Trace gas retrieval from AIUS : Algorithm description 2 and O 3 retrieval assessment 3

AIUS (Atmospheric Infrared Ultraspectral Sounder) is an infrared occultation 14 spectrometer onboard the Chinese GaoFen-5 satellite, which covers a spectral range of 2.4--13.3 μm 15 (750--4100 cm-1) with a spectral resolution of about 0.02 cm-1. AIUS is designed to measure and 16 study chemical processes of ozone (O3) and other trace gases in the upper troposphere and 17 stratosphere around Antarctic. In this study, the corresponding retrieval methodology is described. 18 The retrieval simulations based on the simulated spectra of AIUS have been carried out, with a 19 focus on O3. The relative difference between the retrieved and the true O3 profiles is within 5% from 20 the 15km to 70km and about 10% below 15km. The corresponding averaging kernels illustrate that 21 the overall retrieval information mainly come from the spectra, not the a priori. The retrieval 22 experiments also demonstrate that the shape of the retrieved profiles resembles the shape of the 23 true profile even if the shape of the a priori profile is different from that of the true profile. Further, 24 we perform the O3 retrieval from the real ACE-FTS (Atmospheric Chemistry Experiment-Fourier 25 Transform Spectrometer) measurements and compare the results with the official ACE-FTS Level-2 26 products. Overall, both profiles agree well in the stratosphere where the retrieval sensitivity is 27 high. The relative difference between both profiles is about 15% below 70km, which may due to the 28 measurement errors and different forward model parameters. 29


Introduction
The annual occurrence of the Antarctic ozone hole has been well documented.For studying ozone recovery, many efforts have been made to understand the chemical and dynamical processes around Antarctic [1][2][3].Occultation and limb sounding techniques have provided an important way for remotely observing Earth's middle atmosphere.These measurements have greatly promoted our understanding of the chemical process of atmospheric composition in the upper troposphere and stratosphere by providing profiles measurments with different altitudes.As compared to nadir-viewing measurements, occultation/limb sounding measurements have higher vertical resolution, which can be used to derive vertical information of atmospheric components.Furthermore, high-resolution atmospheric mid-infrared spectra are suitable for detection of many trace species, since a wide variety of vibrational-rotational bands with molecular absorption lines are found within this spectral range.Recently, many occultation observation/limb sounding sensors have been developed and provided abundant profiles of trace gases, such as O3, CO, H2O, NO, etc [4][5][6][7][8][9].
AIUS is one of six payloads onboard the Chinese GaoFen-5 satellite that is expected to launch in May, 2018.AIUS is the first occultation spectrometer developed in China, which is designed to detect the trace gases over the Antarctic.AIUS will operate in a solar synchronous orbit, with a nominal height of 700 km.The instrument is a Fourier transform infrared spectrometer and its main objective is to measure the O3 and other species in the stratosphere and upper troposphere in order to study the ozone change over the Antarctic.
The aim of this study is to introduce the trace gas retrieval algorithm developed for AIUS and to assess its performance based on ozone retrievals.In Section 2, the instrument parameters and level 1 processing of AIUS are introduced briefly.Section 3 describes the retrieval algorithm in detail.
Integrated atmosphere profiles dataset is presented and a sensitivity analysis of atmosphere profiles is showed in Section 4. In Section 5, the simulated spectra and the ACE-FTS observation spectra are adopted to retrieve O3 profiles and to assess the retrieval performance.

AIUS instrument
AIUS is a Fourier transform infrared spectrometer for the detection of occultation transmittance spectra in the middle and upper atmosphere, which has similar characteristics to ACE-FTS.Both instruments have a spectral resolution of 0.02 cm -1 .AIUS covers the spectral range from 750 cm -1 to 4100 cm -1 , while ACE-FTS covers 750--4400 cm -1 .It is a dual-band system composed of MCT (mercury cadmium telluride, 750--1850 cm -1 ) and InSb (1850--4160 cm -1 ).AIUS covers an altitude range from 8 to 100 km and has a field of view of 1.25 mrad.The latitude coverage of AIUS measurements is about 55°S to 90°S, which is mostly over Antarctica.GF5-AIUS level 0 is original auxiliary and interferogram data in binary format and level 1 is HDF5 format file includes reconstructed spectra and processed auxiliary data.GF5-AIUS level 0 to level 1 processing includes three steps.The first step is the acquisition and processing of auxiliary data.By unpacketizing the auxiliary data package, the information of observation, such as acquisition time, sun position and satellite position, is acquired.The geometric parameters, the height and the latitude and longitude coordinates, are calculated from the information of the sun and satellite.The second step is to reconstruct the spectra from the original interferogram.However, since the AIUS is an interferometer, the interferogram will contain some spikes produced by the effect of energetic particles due to space electromagnetic environment on orbit, which will contaminate the complete spectra.Thus, some processes have to be involved to correct these errors.
The nonlinear behavior of the detectors is expected and characterized on-ground, which requires an additional correction.This nonlinearity correction will be consolidated in-flight using commissioning phase data.After that, the FFT is performed to compute the spectra.The last step is to evaluate the spectra's quality by standard deviation or mean value of imaginary part of the calculated spectra and then make the mark to show if the spectra is well reconstructed."0" is for good quality and "1" for bad quality.
Level 1 data is the spectra data which are the relative intensities of each tangent heights using DN (digital number) values.Our inversion takes the transmittance converted from the Level 1 data.
In addition to the observation of the Sun outside and inside the atmosphere, GF5-AIUS also observes the deep space to remove the instrumental emission.Commonly, the transmittance (ℎ, ) at tangent point h of wave number can be calculated by the following equation: Where (ℎ, ), ( ) and ( ) are the digital counts of the observation of signal at tangent point h, the solar radiation outside atmosphere and the deep space signal.

Retrieval methodology of AIUS
Accurate knowledge of pointing and p/T information is important to high-precision quantitative retrieval of abundances of atmospheric species from occultation observed transmittances.The tangent height correction for AIUS is carried out by employing the triangular iteration with tangential strides technique in a microwindow of N2 continuum absorption, whereas the scheme of p/T retrieval is by introducing the hydrostatic equation into the iterative process of optimal algorithm.Details of the design and development of these two algorithms are introduced in our other two papers in preparation.

Inversion model
The inversion algorithm employed in this study is based on OEM (Optimal Estimation Method) proposed by Rodgers [10].Since OEM is generally applicable and facilitates a theoretical error analysis, this method has been widely used in the inversion of atmospheric state parameters using infrared and microwave remote sensing measurements, with nadir, occultation or limb viewing [11][12][13][14][15][16].OEM stabilizes the inversion process by taking into account the statistical information about the atmospheric variability, which has been investigated by many studies [17][18][19][20][21][22][23].
Our inversion scheme is adapted from the retrieval software Qpack 2.0 [23] that uses LM (Levenberg-Marquardt) approach for a nonlinear least squares fitting.The LM iteration method adopted in the Qpack is the same as the LM iteration method modified by Rodgers [17].By introducing a constraint factor γ, the next iterate is yielded by: The inverse of the solution covariance in equation ( 2) is given by： And the cost function ( ) is given by: where is the forward model, is a series of observations value, is the state of the atmosphere, is the covariance matrix of the observation error and is the matrix of weighting function.The a priori state vector is denoted by , with its covariance matrix And is the number of vector.
In our retrieval scheme, retrieval experiments are made based on many simulated spectra and ACE-FTS observation data to decide an optimal choice of γ.After statistical analysis, the factor of γ is defined as a linear scaled function to the cost function.It will be updated at each iteration, which is given by the following equation.Here, is a constant and it is different for different atmospheric species.
The definition of the a priori covariance matrix follows Gaussian statistics and considers the correlation between different components of the state vector and the forward model vector.Different types of the correlation function [24] for computing the correlation have been tested based on the retrievals from simulated and observed ACE-FTS data.In this study, we employ the linear correlation function: where i and j are position indexes, z is the position, lc is the correlation length and |*| signifies the absolute value.σ is the standard deviation calculated from the a priori.
In the retrieval scheme of AIUS, we adopt the " " in the Qpack 2.0 as the threshold of convergence.The iteration is considered converged in the condition that the value of is smaller than 0.01.The definition of is that: where is the length of the state vector.

Adopted forward model
An accurate modeling of the radiative transfer through the atmosphere plays an important role in the inversion.The forward model adopted in the retrieval algorithm of AIUS is the RFM (Reference Forward Model) with the latest release version v4.36 [25].RFM is a GENLN2-based 4. Continua for H2O, O2, N2 and CO2 are included [27][28][29][30][31].
For all considered microwidows, scattering can be negligible and is not taken into accout in our retrieval scheme.

Microwindows
The spectral resolution of AIUS is about 0.02 cm-1.Because of this, the number of data points from each absorption band becomes unrealistic for an efficient inversion process.Furthermore, one should avoid the effect of interfering species on the retrieval of the target species and have the best information on the retrieval.Thus, the retrieval is performed using a set of narrow spectral interval (called "microwindow") instead of an entire spectral band.
To select an appropriate set of microwindows, a sensitivity analysis with Jacobians is required.
First of all, we select the spectral points which are sensitive to the target gas on each cutting height and are not sensitive to the interference gas according to the Jacobians of target and the interference species.Then, the selected spectral points are grown on the basis of information entropy to generate a series of continuous window.Finally, all the selected microwindows at different tangent height are combined.
The absorption lines of O3 in the infrared band are mainly located near 9.6 μm and the main interfering gases of O3 in this spectral band include CO2, H2O and N2O.The chosen microwindows for O3 retrieval are shown in Figure 1.For O3 retrieval, about 20 microwindows are selected, covering from 5 km to 95 km.Microwindows in the range of 1000--1070 cm -1 are sensitive at higher altitudes, while others are sensitive at lower altitudes.Figure 1 The microwindows selected for O3 retrieval.

Integrated Atmospheric profiles
The forward model generates a numerical simulation of measurements based on the given atmospheric state.In other words, the accuracy of the simulated measurements depends on the reliability of the atmospheric parameters used in the forward model.In our retrieval scheme, we  The next step is to combine the two sets of profiles.Since ACE-FTS and AIUS have similar instrument characteristics, the ACE-FTS product is chosen in case that the profile of a particular species at the same geolocation and time can be found in both ACE-FTS and MLS datasets.Finally, profiles of the missing species are read from the AFGL dataset.The species profiles imported from AFGL dataset include NH3, HBr, HI, PH3, H2S, F11, F12, F13, F21, F22, F114, F115 and HNO4.These species profiles from FASCOD (Fast Atmospheric Signature Code) Model 1-6 are resampled and packed into the monthly geographic grids.In the end, the integrated atmospheric species profiles dataset is produced.

Data simulation and sensitivity analysis
A comparison between the integrated atmospheric and AFGL profiles is carried out by simulating the ACE-FTS spectra.The simulation is made with the geolocation and geometry parameters of the ACE-FTS instrument.Figures 3 and 4 compare the simulated ACE-FTS using the two atmospheric profiles database to the observed spectra in two spectra ranges.The simulated spectra 1 and 2 stand for the ones using the integrated atmospheric and AFGL profiles, respectively.Figures 3 and 4 show that in both spectral ranges, the simulated spectra using the integrated atmospheric profiles are obviously more close to the ACE-FTS observed spectra than those using the AFGL atmospheric profiles.The two comparison experiments demonstrate that the simulated spectra are very sensitive to the atmospheric profiles and that the simulated spectra using the dataset of integrated atmospheric profiles agree well to the actual measurements.The O3 retrieval performance is first assessed by using simulated measurements.The microwindows selected in section 3.3 are adopted.Two O3 profiles picked from two grids of the integrated atmospheric dataset (75°S, 150°W in October and 65°S, 90°E in March) are taken as the true profiles to simulate spectra of AIUS.Then, the artificial noise with SNR = 300 is added to the simulated spectra.Details of retrieval configuration are specified in Table 1.The retrieved profiles are shown in Figure 5 and 6.The a priori, true profile and retrieval profile of O3 are shown in figure 5(a) and 6(a).The shape and the values of retrieval profiles are consistent with the true profiles.The relative difference between the retrieval and true profiles presented in figure 5(b) and 6(b) shows that it is within ±5% below 60 km, within ±7% from 60 km to 80 km.The averaging kernels in figure 5(c) and 6(c) illustrate that the retrieval information mainly comes from the measurements.As the residual in both experiments seems nearly identical, only the one in the first experiment is shown in Figure 7.The lowest to the highest tangent heights is from left to right.The residuals at each tangent height are within ±0.02, which are very small.

Assessment of retrieval algorithm based on simulated spectra
Figure 7 The residuals of the first retrieval experiment.
In the above retrieval experiments, = 0.8 • _ , but the shape is same.Thus, more retrieval experiments are made to assessment the dependence of the AIUS algorithm on the shape of the a prior profile.In this experiment, the ACE-FTS O3 level 2 products are taken as the true profiles.
The information of five products selected is shown in table 2. The a prior profiles are from the mean monthly profiles of MLS O3 level 2 products, which indicates that the shape of the a prior profiles can be different from that of the true profiles.Similarly, the artificial noise with same SNR is added randomly to the simulated spectra.O3 retrieval is performed and the results for these five retrieval experiments are similar.Thus, only results of two retrieval experiments using the O3 products from scenes of 40993 and 38154 are presented in Figures 8 and 9, respectively.The two scenes are located in Antarctica and Arctic, respectively.Figures 8(a) and 9(a) show that the shape of the retrieval profiles is almost the same with the true profiles even that the shape of the a prior profiles is different from that of the true profiles.
Figures 8(b) and 9(b) illustrate that the relative difference between the retrieval O3 profiles and the true O3 profiles is almost within 5% from 10 km to 70 km, about 10% near 10 km.However, the relative difference will reach beyond 30%.The reasons may be due to the low concentration of O3 profiles and the retrieval above 70 km is dominated by the a priori information The averaging kernels in Figures 8(c) and 9(c) are similar as those in Figures 5(c) and 6(c), which indicate that the retrieval information mainly comes from the measurement in the troposphere and stratosphere.We also check the residuals of these five retrieval experiments, which are consistent with the residuals in Figure 7.All residuals of these five retrieval experiments are within ±0.02.
The retrieval experiments using synthetic AIUS spectra demonstrate that the algorithm produces reasonable results and sufficient retrieval sensitivity.

O3 retrieval based on ACE-FTS measurements
Under real-world conditions, in addition to the thermal noise of the instrument, the actual measurements are influenced by more factors.To evaluate the influence of various uncertainties on the retrieval algorithm of AIUS, we adopt the level 1 products of ACE-FTS to perform the O3 retrieval experiments, as AIUS expects to perform measurements with similar characteristics.All the a prior profiles of O3 and other species are taken from the dataset of integrated atmospheric profiles.
The level 1products used are those five scenes of ACE-FTS observation data in table 2. Since the results for these five retrieval experiments are similar, only results of two retrieval experiments from scene 40993 and 38154 are presented.8(c) and 9(c), it still reveals that the retrieval information mainly comes from the measurement in the stratosphere.The statistical analysis of the residuals demonstrate that about 90% residuals are within ±0.02, with some points reaching ±0.06, demonstrating the retrieval fits very well.Our algorithm dedicated to AIUS performs stable and delivers comparable results using ACE-FTS real measurements.

Discussion and conclusions
In this study, we have introduced a retrieval algorithm developed for an infrared occultation spectrometer called AIUS.The retrieval algorithm comprises a forward model based on RFM and an OEM framework adapted from Qpack, which employs the LM iteration method.The retrieval experiments of ozone retrievals were carried out based on simulated spectra and ACE-FTS measurements.
In the condition of experiments on simulated spectra, there are some differences depending on the profile shape of the a prior.When the shape of the a prior is the same as the true profile, the relative difference between the retrieval profile and the true profile is within ±5% below 60 km and within 7% in the range of 60-80 km.When the shape of the a prior is and the true profile is different, the retrieval profile shape still keep close to the true profile.The relative difference is a litter bigger.
It is mainly within 5% below 60 km, but can reach 10% near 10 km and 10-15% from 60 km to 70 km.
However, the relative difference is in a reasonable range.And the averaging kernels achieved illustrate that the retrieval information mainly comes from the simulated observation spectra.Thus the retrieval experiments based on simulated spectra indicate that the retrieval algorithm of AIUS work fine and successful.
When it comes to experiments based on ACE-FTS observation data, the retrieval algorithm of AIUS also behaves well.The retrieval experiments show that the relative differences between them are greater than those in the retrieval experiments using simulated spectra.The greater relative differences may be produced by the following reasons.Firstly, although the instrument parameters AIUS and FTS are similar, there must be different in some of the details.Thus, some errors will be brought by using ACE-FTS observation spectra as the AIUS observation spectra.Secondly, the ACE-FTS levels are not the true profiles.They also have uncertainties, which will make the relative difference greater.The last and the most important reason is the greater uncertainty of the observed spectra, which will generate some errors between the simulated spectra by the forward model and the observation spectra in the retrieval process.Nevertheless, the retrieval profiles still agree well with the ACE-FTS level 2 products and the range of the relative differences is satisfactory.
All the retrieval experiments based on the simulated spectra and the measured spectra of ACE-FTS indicate that the retrieval algorithm of AIUS is reliable and robust.Overall, the retrieval profiles agree well with the true profiles or the ACE-FTS level 2 profiles.However, the uncertainties of the retrieval profiles at lower tangent height are still requiring further investigations.After the instrument is launched, we will improve the retrieval algorithm by fine-tuning the forward model parameters according to the characteristics of the AIUS observed spectra and the instrument performance.In addition, an extensive retrieval error characterization is on-going and will be consolidated during the operational phase.
compute a dataset of integrated atmospheric profiles based on MLS (Microwave Limb Sounder) level 2 products, ACE-FTS level 2 products and the profiles from AFGL(Air Force Geophysics Laboratory) atmospheric models.The ACE-FTS level 2 v3.6 and the MLS level 2 (v4.2) products between 2014 and 2016 are considered.We classify and store the species profiles month by month for each set of products.Then, the monthly mean profiles are acquired and classified into different coordinate grids, which is discretized with a 5° latitude and 30° longitude spacing..That is, both of two set of dataset are classified by month and coordinate grid.A diagram of constructing the integrated atmospheric profiles is shown in Figure 2.

Figure 2
Figure2The technological process of constructing the integrated atmospheric profiles.

Figure 5
Figure 5 O3 retrieval experiment based on simulated spectra at 75°S, 150°W in October.(a)Retrieved profile; (b) Relative difference between retrieved and true profiles; (c) Averaging kernel.

Figure 6 O3
Figure 6 O3 retrieval experiment based on simulated spectra at 65°S, 90°E in March.(a)Retrieved profile; (b) Relative difference between retrieved and true profile; (c) Averaging kernel.

Figure 8 Figure 9
Figure 8 O3 retrieval experiment based on O3 product from scene 40993 of ACE-FTS.(a)Retrieved profile; (b) Relative difference between retrieved and true profile; (c) Averaging kernel.

Figure 10 O3
Figure 10 O3 retrieval experiment based on FTS observation spectra from scene 40993.(a)Retrieved profile; (b) Relative difference between retrieved and FTS level 2 product; (c) Averaging kernel.

Figure 11
Figure 11 O3 retrieval experiment based on FTS observation spectra from scene 38154.(a)Retrieved profile; (b) Relative difference between retrieved and FTS level 2 product; (c) Averaging kernel.
[26]-by-line radiative transfer model originally developed at AOPP, Oxford University, under an ESA contract to provide reference spectral calculations for the MIPAS (The Michelson Interferometer for Passive Atmospheric Sounding) instrument launched on the ENVISAT (Environmental Satellite) in 2002.It has been subsequently developed into a general purpose code suitable for a variety of different spectroscopic calculations.Von Clarmann[26]has compared five forward models including the RFM.The inter-comparison experiment showed that the overall inter-consistency of spectra for all participants is good, which also can demonstrate that the RFM works fine and reliable.
2. It can provide Jacobians for p, T, VMR, line-of-sight pointing and surface temperature and emissivity.3.Cross sections can be computed from HITRAN (High-resolution Transmission) spectroscopic database or read from external files.

Table 2
Information of O3 L2 products from ACE-FTS.
The relative difference of these two retrieval experiment below 70 km is mainly within 10%, with some points reach 15%-20%.The relative difference here is larger mainly because of the uncertainties in the measurements and different forward model parameters.The bias of the ACE-FTS O3 products is +1 to +8% in the stratosphere(16-44 km)and can be up to +40% (+20% on average) above 45 km(Jones A., et al., 2012;     Dupuy E., et al., 2009).Although the averaging kernels in Figures10(c) and 11(c) are somewhat broader than those in Figures