Errors induced by different approximations in handling horizontal atmospheric inhomogeneities in MIPAS/ENVISAT retrievals

MIPAS (Michelson Interferometer for Passive Atmospheric Sounding) is a mid-infrared limb emission sounder that operated on board the polar satellite ENVISAT from 2002 to 2012. The retrieval algorithm used by the European Space Agency to process MIPAS measurements exploits the assumption that the atmosphere is horizontally homogeneous. However, previous studies highlighted that this assumption causes significant errors on the retrieved profiles of some MIPAS target species. In this paper we quantify the errors induced by this assumption and evaluate the performances of three different algorithms 5 that can be used to mitigate the problem. We generate synthetic observations with a high spatial resolution atmospheric model and carry out the retrievals with four alternative methods. The first assumes horizontal homogeneity (1D retrieval), the second includes a model of the horizontal gradient of atmospheric temperature (1D plus temperature gradient retrieval), the third accounts for an horizontal gradient of temperature and composition (1D plus temperature and composition gradient retrieval), while the fourth is the full two-dimensional (2D) inversion approach. 10 Our results highlight that the 1D retrieval implies errors that are significant for averages of profiles. Furthermore, for some targets (e.g. T, CH4 and N2O below 10 hPa) the error induced by the 1D approximation becomes visible also in the individual retrieved profiles. The inclusion of any kind of horizontal variability model improves all the targets with respect to the horizontal homogeneity assumption. For temperature, HNO3 and CFC-11 the inclusion of an horizontal temperature gradient leads to a significant reduction of the error. For other targets as H2O, O3, N2O, CH4, the improvements due to the inclusion of an 15 horizontal temperature gradient are minor. In these cases, the inclusion of a gradient in the target volume mixing ratio leads to significant improvements. Among all the methods tested in this work, the 2D approach, as expected, implies the smallest errors for almost all the target parameters. This residual error of the 2D approach is the smoothing caused by the retrieval grid, that is coarser than that of the atmospheric model. 1 Atmos. Meas. Tech. Discuss., doi:10.5194/amt-2016-68, 2016 Manuscript under review for journal Atmos. Meas. Tech. Published: 27 April 2016 c © Author(s) 2016. CC-BY 3.0 License.


Introduction
Satellite limb scanning spectrometers have been widely used to measure atmospheric composition and its evolution with time. In many cases the atmospheric composition is obtained from these measurements with retrieval schemes that assume a horizontally homogeneous atmosphere (the so called one-dimensional, or 1D retrieval approach). In most of the stratosphere this assumption does not produce huge systematic errors. However, in the case of strong horizontal variability, retrieved profiles 5 may be affected by significant error.
In order to quantify this error, we exploit the measurements of the MIPAS (Michelson Interferometer for Passive Atmospheric Sounding) instrument, that operated onboard the ENVISAT satellite from March 2002 to April 2012. The instrument observed the atmospheric mid-infrared emission spectrum using the limb-scanning observation technique (Fischer et al., 2008).
In this spectral region several minor atmospheric constituents are active, and from the inversion of the spectrum it is possible 10 to determine their volume mixing ratio (VMR) vertical profile in the height range from 6 to 70 km. Due to the polar orbit of ENVISAT, MIPAS measured during day-time in the descending (DX) part of the orbit and during night-time in the ascending (AX) part. Comparing MIPAS/ENVISAT CFC-11 profiles with ACE (Atmospheric Chemistry Experiment) matching measurements, Höpfner et al. (2007) discovered unrealistic differences between MIPAS night-side and day-side CFC-11 VMRs. These discrepancies were thoroughly investigated by Kiefer et al. (2010) and were attributed to the unmodelled horizontal variability 15 of the atmosphere in the ESA Level 2 processor. Similar horizontal gradients of temperature or composition are sounded by the instrument line of sight with opposite sign in the ascending and the descending parts of the orbit. This sign difference causes opposite systematic errors in the profiles retrieved from the measurements acquired in the ascending and descending parts of the orbits.
In order to account for the horizontal inhomogeneities of the atmosphere, tomographic inversion codes with the capability 20 of a full two-dimensional (2D) model were developed for MIPAS (e.g. GMTR (Carlotti et al., 2006), MORSE (Dudhia et al., 2005), RET2D (von Clarmann et al., 2003) and the 2D-option of the RCP (Steck et al., 2005)), for SCIAMACHY (Scanning Imaging Absorption Spectrometer for Atmospheric Chartography) (Pukite et al., 2008) and for MLS (Microwave Limb Sounder) (Livesey et al., 2006). Given the complexity of the 2D retrieval models, von Clarmann et al. (2009) andKiefer et al. (2010) evaluated the representation of the horizontal variability of the atmosphere with a temperature (T) horizontal gradient 25 model in the MIPAS 1D retrieval codes. However, to date, the impact of neglecting the horizontal variability of the atmosphere and the relative improvements that can be achieved including a horizontal gradient model are still to be quantified. In this study we quantify the error due to the 1D assumption on MIPAS retrievals on the basis of synthetic observations produced with a highly resolved atmosphere (1.4°in latitude) derived from the chemistry climate model EMAC (ECHAM/MESSy Atmospheric Chemistry, Jöckel et al. (2006)) and the 2D FM (Forward Model internal to the GMTR system). We retrieve the 30 atmospheric state from these synthetic observations using, alternatively, the standard GMTR algorithm and three ad-hoc modified versions of the same code. The first modified version accounts for the horizontal variability by including user-supplied a-priori horizontal gradients of temperature, the second includes user-supplied gradients of atmospheric composition, while the third modified version emulates the 1D retrieval algorithm. The differences between the retrieved and the true atmospheric state profiles provide an estimate of the error caused by the retrieval approach.
The paper is structured as follows: in Sect. 2 we describe the method used to evaluate the size of the errors implied by the different retrieval approaches. In Sect. 3 we discuss the results of our tests. Finally, the conclusions are given in Sect. 4.

5
When analysing real measurements the true atmospheric state is not known. For an accurate assessment of the systematic retrieval errors due to different approaches used to account for the horizontal variability, we therefore use synthetic observations based on data from a high resolution simulation of EMAC and on a 2D FM which is as accurate as possible. We then apply different retrieval algorithms to these observations and evaluate the errors on the basis of the differences between retrieved and reference target parameters.

Atmospheric model
The reference atmosphere used to produce the synthetic spectra was extracted from a high resolution (T85 truncation, corresponding to a horizontal resolution of 1.4°x1.4°) simulation of the chemistry climate model EMAC (version 1.10;Jöckel et al. (2006)) for the year 2011. In the EMAC simulation, a Newtonian relaxation technique towards meteorological analyses for the prognostic variables temperature, vorticity, divergence and the surface pressure was implemented to reproduce realistic 15 synoptic conditions. We applied this nudging technique using the ERA-Interim reanalysis (Dee et al., 2011) from the European Centre for Medium-range Weather Forecasts (ECMWF). In this EMAC simulation a comprehensive treatment of tropospheric and stratospheric chemistry was included. Model output includes temperature, pressure, geopotential height, H 2 O, O 3 , HNO 3 , N 2 O, CH 4 , NO 2 , CFC-11, CFC-12, N 2 O 5 , ClONO 2 and CCl 4 on 39 model levels. The geopotential height at the surface was also given and used for the conversion to geometric height. To investigate possible seasonal variability of the error due to hori- The results of Kiefer et al. (2010) are based on the assumption that the average atmosphere in a given latitude band should not depend on longitude, therefore with a perfect retrieval scheme the zonal averages of retrieved parameters should be equal when computed from measurements in the ascending or descending parts of the orbit. In the case of retrieval schemes that do not consider properly the horizontal variability, a systematic difference between the averaged ascending and the descending 30 measurements will appear. We call this difference "AX-DX difference". In order to more clearly simulate this issue, we modified the above mentioned reference atmospheres to make them identical in the ascending and descending parts of each orbit.
If the error due to the measurement noise is sufficiently small, observed AX-DX differences in the retrieved data can therefore be exclusively attributed to the treatment of the horizontal variability in the retrieval.

Synthetic observations
The synthetic observations used in our analysis are produced with the 2D FM internal to the GMTR code. In this FM the discretization of the atmosphere is sufficiently fine to accurately model the small-scale structures of the reference atmosphere In order to focus our analysis on the error caused solely by the approximations in modelling the horizontal variability of temperature and the target gas, for the generation of synthetic observations we modified the reference atmosphere as follows: The observations used for the retrieval of the VMR of a given gas were generated assuming for both temperature and target  From previous studies (mentioned in Sect. 1) we know that the size of the error induced by the 1D assumption in MIPAS retrievals is comparable to that of the error due to measurement noise. Therefore, to better highlight the error induced by the horizontal variability model we avoided the masking effect of the noise error by adding to the synthetic observations a pseudo-random noise with standard deviation much smaller (a factor of 40) than that of real MIPAS measurements.

Retrieval algorithms 20
We carried out the retrievals on these synthetic observations using four algorithms. All of them were based on the GMTR algorithm of Carlotti et al. (2006).
The four algorithms, however differ in modelling the horizontal variability of the atmosphere: In the 1D algorithm the atmosphere is assumed horizontally homogeneous; in the 1D+grad(T) algorithm the atmosphere is assumed horizontally homogeneous but a prescribed horizontal temperature gradient is included; in the 1D+grad(T,VMR) algorithm the atmosphere is 25 assumed horizontally homogeneous but a prescribed horizontal gradient is included for temperature and the VMR of the target species. Finally, the full 2D atmospheric variability is modelled in the 2D algorithm.
While in the first three retrieval methods each limb scan is processed individually with a Global Fit (Carlotti, 1988) approach, in the 2D retrieval the measurements of a full orbit are simultaneously used for the retrieval of the 2D distribution (Carlotti et al., 2006). Furthermore, while in the second and third retrieval methods the horizontal gradients are externally provided by the 30 user (fixed gradients), in the 2D retrieval they are represented by the 2D retrieved distribution.
The horizontal gradients used in the 1D+grad(T) and 1D+grad(T,VMR) tests are obtained from the 1D retrieved atmosphere. Note that, in the 2D approach, a vertical profile was retrieved at the average position of each measured limb scan. Since the spacing between adjacent limb scans is of the order of 400 km, it follows that the 2D retrievals are affected by the so-called smoothing error due to a retrieval grid step coarser than the step adopted in the reference atmosphere. 5 The target profiles we retrieve from the synthetic observations are pressure, temperature (pT joint retrieval), the VMR of H 2 O, O 3 , HNO 3 , N 2 O, CH 4 and CFC-11. For the assessment of the error for each target we first retrieve pT and use it in the subsequent retrieval of the VMR of the target gas under consideration. All the retrievals are performed on a fixed altitude grid coinciding with the nominal limb-scan of the MIPAS mission after January 2004 (Raspollini et al., 2013). The altitudes of the grid are: 72, 66, 62, 58, 54, 50, 46, 43, 40, 37, 34, 31, 29, 27, 25, 23, 21, 19.5, 18, 16.5, 15, 13.5, 12, 10.5, 9, 7.5, 6 km. The 10 retrieval analysis are operated on 3 cm −1 spectral intervals (the so called Micro Windows, MWs) containing information on the target parameters (Raspollini et al., 2013) and are the same as those used for MIPAS operational data processing with the ESA Level 2 processor Version 6.

Quantifiers
In order to characterize the performance of the different approaches employed to model horizontal variability, we first group 15 the profiles resulting from synthetic retrievals (x ret ) in 15-degrees latitude bands, spanning the range from 90°N to 90°S. The latitude bands are numbered with the index k = 1, ..., 12. In each latitude band k, we then interpolate the retrieved profiles to fixed pressure levels i = 1, ..., n p and, separately for the profiles belonging to the AX and DX parts of the orbits, we calculate, for each pressure level, the following quantity: where j = 1, ..., n k numbers the retrieved (x ret (i, j)) and reference (x ref (i, j)) profiles within each latitude band k. The quantity defined in Eq. (1) represents the estimated bias, as a function of pressure and latitude band. The difference between dif f (i, k) evaluated for the AX and DX parts of the orbits, mimics the "AX-DX difference" analyzed by Kiefer et al. (2010) In Fig.s 2, 3 and 4 the average AX-DX differences in the 60°S -45°S latitude band for temperature and different target species are shown. In agreement with Kiefer et al. (2010), the AX-DX differences significantly deviate from zero for all the considered target species from the 1D retrieval. Since the reference atmosphere used to generate the synthetic observations was symmetric with respect to the South Pole and the measurement noise was very small, the observed differences can only be the different retrieval approaches. In each panel of these figures, the gray dot-dashed line represents the average noise error obtained in the standard Level 2 processing. This error will be referred to as "RND" error and is reported in the plots to evaluate the significance of the error obtained with the different models of horizontal variability. The right panels of these figures refer to the "whole orbit" scenario described in Sect. 2.4, considered to provide an overall picture of the investigated model error.
The averages of the RMSE's over selected pressure ranges for each target are reported in Table 1.

25
In the case of temperature, the 1D method provides largest RMSE in Polar Winter and Mid Latitudes conditions and the smallest RMSE in the Equatorial scenario (Fig. 5). As expected, this result correlates directly with the amplitude of the horizontal temperature gradients. The RMSE obtained for temperature in 1D retrievals is always larger than the RND error, with the exception of the pressure range from 10 to 70 hPa (≈ 19 − 31 km) in the Equatorial region. Over the whole orbit scenario, the RMSE averaged over the whole pressure range is about 1.2 K. For 1D H 2 O retrieval (Fig. 5) the smallest RMSE is obtained 30 in Polar Summer conditions, and in general the RMSE is well below the RND error. Over the whole orbit scenario, the RMSE averaged over the pressure range 0.1-70 hPa is about 5 % while it is 16 % in the 70-200 hPa range(see Table 1). In the case of O 3 (Fig. 6) scenario of the same order as the RND error. RMSE calculations for 1D HNO 3 retrievals (Fig. 6) show that the largest RMSEs are obtained for Polar Winter and Mid Latitudes conditions. In these cases the RMSE is larger than the RND error. A similar behaviour is observed for N 2 O and CH 4 (Fig. 7) with an average RMSE of 5 %. Finally, for CFC-11 we get an average RMSE of 7 % in the 25-100hPa region and 3 % in the 100-300hPa region when using the 1D approach.
These results show that the introduction of all of the models for horizontal variability produce improvements for all the 5 targets ( Table 1). The temperature RMSEs are reduced to less than 1 K when horizontal gradients are modelled and to less than 0.5 K in the case of 2D retrievals. H 2 O RMSEs can be reduced down to 3 % in the 0.1-70 hPa region and to 10 % in the 70-200 hPa region by modelling gradients. The error on O 3 reduces to a few percent below 40 hPa and above 0.2 hPa (see Fig. 6).
In the case of HNO 3 , both modelling of horizontal gradients and the 2D approach mitigate the effect of horizontal variability (only few percent differences remain) over the whole altitude range. In the case of N 2 O and CH 4 , modelling the T and VMR 10 horizontal gradients and the 2D approach greatly reduces the error, in particular in the altitude range of their peak VMRs. The CFC-11 1D retrieval is heavily influenced by the horizontal variability with a large (around 15 %) error above 100 hPa. This error can be greatly reduced when atmospheric variability is taken into account ( Fig. 4 and Fig. 7).
The modelling of a temperature horizontal gradient produces a significant reduction of the error in temperature, HNO 3 , CFC-11. H 2 O retrievals also improve partially at high altitudes. The reduction of error is marginal for the other VMR retrievals. 15 Modelling also the horizontal VMR gradient produces a further reduction of the RMSE. The largest improvements are obtained in O 3 , CH 4 and N 2 O retrievals, while H 2 O at high altitudes and CFC-11 benefit very little from this additional sophistication.
The RMSE's obtained with the 2D approach, reported in the last column of Table 1, are generally smaller than those obtained with any of the simpler horizontal gradient models. Improvements given by the use of different approaches to model horizontal gradients with respect to 1D case are summarised in Table 2.

Conclusions
In this work we quantify the error induced by neglecting the horizontal variability of the atmosphere in MIPAS retrievals, and characterize possible alternative retrieval approaches that could help to reduce this error. Our study is based on synthetic limb observations generated with an accurate 2D forward model that assumes a known atmospheric state taken from a high resolution model (EMAC). We evaluate the relative performance of some different retrieval approaches: the simple 1D model, 1D approximation becomes significant compared to noise error also in the individual retrieved profiles. For the other target parameters this effect is expected to be important only for averages of profiles.
Modelling a temperature horizontal gradient improves temperature (error reduced to 0.6 K), HNO 3 and CFC-11 retrievals (as already reported in (Kiefer et al., 2010)). The effect on the retrieval of the other considered molecules is minor. As already mentioned in Carlotti et al. (2013), this is due to the fact that the 1D retrieved temperature profiles, even if differing from the real temperature, represent "effective" profiles that partially compensate for the horizontal inhomogeneity error. Thus, modelling the horizontal temperature gradient improves the accuracy of the temperatures but only marginally the quality of 5 some retrieved VMRs. The amplitude of this compensation effect depends on MWs used.
Modelling both temperature and VMR gradients reduces the error to 3-10% for H 2 O, 2-9% for O 3 , 4-9% for HNO 3 , 4% for N 2 O, 3% for CH 4 while no improvement is obtained for CFC-11. The improvements obtained for O 3 , CH 4 and N 2 O are particularly important, also because they are concentrated in the altitude region where the VMRs have their maximum values.
The horizontal temperature and VMR gradient values used in our tests are derived from the corresponding atmospheric 10 fields retrieved with the 1D assumption. We consider these gradients relatively accurate. We verified, however, that using less accurate gradients, such as those that can be inferred e.g. from ECMWF analyses, usually produces a less significant reduction of the retrieval error.
The 2D retrieval approach produces the smallest error in modelling the horizontal variability of the atmosphere. We note that the real benefits of the 2D approach are even more evident when looking at the vertical distribution of the errors: the 2D