Ten years of MIPAS measurements with ESA Level 2 processor V6 – Part 1: Retrieval algorithm and diagnostics of the products

Atmos. Meas. Tech., 6, 2419–2439, 2013 www.atmos-meas-tech.net/6/2419/2013/ doi:10.5194/amt-6-2419-2013 © Author(s) 2013. CC Attribution 3.0 License. Atmospheric Measurement Techniques Open Access Ten years of MIPAS measurements with ESA Level 2 processor V6 – Part 1: Retrieval algorithm and diagnostics of the products P. Raspollini1, B. Carli1, M. Carlotti2, S. Ceccherini1, A. Dehn11, B. M. Dinelli3, A. Dudhia4, J.-M. Flaud5, M. López-Puertas7, F. Niro6, J. J. Remedios8, M. Ridolfi2, H. Sembhi8, L. Sgheri9, and T. von Clarmann10 1Istituto di Fisica Applicata “N. Carrara” (IFAC) del Consiglio Nazionale delle Ricerche (CNR), Firenze, Italy 2University of Bologna, Bologna, Italy 3Istituto di Scienza dell’Atmosfera e del Clima (ISAC) del Consiglio Nazionale delle Ricerche (CNR), Bologna, Italy 4Atmospheric, Oceanic and Planetary Physics, Clarendon Laboratory, Oxford University, UK 5Laboratoire Interuniversitaire des Systèmes Atmosphériques (LISA) CNRS, Univ. Paris 12 et 7, France 6SERCO SpA c/o European Space Agency ESA-ESRIN, Frascati, Italy 7Instituto de Astrofísica de Andalucía (CSIC), Granada, Spain 8Earth Observation Science, Department of Physics and Astronomy, University of Leicester, UK 9Istituto per le Applicazioni del Calcolo (IAC) del Consiglio Nazionale delle Ricerche (CNR), Section of Florence, Italy 10Karlsruhe Institute of Technology (KIT), Institute for Meteorology and Climate Research (IMK), Karlsruhe, Germany 11ESA-ESRIN, Frascati, Italy Correspondence to: P. Raspollini ([email protected].it) Received: 4 December 2012 – Published in Atmos. Meas. Tech. Discuss.: 15 January 2013 Revised: 15 July 2013 – Accepted: 5 August 2013 – Published: 23 September 2013 Abstract. The MIPAS (Michelson Interferometer for Passive Atmospheric Sounding) instrument on the Envisat (Environmental satellite) satellite has provided vertical profiles of the atmospheric composition on a global scale for almost ten years. The MIPAS mission is divided in two phases: the full resolution phase, from 2002 to 2004, and the optimized resolution phase, from 2005 to 2012, which is characterized by a finer vertical and horizontal sampling attained through a reduction of the spectral resolution. While the description and characterization of the products of the ESA processor for the full resolution phase has been already described in previous papers, in this paper we focus on the performances of the latest version of the ESA (European Space Agency) processor, named ML2PP V6 (MIPAS Level 2 Prototype Processor), which has been used for reprocessing the entire mission. The ESA processor had to perform the operational near real time analysis of the observations and its products needed to be available for data assimilation. Therefore, it has been designed for fast, continuous and automated analysis of observations made in quite different atmospheric conditions and for a minimum use of external constraints in order to avoid biases in the products. The dense vertical sampling of the measurements adopted in the second phase of the MIPAS mission resulted in sampling intervals finer than the instantaneous field of view of the instrument. Together with the choice of a retrieval grid aligned with the vertical sampling of the measurements, this made ill-conditioned the retrieval problem of the MIPAS operational processor. This problem has been handled with minimal changes to the original retrieval approach but with significant improvements nonetheless. The Levenberg– Marquardt method, already present in the retrieval scheme for its capability to provide fast convergence for nonlinear problems, is now also exploited for the reduction of the ill-conditioning of the inversion. An expression specifically designed for the regularizing Levenberg–Marquardt method has been implemented for the computation of the covariance matrices and averaging kernels of the retrieved products. The regularization of the Levenberg–Marquardt method is controlled by the convergence criteria and is deliberately kept weak. The resulting oscillations of the retrieved profile are a posteriori damped by an innovative selfadapting Tikhonov regularization. The convergence criteria and the weakness of the self-adapting regularization ensure Published by Copernicus Publications on behalf of the European Geosciences Union. 2420 P. Raspollini et al.: Ten years of MIPAS that minimum constraints are used and the best vertical resolution obtainable from the measurements is achieved in all atmospheric conditions. Random and systematic errors, as well as vertical and horizontal resolution are compared in the two phases of the mission for all products, namely: temperature, H2O, O3, HNO3, CH4, N2O, NO2, CFC-11, CFC-12, N2O5and ClONO2. The use in the two phases of the mission of different optimized sets of spectral intervals ensures that, despite the different spectral resolutions, comparable performances are obtained in the whole MIPAS mission in terms of random and systematic errors, while the vertical resolution and the horizontal resolution are significantly better in the case of the optimized resolution measurements. 1 Introduction The Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) is a limb-viewing Fourier transform spectrometer that sounded the emission of Earth’s atmosphere in the spectral range from 685 to 2410cm−1on board the ESA (European Space Agency) Envisat (Environmental satellite) satellite (Fischer et al., 2008). Its unique observation of the atmospheric emission has provided day and night and regularly spaced sampling that exhaustively characterizes the chemical and physical processes occurring in the atmosphere from 6 to 70km altitude, for observations made in nominal mode, and up to 170 km for observations made in special modes. Table 1 summarizes the main characteristics of the MIPAS spectral bands with the indication of the main molecules emitting in each of them. The satellite was launched on 1 March 2002, and in the first two years of operation (from July 2002 to March 2004) MIPAS acquired, nearly continuously, measurements at full spectral resolution (full resolution (FR) measurements, characterized by the spectral sampling of 0.025cm−1). On 26 March 2004 FR measurements were interrupted because of anomalies in the velocity of the interferometer drive unit of MIPAS and the analysis of instrument reliability and performance recommended the use of a shorter interferometric sweep, corresponding to both a lower spectral resolution (0.0625cm−1) and a shorter measurement time (1.8s instead of 4.5s). Test measurements with reduced spectral resolution were successfully performed in August/September 2004 and, accordingly, the reduction in the measurement time was exploited to make more frequent observations both in the vertical (limb) domain and in the horizontal domain (along the orbit). With these changes, which provide, for the operational data products, an optimized compromise between spectral and spatial resolutions (optimized resolution, OR), MIPAS restarted operations on 9 January 2005 with a duty cycle shorter than 40%. Since then, due to the recovering performance of the drive unit, the duty cycle was progressively increased until 1 December 2007 when a 100% duty cycle Table 1. MIPAS spectral bands: spectral range, NESR, most abundant molecules. Spectral FR NESR OR NESR range [nWcm2[nWcm2Most abundant Band [cm−1] srcm−1] srcm−1] molecules A 685–970 30–40 20–25 CO2, O3, H2O, HNO3, NO2, CFC-11, CFC-12, ClONO2 AB 1020–1170 20 13 O3, N2O, CFC-12 B 1215–1500 15 9.5 N2O5, N2O, CH4, H2O, SO2, HOCl, ClONO2 C 1570–1750 3–5 2–2.5 H2O, HNO3, NO2, ClONO2 D 1820–2410 3–5 2–2.5 CO2, O3, NO, CO was again attained. MIPAS was successfully operated with this full duty cycle until 8 April 2012, when an Envisat anomaly occurred resulting into the loss of communication between ground and satellite and the end of MIPAS observations (ESA, 2012a). MIPAS was one of the first Envisat instruments to be fully operational after the launch, providing very high quality Level 1 and Level 2 products. The ESA operational near real time analysis provided from the very beginning vertical profiles of temperature and of volume mixing ratio (VMR) of H2O, O3, HNO3, CH4, N2O and NO2from pole to pole, approximately following the orbital track. In parallel, three other main scientific algorithms have been developed to process MIPAS data. These are the Geofit Multi-Target Retrieval (GMTR) (Carlotti et al., 2006; Dinelli et al., 2010), based on the optimal estimation approach (Rodgers, 2000) and performing a two-dimensional analysis of MIPAS measurements, explicitly handling horizontal inhomogeneities; the algorithm obtained by the joint effort of the Institut für Meteorologie und Klimaforschung (IMK) at Forschungszentrum Karlsruhe and the Instituto de Astrofísica de Andalucía (IAA) (von Clarmann et al., 2003b, 2009b), using Tikhonovregularization,capable ofhandlingdeviations from local thermodynamic equilibrium (non-LTE) and taking into account a horizontal gradient of temperature along the line of sight; the algorithm MORSE developed at Oxford University (Dudhia, 2008; Moore and Remedios, 2010), based on the optimal estimation approach (Rodgers, 2000) and using the Reference Forward Model (Dudhia, 2005). The four retrieval algorithms differ for some assumptions in the forward model, for the spectral intervals used for the analysis and for the retrieval approach, and a profitable cross-fertilization has occurred among them. Studies have been performed for the FR measurements proving that in general consistent results for the operational species are obtained by the different algorithms (see von Clarmann et al., 2003a; Fischer et al., 2008), while studies on the OR measurements are currently ongoing and will be reported in later publications. Other retrieval schemes, used principally for the retrieval of CFCs from MIPAS measurements, are OPERA (Moore and Remedios, 2008) and JURASSIC (Hoffmann et al., 2008), which use optimal estimation on spectrally integrated radiances. Atmos. Meas. Tech., 6, 2419–2439, 2013 www.atmos-meas-tech.net/6/2419/2013/ P. Raspollini et al.: Ten years of MIPAS 2421 This paper is focused on the ESA processor that was used during the Envisat mission for both the near real time analysis, whose requirement is the distribution of the products within three hours from the measurement time, and for the offline analysis, performed on consolidated Level 1 data, that benefits from a posteriori knowledge related to calibration, auxiliary data and precise orbit information. The capacity of operating in near real time made the MIPAS ESA dataset particularly suitable for the use in operational data assimilation systems. Indeed, near real time MIPAS ozone profiles were actively assimilated at the ECMWF (European Centre for Medium-Range Weather Forecasts) from October 2003 until the end of March 2004 (Dethof, 2003), and, after the interruption in 2004, from 8 December 2011 until 8 April 2012. The assimilation of MIPAS ozone data at the ECMWF was proven to substantially improve the quality of the ECMWF ozone analyses (Dragani, 2012; Thépaut et al., 2012), in particular the good vertical resolution of MIPAS in the stratosphere could provide a very useful constraint on the ozone analyses. The description and characterization of the ESA processor’s products of the full resolution phase was already described in Ridolfi et al. (2000) and Raspollini et al. (2006). In this paper we focus on the performances of the latest version of the ESA processor ML2PP (MIPAS Level 2 Prototype Processor) V6, which has been used for reprocessing the entire MIPAS mission, i.e., including both phases. The complete ML2PP V6 database has been released in 2012 (ESA, 2012b), data access is provided via fast registration at https: //earth.esa.int/web/guest/data-access/browse-data-products. The ML2PP V6 dataset contains the upgrades that were needed after the change of the operating mode in 2005 both in the algorithm, to cope with the finer altitude sampling of the OR measurements, and in the spectral intervals selected for each retrieval, to cope with the reduced spectral resolution. Since the retrieval is performed at the grid of the measured tangent altitudes and this grid is significantly finer, for the OR measurements, than the MIPAS instantaneous field of view (IFOV, 3km) in the upper troposphere and lower stratosphere, the retrieval of the OR measurements resulted in an ill-conditioned problem and required a regularization approach that was not previously needed for the analysis of the FR measurements. Furthermore, in order to minimize the total error in the two phases of the mission, spectral intervals specifically optimized for each of them were used. Even if the whole MIPAS mission has now been reprocessed with the same algorithm, the different vertical and horizontal samplings and the different spectral intervals used in the two phases of the mission represent a discontinuity in the measurements whose impact on the products has been carefully investigated. This analysis is split in two parts. The first part, covered by this paper, makes an overview of the choices made for the inversion of the OR measurements starting from the retrieval approach designed for the FR measurements. The paper is then focused on the description of the upgraded diagnostics used for the characterization of the Level 2 products and the comparison of the performances in the two phases of the mission in terms of random and systematic errors and spatial resolution. The second part, covered by a companion paper (Raspollini et al., 2013), will study whether the discontinuity in MIPAS measurements in the two phases has an impact on the bias of the products between the two phases of the mission. 2 Characteristics of the two phases of the MIPAS mission In both phases of the mission different measurement modes are used to observe different processes in the atmosphere with either better sampling or better altitude coverage. Corresponding modes in the two phases of the mission are meant to achieve the same scientific objectives but may slightly differ for the altitude coverage and for the altitude grid. The general objectives of the different measurement modes are shortly reviewed. The nominal mode (NOM) is the basic mode used to study chemistry and transport and to provide a database for climatology, trend analyses and near real time applications. It is designed to cover the upper troposphere, the stratosphere and the lower mesosphere (approximated boundaries 6–70km). The upper troposphere–lower stratosphere (UT–LS) measurement mode, called UTLS-1, is tailored to studies of atmospheric processes in the UT–LS region (including the tropical tropopause layer). It provides a trade-off between vertical and horizontal resolution as well as vertical coverage, ensuring a fine vertical and along-track sampling between the upper troposphere and the middle stratosphere. The middle atmosphere (MA) mode covers most of the stratosphere, the mesosphere and the lower thermosphere (from 18 to 102km). This mode is dedicated to studying linkages between the upper atmosphere and the stratosphere, i.e., the global circulation and transport of CO and NOx from the mesosphere down to the stratosphere in polar winter hemispheres, as well as solar proton events affecting both the upper atmosphere and the stratosphere. This mode is also used to monitor the quality of operational retrievals that neglect deviations from local thermodynamic equilibrium (non-LTE). The upper atmosphere (UA) mode covers all the mesosphere and the lowest part of the thermosphere and is mainly dedicated to measurements of high-altitude NO and temperature. Table 2 summarizes the characteristics of the most used modes in the two phases. For FR measurements details are provided only for the NOM mode, which was the most used one in the first phase. For OR measurements details are provided for the NOM, UTLS-1, MA and UA measurement modes. UTLS-1 mode was the prevalent mode in the years 2005 and 2006. Then, since December 2007, when MIPAS www.atmos-meas-tech.net/6/2419/2013/ Atmos. Meas. Tech., 6, 2419–2439, 2013 2422 P. Raspollini et al.: Ten years of MIPAS Table 2. Characteristics of FR and OR measurements for the most used measurement modes of the two phases of the mission. FR measurements (from June 2002 to March 2004) Spectral resolution: 0.025cm−1 Measurement mode Horizontal sampling No. of scans Vertical sampling NOM 550km 17 3 km step 5 km step 8 km step 6–42km 42–52km 52–68km OR measurements (from January 2005 to April 2012) Spectral resolution: 0.0625cm−1 Measurement mode Horizontal sampling No. of scans Vertical sampling NOM 410km 27 1.5km step 2 km step 3 km step 4 km step 4.5km step 6–21km 21–31km 31–46km 46–62km 62–71km UTLS-1 290km 19 1.5km step 2 km step 3 km step 4.5km step 8–21.5km 21.5–27.5km 27.5–33.5km 33.5–51.5km MA mode 430km 29 3 km step 18–102km UA mode 375km 35 3 km step 5 km step 42–102km 102–172km returned to the 100% duty cycle, regular observations were made with a period of 10 days, consisting of 8 days of NOM mode measurements, 1 day of MA mode and 1 day of UA mode. In OR measurements, NOM and UTLS-1 modes are characterized by a floating-altitude measurement grid. This means that the limb sounding grid is shifted rigidly with the lowest measured altitude tvarying with the latitude, θ, according to t=A+Bcos(2θ) −Ccos(90◦−abs(θ)). In this equation A=12km, B=0 and C=7km for the NOM mode and A=8.5km, B=3km and C=0 for the UTLS-1 mode. The floating-altitude sampling grid is meant to follow roughly the tropopause height along the orbit with the requirement to collect at least one spectrum within the troposphere while avoiding too many spectra affected by clouds. For a detailed description of all measurement modes used in the two phases of the mission see alsoOelhaf (2008), while for a detailed calendar of MIPAS measurements see Dudhia (2008). The MIPAS ML2PP V6 dataset covers all described measurement modes, although MA and UA modes are analyzed by the ESA processor only up to 70km, since above this altitude the impact of non-LTE cannot be neglected and nonLTE effects are not handled in the forward model of the ESA processor. Analysis of MA and UA modes on the full altitude range are performed with the IMK-IAA algorithm (García-Comas et al., 2012; Bermejo-Pantaleon et al., 2011), while the analysis of UTLS-1 mode with IMK processor is described in Chauhan et al. (2009). 3 Upgrades in the code The measurements of the first phase of the MIPAS mission were originally reprocessed by the ESA Instrument Processing Facilities (IPF) V4.1 and V4.2, based on the Optimized Retrieval Model (ORM) code described in Ridolfi et al. (2000) and in Raspollini et al. (2006). These measurements were also validated with respect to correlative measurements (Ridolfi et al., 2007; Cortesi et al., 2007; Wang et al., 2007; Payan et al., 2009; Wetzel et al., 2007, 2013, all contained in a MIPAS Special Issue, 2006). The main features of the algorithm originally designed for the analysis of the FR measurements are as follows. 1. Use of microwindows (MWs), i.e., selected spectral intervals containing relevant information on target parameters and minimizing the systematic errors, which arise chiefly from approximations in the forward model and instrument errors (Dudhia et al., 2002; von Clarmann and Echle, 1998). 2. The forward model computes the radiative transfer integral properly taking into account the atmospheric vertical inhomogeneities but assuming homogeneity in the horizontal direction. Atmosphere is assumed to be in LTE and in hydrostatic equilibrium. The characteristics of the instrument (instrument line shape (ILS) and IFOV) are accurately modeled. The impact of unaccounted atmospheric effects (non-LTE, interfering species, etc.) is minimized through the MW selection. Scattering is not included in the radiative transfer integral, and the spectra affected by thicker clouds, identified by the cloud filtering algorithm (Spang et al., 2002, 2004; Raspollini et al., 2006), are not included in the analysis. 3. The altitude grid of the retrieval is identified by the tangent points of the limb measurements. Only for some species, characterized by a low information content, a retrieval grid coarser than the measurement grid is used in order to avoid a too large ill-conditioning. Atmos. Meas. Tech., 6, 2419–2439, 2013 www.atmos-meas-tech.net/6/2419/2013/ P. Raspollini et al.: Ten years of MIPAS 2423 4. For each scan, sequential retrieval of the target species is performed (first H2O, then O3, HNO3, CH4, N2O and NO2) after the simultaneous retrieval of the pressure corresponding to the tangent altitudes and the related temperature values (pT retrieval). 5. MW-dependent continuum absorption cross-section profiles and MW-dependent, but height-independent offset calibration values are jointly retrieved with either VMR or pT retrieval. 6. Initial guess of the target species is determined using the profiles retrieved in the previous scan of the orbit appropriately combined with climatological and ECMWF profiles (if available). 7. Assumed profiles of the interfering species are given, whenever available, by the profiles retrieved in the previous retrievals (either the previous scan or the previous retrievals of the same scan) appropriately combined with climatological and ECMWF profiles (if available). 8. Global fit analysis (Carlotti, 1988) is performed, consisting of the simultaneous fit of the whole limb scanning sequence of the spectra acquired at different tangent altitudes. 9. Nonlinear least squares fit is used with the Levenberg– Marquardt minimization and regularizing method (Levenberg, 1944; Marquardt, 1963; Hanke, 1997). In the following sections, the main changes to the retrieval algorithm are described relative to the algorithm for FR measurements reported in Ridolfi et al. (2000) and in Raspollini et al. (2006). These include the adaptations to the Levenberg–Marquardt method, already utilized in the original FR algorithm, to avoid the ill-conditioning of the retrieval approach and an a posteriori self-adapting Tikhonov regularization technique. Diagnostics of the products specifically studied for the regularizing Levenberg–Marquardt method is also included as well as upgrades to the auxiliary data. Finally, new products are described. 3.1 The regularizing Levenberg–Marquardt method The ESA processor, being specifically designed for the near real time analysis of MIPAS measurements, had to be capable of operating in an automatic way for a long period. These requirements, together with the choice of making a minimal use of external constraints in order to avoid biases in the retrieved profiles, guided our design of the retrieval approach. Let ybe the m-dimensional vector of observations with error covariance matrix Syand f(x)the forward model, a nonlinear function of the n-dimensional atmospheric state vector x. Due to nonlinearities, the problem is solved in a context of Newtonian iterations where f(x)is linearized: f(x)=f(xi)+Ki(x−xi), (1) with iindex of iteration and KiJacobian matrix ∂f ∂xcalculated at the linearization point xi. The least squares solution of the inverse problem minimizes the cost function: χ2=(y−f(x))TS−1 y(y−f(x)). (2) Minimization of χ2leads to the Gauss–Newton iteration: xi+1=xi+KiTS−1 yKi−1KiTS−1 y(y−f(xi)). (3) In our application we modify Eq. (3) exploiting the Levenberg–Marquardt (Marquardt, 1963; Levenberg, 1944) method: xi+1=xi+KiTS−1 yKi+αiDi−1KiTS−1 y(y−f(xi)), (4) where Diis chosen to be a diagonal matrix with elements equal to those in the diagonal of KiTS−1 yKi. Considering that the elements of the state vector are not homogeneous, this approach allows us to provide a correction that is scaled with the error of each element. The parameter αiis adjusted according to a damping– undamping strategy, see e.g., Lampton (2004). The iterations start with a small α0. At each iteration, if the new state xi+1 provides a reduction of the chi-square (χ2(xi+1)<χ2(xi)), then xi+1is accepted and αi+1is selected such that αi+1< αi. If the state xi+1provides an increase of the chi-square (χ2(xi+1)>χ2(xi)), then xi+1is rejected and the iteration is repeated with a larger value of αi. The iteration is performed until a final iteration criterion is fulfilled (see below). The Levenberg–Marquardt method has two distinct effects. The first effect is the reduction of the correction applied to the state vector at each iteration, while the correction vector itself is rotated from the Gauss–Newton step direction obtained from Eq. (4) with αi=0 towards the opposite direction of the gradient of χ2(x), i.e., the steepest descent direction. It follows that, with a large enough αi, the χ2of the iterates monotonically decreases. By reducing the step length, the Levenberg–Marquardt method avoids making a too large correction, taking the solution outside of the linear approximation range. The second effect, that has been highly exploited for the analysis of the OR measurements due to the increased illconditioning of the retrieval problem, is that the inversion of the possibly ill-conditioned matrix KiTS−1 yKiis avoided and replaced by the inversion of the matrix KiTS−1 yKi+ αiDi, which is better conditioned. This is particularly important when the cost function to be minimized has nearly flat valleys or, which is equivalent, there are subsets of the state space where the cost function has a nearly constant minimum value. The regularizing effect of the Levenberg– Marquardt method is discussed in Hanke (1997), Engl et al. (2000), Doicu et al. (2004), Pujol (2007), Doicu et al. (2010), Hochbruck and Honig (2010), Jin (2010), and Böckmann et al. (2011). www.atmos-meas-tech.net/6/2419/2013/ Atmos. Meas. Tech., 6, 2419–2439, 2013 2424 P. Raspollini et al.: Ten years of MIPAS Theregularizing Levenberg–Marquardt method is,according to Hanke (1997), a semiconvergent method. Since the regularizing effect decreases with the number of iterations, the noise error increases, and the iterates may not converge in the xspace. The final iteration criteria of the Levenberg–Marquardt iterations should be implemented taking into account two conflicting requirements. On one hand we must avoid stopping the iterations too early, with values of χ2too far from the minimum. On the other hand, the iterations must be stopped before the noise error becomes too large. In the literature mentioned above, the consistency criterion is favored as a final iteration criterion, i.e., the iteration is stopped as soon as the χ2is only slightly larger than its expected minimal value of 1. For MIPAS this criterion cannot be applied because we do not have a reliable expectation value for the minimum of the reduced χ2as a consequence of the variability of the systematic errors. Instead, we use dedicated final iteration criteria. The Level 2 processor originally used for the analysis of the FR measurements terminated the retrieval iterations (see Raspollini et al., 2006) when at least one of the following two conditions was fulfilled. 1. The relative difference between the actual χ2and its predicted value in the assumption of the linear forward model is smaller than a predefined threshold t1. 2. The maximum inter-iteration relative correction to the target profile vector is less than a predefined threshold t2. In ML2PP V6, the final iteration criteria have been further improved in order to better handle the conflicting requirements in the case of the ill-conditioned retrievals encountered with OR observations. In particular, in ML2PP V6 the condition (1) on the relative difference between χ2and linear χ2, being a necessary, but not sufficient, condition to guarantee that a local minimum has been reached, is checked only if the actual χ2is less than a predefined threshold t5. Furthermore, two other conditions have been added, the fulfillment of one of the four being sufficient to stop the retrieval. The two additional conditions are as follows. 3. The relative inter-iteration change of χ2is less than a threshold t3. This condition is checked only if the actual χ2is less than the threshold t5. 4. The n-dimensional state vector xiat the current iteration (i) is compatible with the state vector xi−1at the previous iteration, within a fraction t4of its error bars represented by the covariance matrix Si(see Eq. 7). s(xi−xi−1)TS−1 i(xi−xi−1) n< t4(5) The two newly added final iteration criteria allow to reduce, on average, the number of iterations by 18%, while the resulting average χ2does not increase. The average number of iterations for pT retrieval is about 4, while it is on average about 3–3.5 for the other retrievals with the exception of NO2, for which the number of iterations is generally 1 or 2. Both the chosen thresholds and the fact that the iteration is stopped when one of the final iteration criteria is fulfilled ensure that iterations not achieving a significative reduction of the χ2are avoided. Because of the ill-conditioning, failing to stop the iterations may produce an unwanted increase of the noise error in the solution, and may result in oscillating profiles. On the other hand, slightly oscillating profiles due to ill-conditioning guarantee that a weak constraint has been used and are therefore tolerable, also considering that the adaptive a posteriori regularization will reduce these oscillations (see Sect. 3.3). 3.2 Diagnostics of the Levenberg–Marquardt solution In ill-conditioned retrievals the Levenberg–Marquardt solution depends, to some degree, on both the initial guess of the state vector and the pathway followed by the iterative minimization procedure. The same dependence exists also for the covariance matrix and the averaging kernels (for their definition see Sect. 4.2) of the Levenberg–Marquardt solution. For a proper calculation of the covariance and averaging kernel matrices of the Levenberg–Marquardt solution, ML2PP V6 uses an algorithm (Ceccherini and Ridolfi, 2010) in which all the retrieval iterations and the Levenberg– Marquardt damping are rigorously taken into account. This is particularly important in the retrieval of OR measurements, since, due to the ill-conditioning of the problem, the Levenberg–Marquardt parameter can be significantly different from zero. To summarize the equations used, let ibe the iteration count and cits value at convergence. For i=0,...,c, we define the sequence of gain matrices: (Ti)jk ≡∂(xi)j ∂yk .(6) With this definition, the covariance Scand the averaging kernel Acmatrices of the Levenberg–Marquardt solution xcare given by Sc=TcSyTT c,(7) Ac=TcKc.(8) Matrices Tican be obtained by deriving the Levenberg– Marquardt iterative formula (Eq. 4). Considering that the initial guess x0does not depend on the observations y, we obtain the following recursive expression: Atmos. Meas. Tech., 6, 2419–2439, 2013 www.atmos-meas-tech.net/6/2419/2013/ P. Raspollini et al.: Ten years of MIPAS 2425          T0=0 Ti+1=KiTS−1 yKi+αiDi−1KiTS−1 y+ +I−KiTS−1 yKi+αiDi−1KiTS−1 yKiTi. (9) It can be easily shown that in well-conditioned retrievals reaching the exact numerical convergence the covariance and the averaging kernel matrices calculated with Eqs. (7), (8) and (9) coincide with those calculated assuming the last iteration as a Gauss–Newton iteration (αc=0). On the other hand, in ill-conditioned retrievals and/or in retrievals stopped with a physically meaningful final iteration criterion, the Levenberg–Marquardt solution and its diagnostic tools deviate from those predicted by the Gauss–Newton formulas. Additional tests and discussions on this algorithm can be found in Ceccherini and Ridolfi (2010). The use of this procedure ensures that in ML2PP V6 both covariance and averaging kernel matrices are properly computed even when the Levenberg–Marquardt procedure terminates with a Levenberg–Marquardt parameter significantly different from zero. 3.3 A posteriori regularization As noted in Sect. 3.1, the profiles retrieved using only the Levenberg–Marquardt regularization often exhibit unphysical oscillations. In the Level 2 ESA processor ML2PP V6 these oscillations are damped with a Tikhonov (Tikhonov, 1963) regularization scheme applied, a posteriori, to the Levenberg–Marquardt solution. The expression for the a posteriori regularized solution is x=S−1 c+λR−1S−1 cxc+λRxa.(10) The regularization matrix Ris obtained using the first derivative operator, and xais an a priori profile, which, in our case, is the null vector. This type of regularization is also used by the MIPAS IMK scientific processor (von Clarmann et al., 2003b, 2009b), but contrary to their approach, where the regularization is performed during the iterations and the same regularization strength λis used for all profiles, the ESA processor performs the a posteriori regularization and determines, for each profile, the optimal regularization strength λon the basis of the so-called error consistency method, first introduced in Ceccherini (2005). This method selects the scalar λon the basis of the requirement that the regularized and un-regularized profiles should be compatible within the random error of the regularized profile, adapting its strength on the basis of the measurement error. This criterion leads to an analytical formula for the calculation of the regularization parameter λ: λ=rn (xa−xc)TRScR(xa−xc),(11) 0 50 100 150 200 01/01/07 03/01/07 05/01/07 07/01/07 09/01/07 11/01/07 01/01/08 03/01/08 05/01/08 07/01/08 09/01/08 11/01/08 01/01/09 O3 regularization strength (km2/ppmv4) Time 80N-90N 65N-80N 20N-65N 20S-20N 65S-20S 65S-80S 80S-90S Fig. 1. Time evolution of the regularization strength used in ozone retrieval from January 2007 to December 2008 for the different latitude bands indicated in the plot’s key. Points represent weekly means. where Scis the covariance matrix of the profile retrieved with the regularizing Levenberg–Marquardt method (Eq. 7). As shown in Ceccherini (2005) and in Ceccherini et al. (2007a), this regularization parameter provides a significant but rather weak regularization. The existence of an analytical expression makes the error consistency method particularly suitable for implementation in operational retrievals, where the regularization is applied, without direct user supervision, to large sets of profiles with variable noise errors. Figure 1 represents the time evolution of the regularization strength for the ozone retrieval from January 2007 to December 2008 for different latitude bands. The regularization strength presents significant latitudinal and seasonal behavior, that, according to Eq. (11), is anti-correlated with the retrieval error of the profile obtained with the regularizing Levenberg–Marquardt method. The possibility of adapting the regularization strength to each observation according to its random error makes the biasintroducedby theregularization always comparablewith the random error. Furthermore, by ensuring that the relative weight of the measurements and the constraint in the cost function to be minimized is maintained approximately constant, the same relative regularization is applied to the profile even when the information content of the measurements changes significantly, with a consequent small variation of the vertical resolution (see Sect. 4.2). By application of the regularization after a preceding Levenberg–Marquardt retrieval, a completely self-adapting approach is possible that exploits the profile obtained by the regularizing Levenberg–Marquardt method to compute the retrieval error dependent regularization strength. A posteriori regularization was preferred to the use of the regularization within the iterations because the interaction of the two adaptive approaches (Levenberg–Marquardt and regularization www.atmos-meas-tech.net/6/2419/2013/ Atmos. Meas. Tech., 6, 2419–2439, 2013 2426 P. Raspollini et al.: Ten years of MIPAS with error consistency method) makes the retrieval more instable and the convergence slower. After the a posteriori regularization the covariance and averaging kernel matrices, computed in Eqs. (7) and (8), are updated according to S=S−1 c+λR−1S−1 cS−1 c+λR−1,(12) A=S−1 c+λR−1S−1 cAc.(13) Since the strength of the regularization is driven by a single scalar parameter λindependent of altitude, the error consistency method is not suitable to regularize the water vapor profile for which the VMR and its absolute retrieval error change by two orders of magnitude across the MIPAS retrieval range (6–70km). An attempt was made to fix this problem by applying the regularization to the logarithm of thewater VMR profile,which isequivalent toconsideringthe relative error instead of the absolute one. However, this approach fails when, because of the retrieval errors, a negative value of the water vapor VMR is retrieved. The constraining of the negative retrieved values to 10−10 parts per million per volume (ppmv), as described in Sect. 3.6.1, did not help, because for this small value the approximation of the linear error propagation from the profile to the logarithm of the profile fails. In ML2PP V6 this problem with water vapor VMR regularization is temporarily avoided by disabling the a posteriori regularization in water vapor retrievals. In future ESA processor releases this problem will be tackled with a more sophisticated, self-adapting and altitude-dependent regularization scheme first proposed in Ridolfi and Sgheri (2009) and subsequently optimized for the near real time retrieval processors in Ridolfi and Sgheri (2011). 3.4 Upgrades in the auxiliary data In addition to the changes in the algorithm, the analysis of the OR measurements required also new auxiliary data. The main change was made in the MW database, i.e., the database of the spectral intervals selected for the retrieval containing the best information on the target species and being less affected by systematic errors. The MW selection is based on the minimization of the total error, including both random and systematic errors (see Sect. 4.1). The change of the spectral resolution modifies the contribution of each of these errors and leads to a different optimized selection of MWs in the two phases of the mission. Furthermore, the MWs for the analysis of the OR measurements were selected using some modified estimation of these errors, according to the improved knowledge on some MIPAS instrument errors as described in Sect. 4.1. Tables 3, 4 and 5 list the MWs selected for each species for the analysis of FR and OR measurements. The MWs used for the analysis of the FR measurements are the same as described in Raspollini et al. (2006). The spectral intervals analyzed in the OR measurements are 3–4 times, depending on the different species, wider than those of the old operation mode, even if, because of the reduced spectral resolution, the number of measured spectral points is only 1.2–1.6 times greater. Some points of these MWs are masked (i.e., are not used in the retrieval), and the masks are different at different altitudes. In general the two sets of MWs have only a small number of spectral points in common. The use of two separate sets of MWs, further than the change in the measurement scenario, represents a discontinuity between the two phases of the mission. The impact of this discontinuity on the retrieval performances is investigated in terms of random and systematic error and spatial resolution in the subsequent sections, while the possible presence of bias between the two phases of the mission due to the different systematic errors affecting the two sets of MWs and to the different measurement scenario will be investigated in a subsequent companion paper (Raspollini et al., 2013). Further changes in the auxiliary data involve the MIPAS dedicated spectroscopic database. ML2PP V6 uses V3.2 of the spectroscopic database. With respect to V3.1 described in Raspollini et al. (2006), V3.2 includes updates in NH3, OCS, NO, H2O2, HNO3, as well as updated pressure broadening (and its temperature dependence) of H2O at 948.26288cm−1. The climatological profile dataset used (IG2 V4.1) is described in Remedios et al. (2007). 3.5 New products Starting with ML2PP V6, four additional target species, namely, CFC-11, ClONO2, N2O5and CFC-12, have been operationally processed. These species are retrieved sequentially in this order after the retrieval of the original target species. With the addition of these new target species not only more variables of the atmospheric chemistry are determined providing a more comprehensive overview of the overall atmospheric composition, but also a better understanding of the observed spectrum is attained. Indeed, the use of the retrieved profiles of these species, instead of the IG2, as assumed profiles in the retrieval of the other target species, reduces the errors due to the mutual interference of the species. The analysis of these species performed by the other MIPAS algorithms, for either a part of the mission or the total mission, are reported in Dudhia (2008), Höpfner et al. (2004), Kellmann et al. (2012), and Mengistu Tsidu et al. (2004). CFC species are crucial for ozone depletion in the upper stratosphere and in the polar regions due to the chlorine released by their photolytic decomposition in the stratosphere; furthermore, since CFCs and most of their replacements are strong infrared absorbers, they contribute significantly to the anthropogenic greenhouse effect. Continuous measurements of these long-lived trace gases are useful to validate transport in atmospheric models. The study of the trends of these species during the whole MIPAS mission Atmos. Meas. Tech., 6, 2419–2439, 2013 www.atmos-meas-tech.net/6/2419/2013/ P. Raspollini et al.: Ten years of MIPAS 2427 0 10 20 30 40 50 60 70 80 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Altitude (km) Ozone absolute noise error (ppmv) Latitude band: 65S-90S DJF MAM JJA SON 0 10 20 30 40 50 60 70 80 0 5 10 15 20 25 30 Altitude (km) Ozone percent noise error (%) Latitude band: 65S-90S DJF MAM JJA SON Fig. 2. Absolute (left plot) and percent (right plot) noise error of O3profile averaged on all profiles of the 65–90◦S latitude band in the four seasons of year 2008 (December 2007, January and February 2008 (DJF); March, April and May 2008 (MAM); June, July and August 2008 (JJA); September, October and November 2008 (SON)). Table 3. Spectral intervals selected for the retrieval of pressure and temperature, H2O, O3and HNO3in the two phases of the mission. FR OR Spectral interval [cm−1] Altitude range [km] Spectral interval [cm−1] Altitude range [km] pT 685.7–685.825 33–47 703.375–703.875 21–37 686.4–689.4 30–68 719.0625–720.625 27–66 694.8–695.1 27–36 740.9375–743.9375 15–70 700.475–701.1 21–30 791.625–792.25 9–21 728.3–729.125 15–27 937.5–940.5 6–23 741.975–742.25 15–24 942.31–944.62 6–27 791.375–792.875 6–33 H2O 807.85–808.45 9–18 953.6875–956.6875 6–40 946.65–947.7 6–18 1223.75–1226.25 7.5–18 1645.525–1646.2 27–60 1387.5625–1390.5 12–70 1650.025–1653.025 15–68 1391.75–1394.75 12–54 1649.875–1652.875 15–66 O3 763.375–766.375 6–68 729.25–732.25 15–42 1039.375–1040.325 52–68 756.625–759.625 9–36 1122.8–1125.8 6–68 1043–1046 27–68 1117–1120 6–42 1123.5625–1126.5625 9–68 HNO3 876.375–879.375 6–42 836.875–839.875 6–42 885.1–888.1 6–42 859.5625–862.5625 9–42 877.0–880.0 6–42 893.625–896.625 6–42 918.9375–921.9375 9–42 www.atmos-meas-tech.net/6/2419/2013/ Atmos. Meas. Tech., 6, 2419–2439, 2013 2434 P. Raspollini et al.: Ten years of MIPAS 0 10 20 30 40 50 60 70 -0.2 0 0.2 0.4 0.6 0.8 1 O3 AK DoF=15 FR measurements 0 10 20 30 40 50 60 70 -0.2 0 0.2 0.4 0.6 0.8 1 O3 AK DoF=21.5 OR measurements Fig. 8. O3averaging kernels for two representative scans of FR (left plot) and OR (right plot) measurements. 0 10 20 30 40 50 60 70 80 1 2 3 4 5 6 7 8 9 10 Altitude (km) O3 vertical resolution and vertical step (km) OR vert. res. OR step FR vert. res. FR step Fig. 9. Vertical resolution profile and vertical retrieval steps for ozone profiles retrieved from FR measurements (green curves) and OR measurements (red curves), as indicated in the plot’s key. A set of horizontal averaging kernels (HAKs), characterizing the horizontal smoothing of MIPAS measurements, has been computed as described in von Clarmann et al. (2009). This set includes HAKs for the MIPAS IG2 atmospheres (Version 4.1, Remedios et al., 2007), i.e., six latitude bands and four seasons for each year and for both FR and OR measurements. The HAKs were calculated assuming the measurement characteristics corresponding to the nominal measurement modes of both the FR and the OR scenarios (see Table 2). For all the considered cases, the HAKs have a single maximum, therefore it is meaningful to quantify their horizontal spread with the FWHM. We compute this quantity using the same method used for the estimation of the vertical resolution (see Sect. 4.2). The FWHM of the HAKs shows quite small variations as a function of both latitude and season, therefore here we show only the FWHM relating to a single month (July) and the average over the six latitude bands. Figures 13 (for FR) and 14 (for OR) show the FWHM of HAKs as a function of 0 10 20 30 40 50 60 70 80 2 3 4 5 6 7 Altitude (km) Ozone vertical resolution (km) Latitude band: 65S-90S DJF MAM JJA SON Fig. 10. Ozone vertical resolution profile averaged on all profiles of the 65–90◦S latitude band in the four seasons of 2008 (DJF, MAM, JJA and SON 2008). altitude. Each plot contains lines related to temperature and to the VMR of six MIPAS species, as indicated in the plot’s key. In general, below about 40km the FWHM of the FR HAKs is between 200 and 300km for all MIPAS products; and those corresponding to OR are slightly smaller. Above 40km, the FR HAKs is between 300 and 600km, while those ofORare significantlybetter, stillbelow300km exceptat the uppermost altitude. Since the horizontal sampling step of MIPAS limb scans is about 510km for FR measurements and about 410km for OR measurements (see Table 2), in both cases the atmosphere turns out to be horizontally undersampled at most altitudes. Because of this undersampling, the horizontal resolution of MIPAS measurements in the nominal mode is better quantified by the horizontal sampling (see Table 2) rather than by the FWHM of the HAKs. Another interesting feature of the MIPAS HAKs is the horizontal shift (or displacement) existing between the Atmos. Meas. Tech., 6, 2419–2439, 2013 www.atmos-meas-tech.net/6/2419/2013/ P. Raspollini et al.: Ten years of MIPAS 2435 0 10 20 30 40 50 60 70 80 1 2 3 4 5 6 7 8 9 10 Altitude (km) Vertical resolution (km) FR measurements T H2O O3 HNO3 CH4 N2O NO2 CFC-11 CFC-12 N2O5 ClONO2 Fig. 11. Vertical resolution profile of T, H2O, O3, HNO3, CH4, N2O, NO2, CFC-12, CFC-11, ClONO2and N2O5retrieved from FR measurements. 0 10 20 30 40 50 60 70 80 1 2 3 4 5 6 7 8 9 10 Altitude (km) Vertical resolution (km) OR measurements T H2O O3 HNO3 CH4 N2O NO2 CFC-11 CFC-12 N2O5 ClONO2 Fig. 12. Vertical resolution profile of T, H2O, O3, HNO3, CH4, N2O, NO2, CFC-12, CFC-11, ClONO2and N2O5retrieved from OR measurements. geolocation of the tangent point and the point where most of the information comes from. While the retrieved profiles are assumed as geolocated at the tangent points of the limb scan from which they are retrieved, most of the information contributing to the retrieved values comes from air masses shifted towards the satellite with respect to the tangent points. This shift is positively correlated to the opacity of the atmosphere in the spectral region used for the retrieval, and hence it is important in case of large opacity of the MWs used in the retrieval and in presence of significant horizontal variability oftheatmosphere. Intheseconditions theshiftmay reach,for temperature, the value of 150–200km. Further details on this shift can be found in von Clarmann et al. (2009a), Carlotti and Magnani (2009), and Carlotti et al. (2013). 0 10 20 30 40 50 60 70 0 100 200 300 400 500 600 Altitude (km) FWHM of Horizontal AKs (km) FR, July 2002 T H2O O3 HNO3 CH4 N2O NO2 Fig. 13. FWHM of FR horizontal averaging kernels relating to temperature, and the VMR of H2O, O3, HNO3, CH4, N2O, NO2. The assumed atmosphere is the one from IG2, July 2002. 0 10 20 30 40 50 60 70 0 100 200 300 400 500 600 Altitude (km) FWHM of Horizontal AKs (km) OR, July 2006 T H2O O3 HNO3 CH4 N2O NO2 Fig. 14. FWHM of OR horizontal averaging kernels relating to temperature, and the VMR of H2O, O3, HNO3, CH4, N2O, NO2. The assumed atmosphere is the one from IG2, July 2006. 5 Conclusions With almost ten years of measurements, MIPAS products constitute an extended and valuable dataset, important for studies of trends, climatology, and in general for the study of the physics and chemistry of the atmosphere. The MIPAS mission is divided in two phases: the so-called FR phase, in the first two years of operation (from July 2002 to March 2004) when the instrument acquired, nearly continuously, measurements at full spectral resolution (sampled at 0.025cm−1); and the so-called OR phase (from January 2005 to April 2012), in which the instrument operated with a reduced spectral resolution (0.0625cm−1), but improved spatial resolution, that is with more frequent observations both in the vertical (limb) domain and in the horizontal domain (along the orbit). www.atmos-meas-tech.net/6/2419/2013/ Atmos. Meas. Tech., 6, 2419–2439, 2013 2436 P. Raspollini et al.: Ten years of MIPAS The ESA processor has been specifically designed for operating in near real time, and hence for working automatically in different atmospheric conditions, aimed to use the minimum amount of a priori information that may introduce a bias in the profiles. The algorithm, originally designed for the scenario of the FR measurements, required some modifications for the analysis of the OR measurements, to fully exploit the dense vertical sampling of the OR measurements with a proper handling of the ill-conditioned problem coming from the use of a retrieval grid finer than the IFOV of the instrument. Looking for self-adapting constraints, the ill-conditioned problem of the OR measurements is handled with the regularizing Levenberg–Marquardt approach during the iterations and an a posteriori regularization with a self-adapting constraint dependent on the random error of each profile. An accurate method specifically designed for the regularizing Levenberg–Marquardt approach is used for the computation of the diagnostic quantities (covariance and averaging kernels). The innovative solutions implemented in ESA processor and discussed in the paper can be useful for the analysis of future limb-sounding missions. An overview of the performance of the ESA processor ML2PP V6, used for the re-analysis of the entire MIPAS mission, is presented for all the operational species, i.e., H2O, O3, HNO3, CH4, N2O, NO2, CFC-11, CFC-12, N2O5, ClONO2, further than temperature, and a comparison between the two phases has been carried out. The performed analysis shows that the random and systematic error performances, thanks to the redundant information on the target species present in MIPAS spectra and the consequent use of dedicated MWs in the two phases (larger spectral intervals being used for OR measurements), are generally comparable in the two phases. The single scan random error varies between 5 and 20% for most species and most altitudes. For the weakest species, near the boundaries of the retrieval range, the percent random error may be significantly larger than these values. The systematic errors are generally larger than the random errors, especially for the OR measurements. The profiles from OR measurements are characterized by an improved horizontal sampling (about 510km for FR measurements, about 410km for OR measurements) and an improved vertical resolution (varying, in the altitude range 10– 40km, between 3 and 5km for FR measurements, between 1.5 and 4km for OR measurements) for most species. In general, for the species we have analyzed, the OR measurements provide higher quality products than FR measurements. The random errors, as well as the systematic errors, are dependent on the latitude and season. On the contrary, thanks to the use of a self-adapting regularization schemes in the retrieval algorithm, a small variation of the vertical resolution is obtained for different atmospheric conditions. The minimal use of external constraints, which are prone to introduce biases in the solution, makes ESA processor products suitable for the climatological studies. The use of different MWs in the two phases and in general thechange in the measurementscenario impose some caution when using the full ten year dataset to extract trends. This issue will be further investigated in a subsequent companion paper (Raspollini et al., 2013). Supplementary material related to this article is available online at http://www.atmos-meas-tech.net/6/ 2419/2013/amt-6-2419-2013-supplement.pdf. Acknowledgements. This work has been performed under the ESA study “Support to MIPAS Level 2 product validation”, contract ESA-ESRIN no. 21719/08/I-OL. The authors are grateful to the Astrium team that developed the industrial prototype ML2PP using the ORM code as reference, to Thorsten Fehr and Rolf von Kulhmann for the coordination of the MIPAS Quality Working Group activities and to Michael Kiefer for the work done within the MIPAS Quality Working Group. Edited by: A. Lambert References Bermejo-Pantaleón, D., Funke, B., López-Puertas, M., GarcíaComas, M., Stiller, G. P., von Clarmann, T., Linden, A., Grabowski, U., Höpfner, M., Kiefer, M., Glatthor, N., Kellmann, S., and Lu, G.: Global observations of thermospheric temperature and nitric oxide from MIPAS spectra at 5.3µm, J. Geophys. Res., 116, A10313, doi:10.1029/2011JA016752, 2011 Böckmann, C., Kammanee, A., and Braunss, S.: Logarithmic convergence rate of Levenberg-Marquardt method with application to an inverse potential problem, J. Inverse and Ill-Pose. P., 19, 345–367, doi:10.1515/JIIP.2011.034, 2011. 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