values that are lower, equal to, or greater than the average of the values, respectively (see legend). Percentages in braces after the flight ID indicate the spatial coverage of the prediction throughout the catchment. Meteorological state variables from the superimposed flight lines are used in the respective LTFM prediction (illustration identical with Fig. 2). natural variability of Bo within the land covers ranges from 48 % (rainfed agriculture) to 79 % (marshland). Water absorbs strongly in the near infrared, leading to negative EVI values that are not indicative of vegetation greenness. Hence EVI values for water surfaces are discarded, and the land cover “water” cannot be modelled by the present ERFs. 3.3 Uncertainty Metzger et al. (2012) have shown that turbulent flux measurements with the WSMA platform and instrumentation are unbiased, and precise to within 8 %. Uncertainty due to the limited sampling size of turbulent eddies is estimated using the methods of Lenschow and Stankov (1986) and Lenschow et al. (1994). Details on the implementation can be found in Metzger et al. (2012). For a single flux measurement, the www.biogeosciences.net/10/2193/2013/ Biogeosciences, 10, 2193–2217, 2013
APPENDIX E: METZGER ET AL. (2013) 123 2210 S. Metzger et al.: Spatially explicit regionalization of airborne flux measurements Fig. 12. Left: MLFR of Bowen ratio between the first and the second flight pattern on every measurement day. The weight of each data point in the relationship is represented by the size of the circles. Right: time series of Bo for different land covers throughout the measurement campaign. In both images the error bars represent the Gaussian sum of the natural variability in each land cover class and the ensemble random error in the LTFM procedure. The land cover colour code and corresponding abbreviations are identical with Fig. 2. Fig. 13. MLFRs of median observed and predicted fluxes along 42 flight lines. The error bars correspond to the variability of the fluxes along the flight line, and the weight of each data point in the relationship is represented by the size of the circles. systematic (and random) components of this sampling uncertainty range from <1 % (57 %) for Hto <1 % (121 %) for LE. Table 4 summarizes above uncertainty sources, as well as additional sources which are discussed in the following. In order to assess the uncertainty arising from the spatiotemporal analyses (Sect. 2.5.1), we compare the median observed and predicted fluxes along all flight legs (Fig. 13). The LTFM predictions slightly overestimate the observed fluxes (H=5%, LE=5 %), but in both cases the 99.9 % confidence intervals include unity slope. The median differences of dH=2 % (40 %), and dLE =4 % (47 %) agree marginally more closely. Moreover, the median residuals between fitted and observed values emphasize that the BRT fitting technique is unbiased (Table 4). Subsequently, we assess the predictive performance of the BRT response function in light of missing state variable combinations in the training data. For this purpose one flight at a time was omitted from the training data, and the incompletely trained BRT model was used to predict the missing data. The resulting median differences amount to 11 % (69 %, N=7311) for Hand 18 % (77 %, N= 7265) for LE. During prediction, cases where one or more state variables exceed their respective range during training were excluded. As a consequence the sample size is ≈14 % smaller than the total number of observations (N=8466). Lastly, we consider the uncertainty resulting from disregarding part of the spatio-temporal variability in the state variables during BRT predictions. For this purpose we quantify the disregarded parts of the natural variability, and propagate it through the full BRT model. The resulting median differences amount to 13 % (77 %) and 14 % (75 %) for Hand LE, respectively, and are dominated by the effect Biogeosciences, 10, 2193–2217, 2013 www.biogeosciences.net/10/2193/2013/
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ERKLÄRUNG 131 Erklärung Hiermit erkläre ich, dass ich die Arbeit selbständig verfasst und keine anderen als die von mir angegebenen Quellen und Hilfsmittel benutzt habe. Ferner erkläre ich, dass ich anderweitig mit oder ohne Erfolg nicht versucht habe, diese Dissertation einzureichen. Ich habe keine gleichartige Doktorprüfung an einer anderen Hochschule endgültig nicht bestanden. Bayreuth, 2013-04-15 Stefan Metzger