KLIMA-IASI upgrades in forward and inverse modeling

The main upgrades introduced in the KLIMA-IASI code with respect to the MARC and REFIR retrieval systems concerned:

• The implementation of a new interface (the pre-processor) between the input data required for the inversion of IASI spectra and the KLIMA-IASI processor (i.e., IASI Level 1b and Level 2 products and auxiliary data)
• The modifications of the FM and RM modules, aimed at improving the accuracy of the simulation (e.g., use of a band dependant surface emissivity), at modelling the instrumental features of the IASI spectrometer (Instrument Spectral Response Function, Radiometric Noise, Field of View) and at providing, as part of the retrieval products, CO₂ column values and errors.

Here we focus on the new features of the KLIMA–IASI processor, which are individually described in the following sub-sections.

Use of an atmospheric vertical grid expressed in terms of pressure

The stratification of the atmosphere adopted for the RT calculations and the vertical retrieval grid are both expressed in terms of pressure levels. The corresponding altitude levels can be reconstructed from the temperature profile, assuming hydrostatic equilibrium. This choice facilitate the comparison with the assimilated profiles generally provided on a pressure grid (e.g., ECMWF fields, Carbon Tracker model output). Moreover, the pressure grid is independent on the orography of the surface, and the information provided by IASI L2 on the pressure at the Earth surface is sufficient to reconstruct the stratified atmospheric structure.

Surface Emissivity

The Earth’s surface emissivity model has been modified, in order to exploit the band dependent emissivity information available from IASI L2 operational products. IASI emissivity values are provided as average values over 12 spectral bands from ~770 cm^-1 (13 mm) to ~2777 cm^-1 (3.6 mm). The KLIMA-IASI code has been designed to perform forward model calculations over the IASI spectral range subdivided in 47 independent band 45 cm^-1 wide. The spectral radiance measured in each band can thus be simulated using the corresponding Earth’s surface emissivity value as obtained from IASI L2 products (whenever a valid IASI L2 emissivity value is not provided, surface emissivity equal to 1 is assumed). A band dependent value of Earth’s surface temperature is accordingly retrieved, when this quantity is included in the state vector.

Retrieval of columnar values

Columnar values have been added to the standard output of the inversion process, in order to provide direct access to the information on total and partial columns of the retrieved atmospheric constituents and, in particular, of carbon dioxide. For each retrieved species the KLIMA code outputs the differential column profile on the atmospheric grid on which the forward model performs the radiative transfer calculation. Taking into account the linear relationship between the vertical VMR profile of a species x_vmr and the associated profile of differential columns y_column, it is straightforward to calculate the VCM of the latter:

y_column = J x_vcm

where J is the Jacobian matrix of the differential column profile with respect to the VMR profile.

If we indicate with VCM_y and VCM_x the variance-covariance matrix of the differential column and of the VMR profile, respectively, we can write:

VCM_y = J VCM_x J^T

The total column can be calculated by adding up all the elements of the differential column profile vector (or, for partial columns, of the elements in the pressure range of interest). Correspondingly the VCM of the total column is the sum of all the elements of the differential column VCM. If a multi-target retrieval approach is adopted, including the interfering species as part of the state vector and other uncertainties on FM parameters in the a priori VCM, the VCM of the retrieved products accounts for the total error budget. This property holds also for the VCM of the differential column profile.

Measurement Space Solution Method

The standard output of the KLIMA-IASI processor provides the set of input data required to perform the calculations of the Measurement Space Solution Method. A detailed descritpion of the method can be found in the paper by (Ceccherini et al., 2009).

IASI Instrument Spectral Response Function

The IASI Instrument Spectral Response Function (ISRF) may be calculated from the data provided by EUMETSAT, via the UMARF archive, in the file:

IASI_SDB_xx_M02_20070705200000Z_20070705200000Z_20070705161317Z_IAST_IASISPECDB.nat

As explained in detail in IASI Level 1 product guide, the ISFR depends on the IFOV number, the corner cube direction and on wave number. Figure 1 shows the average ISRF between ±16 cm^-1.

Figure 2 shows the standard deviation of the ISRF with respect to the IFOV number, the corner cube direction and averaged on the wave number. The standard deviations are always less than 1%. As a consequence, the dependence on the IFOV number and on the corner cube direction can be neglected, and only the wave number dependence is taken into account by the KLIMA-IASI FM.

Figure 1

IASI ISRF averaged on all the dependences between ± 16 cm^-1

Figure 2

Standard deviation of the ISRF with respect to the IFOV number,

the corner cube direction and averaged on the wave number between ± 16 cm^-1

The sounder spectra database provides an undersampled ISRF (typical spectral sampling interval 15 cm^-1).

Figure 3 shows some example of the under-sampled ISRF. The associated standard deviations with respect to the IFOV number, the corner cube direction are shown in Figure 4. This figure shows that the standard deviation increases with increasing wave number, but is always less than 3%. These smooth functions can now be used to over-sample every needed wave number. The KLIMA algorithm interpolates the under-sampled ISRF to obtain a frequency dependent ISRF.

Figure 3

IASI ISRF provided for 650, 1350, 2055, and 2700 cm^-1

Figure 4

Standard deviation of the IASI ISRF with respect to the IFOV number,

he corner cube direction related to the wave numbers reported in Figure 3

IASI Field of View

The IASI Instantaneous Field of View (IFOV) has a diameter of 14.65 mrad, which corresponds to a ground resolution of 12 km at nadir and a satellite altitude of 819 km (see IASI Level 1 Products Guide). For homogenous horizontal atmosphere and homogenous surface, the FOV effect is negligible. In Figure 5 we show the difference between simulated spectral radiance at nadir and at +5 deg from nadir (corresponding to a FOV with ground resolution of 50 km). The difference is compared with the nominal noise of IASI instrument.

Figure 5

IASI Field of View Effect

Basic features of KLIMA

forward and inverse models

The KLIMA algorithm consists of two distinct modules, that can operate independently to produce simulated observations or be combined for inverse processing of real or synthetic data: the Forward Model and the Retrieval Model. The Forward Model (FM) simulates wideband nadir radiances measured at the top of the atmosphere using line-by-line Radiative Transfer (RT) calculation. The code computes the radiance that reaches the instrument, and simulates the instrumental effects. Assuming a uniform layered atmosphere, the RT is implemented using the Curtis-Godson (Houghton, 2002) values of temperature and pressure for each species in each layer. The atmospheric line-shapes are modelled with a modified Voigt profile in which the Lorentz function is replaced with the Van Vleck-Weisskopf function (Van Vleck and Weisskopf, 1945). The spectroscopic database used for the simulations is HITRAN 2004 (Rothman et al., 2005) with recent updates for the air broadened half widths provided by Gordon et al. (2007). The atmospheric continuum is modelled according to the work by Clough et al. (2005) considering the contribution of water vapour lines external to the region of 25 cm^-1 from the line centre.

For CO₂ a dedicated spectroscopic database and line-shape has been adopted in order to take into account the line-mixing effect (Niro et al., 2005a,b). The retrieval procedure (Carli et al., 2007) is designed as a global-fit, multi-target retrieval, based on the constrained Non-linear Least-Square Fit (NLSF) approach: the cost function to be minimized takes into account the a priori information (Optimal Estimation approach) and the Marquardt parameter (Rodgers, 2000). Tsimultaneously he retrieval algorithm enables us to fit the wideband spectrum to find more quantities (multi-target retrieval) in order to best account for the errors due to the interfering unknowns. Alternatively, the systematic effects can be taken into account using the complete variance-covariance matrix (VCM) defined as the VCM of the measurement errors plus the VCM of the errors in the estimates of the FM parameters (systematic errors).Von Clarmann et al. (2001) have demonstrated that in a retrieval that converges at the first iteration the two procedures provide the same results for the single target. Retrieval tests have also shown that in the case of strong interferences the non-linear effects become significant and that the properties demonstrated by von Clarmann, which are valid for a single iteration, are no longer verified. In this case, the non-linearities of the inversion problem are better handled by using the multi-target retrieval approach. The results of these tests are in agreement with the conclusions reached by Livesey et al., (2006) who account for the interference of the temperature error in the VCM of the retrieval, but adopt at the same time a two-step retrieval, in order to make sure that a single iteration is sufficient in the second step. Therefore, for the adaptation of the KLIMA algorithms to the processing of IASI data we will implement this second procedure. A procedure that adopts multi-target retrieval for the interfering species and a complete VCM for the other FM uncertainties does reduce the effects of systematic errors (because the retrieval procedure weights the individual measurements according to their total error and correlations) and makes possible the exploitation of broad band measurements (because the systematic errors are no longer a constraint that imposes the use of microwindows).

Heritage of the MARC and REFIR

retrieval codes

The KLIMA-IASI Retrieval Code

In this section, a general overview of the KLIMA-IASI prototype software system, as resulting from the adaptation and optimisation work undertaken during Phase 1 of the project, is presented. A brief description of the retrieval code is given, summarizing the basic features of the forward and inverse models. along with the heritage of previously developed codes which have been designed and implemented for different applications. The characteristics of the program, which are directly inherited from existing algorithms, are identified and reference is made to technical documentation and to scientific literature for background information and more detailed description of common choices adopted for forward and inverse modelling by both the KLIMA-IASI and its precursors. The main focus of the section is on the elements of innovation introduced in the KLIMA-IASI retrieval code and on new methodologies that are proposed for both data analysis and diagnostic purposes.

• Basic features of KLIMA forward and inverse model

• Heritage of the MARC and REFIR retrieval codes

• KLIMA-IASI upgrades in forward and inverse modelling