Impact of time and spatial averages on the energy balance closure

IMPACT OF TIME AND SPATIAL AVERAGES ON THE ENERGY BALANCE CLOSURE A dissertation submitted to the Bayreuth Graduate School of Mathematical and Natural Sciences University of Bayreuth, Germany to attain the academic degree of Doctor of Natural Sciences (Dr. rer. nat.) presented by Doojdao Charuchittipan M.Sc. born 9 April 1977 in Koh Samui, Thailand Thesis Supervisor PROF. DR. THOMAS FOKEN Bayreuth, 2013 IMPACT OF TIME AND SPATIAL AVERAGES ON THE ENERGY BALANCE CLOSURE presented by DOOJDAO CHARUCHITTIPAN, M.Sc. supervised by PROF. DR. THOMAS FOKEN DEPARTMENT OF MICROMETEOROLOGY UNIVERSITY OF BAYREUTH This doctoral thesis was prepared at the Department of Micrometeorology, University of Bayreuth from August 2009 until April 2013 and was supervised by Prof. Dr. Thomas Foken. This is a full reprint of the dissertation submitted to attain the academic degree of Doctor of Natural Sciences (Dr. rer. nat.) and approved by the Bayreuth Graduate School of Mathematical and Natural Sciences (BayNAT) of the University of Bayreuth. Date of submission: 5 June 2013 Date of defense: 16 July 2013 Director: Prof. Dr. Franz Xaver Schmid Doctoral Committee: Prof. Dr. Thomas Foken, 1st reviewer Prof. Dr. Bernd Huwe, 2nd reviewer Prof. Dr. Andreas Held, Chairman Dr. Johannes L¨uers Acknowledgements I wish to express my gratitude to: My supervisor, Prof. Dr. Thomas Foken, who always shares his profound knowledge with his students. His endless support and guidance along with his valuable discussion in all stage of my works are very meaningful for completing this thesis. Current and former members of the department of Micrometeorology at the University of Bayreuth, for their assistance and support throughout my years in Bayreuth. Their contributed discussion and comments are very helpful to my works. In particular Dr. Rafael Eigenmann, for kindly translating my abstract from English into German and Dr. Wolfgang Babel, who partially involved in my submitted paper and edited my abstract. Dr. Johannes L¨uers and Prof. Dr. Andreas Held for being part of my mentorate committee. Prof. Dr. Bernd Huwe for being the second reviewer. Everyone in the ELSH project, in particular Dr. Frank Beyich and Jens-Peter Leps of Deutscher Wetterdienst, for providing many data from the LITFASS-2003 experiment that were extensively analyzed throughout my thesis. Also, Prof. Dr. Jens Bange, Yvonne Breitenbach and Dr. Daniel Villagrasa of the Institute for Geoscience, Eberhard Karls Universit¨at T¨ubingen, for providing the Helipod data, which allows me to carry out the analysis in the spatial average part very effectively. Dr. Matthias Mauder, for providing many useful discussions and comments to my paper. This is very helpful for my analysis in the time average part. He also provided the wavelet analysis code, which I have modified to use in many parts of this thesis. Dr. Natascha Kjlun, for allowing me to use her LPDM-B footprint model. This is a very essential tool for my analysis in the spatial average part. Dr. Bernhard Winkler of Rechenzentrum at the University of Bayreuth, for guiding me through the University Linux cluster. This is also help for me to run the footprint model a lot more faster. All the co-authors of my submitted paper, for their contributions to the manuscript. Everyone who participated in the LITFASS-2003 experiment, who has produced many good quality data, which I have used throughout my thesis. Pira Korsieporn, Boripont Manmontri, Suparat Chuechote, Krist Dacharux, and Weeraya Donsomsakulkij for proofreading my thesis. My family, who constantly supports me through out my study. I was financially supported by the German Research Foundation (DFG) within the projects FO 226/20-1 between August 2009 - September 2012 and granted a doctorate finalizing funding from B¨uro der Frauenbeauftragten of University of Bayreuth from October 2012 to December 2012. I am very thankful for all these supports. Abstract Secondary circulations are large and relatively stationary eddies, which are caused by the surface heterogeneity and normally reside away from the ground. They are believed to be the cause of the energy balance closure problem at the earth’s surface, because their contribution to the turbulent fluxes is missed by a fixed eddycovariance tower measurement that has a typical averaging time of 30 minutes. In this thesis, data from the LITFASS-2003 experiment was used to investigate the impact of time and spatial averages on the energy balance closure. This data consisted of many observations over a large heterogeneous landscape that could generate secondary circulations; some of which might be still near the earth’s surface. For the time average analysis, the averaging time was extended to increase the possibility that secondary circulations were picked up by the sensor. Two approaches, which were the modified ogive analysis and the block ensemble average, were applied to analyze the data from ground-based measurements. The modified ogive analysis requiring a steady state condition, could extend the averaging time up to a few hours and suggested that an averaging time of 30 minutes was still overall sufficient for the eddy-covariance measurement over low vegetation. The block ensemble average, on the contrary, did not require a steady state condition, but could extend the averaging time to several days. However, this approach could only improve the energy balance closure for some sites during specific periods, when secondary circulations existed in the vicinity of the sensor. Based on this approach, it was found that the near-surface secondary circulations mainly transported sensible heat, which led to an alternative energy balance correction by the buoyancy flux ratio approach, in which the attribution of the residual depended on the relative contribution of the sensible heat flux to the buoyancy flux. The fraction of the residual attributed to the sensible heat flux by this energy balance correction was larger than in the energy balance correction that preserved the Bowen ratio. In the spatial average analysis, two energy balance correction approaches, the buoyancy flux ratio and the Bowen ratio approaches, were applied to the areaaveraged fluxes (composite fluxes) in order to include contribution from secondary circulations. These composite fluxes were aggregated from multiple ground-based measurements. The energy balance corrected fluxes were validated against the spatial average fluxes, which were measured by an aircraft and a large aperture scintillometer (LAS). In this validation, the backward Lagrangian footprint model was used to estimate the source area of the measurement. It was found that both energy balance correction approaches did improve the agreement between time and spatial averages fluxes. This suggested that the contribution from secondary circulations could be properly accounted by the energy balance correction. All findings in this thesis, therefore, depict that secondary circulations significantly transport energy in the atmospheric surface layer. The energy balance correction, accomplished by using either the Bowen ratio approach or the buoyancy flux ratio approach, is necessary to estimate the actual vertical transport of energy at the earth’s surface. Zusammenfassung Sekund¨are Zirkulationen sind große, nahe zu station¨are Eddies, die durch Oberfl¨achenheterogenit¨aten verursacht werden und sich normalerweise entfernt vom Boden befinden. Es wird angenommen, dass sie die Ursache f¨ur das Energiebilanzschließungsproblem an der Erdoberfl¨ache sind, da ihre Beitr¨age zu den turbulenten Fl¨ussen nicht von den r¨aumlich station¨aren Masten der Eddy-Kovarianz-Messung, deren typisches Mittelungsintervall 30 Minuten ist, erfasst werden. In dieser Arbeit werden Daten aus dem LITFASS-2003 Experiment verwendet, um den Einfluss der zeitlichen und r¨aumlichen Mittelung auf die Energiebilanzschließung zu untersuchen. Das Experiment bestand aus umfassenden Messungen ¨uber stark heterogener Landschaft und bot somit die M¨oglichkeit, eine Vielzahl an Aspekten sekund¨arer Zirkulationen zu untersuchen. In Bezug auf die zeitliche Mittelung wurde das Mittelungsintervall ausgedehnt, um den Beitrag potentieller sekund¨arer Zirkulationen zu ber¨ucksichtigen. Zwei Ans¨atze wurden mit Hilfe der Bodenmessungen angewandt: die modifizierte Ogivenanalyse und die Blockmittelungsmethode. Die modifizierte Ogivenanalyse, die station¨are Bedingungen bentigt, kann die Mittelungszeit bis zu mehreren Stunden ausdehnen und zeigt, dass die Mittelungszeit von 30 Minuten im Allgemeinen f¨ur Eddy-Kovarianz-Messungen ausreicht. Die Blockmittelungsmethode, die keine station¨aren Bedingungen bentigt, kann die Mittelungszeit auf mehrere Tage ausdehnen. Jedoch kann sie die Energiebilanzschließung nur f¨ur einige Standorte und nur zu bestimmten Zeiten, in denen sich die sekund¨aren Zirkulationen in der N¨ahe des Sensors befinden, verbessern. Diese bodennahen sekund¨aren Zirkulationen transportieren haupts¨achlich f¨uhlbare W¨arme. Diese Ergebnisse f¨uhren zu einer alternativen Korrektur der Energiebilanzschließung durch die Methode des Auftriebsstromverh¨altnisses, welches den grßeren Anteil des Residuums dem f¨uhlbaren W¨armestrom zuordnet. Bei der r¨aumlichen Mittelung wurde die Energiebilanzschließungskorrektur auf die fl¨achengemittelten oder zusammengesetzten Fl¨usse, die aus mehreren Bodenmessungen zusammengefasst wurden, angewandt, um Beitr¨age von sekund¨aren Zirkulationen mit einzubeziehen. Diese energiebilanzkorrigierten Fl¨usse wurden gegen Flugzeugmessungen und einem Grossfl¨achen-Scintillometer (LAS), die beide fl¨achengemittelte Fl¨usse liefern, unter Zuhilfenahme eines Footprintmodells validiert. Es xiv NOMENCLATURE ˜cMesoscale term of variable c Cow,c Cospectrum dDisplacement height [m] fFrequency [Hz] FArea-averaged flux FcCO2flux [µmol m−2s−1] FsFlux footprint F30 Turbulent flux at 30 minutes F4hr Turbulent flux at 4 hours gGravitational acceleration (9.80 m s−2) h0Elevation or height above sea level [m] hcCanopy height [m] HHyperbolic hole size I↑longwave up-welling radiation [W m−2] I↓longwave down-welling radiation [W m−2] kvvon Karman constant (≈0.4) K↑shortwave up-welling radiation [W m−2] K↓shortwave down-welling radiation [W m−2] LObukhov length [m] pAir pressure [N m−2or Pascal] PTime period [s] ogw,c Ogive function Q∗Net radiation [W m−2] QBBuoyancy flux [W m−2] QELatent heat flux [W m−2] QEBC−Bo ELatent heat flux as corrected by the Bowen ratio approach [W m−2] QEBC−HB ELatent heat flux as corrected by the buoyancy flux ratio approach [W m−2] ˜ QEMesoscale flux of latent heat [W m−2] QGGround heat flux [W m−2] QHSensible heat flux [W m−2] QEBC−Bo HSensible heat flux as corrected by the Bowen ratio approach [W m−2] NOMENCLATURE xv QEBC−HB HSensible heat flux as corrected by the buoyancy flux ratio approach [W m−2] ˜ QHMesoscale flux of sensible heat [W m−2] QiThe ith quadrant Ri Bulk Richardson number Res Residual SW Source weight matrix SWnor Normalized source weight matrix tTime [s] TTemperature [K] (u, v, w) Velocity components [m s−1] u∗Friction velocity [m s−1] UWind speed [m s−1] xFetch distance [m] zHeight above ground or vertical displacement [m] z0Surface roughness length [m] ziBoundary layer depth or mixed layer height[m] zmMeasurement height [m] δInternal boundary layer height [m] ∆ttime step [second] ∆max Maximum flux difference ηWidth of an error band θWind direction or undisturbed wind sector [Degree] λHeat of evaporation of water [J kg−1] ρAir density [kg m−3] τTime period [s] Single-used symbols are explained in the text and may not appear in this list. 1 Introduction The atmospheric boundary layer (ABL) is the lowest 1-2 km of the atmosphere. Its most bottom part, the atmospheric surface layer (ASL), is the most immediately affected by the earth’s surface. This is where the vital exchanges of energy and matter, such as momentum, sensible heat and water vapor, between the earth’s surface and the atmosphere take place. Full details of the ABL and ASL are available in many textbooks, for example Stull (1988), Kaimal and Finnigan (1994) and Foken (2008b). To deepen our understanding of the ASL and all the exchange processes, micrometeorologists have conducted many experiments since about the 1920’s. They quantify these exchange processes with the surface fluxes of energy and matter, which are currently widely measured by the eddy-covariance (EC) measurement (Aubinet et al., 2012) on a fixed-tower system. The extensive developments of the sonic anemometer and gas analyser, which are important instruments in the EC measurement, over the past 10-20 years not only made the EC measurement a lot easier, but also allow us to measure fluxes continuously over a long period. With the ability to measure the carbon dioxide and other traced gases fluxes, the EC measurement has became even more popular in the ecological research. Nowadays, there is a global network of EC measurements, FLUXNET (Baldocchi et al., 2001), which continuously monitors the exchange of energy and matter between the biosphere and the atmosphere on a long-term basis since 1990’s. Such measurement is indeed an integral part of many atmospheric models. For instance, the information on the ASL provides parameter inputs into the numerical weather prediction model (NWP), where the knowledge on surface fluxes is very important (Warner, 2011). Therefore, the accuracy of the EC measurement is definitely very crucial to many branches of research as well as our daily lives. 2 1. INTRODUCTION 1.1 Energy balance closure at the earth’s surface This thesis develops around one of the major concerns in the ASL, the energy balance closure problem, which has been aware of since 1980’s. Many micrometeorological experiments over low vegetation, for example the EBEX-2000 experiment (EBEX, ‘Energy Balance Experiment’, Oncley et al., 2007) and the LITFASS-2003 experiment ((LITFASS, ‘Lindenberg Inhomogeneous TerrainFluxes between Atmosphere and Surface: a long-term Study’, Beyrich and Mengelkamp, 2006), show that the available energy, which is the sum of the net radiation and the ground heat flux, is larger than the sum of the sensible and latent heat fluxes. To conserve energy, the missing energy is replaced by the residual. Then for the homogeneous and stationary ASL, the energy budget equation over low vegetation at the earth’s surface becomes Res =−Q∗−(QG+QH+QE),(1.1) where Res is the residual, Q∗is the net radiation, QGis the ground heat flux, QH is the sensible heat flux, and QEis the latent heat flux. Each energy flux in Eq. 1.1 is positive, when it is transported away from the ground. Among all energy fluxes in Eq. 1.1, Q∗is mostly the largest, however, come with a good measurement accuracy, while QGis mostly the smallest. Therefore, measurement accuracies of both Q∗and QGdo not account for the energy balance closure (Kohsiek et al., 2007; Liebethal et al., 2005) and the residual is most likely caused by an EC tower measurement, which is normally used for measuring QH and QE. An EC tower measurement is technically a fixed point in space that can only measure eddies, which have moved pass the sensor. If eddies are stationary or moving very slowly, they may not or never move pass the sensor within a typical averaging time of 30 minutes. Therefore, their contributions are definitely missed by an EC tower measurement. More details of the energy balance closure as well as additional comments on surface fluxes measurement can be found in Foken (2008a), Mahrt (2010), Foken et al. (2011) and Leuning et al. (2012). 1.2 Secondary circulations According to several studies by a large-eddies simulation (LES), the energy imbalance can be significantly improved by including low frequency contributions from the secondary circulations (SC) or turbulence organized structure (TOS, Inagaki et al., 2006; Kanda et al., 2004; Steinfeld et al., 2007). SC are large scale eddies 1. INTRODUCTION 3 (several kilometers) and relatively stationary (either static or move very slowly). They are generated by the surface heterogeneity (Stoy et al., 2013) and normally move away from the ground. Their contributions to the low frequency part of the turbulent spectrum may not be entirely captured by an EC tower measurement, which is operated near the earth’s surface and typically averaged over a period of 30 minutes. This result in the underestimation of QHand QE, which are normally measured by an EC tower. In this thesis, data from the LITFASS-2003 experiment was used to study the energy balance closure under the impact of time and spatial averages. This experiment collected high quality data set with many instruments over a large heterogeneous landscape, which could generate SC. Some of which might still reside near the earth’s surface and would show their influences over the energy balance closure. More details of the LITFASS-2003 experiment and its energy balance closure can be found in Beyrich and Mengelkamp (2006) and Foken et al. (2010). 1.2.1 Time average An EC measurement on a fixed tower seems to be the most convenient way to measure surface fluxes. Given that 30-minute averaging time can be too short, the averaging time extension beyond 30 minutes may increase the possibility of slow moving eddies to move past the sensor. There are two approaches for investigating the averaging time extensions, the ogive analysis (Desjardins et al., 1989; Oncley et al., 1990) and the block ensemble average (Bernstein, 1966, 1970; Finnigan et al., 2003). The ogive analysis uses the turbulent spectra to estimate the turbulent fluxes at different frequency ranges. Hence it is possible to evaluate how much the low frequency parts contribute to the turbulent fluxes measured by the EC method. In Foken et al. (2006), the ogive analysis was applied to the data measured over the maize field (station A6) of the LITFASS-2003 experiment. It was mainly focused on the data from three selected days, which the averaging time was extended up to 4 hours. It was found that the time extension would not significantly increase the turbulent fluxes. For the block ensemble average, low frequency contributions from long term fluctuations over several hours to days are added to the total fluxes . In Mauder and Foken (2006), it was also applied to the data set from the same maize field of the LITFASS-2003 experiment (A6). The selected long period was 15 days, while the block ensemble averaging period was varied from 5 minutes to 5 days. This 4 1. INTRODUCTION study shows that the block ensemble average can close energy balance at a longer averaging time. In this thesis, both ogive analysis and block ensemble average were applied to data from all EC towers of the LITFASS-2003 experiment. If SC does matter to the energy balance closure, this study would reveal an appropriate energy balance correction in order to estimate the actual vertical transport of energy at the earth’s surface. 1.2.2 Spatial average Even the averaging time extension can increase the possibility to measure slow moving SC, a fixed-tower measurement is still unable to detect stationary SC. To overcome this weakness, a measurement which can collect data from multiple locations almost instantly is suggested. The appropriate statistics of this measurement are the spatial averaged statistics. This type of measurement was available during the LITFASS-2003 experiment with the Helipod (Bange and Roth, 1999; Bange et al., 2002) and the large aperture scintillometer (LAS). These measurements can sample both stationary and slow moving SC. Therefore, they can be used to validate the energy balance corrected fluxes as suggested from the time average analysis. This validation needs an additional tool to relate the time and spatial averages together. In this thesis, the footprint analysis was used for this task. Both studies in time and spatial averages would reveal how SC contribute to the surface fluxes as well as the necessity to include this contribution to the actual vertical transport of energy, which would lead to the suggestion of appropriate parameterizations in the ASL. 2 Tools To carry out all investigations in this thesis, many tools, which could be some mathematical techniques or atmospheric models, are required. All necessary ones are presented in this chapter. 2.1 Averaging operators Since the atmospheric turbulence is non-linear, meteorologists analyse and report the atmospheric properties like wind velocity, temperature and humidity, in term of statistics. These statistics can be obtained through suitable averaging operators, which produce representative statistics of the interested system. There are three different averaging operators: time average, spatial average and ensemble average. Only brief descriptions of each operator are presented here. Intensive details of these operators when apply to the atmospheric data can be found in any introductory books in the atmospheric sciences. For simplification, one dimensional flow is assumed. In this case, any variable f(x, t) is a function of space (x) and time (t). 2.1.1 Time average: The time average of fis denoted by f. It is calculated from set of data collected at a fixed point in space over time interval P. It can be defined in both discrete and continuous data set as discrete f=1 N N X i=1 f(x, i),(2.1) continuous f=1 PZt0+P t0 f(x, t)dt, (2.2) 6 2. TOOLS where Nis the number of data points in a time interval P. For discrete case t=i∆tand ∆t=P/N (2.3) 2.1.2 Spatial average: The spatial average of fis denoted by sfand calculated from set of data collected at an instant of time over a spatial domain X. It can be defined as discrete sf=1 N N X j=1 f(j, t),(2.4) continuous sf=1 XZx0+X x0 f(x, t)dx, (2.5) where Nis the number of data points in a spatial domain X. For discrete case x=j∆xand ∆x=X/N (2.6) This averaging operator may extend to an area or a volume average. 2.1.3 Ensemble average: The ensemble average of fis denoted by hfi, and calculated from nidentical experiments. It is defined as hfi=1 N N X i=1 fi(x, t),(2.7) where Nis the number of data points collected from nidentical experiments. The representative statistics, which can apply to all the governing equations, must satisfy the ’Reynolds averaging rules’ (section 2.2). Among these three averaging operators, only the ensemble average is qualified. In controllable experiments, where number of experiments can be repeated with the same conditions, the ensemble average is possible. Unfortunately, in the uncontrollable atmosphere, experiments cannot be repeated with the same conditions. However, under a specific circumstance, when the atmosphere is homogeneous (statistics do not change with space) and stationary (or steady state condition, statistics do not change with time), 2. TOOLS 7 all three averaging operators are equivalent. This is known as the ergodic condition. f=sf=hfi(2.8) 2.2 Reynolds averaging rules Let’s assume that the atmosphere is homogeneous and stationary, which makes the ergodic condition to be valid. Under such condition, the time average of variable f is constant over a period Pand a spatial domain X. Therefore, at any point in this period and spatial domain, f(x, t) = hf(x, t)i+f′(x, t) = f+f′(x, t),(2.9) where the turbulence term f′(x, t) is the fluctuation from the mean. This expression is known as the ‘Reynolds decomposition’. By applying the Reynolds decomposition to atmospheric variables fand g, they obey the ’Reynolds averaging rules’, which are (i)f+g=f+g(2.10) (ii)k f =k f (2.11) (iii)f g =f g (2.12) (iv) lim fn= lim fn(2.13) With kis constant and fnis a sequence of functions. The last averaging rule can be interpreted as the commutation between the averaging and differential (or integral) operators, such that ∂f ∂t =∂f ∂t and Zb a f dt =Zb a f dt (2.14) This leads to f=f(2.15) f′= 0 (2.16) fg =f g +f′g′(2.17) More details of Reynolds averaging rules when apply to meteorology can be found in most elementary textbook or many early publications in atmospheric sciences such 14 3. DATA Figure 3.1: Map and land use of the LITFASS area. The land use fractions were obtained in 2003, while the map represent the terrain in 2013 (maps were generated by Google Earth and Google map chart). 3.2 Eddy-covariance tower measurements 3.2.1 Measuring stations There were 16 EC systems installed on multiple towers during the LITFASS-2003 experiment. All of them were operated individually as a single-point measurement, in which the representative statistics are the time average statistics. Each EC system or a turbulence complex consisted of a sonic anemometer and a hygrometer, which could measure wind velocity, temperature and moisture. This measurement allowed estimations of the sensible and latent heat fluxes by the EC technique. An estimation of the CO2flux was also possible, if the hygrometer could measure the CO2concentration. Fourteen EC systems were installed on small towers, each of which was part of a micrometeorological measuring station. These stations were operated as groundbased measuring stations on 13 sites. They were mostly scattered over the agricultural fields on the eastern part of the LITFASS area. Two stations, NV2 and NV4, were installed on the same grassland, but they were oriented to different wind 3. DATA 15 sectors. In this thesis, results from these two stations were combined and reported as one station NV. The other two EC systems were installed on the MOL tower at 50 m and 90 m height, which was a few meters away from NV2 and NV4. Instead of keeping high frequency raw data, all measuring stations kept short-term statistics at every 5 or 10 minutes. The long-term statistics can be calculated from these short-term statistics with Eq. 2.18. A brief summary with information about all measuring stations used in this thesis is shown in Table 3.1. To measure all energy balance components in Eq. 1.1, the net radiation and ground heat flux were also measured in all 14 ground-based stations. For the net radiation measurement, four components net radiometers were installed to measure both down-welling and up-welling components of the shortwave and longwave radiations. Therefore, the net radiation could be estimated from Q∗=K↑+K↓+I↑+I↓(3.1) where K↑,K↓,I↑and I↓are the shortwave up-welling radiation, shortwave down-welling radiation, longwave up-welling radiation and longwave down-welling radiation respectively. For the ground heat flux over the terrain, the following quantities were measured at different depths; soil humidity, soil temperature and soil heat flux. Using these parameters, there are two different ways to estimate the soil heat flux at a specific depth. The first approach is by a direct measurement with the heat flux plate. This approach is known as the PlateCal approach. The second approach, the GradCal approach, uses the vertical temperature gradient to determine the soil heat flux at a specific depth. More details of these two approaches can be found in Liebethal et al. (2005). Once the soil heat flux at a specific depth was known, it was extrapolated up to the surface by using the change in heat storage of the soil (calorimetry). It must be noted that the soil humidity measurement of the A5 (rye) station was mostly not available, because of the defective sensor. Since this station was just around 100 m away from the A6 (maize) station, the soil humidity measurement of the A6 station was used to determined the ground heat fluxes of the A5 station. Due to the high heat capacity of water, the whole lake (FS) could be approximated as a big heat reservoir. Therefore, the heat released or consumed at the lake surface can be estimated from the change in heat storage of the lake. The ground heat flux of the lake was determined from the temperature profile of the lake by assuming well-mixed conditions in a shallow lake (Nordbo et al., 2011). 16 3. DATA Table 3.1: Brief information of EC stations in the LITFASS-2003 experiment during 20 May 2003 12:00 UTC - 18 June 2003 00:00 UTC. Notations: Sta = Station, Op = Operator, zm= measurement height, θ= undisturbed wind sectors (clockwise), hc= canopy height, h0= elevation or height above sea level [m], Res = mean residual between 10:00 - 12:00 UTC, which is also reported as a percentage to the available energy (Res/(−Q∗−QG)). Full details can be found in Beyrich and Mengelkamp (2006) and Mauder et al. (2006). Sta Surface Op1Turbulence zmθ hch0Latitude Longitude Res(%) sensors (m) (deg) (m) (m) (deg) (deg) A1 Rye TUDD USA-1/KH20 3.55 90-300 0.95-1.55 69 52◦13′39′′ 14◦04′29′′ - A2 Rape TUDD CSAT3/KH20 3.6 90-330 1.1-1.25 93 52◦12′34′′ 14◦08′18′′ - A3 Barley GKSS CSAT3/KH20 3.25 90-270 0.6-0.7 86 52◦11′31′′ 14◦06′59′′ 109 (26%) A4 Maize GKSS CSAT3/KH20 3.25 90-270 0.05-0.75 75 52◦10′28′′ 14◦07′18′′ 115 (29%) A5 Rye UBT USA-1/KH20 2.8 60-30 0.9-1.50 73 52◦10′09′′ 14◦07′28′′ 147 (31%) A6 Maize UBT CSAT3/LI7500 2.7 90-270 0.1-0.6 73 52◦10′00′′ 14◦07′29′′ 117 (30%) A7 Rape GKSS CSAT3/KH20 3.4 30-240 0.7-0.9 67 52◦09′16′′ 14◦06′10′′ 52 (13%) A8 Triticale WAU CSAT3/LI7500 3.55 30-210 0.8-1.1 52 52◦08′14′′ 14◦10′36′′ 110 (23%) A9 Rape WAU CSAT3/LI7500 3.5 60-210 1-1.2 48 52◦07′26′′ 14◦10′27′′ 107 (23%) NV2 Grass DWD USA-1/LI7500 2.4 60-180 0.05-0.20 73 52◦09′57′′ 14◦07′20′′ 67 (19%) NV4 Grass DWD USA-1/LI7500 2.4 150-330 0.05-0.20 73 52◦09′57′′ 14◦07′20′′ 85 (24%) FS Lake DWD USA-1/LI7500 3.85 180-30 0 43 52◦08′15′′ 14◦06′37′′ 245 (63%) HV Pine forest DWD USA-1/LI7500 30.5 30-330 14 49 52◦10′54′′ 13◦57′09′′ 126 (23%) M50 Grass DWD USA-1/LI7500 50 90-300 0.05-0.20 73 52◦09′57′′ 14◦07′20′′ - M90 Grass DWD USA-1/LI7500 90 90-300 0.05-0.20 73 52◦09′57′′ 14◦07′20′′ - 1DWD - German Meteorological Service; TUDD - University of Technology Dresden; GKSS - GKSS Research Centre Geesthacht; WAU - Wageningen University and Research Centre; UBT - University of Bayreuth 3. DATA 17 3.2.2 Canopy heat storage All kinds of plants store energy in their canopies. This canopy heat storage has two main contributions from the plant material (or biomass) and the air between plants. As reported by Oncley et al. (2007), over low vegetation like a cotton field, both contributions of a canopy heat storage are relatively small and negligible. According to the study in maize and soybean (Meyers and Hollinger, 2004), the stored energy in biomass is significant when a canopy is fully developed, while QGis very low. During the LITFASS-2003 experiment, the maize field began from bare soil and grew up to approximately 0.5 m at the end of the experiment. Therefore, their stored energy in biomass can be neglected. However, a forest’s canopy heat storage is significant (Lindroth et al., 2010) and need to be included in the energy budget equation (Eq. 1.1). Unfortunately, not all required biomass properties of the forest were collected during the LITFASS-2003 experiment and the forest’s canopy heat storage could not be precisely estimated. Hence, all analyses of this site were conducted without a canopy heat storage term. Since a forest’s canopy heat storage during the daytime would release back to the atmosphere during the nighttime, it is more important in the sub-diurnal scale (Haverd et al., 2007). Therefore, the omission of a forest’s canopy heat storage would have minimal effect over a long-term basis. 3.2.3 Data selection for the ogive analysis and block ensemble average There were two analyses in the time average part (Chapter 4), the ogive analysis and block ensemble average. Both of them were applied to data from EC towers as listed in Table 3.1. Most of the required data was available since 20 May 2003 12:00 UTC, so the period between 20 May 2003 12:00 UTC - 18 June 2003 00:00 UTC was chosen to be analyzed in this thesis. To ensure high data quality as well as to minimize the irrelevant factors, which might influence turbulent fluxes, different data selection criteria were applied to the data in both ogive analysis and block ensemble average parts separately. For the ogive analysis, the averaging time was extended to up to 4 hours. This 4-hour period consisted of 8 consecutive subperiods (or blocks) of 30 minutes. The ogive analysis over any 4-hour periods was carried out only if all blocks satisfy the selection criteria. The first selection criterion is the same as that found in Mauder et al. (2006), which is that the sonic anemometers must not be disturbed either by the internal boundary layer due to the surface heterogeneity, or the flow distortion 18 3. DATA caused by obstacles. The internal boundary layer height can be estimated from (Raabe, 1983) zm≤δ= 0.3√x, (3.2) where zmis the measurement height, δis the internal boundary layer height and xis the distance from the sensor to boundary of the next land use. To keep the measurement undisturbed, zmmust not exceed δ. Hence, any wind direction, whose corresponding xdid not satisfy Eq. 3.2, were excluded from the investigation. The undisturbed wind sectors (θ), from both internal boundary layer and flow distortion, of each measuring station are listed in Table 3.1. Additionally, footprint climatology was used to confirm that the target land use has a significant contribution to the measurement. This contribution varied over the stability range. Any wind sectors whose contribution from target land use is less than 80%, were also excluded from the investigation. The next data selection criterion involves a steady state condition of the time series, which is indicated by the steady state flag (section 2.3). Accepted high quality data have quality flag 1-3. In this thesis, the ogive analysis of the energy balance components (QHand QE) and CO2flux (Fc=w′c′CO2) were considered separately. For the energy balance components, only the steady state flags of friction velocity (u∗), QHand QEwere considered. The ogive analysis was applied to any periods only when all these three steady state flags qualified. For Fc, the ogive analysis was applied on any period only when the steady state flag of u∗and CO2qualified. The transition period was avoided by excluding the time period covering one hour before to one hour after both sunrise and sunset from the ogive analysis. The threshold values of each turbulent flux was set as a minimum requirement for the analysis. For u∗, which indicates the level of turbulence (Massman and Lee, 2002), its threshold value is 0.1 ms−1. This was set to rule out very small turbulent fluxes, which might result from instrumentation noise. This limit normally excludes periods with very weak wind as well. For QH,QEand Fc, their threshold values were formulated to avoid complication with their measurement errors. According to Mauder et al. (2006), based on 30-minute averaging time, the measurement errors of QHand QEare 10% - 20% of the turbulent flux at 30 minutes or 10 - 20 W m−2, whichever is larger. For u∗and Fc, their measurement errors are 0.02-0.04 ms−1and 0.5-1 µmol m−2s−1respectively (Meek et al., 2005). Therefore, in this thesis, the threshold values of QHand QEwere set to be 20 W m−2, while the threshold value of Fcwas set to be 1 µmol m−2s−1. Unusually large uncertainty of Fcduring the night time was taken into account by using only data periods with u∗greater than 3. DATA 19 Table 3.2: Information about selected Helipod flight legs. Notations: zm= average height above ground, θ= average wind direction, zi= boundary layer height Properties 7 Jun 2003 14 Jun 2003 13:40-13:50 9:20-9:30 zm(m) 85 88 Direction North to South Northwest to Southeast Distance (km) 18.5 20.1 θ(deg) 254 279 zi(m) 1350 1800 Meteorological conditions after heavy rain events dry Land use coverage mainly farmland mainly forest and farmland 0.25 ms−1(Hollinger and Richardson, 2005). Similar selection criteria could not apply in the block ensemble average approach, as it involved averaging times of several hours to days. Therefore, the quality control of this part was done by discarding any periods with more than 10% of missing raw data. This missing data could have resulted from various factors, such as electrical black out. 3.3 Aircraft measurements The aircraft measurements in the LITFASS-2003 experiment were done by the Helipod. The Helipod is a turbulence measurement system, which attaches below a helicopter by a 15 m rope. It collected data at 100 Hz, while the helicopter was moving at a speed of 40 ms−1. This speed is much faster than the wind speed and the sampling rate is fast enough to sample the data within the evolution time scale of eddies. The Helipod is outside the down-wash area of the helicopter, which creates a smaller disturbance than a conventional research aircraft. During the LITFASS2003 experiment, there were 27 flights over 16 days. More details of the Helipod measurements can be found in Bange and Roth (1999) and Bange et al. (2002). Two selected flights legs on 7 and 14 June 2003 were used in the spatial average part. Brief information of each flight leg are presented in Table 3.2, while the outline of the flight paths are presented in chapter 5. According to Lenschow and Stankov (1986) and Lenschow et al. (1994), to measure flux with a good accuracy, the flight distance must be as large as possible. Distances of these two selected 20 3. DATA flights were greater than 10zi, which meet the suggestion in Lenschow and Stankov (1986). The integral time scale of these two flights, which is used to estimate flux uncertainty, could be properly calculated without any approximation as well (Bange et al., 2006a). The instantaneous fluxes along the flight path of both flights were calculated by a moving average approach. By varying the window size from 500 m to 10 km, 10% uncertainty of the entire flight’s flux, in both QHand QEhave been reached at the window size of 2 km for both selected flights. Therefore, a window size of 3 km was used for a comparison purposes through-out this thesis. 3.4 Scintillometer A large aperture scintillometer (LAS) can be used to determine the sensible heat flux by measuring the structure parameter of the refractive index. It is operated at a near-infrared wavelength and suitable for estimating the sensible heat flux over path lengths of several kilometers. In 2003, there were three LASs installed over the LITFASS area. In this thesis, the surface sensible heat flux, which was measured by the LAS over the farmland, was compared with the spatial average flux measured by the Helipod as well as surface fluxes estimated from the footprint model. This LAS had a transmitter installed on the MOL tower, while the receiver was at the observatory in Lindenberg. The outline of this LAS path is presented along with the selected Helipod flight paths in chapter 5. The effective beam was 43 m in height and covered the path length of 4.7 km. More technical and theoretical details of this LAS can be found in Meijninger et al. (2006) and the references thereafter. 3.5 Boundary layer height Boundary layer height (zi) or mixed layer height is the height at which the surface forcings are no longer in effect. For this thesis, it was an input parameter of the LPDM-B footprint model (section 2.6) and was used as an initial point of surface flux extrapolation. There are two basic approaches to determine zinowadays , which are an estimation from profile data and parameterizations by a model. Details of most available methods in the literature can be found in Seibert et al. (2000). For the LITFASS area, ziis estimated from the high-resolution vertical profiles of temperature, humidity and wind, which are obtained from the operational ra- 3. DATA 21 diosoundings. In this area, the operational radiosoundings are routinely released four times a day at the MOL (WMO station code 10393). Full details of ziestimations at this station can be found in Beyrich and Leps (2012). Each radiosonde, which is released at 00:00, 06:00, 12:00 and 18:00 UTC daily, collects the data at every 5 second and rises up at about 5 ms−1. There are different criteria for estimating zi, however, the one evaluated from the Richardson number is selected to be a standard output. The bulk Richardson number (Ri) is defined as Ri(z) = (z−h0)(g/θ0) (θ(z)−θ0) U2(z),(3.3) where zis the height above ground, g= 9.80 ms−2is the gravitational acceleration, Uis wind speed and h0is the elevation of the released site, which is 112 m above sea level for the MOL. ziis then determined from the first level where Ri exceed 0.2. There are many reasons to choose the Richardson number approach as a standard output. Firstly, it considers both thermal and mechanical effects of the turbulence. Secondly, it provides a consistent data set, and finally, it is consistent with the value from operational Numerical Weather Prediction (NWP) model output. Other than the Richardson number approach, the MOL also estimates zifrom many different criteria, such as the level of maximum potential temperature gradient, the level of maximum humidity gradient and from a parcel method. In an ideal atmosphere, zifrom all criteria are not much different. Therefore, the deviation of zifrom all criteria are used to estimate the measurement uncertainty and assign a quality flag. 3.6 Roughness length and displacement height The roughness length (z0) and displacement height (d) are also input parameters of the LPDM-B. For an individual ground-based tower, the calculations of these two parameters were adapted from Martano (2000). The first step was to select 30-minute runs with neutral stratification (|z/L| ≤ 0.05). All these runs must be during the daytime, had acceptable wind direction as listed in Table 3.1, and had QHand QElarger than 20 Wm−2. For the neutral stratification, the wind speed has a logarithmic profile as U(z) = u∗ kv ln z−d z0,(3.4) 22 3. DATA where Uis wind speed, zis a height above ground, u∗is the friction velocity and kv= 0.4 is von Karman constant. Next was to take u∗from the measurement and assign the initial values of z0and dto be 0.1hcand 2hc/3 respectively (hcis a canopy height). Subsequently z0and dwere varied iteratively until the different between U(z) and the measured wind speed reached its minimum. The values of z0and d were taken at this minimum. Finally, a daily average was made to estimate z0and dfor each day. 3.7 Composite fluxes For each land use in the LITFASS area, their representative fluxes or composite fluxes of each 30-minute period were aggregated from turbulent fluxes with accepted quality flags of all ground-based measurements. Detailed formulations can be found in Beyrich et al. (2006). In principle, all ground-based stations were grouped according to their land uses such as grass (NV2 and NV4), maize (A4 and A6), rape (A2, A7 and A9), cereals (A1, A3, A5 and A8), lake (FS) and forest (HV). For the land use with one measuring station, like lake and forest, the composite fluxes were taken from measured turbulent fluxes, which had accepted quality flags and covered undisturbed wind sectors. For the grassland, where two measuring stations were installed on the same field and each station was oriented to different wind sectors, the composite fluxes were taken from the station with undisturbed wind sector (Table 3.1). For example, if the wind direction at one 30-minute period is 150 degree, the composite fluxes of the grassland of this period are the fluxes measured by NV2 station. For maize, rape and cereals, where two or more measuring stations were installed on different fields, the formulation of composite fluxes was more complicated. The 30-minute fluxes of all stations needed to be normalized before averaging together as composite fluxes. For each land use, the normalization factor of each station was determined from a linear regression over the time period, when data from all stations in each group was available with good quality. For example, in case of the composite flux of latent heat of cereals, all period with good quality latent heat fluxes of A1, A3, A5 and A8 were selected. The linear regression lines of each station were formed over these data. The normalization factors of each station were determined from the value from these regression lines. On 29 May 2003, the value from these regression lines of A1, A3, A5 and A8 were 1.1, 0.75, 1.3 and 0.9 respectively. Hence, their normalization factor of latent heat flux of each station on this day are 0.9 (=1/1.1), 3. DATA 23 1.33 (=1/0.75), 0.75 (=1/1.3) and 1.1 (=1/0.9) respectively. Once normalized, the average value of normalized latent heat fluxes was taken as a composite flux. The composite fluxes of grass, maize, rape and cereals were combined together as composite fluxes of the farmland. This farmland composite fluxes were combined with composite fluxes of lake and forest to form the composite fluxes or area-averaged fluxes of a whole LITFASS area. With this composite flux formation process, the composite flux of all energy balance components was created. In this thesis, the same principle was also applied to estimate the composite quantity of u∗,z0and das well. All these composite fluxes were used with the footprint analysis in the spatial average part. 30 4. TIME AVERAGE hai ˜a1 a1 ˜a2 a2 ˜a3 a3 ˜aN aN ... ... (a) over period NP a(t) 0 P 2P 3P NP 0 a′ n ˜an an hai (b) the nth block of period P t a(t) (n−1)P nP 0 Figure 4.2: The block ensemble average and triple decomposition of a(t). (a) Over a long period NP, the block ensemble average haiis constant, while the time average of an individual block an is not constant and deviates from the block ensemble average by ˜an. (b) At any point in the nth block, a(t) can be decomposed with a triple decomposition (Eq. 4.11). Finnigan, 1994), is not a long term coordinate. It sets wof each nth period to zero and acts as a high-pass filter. In this thesis, the long term coordinate was obtained with the planar fit rotation (section 2.4), which determines the rotation angle from multiple periods. This rotation set the block ensemble average of vertical velocity of the period NP to zero (hwi= 0), while the mean vertical velocity in each period P is not necessary zero. Thus the block ensemble average of the vertical flux becomes hwci=h˜w˜ci+w′c′(4.13) According to Finnigan et al. (2003), the mesoscale flux ˜w˜chas two roles, which are 1. To balance the unsteady horizontal flux divergence and transient changes in source and storage terms. 2. To carry the low frequency contribution to the long-term vertical flux. The first role can cause ˜w˜cto become very large in any arbitrary periods, which 4. TIME AVERAGE 31 can be much larger than the mean vertical flux itself. This role is believed to be a transient effect. Therefore, if a long averaging period NP is long enough, this role would be suppressed and minimized. Then only the second role would contribute to the vertical flux. To further suppress the diurnal effects, a long period over a few days would help to balance the strong daytime fluxes with the weak nighttime fluxes as well as suppress any extreme days in between. Therefore, only the low frequency part of the diurnal effects would be left at the end, which would show as a weak inflection at this scale. However, a long period over a few days would also intensify errors in ˜w˜c. These errors may be from instrumentation drift, gaps and some synoptic scale events. The LITFASS-2003 experiment lasted only about a month and was well installed, therefore, instrumentation drift can be neglected. Hence, any long period, which is not influenced by any synoptic events with minimum gaps, is suitable for the investigation by the block ensemble average. Note that over long averaging period, hQ∗iand hQGiare stable. This means that hResionly depends on hQHi and hQEi. This block ensemble average was applied to the data set from the Amazonian rain forest in Finnigan et al. (2003). From this article, the residual reaches zero at around 4 hours. A similar strategy was applied on the 15-day data set from the maize field (A6) of the LITFASS-2003 experiment during 2 June 2003 18:00 UTC - 18 June 2003 00:00 UTC (Mauder and Foken, 2006). Overlapping blocks ensemble average was used, with the starting point of each consecutive block being shifted by 5 minutes. The period Pof the block ensemble average was varied from 5 minutes to 5 days. The flux corrections as mentioned in the section 2.3 were applied in each individual blocks. It is shown that the energy balance is closed within a day and mainly caused by the increase of hQHi. In this thesis, to investigate whether the block ensemble average could generally close the energy balance, the block ensemble average was applied to the same data set as in the MOG (all listed station in Table 3.1, except A1 and A2) and used an identical period as in Mauder and Foken (2006). The moving block average was chosen, as it could span throughout the entire period of interest. The starting points of each consecutive block was shifted by 10 minutes, because many data sets to be used in this analysis are only available at every 10 minutes. Since data from all EC towers of the LITFASS-2003 experiment was already analyzed over 30-minute period (Beyrich et al., 2006; Foken et al., 2010), it is not necessary to investigate the averaging period shorter than 30 minutes. Therefore, the block ensemble period Pwas varied from 30 minutes to 5 days. The same flux corrections as in Mauder 32 4. TIME AVERAGE and Foken (2006) were also applied here as well. 4.1.3 Scale analysis In the time average analysis, the wavelet analysis (section 2.5) was used to inspect scales of eddies that contribute to the turbulent fluxes. To investigate the low frequency contribution from SC, the low frequency data might be enough. However, it would be more meaningful to compare all possible scales of eddies that can be resolved by an EC tower, in which the raw high frequency data are needed. The wavelet analysis demands a lot of computing resources when analyzing the high frequency data. Therefore, it is almost impossible to apply the wavelet analysis over a long period at once. The available computing resource, employed in this thesis, allowed the calculation of the longest period up to five days for the high frequency data. In this thesis, the wavelet analysis firstly applied to data from A5, A6, NV, M50 and M90 stations, whose raw high frequency data are available. If the separation between small and large scales eddies are very distinctive, the low frequency data would be sufficient to inspect the large scale eddies. 4.2 Results and discussions 4.2.1 Modified ogive analysis For ground-based stations, the data selection criteria (section 3.2.3) ruled out most of nighttime periods in both MOG analyses, because their turbulent fluxes were below thresholds. The measuring stations with broader undisturbed wind sectors, which are A5 (rye), NV (grass) and HV (pine forest), were expected to have more qualified periods. This was confirmed by number of qualified periods from NV and A5 stations. However, number of qualified periods of HV for the MOG of energy balance component was much less than other two measuring stations. This was because many data period from HV randomly had poor steady state flags (flag 4-9) of QEthroughout the day. This was in contrast to data from FS (lake), whose steady state flags of QHwere randomly poor. Because of these unsteadiness in QH and QE, many data periods were removed from HV (forest) and FS (lake) stations. Over low vegetation, steady state flags of QHand QEwere normally good between 6:00 - 16:00 UTC. Some random unsteady period mostly appeared in the afternoon. For all selected measuring stations, steady states flags of Fc(if measurements were 4. TIME AVERAGE 33 available) were randomly poor throughout the day, while steady state flags of u∗ were mostly good (flag 1-3). Hence, passing the steady state criterion, is mainly dependent on the stationary of QH,QEand Fc. At the end, in each measuring station, only 5% -20% of available periods were left for the MOG. They mainly spanned the duration between 6:00 - 16:00 UTC. For the energy balance components, they all had unstable stratification. While for Fc, there were a few periods with stable stratification. The results of the MOG of energy balance component (u∗,QHand QE) and CO2 flux (u∗and Fc) are shown in Table 4.2 and 4.3 respectively. These two tables report the number of qualified periods for the MOG (Tot #, column 1), the average of F30 (F30, column 4, 6 and 9), and the percentage of qualified periods in each ogive case (#, column 5, 8 and 11). All sets of information are reported at two different sizes of error bands (η), 10% and 20%, which must be larger than the threshold fluxes (section 3.2.3). For case 2 and 3, the average of maximum flux difference for each case (h∆maxi, column 7 and 10) is also presented. According to the physical appearance of the surfaces, all selected measuring stations could be classified into three categories, which were lake (FS), low vegetation (A3-A9 and NV) and forest (HV). u∗seemed to be the only one that strictly followed this classification, while QHdid so loosely. F30of u∗and QHwere highest over the forest and smallest over the lake. For low vegetation, F30of u∗closely grouped together, while F30of QHgrouped dispersedly. There was not much difference in F30of QEand Fcbetween forest and low vegetation outside the southern part of the LITFASS area. The southern part of the LITFASS area was significantly affected by the heavy rain events on 5 June 2003, which probably extremized QE and Fcin A7-A9 and FS stations. Both MOG of energy balance components and CO2flux gave quite similar results in u∗. The MOG classified most periods from all sites as Case 1. This suggests that the time extension has almost no impact on u∗regardless of canopy types. Over lake and low vegetation, the MOG classified most qualified period of both QHand QEas Case 1. This suggests that 30-minute averaging time is generally sufficient to capture most of turbulent fluxes. However, there were significant numbers of Case 2 and 3 of both QHand QEin some of low vegetation stations and remarkably forest stations (HV). These periods of Case 2 and 3 of low vegetation sites were closely related to the stationary of QHand QEover 4-hour period. For low vegetation sites, periods of Case 1 of QHand QEusually had 4-hour steady state flag 1, while Case 2 and 3 usually had flag 2 or more. This relation was not obviously observed in the forest site. This implies that when the atmosphere becomes less stationary at longer averaging time, the measured fluxes over low vegetation can 34 4. TIME AVERAGE be either increased or decreased. As number of Case 3 was normally greater than number of Case 2 in both QHand QEfor low vegetation and forest, the averaging time extension would tend to increase QHand QE. For Case 3 in low vegetation, QH broadly increased more than QE. This suggests that the averaging time extension has more impact on QH. The average maximum flux difference h∆maxiincreased with the size of an error band (η), while less number of Case 2 and 3 was observed. This was because the fewer periods left had larger ∆max. Eventually, even with the greatest ∆max added on the top of flux corrections, it was still not enough to close the energy balance. Furthermore, from scalar similarity of QHand QE, these measured fluxes were expected to increase or decrease together. Thus Case 2 or Case 3 in both QHand QEshould be observed simultaneously, which after all rarely happened over low vegetation. It must be noted that in A7 (Rape), the residual was relatively small and quite comparable with the measurement errors of QHand QE. Hence, small fluxes increasing from the averaging time extension might close the energy balance in this site. However, this closure would not be the act of large scale eddies. Table 4.2: Results from the modified ogive analysis of the energy balance components (u∗,QH and QE) of the LITFASS-2003 experiment between 20 May 2003, 1200 UTC - 18 June 2003, 0000 UTC. Notations: Tot # is the number of qualified periods for the MOG; ηis the width of error band, which is set to be 10% and 20% of F30 (average flux at 30 min period of each run) and has a minimum value equals to the measurement error of each turbulent flux; F30is the average of F30 from all runs in each ogive case; # is the percentage of qualified periods in each ogive case; h∆maxiis the average of ∆max (maximum flux difference) from in each ogive case. Note that the unit of each specified flux in column 2 only applies to quantities in column 4, 6, 7, 9 and 10 of the same row. Station Flux ηCase 1 Case 2 Case 3 (Tot #) (%) F30#(%) F30h∆maxi#(%) F30h∆maxi#(%) Forest u∗10 0.68 100.0 - - 0.0 - - 0.0 (ms−1) 20 0.68 100.0 - - 0.0 - - 0.0 HV QH10 261 74.8 205 -33 3.3 224 33 22.0 (Wm−2) 20 252 96.7 237 -56 0.8 217 70 2.4 (123) QE10 107 43.1 128 -33 9.8 119 27 47.2 (Wm−2) 20 112 75.6 126 -45 4.9 125 40 19.5 Rye u∗10 0.30 100.0 - - 0.0 - - 0.0 (ms−1) 20 0.30 100.0 - - 0.0 - - 0.0 A3 QH10 188 93.7 124 -13 1.6 124 15 4.8 (Wm−2) 20 184 100.0 - - 0.0 - - 0.0 (63) QE10 84 92.1 51 -12 4.8 55 11 3.2 (Wm−2) 20 81 100.0 - - 0.0 - - 0.0 Continued on next page 4. TIME AVERAGE 35 Table 4.2 – continued from previous page Station Flux ηCase 1 Case 2 Case 3 (Tot #) (%) F30#(%) F30h∆maxi#(%) F30h∆maxi#(%) Rye u∗10 0.34 96.8 0.25 -0.03 0.9 0.14 0.03 2.3 (ms−1) 20 0.34 99.5 - - 0.0 0.07 0.05 0.5 A5 QH10 148 88.1 99 -15 2.8 85 19 9.2 (Wm−2) 20 143 97.7 - - 0.0 61 36 2.3 (218) QE10 145 89.9 118 -20 4.6 131 23 5.5 (Wm−2) 20 143 97.2 116 -26 0.9 132 30 1.8 Triticale u∗10 0.35 100.0 - - 0.0 - - 0.0 (ms−1) 20 0.35 100.0 - - 0.0 - - 0.0 A8 QH10 180 98.1 117 -18 1.9 - - 0.0 (Wm−2) 20 179 100.0 - - 0.0 - - 0.0 (107) QE10 125 100.0 - - 0.0 - - 0.0 (Wm−2) 20 125 100.0 - - 0.0 - - 0.0 Maize u∗10 0.34 82.9 - - 0.0 0.23 0.04 17.1 (ms−1) 20 0.32 97.4 - - 0.0 0.26 0.06 2.6 A4 QH10 123 75.0 106 -13 2.6 114 42 22.4 (Wm−2) 20 121 84.2 - - 0.0 115 54 15.8 (76) QE10 129 77.6 104 -27 15.8 73 23 6.6 (Wm−2) 20 124 89.5 110 -44 6.6 81 28 3.9 Maize u∗10 0.31 94.0 0.18 -0.03 4.3 0.15 0.03 1.7 (ms−1) 20 0.30 99.1 0.14 -0.04 0.9 - - 0.0 A6 QH10 106 84.6 98 -12 2.6 116 28 12.8 (Wm−2) 20 108 94.9 - - 0.0 92 39 5.1 (117) QE10 134 82.9 77 -20 12.0 80 18 5.1 (Wm−2) 20 127 95.7 91 -37 2.6 57 22 1.7 Rape u∗10 0.28 100.0 - - 0.0 - - 0.0 (ms−1) 20 0.28 100.0 - - 0.0 - - 0.0 A7 QH10 127 90.4 83 -13 8.5 94 12 1.1 (Wm−2) 20 123 100.0 - - 0.0 - - 0.0 (94) QE10 181 98.9 - - 0.0 141 16 1.1 (Wm−2) 20 181 100.0 - - 0.0 - - 0.0 Continued on next page 36 4. TIME AVERAGE Table 4.2 – continued from previous page Station Flux ηCase 1 Case 2 Case 3 (Tot #) (%) F30#(%) F30h∆maxi#(%) F30h∆maxi#(%) Rape u∗10 0.30 100.0 - - 0.0 - - 0.0 (ms−1) 20 0.30 100.0 - - 0.0 - - 0.0 A9 QH10 114 91.7 98 -11 1.7 109 15 6.7 (Wm−2) 20 114 100.0 - - 0.0 - - 0.0 (60) QE10 200 100.0 - - 0.0 - - 0.0 (Wm−2) 20 200 100.0 - - 0.0 - - 0.0 Grass u∗10 0.34 92.5 - - 0.0 0.15 0.02 7.5 (ms−1) 20 0.33 100.0 - - 0.0 - - 0.0 NV QH10 117 93.0 101 -15 6.0 132 23 1.0 (Wm−2) 20 116 99.5 99 -27 0.5 - - 0.0 (201) QE10 131 86.1 95 -19 2.0 118 19 11.9 (Wm−2) 20 140 97.5 94 -31 0.5 114 27 2.0 Lake u∗10 0.21 90.3 0.09 -0.02 1.4 0.16 0.02 8.3 (ms−1) 20 0.20 100.0 - - 0.0 - - 0.0 FS QH10 40 95.8 - - 0.0 31 14 4.2 (Wm−2) 20 40 100.0 - - 0.0 - - 0.0 (72) QE10 197 95.8 93 -15 1.4 121 14 2.8 (Wm−2) 20 193 100.0 - - 0.0 - - 0.0 50 m u∗10 0.54 66.3 0.25 -0.06 8.1 0.36 0.06 25.6 (ms−1) 20 0.49 91.9 0.18 -0.08 3.5 0.28 0.09 4.7 M50 QH10 109 39.5 117 -25 23.3 109 24 37.2 (Wm−2) 20 111 76.7 107 -38 8.1 114 36 15.1 (86) QE10 170 38.4 125 -21 4.7 140 28 57.0 (Wm−2) 20 154 72.1 - - 0.0 143 37 27.9 90 m u∗10 0.61 74.3 0.17 -0.05 2.9 0.44 0.06 22.9 (ms−1) 20 0.57 97.1 0.17 -0.05 2.9 - - 0.0 M90 QH10 118 28.6 110 -21 37.1 115 19 34.3 (Wm−2) 20 117 85.7 104 -33 8.6 85 31 5.7 (35) QE10 207 42.9 190 -62 5.7 171 37 51.4 (Wm−2) 20 196 77.1 172 -97 2.9 155 52 20.0 4. TIME AVERAGE 37 Table 4.3: Results from the modified ogive analysis of CO2flux (u∗and Fc). The description is similar to Table 4.2. Station Flux ηCase 1 Case 2 Case 3 (Tot #) (%) F30#(%) F30h∆maxi#(%) F30h∆maxi#(%) Forest u∗10 0.64 99.5 - - 0.0 0.38 0.06 0.5 HV (ms−1) 20 0.64 100.0 - - 0.0 - - 0.0 (192) FC10 8.68 58.3 8.25 -1.57 12.5 7.43 1.54 29.2 (µmol m−2s−1) 20 8.29 89.1 7.73 -2.48 4.2 8.21 3.23 6.8 Triticale u∗10 0.34 100.0 - - 0.0 - - 0.0 A8 (ms−1) 20 0.34 100.0 - - 0.0 - - 0.0 (124) FC10 15.78 99.2 - - 0.0 15.65 1.89 0.8 (µmol m−2s−1) 20 15.78 100.0 - - 0.0 - - 0.0 Maize u∗10 0.31 97.4 0.26 -0.03 0.9 0.15 0.03 1.8 A6 (ms−1) 20 0.31 100.0 - - 0.0 - - 0.0 (114) FC10 9.09 62.3 7.13 -1.56 14.0 7.34 2.40 23.7 (µmol m−2s−1) 20 8.69 78.9 7.10 -1.70 10.5 7.52 4.09 10.5 Rape u∗10 0.32 100.0 - - 0.0 - - 0.0 A9 (ms−1) 20 0.32 100.0 - - 0.0 - - 0.0 (91) FC10 17.57 96.7 9.21 -1.59 2.2 19.75 2.70 1.1 (µmol m−2s−1) 20 17.41 100.0 - - 0.0 - - 0.0 Grass u∗10 0.33 88.8 - - 0.0 0.27 0.04 11.2 NV (ms−1) 20 0.33 96.6 - - 0.0 0.22 0.05 3.4 (206) FC10 9.95 74.3 8.80 -1.67 14.1 7.65 1.27 11.7 (µmol m−2s−1) 20 9.57 94.7 8.47 -2.74 3.9 9.41 2.82 1.5 50m u∗10 0.52 41.2 0.23 -0.08 3.9 0.44 0.08 54.9 M50 (ms−1) 20 0.50 77.8 0.19 -0.09 2.6 0.35 0.10 19.6 (153) FC10 12.06 15.7 8.84 -3.13 9.8 11.58 2.38 74.5 (µmol m−2s−1) 20 11.68 62.1 8.11 -4.25 5.9 11.42 3.21 32.0 90m u∗10 0.54 40.2 0.25 -0.11 6.9 0.50 0.08 52.9 M90 (ms−1) 20 0.53 77.5 0.23 -0.13 4.9 0.45 0.10 17.6 (102) FC10 13.69 10.8 13.91 -2.46 3.9 10.86 2.82 85.3 (µmol m−2s−1) 20 11.53 42.2 12.08 -3.04 2.0 11.07 3.49 55.9 For Fc, Case 1 was still a majority, with larger fraction of Case 2 and 3 than the energy balance components. Forest also had larger fraction of Case 2 and 3 than did low vegetation. Overall, number of Case 3s was greater than number of Case 2s, and h∆maxiof Fcalso increased with η. The 4-hour steady state flags were 38 4. TIME AVERAGE normally 1 for Case 1 and higher for Case 2 and Case 3. However, Case 2 generally had higher steady state flags than Case 3. This suggests that when the atmosphere becomes less stationary at longer averaging time, the measured Fctends to increase. However, when the degree of unsteadiness becomes stronger, the measured Fcstart to decrease. Number of qualified periods for the MOG of M50 and M90, which measured fluxes on the same tower at different heights, was very low. This should be caused by more unsteadiness at higher measurement height. High number of Case 3s in u∗indicates that the averaging time extension can eventually increase u∗. Large fraction of Case 2 and Case 3 in both QHand QEwere observed at both measurement heights. Additionally, Case 3 were observed simultaneously with either Case 2 or Case 3 in both QHand QE. The measurement heights of these two stations should be high enough (probably outside the ASL) to observe SC regularly. Therefore, all these evidences might imply that outside the ASL, SC can significantly effect QHand QE, which can be observed at a longer averaging time. 4.2.2 Block ensemble average The block ensemble average (Eq. 4.13) of various measuring stations during 2 June 2003 18:00 UTC - 18 June 2003 00:00 UTC, are shown in Fig. 4.3. This period was chosen as a long period NP to repeat Mauder and Foken (2006) with some minor modifications (section 4.1.2). It was found that the result from A6 (Maize) station differed from the original one by less than a measurement errors of QHand QE. Therefore, these modifications still give the comparable results, which would allow modifications to other data sets to be applied confidently. The outcome of block ensemble average was quite unexpected, because it could not close the energy balance in all sites. In all stations, both hQHiand hQEiwere relatively constant in the first few hours. This finding is consistent with the results from the ogive analysis, in which the averaging time extension for a few hours would not much change the measured fluxes. When a block ensemble period Pwas longer than a few hours, the block ensemble average fluxes started to change. In most stations, hQEiwere more steady at longer P. The closures in A4 (maize), A5 (rye) and A6 (maize) were around 15 - 30 hours, which is closed to the results in Mauder and Foken (2006), and were mainly caused by the increase of hQHiwith longer P. Note that there was an abrupt decrease of hQHiat very large Pin A4 (maize). In A9 (rape), the increase of hQHiwith Pcould not close the energy balance, because it was canceled with the decrease of hQEi. The 4. TIME AVERAGE 39 Period (minute)Period (minute) Energy flux density (W m−2) −20 0 20 40 60 80 100 A5 0 20 40 60 80 A6 −20 0 20 40 60 80 100 120 A7 30 40 50 60 70 80 90 100 A8 30 40 50 60 70 80 90 A9 −50 0 50 100 150 NV −100 −50 0 50 100 150 200 FS 0 20 40 60 80 100 HV 101102103104 0 50 100 M50 101102103104 0 50 100 M90 A3 101102103104 20 30 40 50 60 70 <QH> < QE>< Res> A4 101102103104 −100 −50 0 50 100 150 200 Figure 4.3: Block ensemble average fluxes evaluated using data from EC towers of the LITFASS2003 experiment during 2 June 2003 18:00 UTC - 18 June 2003 00:00 UTC. These EC towers covered these following land uses: pine forest (HV), barley (A3), maize (A4, A6), rye (A5), rape (A7, A9), triticale (A8), grassland (NV, M50, M90) and lake (FS). M50 and M90 measured fluxes at 50 m and 90 m heights respectively. 46 4. TIME AVERAGE buoyancy term dominates the shear production term as z/L ≤ −1. This situation is also accompanied by the low friction velocity. Since the free convection was not observed during 1 June 2003 - 5 June 2003, these near-surface SC were reasonably caused by the surface heterogeneity(Stoy et al., 2013). In case of the LITFASS area, this surface heterogeneity included the thermal heterogeneity, which could be induced by the difference in surface temperatures between different land uses. 4.2.3 Scale analysis In this part, the wavelet analysis was applied to the raw high frequency data from A5 (rye), A6 (maize) and NV (grass) in order to resolve scales of turbulence that contribute to the vertical fluxes during 1 June 2003 15:00 UTC - 5 June 2003 15:00 UTC. Wavelet cross-scalograms from these three stations are shown in Fig. 4.7. From these diagrams, there were two turbulent scales. The smaller scale was observed daily during the daytime and transport both QHand QE. This scale ranged from a few seconds to a few minutes and should be captured by the EC measurement with 30minute averaging time. The larger scale mainly transported QHand did not appear on a daily basis. At this larger scale, the positive contribution, which tended to increase QHwas found in the A5 (rye) and A6 (maize), while negative contribution that decreased QHwas found in NV (grass). This conformed with consecutive large ˜ QHin the Hovmøller diagrams of mesoscale fluxes and the increase or decrease of the block ensemble average fluxes at longer P. According to the wind speed of A5 (rye), A6 (maize) and NV (grass), this larger scale corresponded to the inverse frequency and inverse wavenumber of around 4-5 hours and 35 km respectively, which could not be captured by the EC measurement averaging over 30-minute period. At higher measurement height, smaller scale turbulence was slightly larger than the ground-based stations, while larger scale turbulence was found in both QHand QE. For example during 1 June 2003 15:00 UTC - 5 June 2003 15:00 UTC of M50 (50 m), the increase of ˜ QEand decrease of ˜ QHat longer P(Fig. 4.6) were consistent with the pattern in the Hovmøller diagrams of mesoscale fluxes (Fig. 4.5) and larger scale turbulence from the wavelet analysis (Fig. 4.8 a). Application of the wavelet analysis on the low frequency data can still show the larger scale turbulence, while loosing the information of smaller scale ones. Therefore, if only larger scale turbulence was needed to be inspected, this low frequency data would be sufficient. The wavelet cross-scalograms from low frequency data of FS (lake, ∆t= 10 minutes) and A8 (triticale, ∆t= 5 minutes) during 1 June 2003 15:00 UTC - 5 June 2003 15:00 UTC are shown in Fig. 4.8 b and c. For FS (lake), strong negative contribution 4. TIME AVERAGE 47 Figure 4.7: Wavelet cross-scalogram of sensible heat fluxes (upper panels) and latent heat fluxes (lower panels) evaluated using high frequency data from a) A5 (rye), b) A6 (maize) and c) NV (grass). These data sets spanned the period between 1 June 2003 15:00 UTC - 5 June 2003 15:00 UTC. Colors represent the value in W m−and the black solid line is the cone of influence. 48 4. TIME AVERAGE Figure 4.8: Wavelet cross-scalogram of sensible heat fluxes (upper panels) and latent heat fluxes (lower panels) evaluated using high frequency data from a) M90 (90 m), and low frequency data from b) FS (lake, ∆t= 10 minutes) and c) A8 (triticale, ∆t= 5 minutes) These data sets spanned the period between 1 June 2003 15:00 UTC - 5 June 2003 15:00 UTC. Colors represent the value in W m−and the black solid line is the cone of influence. 4. TIME AVERAGE 49 was found in the larger scale turbulence, which was consistent with the consecutive large negative ˜ QHand the decrease of hQHiat longer P. For A8 (triticale), the contribution from larger scale turbulence was not significant in both QHand QE, which was consistent with the block ensemble average and Hovmøller diagrams of mesoscale fluxes. Both patterns from the Hovmøller diagram and wavelet analysis showed the positive or negative mesoscale fluxes. However, they did not actually show what contributes to these fluxes. For the turbulent fluxes, the quadrant analysis can be used by dividing the instantaneous contribution into four quadrants (Shaw, 1985). Since the results from the block ensemble average, Hovmøller diagrams of mesoscale fluxes and wavelet analysis suggested that the main contribution for closing the energy balance were mesoscale fluxes, the principle of quadrant analysis was adopted and applied to the mesoscale fluxes ˜w˜c. Let ˜ T(temperature) and ˜a(absolute humidity) to be the abscissa and ˜w(vertical velocity) to be the ordinate, the four quadrants (Qi, i = 1, ..., 4) are Q1:˜w > 0 and ˜ T > 0 or ˜a > 0 warm air rising or moist air rising, Q2:˜w > 0 and ˜ T < 0 or ˜a < 0 cold air rising or dry air rising, Q3:˜w < 0 and ˜ T < 0 or ˜a < 0 cold air sinking or dry air sinking, Q4:˜w < 0 and ˜ T > 0 or ˜a > 0 warm air sinking or moist air sinking. Q1and Q3contribute to the positive flux, while Q2and Q4contribute to the negative flux. The abscissa and ordinate were then normalized by their standard deviations. The hyperbolic hole of size 0.5 (H= 0.5) was set to classify the strength of the contribution. Any points inside this hole weakly contributed to the mesoscale fluxes and could be neglected. Therefore, points with significant contribution outside the hyperbolic hole must satisfy  ˜w˜ T σ˜wσ˜ T or  ˜w˜a σ˜wσ˜a > H. (4.14) With the quadrant analysis, contributions of the mesoscale fluxes were expected to be identified. To be conformed with the Hovmøller diagram (Fig. 4.4 and 4.5), the same long period NP, which is 20 May 2003 12:00 UTC - 18 June 2003 00:00 UTC, and P= 30 minutes (non-overlapped) were used. Therefore, any points on the quadrant analysis diagram represented the normalized ˜w˜cfrom each non-overlapped 30-minute period. 50 4. TIME AVERAGE ˜ T/σ ˜ T ˜a/σ˜a ˜ T/σ ˜ T ˜a/σ˜a ˜w/σ ˜w A3 −4 −2 0 2 4 −4 −2 0 2 4 −4 −2 0 2 4 −4 −2 0 2 4 A4 −4 −2 0 2 4 −4 −2 0 2 4 −4 −2 0 2 4 −4 −2 0 2 4 A5 −4 −2 0 2 4 −4 −2 0 2 4 A6 −4 −2 0 2 4 −4 −2 0 2 4 A7 −4 −2 0 2 4 −4 −2 0 2 4 A8 −4 −2 0 2 4 −4 −2 0 2 4 A9 −4 −2 0 2 4 −4 −2 0 2 4 NV −4 −2 0 2 4 −4 −2 0 2 4 FS −4 −2 0 2 4 −4 −2 0 2 4 HV −4 −2 0 2 4 −4 −2 0 2 4 M50 −4 −2 0 2 4 −4 −2 0 2 4 −4 −2 0 2 4 −4 −2 0 2 4 M90 −4 −2 0 2 4 −4 −2 0 2 4 −4 −2 0 2 4 −4 −2 0 2 4 Figure 4.9: Quadrant analysis of the mesoscale flux evaluated using data from EC towers of the LITFASS-2003 experiment during 20 May 2003 12:00 UTC - 18 June 2003 00:00 UTC. Each dot represents the normalized mesoscale flux of each 30-minute block, in which the period from 1 June 2003 15:00 UTC to 5 June 2003 15:00 UTC is highlighted using red dots. The blue solid lines represent the hyperbolic hole (H = 0.5) 4. TIME AVERAGE 51 The results of the quadrant analysis of all stations are shown in Fig. 4.9. In these diagrams, all points during 1 June 2003 15:00 UTC - 5 June 2003 15:00 UTC are distinguished from the rest by the red color dots. By considering only strong contribution outside a hyperbolic hole (blue line), it was found that during this period, ˜ QH (via ˜w˜ T) had more contribution from Q1(warm air rising) for A4 (maize), A5 (rye) and A6 (maize), while there was more contribution from Q4(warm air sinking) for NV (grass) and FS (lake). The cancellation between Q1and Q4were found for the rest of the ground-based stations. For ˜ Qe(via ˜w˜a), significant contribution outside the hyperbolic hole was not found in most ground-based stations. These results implied that the increase of hQHiat longer Pin A4 (maize), A5 (rye) and A6 (maize) were caused by warm air near the surface rising, while the decrease of hQHiin NV and FS were caused by warm air aloft sinking. When significant contribution from two opposite sign quadrants was found, their cancellation kept the vertical fluxes constant and only a weak inflection was found at the diurnal scale. For M50 (50 m) and M90 (90 m), even their block ensemble average fluxes did change significantly at longer P, it was very difficult to judge that which specific quadrant significantly contribute to the vertical flux. Since both of them were outside the ASL and always experienced SC, their mesoscale contribution might not behave similarly to the ground-based measurement. 4.3 Energy balance correction All the findings in section 4.2.2 4.2.3 suggest that without assuming steady state condition, the block ensemble average can extend the averaging time to several days, by including the period to period fluctuations or mesoscale fluxes ( ˜w˜c) into the mean vertical flux. However, the increased fluxes are not always enough to close the energy balance. With the assistant of the Hovmøller diagram, which shows variation of mesoscale fluxes over long period, the period when SC exist in the vicinity of the sensor can be uncovered by exhibiting consecutive large mesoscale fluxes. This implies that when SC exist near the earth’s surface, they mainly transport the sensible heat, which supports the poor scalar similarity between the sensible and latent heat fluxes in the low frequency region (Foken et al., 2011; Ruppert et al., 2006). Since SC move very slowly and are very large in size, an EC tower measurement averaging over 30 minutes is unable to detect them. If the sensor is coincidentally at the right time and spot, when SC transport near-ground warm air upward, positive 52 4. TIME AVERAGE contributions from ˜ QHwould yield higher hQHiover long period that can improve the energy balance closure. However, when these near-surface SC transport warm air aloft downward, their negative contribution of ˜ QHwould decrease hQHiat longer averaging time. This suggests that near-surface SC are responsible for the energy balance closure problem rather than the sensor efficiency. To account for low frequency turbulent fluxes caused by SC, it must be accepted that the scalar similarity between the sensible and latent heat fluxes is no longer valid throughout all scales. Therefore, the widely used energy balance correction in Twine et al. (2000), EBC-Bo, which assumes the scalar similarity between sensible and latent heat fluxes by preserving the Bowen ratio would not generally hold. As near-surface SC transport more sensible heat, EBC-Bo may attribute less residual to the sensible heat flux than expected. This leads to an alternative energy balance correction through the buoyancy flux ratio (EBC-HB), in which the convection play a key role. The buoyancy flux, QB, is defined as QB=ρcpw′T′ v,(4.15) where ρis the air density. cpis the specific heat capacity of air at constant pressure. Tvis the virtual temperature, which can be replaced by the sonic temperature (TS) with negligible loss of accuracy (Kaimal and Gaynor, 1991). This means that QB can be directly measured with a good accuracy by the sonic anemometers. The virtual temperature is related to the actual temperature (T) and specific humidity (q) in the same way as the sonic temperature (Schotanus et al., 1983), which leads to QB=ρcpw′T′ v=ρcpw′T′+ 0.61 T w′q′ =QH1 + 0.61 Tcp λ Bo,(4.16) where λis the heat of evaporation of water and Bo is the Bowen ratio. The residual can be partitioned with EBC-HB, which contains both sensible and latent heat fluxes. A fraction of the residual, which would attribute to the sensible heat flux is dependent on the relative contribution of the sensible heat flux to the buoyancy flux, while the remaining go to the latent heat flux. Therefore the corrected sensible and latent heat fluxes with EBC-HB (QEBC−HB Hand QEBC−HB Erespectively) are, QEBC−HB H=QH+fHB ·Res, (4.17) QEBC−HB E=QE+ (1 −fHB)·Res, (4.18) 4. TIME AVERAGE 53 with fHB =QH QB =1 + 0.61 Tcp λ Bo−1 .(4.19) Since this method does not preserve the Bowen ratio, thus Eq. 4.17-4.19 must be calculated iteratively until the Bowen ratio in the Eq. 4.19 converges. The comparison between EBC-Bo and EBC-HB is shown in the Fig. 4.10. Both approaches are identical at very high Bowen ratio, in which all the residual is shifted to the sensible heat flux. For the typical range of Bowen ratio, however, EBC-HB attributes larger fraction of the residual to the sensible heat flux than that by EBC-Bo. This is more consistent with the findings in this chapter. 0.01 0.1 1 10 100 1 10 100 Fraction of residual attribute to QH (%) Bowen ratio EBC−Bo EBC−HB, Tair = 15 oC EBC−HB, −30 oC < Tair < 30 oC Figure 4.10: Fraction of the residual attributed to the sensible heat flux at different Bowen ratios evaluated from two different approaches. The Bowen ratio approach (EBC-Bo, black line) assumes the scalar similarity between the sensible and latent heat fluxes by preserving the Bowen ratio (Twine et al., 2000). The buoyancy flux ratio approach (EBC-HB, gray lines) partitions the residual according to the ratio between the sensible heat flux and the buoyancy flux, and is shown at different temperatures from -30◦C to 30◦C. Even both approaches are identical at very large Bowen ratio, EBC-HB mostly attributes larger fraction of the residual to the sensible heat flux than that by EBC-Bo 5 Spatial average In this chapter, to prove whether the energy balance correction (chapter 4) could properly include contributions from secondary circulations, the energy balance correction was applied on area-averaged fluxes (or composite fluxes), which were aggregated from fluxes measured by multiple EC towers in the LITFASS area. These corrected composite fluxes were supposed to include contribution from secondary circulations and expected to be more comparable with the spatial averaged fluxes, which were measured by the Helipod and LAS. 5.1 Spatial measurement A fixed EC tower measurement, whose turbulent fluxes are obtained through time averaging, has been proven to be effective over the homogeneous surface. With the Taylor’s frozen hypothesis (Taylor, 1938), the time averaged fluxes from the EC measurement can also represent spatial averaged fluxes over a limited area surrounding the tower. However, when the terrain becomes more complex, it would reduce the validity of Taylor’s frozen hypothesis, so the time averaged fluxes may no longer represent the spatial averaged fluxes (Crawford et al., 1996). Moreover, even the averaging time has been extended, a fixed tower never measures contributions from stationary SC (Mahrt, 2010). This drawback suggests that any measurements that operates on the spatial average basis and can probe through stationary SC become necessity. The measurement that operate on a spatial average basis, normally collects data at multiple locations (almost) simultaneously. It normally covers the larger area than a fixed-tower measurement. This type of measurement can be measured by either a fixed instruments, a LAS or an array of fixed towers as examples, or sensors on 5. SPATIAL AVERAGE 55 a moving vehicle, like a tram (Oncley et al., 2009) or an aircraft. All these measurements are expected to included contributions from both moving and stationary SC, which is supported by many literatures. For instance, in Meijninger et al. (2006), spatial averaged fluxes measured by the LAS over the LITFASS area are systematically higher than composite fluxes (section 3.7). Or in Mauder et al. (2008), spatial averaged fluxes from a network of ground-based sensors over agricultural land give additional 50 W m−2in QH. Over the past ten years, many aircraft-based measurements have been conducted and their measured fluxes can be representative in a regional scale (Desjardins et al., 1995). There are many types of aircraft-based measurements performed recently, such as the Helipod (Bange et al., 2002), an Unmanned Aerial Vehicle (Kroonenberg et al., 2012) and a weight-shift microlight aircraft (Metzger et al., 2012). These measurements cannot operate over a long period. Therefore, they rather more compliment to the tower-based measurements than replacement (Desjardins et al., 1997; Mauder et al., 2007a). For the LITFASS-2003 experiment, there were measurements from the Helipod and LAS available (section 3.3 and 3.4). Their measured fluxes were systematically higher, but broadly agreed with the composite fluxes or area-averaged fluxes estimated from ground-based measurements (section 3.7). These composite fluxes were formulated from 30-minute averaged fluxes of multiple EC towers, which might not include the contribution from SC. From the findings in Chapter 4, the missing contributions from SC can be included by the energy balance corrections either with the Bowen ratio approach (EBC-Bo) or Buoyancy flux ratio approach (EBC-HB). Therefore, two additional set of composite fluxes with EBC-Bo and EBC-HB were created from the original set of composite fluxes (without energy balance correction, NC, section 3.7). Each set of composite fluxes consisted of composite sensible and latent heat fluxes of each land use. To test whether these new set of composite fluxes could improve the agreement with the fluxes measured by the Helipod and the LAS, additional aggregation strategy was done. This strategy required the source area of the Helipod, which could be estimated by the footprint analysis. In Metzger et al. (2013), the simple parameterizations model of the backward footprint model (Kljun et al., 2004) was used to determine the source area of the aircraft fluxes. In this thesis, the full version of this footprint model, LPDM-B (section 2.6 or Kljun et al., 2002), was used for this task. This investigation would reveal the connection between the spatial averaged fluxes measured by the Helipod and the LAS with the time averaged fluxes, which 62 5. SPATIAL AVERAGE both flights, the regions with minimum QHseemed to be coincide with the presence of the lakes upwind of the flight paths. These regions are P5-P8 of Fig. 5.3 a and P2-P4 of Fig. 5.3 b. There were more flux variabilities in QHwhen the Helipod passed over the farmland. For the flight on 7 June 2003, which occurred in between two heavy rain events, its QEwas averagely larger than that of the flight on 14 June 2003. Moreover, the southern part averagely showed larger QEthan the northern part of the flight. This was consistent with the rain event on 5 June 2003, which occurred mainly in the southern part of the LITFASS area. Energy density (W m−2) Latitude  P1 P2 P3 P4 P5 P6 P7 P8 52.12 52.14 52.16 52.18 52.2 52.22 52.24 52.26 −100 0 100 200 300 400 500 QH,wavelet QH,mov QE,wavelet QE,mov (a) 7 June 2003 Energy density (W m−2) Latitude  P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 52.12 52.14 52.16 52.18 52.2 52.22 52.24 52.26 −100 0 100 200 300 400 500 QH,wavelet QH,mov QE,wavelet QE,mov (b) 14 June 2003 Figure 5.3: Sensible and latent heat fluxes, deduced from a wavelet analysis (subscript wavelet) and moving average (windows size = 3 km, subscript mov), of the Helipod flight on a) 7 Jun 2003 14:40 - 13:50 UTC and b) 14 Jun 2003 09:20 - 09:30 UTC. Both estimations broadly agree to each other. The wavelet analysis of selected flights are shown in Fig. 5.4. There were the absences of the signal in QHthat coincided with the region of minimum QHin both flights. The absences of QHin the wavelet analysis are a typical signature of the lake. Eddies, which suddenly disappeared, had Fourier period up to 1 km, which corresponded to the inverse wavenumber of 100-200 m. These would be the scale 5. SPATIAL AVERAGE 63 of eddies that transported QHbetween the atmosphere at the Helipod’s height and the surface below. For the flight on 7 June 2003 (Fig. 5.4 a), these scale of eddies extensively transported QE. This indicated that the absence of QHover the lake might be rather caused by the missing of the temperature fluctuations. However, for the flight on 14 June 2003 (Fig. 5.4 b), the wavelet analysis showed the absences in both QHand QEsimultaneously. 14 June was comparatively dry with respect to 7 June. This suggested that the existence of QEover the lake on 7 June would be caused by the wet air mass after the rain event on 5 June 2003. Fractional contributions of each land use Ai(Eq. 5.11) along the flight paths, which were estimated from the LPDM-B model, are shown in Fig. 5.5. By using Eq. 5.12 and 5.13, three set of QH0,footprint and QE0,footprint were calculated from three types of composite fluxes: NC (green lines), EBC-Bo (blue lines) and EBCHB (red lines). These three fluxes, which were estimated from the footprint model, were compared with the fluxes extrapolated from the Helipod (5.14 and 5.15, black lines). It was found that they did mostly show the same tendency. This would suggest that surfaces forcings or source areas as predicted by the footprint were acceptable. QH0,footprint with EBC-Bo and EBC-HB were consistent very well with QH0,helipod when the Helipod was over the farmland and forest. For 7 June 2003, the discrepancy between QH0,footprint and QH0,helipod was large in the southern part, which can be caused by the presence of the lake and the rain events on 5 June 2003. However, this rain event did not much disturbed the measurement of QHin the southern part of the LITFASS area. Hence, the discrepancy between QH0,footprint and QH0,helipod, which was also found over the lake in the flight on 14 June 2003, should be mainly caused by the lake. This discrepancy might be explained by the internal boundary layer over the lake, whose frictional velocity suddenly drops from the surrounding area. This internal boundary layer might trap all particles beyond this lake. Even the footprint model predicted that there were significant contributions from forest and farmland in this area, their contributions could be neglected, if they were beyond the lake. Since the touchdown table does not contain the detailed trajectory of each particle, it is very difficult to precisely remove the trapped particles. Therefore, it must be reminded that when the source area contains fractional of water or lake, its QH0,footprint tends to be over estimated. This condition must be considered carefully and suggests that points with significant contribution from the lake should not be included in the comparison. For QE, which was much disturbed by the rain event, its composite fluxes could 64 5. SPATIAL AVERAGE Figure 5.4: Wavelet cross-scalogram of the Helipod flight on a) 7 June 2003 and b) 14 June 2003. The upper panels represent the sensible heat fluxes, while the lower ones represent the latent heat fluxes. Colors represent the value in W m−1and the black solid line is the cone of influence. 5. SPATIAL AVERAGE 65 be very different from locally measured one. This caused a large discrepancy between QE0,footprint and QE0,helipod throughout the entire flight on 7 June 2003. A spatial shift between QE0,footprint and QE0,helipod were also clearly observed in both flights. This spatial shift was not obviously shown in QH, therefore, it was most likely caused by the scalar similarity between moisture and temperature, which do not hold over the whole frequency range. Hence, small difference would be added up and could be observed at a large observation distance. For the flight on 14 June 2003, which was not disturbed by the rain event, if a spatial shift was taken into account, QE0,footprint with EBC-Bo over the lake tended to be overestimated, while with EBC-HB and NC tended to be underestimated. Therefore, the discrepancies between QE0,footprint and QE0,helipod would be caused by the composite fluxes rather than the presence of the lake. Table 5.1: The surface fluxes from different estimations within the range that least effect by the lake (bounded by vertical dashed lines in Fig. 5.5). These estimations are: NC = No energy balance correction; EBC-Bo = energy balance correction with Bowen ratio approach; EBC-HB = energy balance correction with buoyancy flux ratio approach; and Helipod - mov = the extrapolation to the surface of moving average fluxes (3km windows) of the Helipod Estimation 7 Jun 2003 14 Jun 2003 QH0(Wm−2)QE0(Wm−2)QH0(Wm−2)QE0(Wm−2) LPDM-B - NC 122 170 231 140 LPDM-B - EBC-Bo 163 229 305 186 LPDM-B - EBC-HB 215 177 347 144 Helipod - mov 192 191 281 187 To observe how well can the footprint model predict the surface fluxes, only part of the flight that least influence by the presence of the lake should be considered. This region is bounded by the vertical black dashed lines in Fig. 5.5. The average of QH0,footprint,QE0,footprint,QH0,helipod and QE0,helipod within this range are shown in Table 5.1 and represented by the horizontal dashed lines in Fig. 5.5 (color codes after the solid lines). For 7 June 2003, a fractional contributions from the lake was pretty low. It was found that QH0,footprint with EBC-Bo and EBC-HB did equally well and were much better than NC. Since the composite latent heat fluxes of this flight might not a good representative of this flight segment, the comparison between QE0,footprint and QE0,helipod would be inconclusive. For 14 June 2003, the bounded region was a little bit disturbed by the presence of the lake, which suggested that QH0,footprint could be overestimated. By taking this issue into account, it can be concluded that QH0,footprint with EBC-Bo and EBC-HB did equally well and were much better than NC as well. For QE0,helipod, it was best fit with QE0,footprint with EBC-Bo. However when the spatial shift was considered, average QE0,helipod of this 66 5. SPATIAL AVERAGE flight segment should be lower than estimated. Therefore, QE0,footprint with EBC-HB and NC were acceptable as well. One more thing that may need to be considered is that the Helipod measurement height was clearly not in the ASL and would be in different similarity scaling domain. According to the time average analysis (chapter 4), both sensible and latent heat fluxes significantly change at long block ensemble averaging period in M50 and M90 (measured fluxes at 50 m and 90 m heights respectively). This implies that large scale eddies, which transport the energy at these heights, may not behave similarly to the ones near the earth’s surface and tend to preserve the Bowen ratio. Therefore, the extrapolation to the surface from these measurement heights may fit better with the surface fluxes estimated with EBC-Bo. To get rid of this ambiguity, the spatial average measurements conducted near the earth’s surface are needed. Part of the flight on 7 June 2003 was right above the LAS path over the farmland (section 3.4 and Fig. 5.2). The source areas of this Helipod’s segment and the LAS should not be much different, in which both measured sensible fluxes would be comparable. The comparison between sensible heat fluxes measured from this Helipod segment, measured by the LAS, and estimated from the footprint model is shown in Fig. 5.6. For the entire flight on 7 June 2003, the measurement error of the sensible heat flux was around 33 W m−2and the measurement error for the flight segment above the LAS should be not much different. Sensible heat flux, which was measured over this flight segment, was QH,helipod =166 W m−2(upper black circle). Its extrapolation down to the surface was QH0,helipod = 175 W m−2 (lower black circle). The surface sensible heat flux deduced from the LAS was QH0,LAS = 171 W m−2and represented by blue diamond. It was actually within the measurement error of the Helipod. All surface fluxes estimated from the footprint model are represented by the red symbols. QH0,helipod and QH0,LAS seemed to be best fit with QH0,footprint with EBC-Bo (156 W m−2). Nevertheless, they were also in good agreement with QH0,footprint with EBC-HB (208 W m−2). Moreover, the southern part of this flight segment had small contribution from the lake, which implied that all sets of QH0,footprint would be slightly overestimated. When this issue was taken into account, all footprint estimated fluxes (all red symbol), should be a little bit shifted to the left. This would lead to the same conclusion earlier that both EBC-Bo and EBC-HB are equally good for predicting the surface sensible heat flux by the footprint model and they are much better than no energy balance correction at all. 5. SPATIAL AVERAGE 67 Figure 5.5: The comparison between the surface fluxes estimated from the footprint model and extrapolated fluxes from the Helipod (black). The footprint estimated surface fluxes were calculated from three types of composite fluxes, without energy balance correction (green), with EBC-Bo (blue) and with EBC-HB (red). Part of the flight that least influence by the presence of the lake are bounded by the vertical black dashed lines 68 5. SPATIAL AVERAGE 0 50 100 150 200 250 0 10 20 30 40 50 60 70 80 90 QH (W m−2) z (m) NC EBC−Bo EBC−HB Helipod LAS Figure 5.6: This diagram shows the comparison of surface fluxes on 7 June 2003, which was estimated from the flight segment above the LAS path over the farmland. The black circles represent sensible heat fluxes as measured by the Helipod (upper) and extrapolated to the surface (lower). All red symbols represent surface sensible heat fluxes estimated from the footprint model with no energy balance correction (triangle), EBC-Bo (circle) and EBC-HB (square). The blue diamond represents surface fluxes estimated from the LAS. 5.3.2 Tower Three sets of surface fluxes estimated with the LPDM-B model were created in the same way as Eq. 5.12 and 5.13 for all selected 30-minute runs of M50 and M90. The comparisons of these fluxes with the surface fluxes extrapolated from the tower (Eq. 5.16 and 5.17) are shown in Fig. 5.7. Unlike the Helipod, QH0,tower was best fit by QH0,footprint with no energy balance correction, while QE0,tower was equally good for all three sets of QE0,footprint. From the time average analysis (chapter 4), it was shown that both M50 and M90 normally experienced SC. However, within 30 minutes contributions from SC were not yet fully included. Therefore, the measured fluxes should be more comparable to the uncorrected fluxes. Additionally, at these two measurement heights, the steady state conditions or homogeneous conditions might no longer hold. This means their time averaged statistics could represent neither time-averaged nor spatial-averaged statistics of the source area and the relation with the composite fluxes as in Eq. 5.1 might not be applicable. 5. SPATIAL AVERAGE 69 0 100 200 300 400 0 50 100 150 200 250 300 350 400 QH0,footprint (W m−2) QH0,tower (W m−2) NC EBC−Bo EBC−HB 0 50 100 150 200 250 300 0 50 100 150 200 250 300 QE0,footprint (W m−2) QE0,tower (W m−2) a) M90 0 100 200 300 400 0 50 100 150 200 250 300 350 400 QH0,footprint (W m−2) QH0,tower (W m−2) NC EBC−Bo EBC−HB 0 50 100 150 200 250 300 0 50 100 150 200 250 300 QE0,footprint (W m−2) QE0,tower (W m−2) b) M50 Figure 5.7: The comparison between the footprint surface fluxes and the surface fluxes extrapolated from M50 and M90 tower. 6 Conclusions In this thesis, data from the LITFASS-2003 experiment was analyzed to study the energy balance closure problem at the earth’s surface, which has been believed to be caused by the secondary circulations. The analysis was carried out in both time and space domains, from which several conclusions were drawn. The time domain analysis mainly involved data from ground-based eddy-covariance towers, whose representative statistics were time-averaged statistics. To increase the possibility that secondary circulations were picked up by the sensor, the eddycovariance averaging time was extended beyond a typical value of 30 minutes. This time extension strategy was accomplished through the ogive analysis (Desjardins et al., 1989; Oncley et al., 1990) and the block ensemble average (Finnigan et al., 2003). The ogive analysis requires a steady state condition, restricting the time extension to only a few hours. In this thesis, the modified ogive analysis was formulated to deal with low frequency data, which allowed the investigation to include low frequency data from all available ground-based stations. Employed this approach, it was found that an averaging time extension up to four hours would not significantly improve the energy balance closure in all ground-based stations. The time extension, moreover, had more impact over tall vegetation. Sensible heat flux, latent heat flux and CO2flux were more sensitive to the time extension than friction velocity. Over low vegetation, the increase of these three turbulent fluxes with the time extension was related to the unsteadiness of the longer averaging period. The increase of the sensible heat flux was overall higher compared to one of the latent heat flux. Over a longer period, the increase or decrease of sensible and latent heat fluxes might not change proportionally as expected. For 4-hour averaging time in low vegetation, the sensible heat flux averagely increased by 15 - 45W m−2, while the latent heat 6. CONCLUSIONS 71 flux averagely increased by 10 - 25 W m−2. These amount of energy increased were not overall enough to close the energy balance in all low vegetation measurements of the LITFASS-2003 experiment. Therefore, the 30-minute averaging time is still sufficient for the eddy-covariance measurement over low vegetation. The block ensemble average, which does not require a steady state condition, can extend the averaging time to several days by including period to period fluctuations or mesoscale fluxes ( ˜w˜c) to the mean vertical flux. These mesoscale fluxes indeed include low frequency contribution not only from secondary circulations, but also from other large scale events (for example a synoptic scale event). It was shown from the LITFASS-2003 data that there existed large scale eddies, which were believed to be secondary circulations, near the earth’s surface. During the period between 1 June 2003 to 5 June 2003, when secondary circulations existed in the vicinity of the sensor and were not influenced by other large scale events, consecutive large mesoscale fluxes of temperature ( ˜w˜ T) were found through the Hovmøller diagrams of mesoscale fluxes. During this period, the wavelet analysis suggested that these near-surface secondary circulations spanned a time and a spatial extension of 4-5 hours and 30-40 km respectively. Additionally the quadrant analysis of mesoscale fluxes in this period showed that positive contribution of the large mesoscale fluxes was mainly from the first quadrant, in which near-ground warm air was transported upward, while the negative contribution was mainly from the forth quadrant, in which warm air aloft was transported downward. 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Boundary-Layer Meteorology 78:191–210 Appendix A Individual contribution to the joint publication Charuchittipan, D., Babel, W., Mauder, M., Leps, J.-P., and Foken, T.: Extension of the averaging time of the eddy-covariance measurement and its effect on the energy balance closure, submitted to Boundary-Layer Meteorology •I partly developed the idea of this manuscript. I conducted the whole data analysis, wrote the text and act as the corresponding author of the manuscript. •Wolfgang Babel developed the proposed new energy balance closure correction algorithm together with me and realised the respective part in the conclusions. •Matthias Mauder initiated the use block ensemble average and wavelet analysis to the data from the LITFASS-2003 experiment. He also participate in the LITFASS-2003 experiment. •Jens-Peter Leps provided data from several measuring stations of the LITFASS2003 experiment. He also participate in the LITFASS-2003 experiment. •Thomas Foken encouraged the structure of the manuscript and contributed with many scientific discussions. Furthermore, he initiated the project related to the manuscript. Declaration / Erkl¨arung I hereby declare, to the best of my knowledge and belief, that this thesis does not contain any material previously published or written by another person, except where due reference has been made in the text. This thesis contains no material, which has been previously accepted or definitely rejected for award of any other doctoral degree at any university or equivalent institution. Hiermit erkl¨are ich, dass ich die vorliegende Promotionsarbeit selbst¨andig verfasst und keine anderen als die angegebenen Quellen und Hilfsmittel benutzt habe. Hiermit erkl¨are ich, dass ich nicht bereits anderweitig versucht habe, diese Dissertation ohne Erfolg einzureichen oder mich einer Doktorprfung zu unterziehen. Hiermit erkl¨are ich, dass ich die Hilfe von gewerblichen Promotionsberatern bzw. -vermittlern weder bisher in Anspruch genommen habe, noch knftig in Anspruch nehmen werde. Bayreuth, den Doojdao Charuchittipan