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).
