The forward model: σ-IASI

The radiative transfer code σ-IASI [Amato et al. 2002] consists of a monochromatic radiative transfer model, which has been designed for the fast computation of spectral radiance and its derivatives (Jacobian) with respect to a given set of geophysical parameters.

The forward model σ-IASI has been initially developed in the framework of a long collaboration between UniBas (formerly DIFA (Department of Environmental Engineering and Physics of the University of Basilicata) and EUMETSAT to assist the various developing phases of IASI.

The code uses a look-up table for the optical depth. The look-up table is derived from the LBLRTM (Line-by-Line Radiative Transfer Model) model (e.g., the latest version of σ-IASI uses LBLRTM version 12.2). The forward module is based on 60 pressure layers, spanning the atmosphere from the ground level to the top level assumed to be at 0.005 hPa. The model computes spectral radiances and analytical Jacobian derivatives of any surface (ground or thick cloud if needed) and/or atmospheric parameter.

IASI radiances are obtained through convolution with the IASI Instrumental Spectral Response Function (ISRF). LBLRTM and σ-IASI share the same spectral line library. This is the Atmospheric Environmental Research or AER v_3.2 line parameter database with the continuum absorption MT_CKD 2.5.2 (e.g. see http://rtweb.aer.com/lblrtm_frame.html ). The AER line database adopts HITRAN2008 with exceptions for H2O, CO2, and O2. For what concerns the IASI spectral range, the H2O line positions and intensities for the wavenumber region from 10 to 2500 cm-1 are from [Coudert et al., 2008] ; CO2 absorption optical depth calculations take advantage of the first order line coupling coefficients re-calculated using the formalism of [Niro et al., 2005].

In the published version of σ-IASI, the atmospheric state vector is specified by surface temperature and emissivity, atmospheric profiles of temperature, plus mixing ratios profiles of H2O, HDO, CO2, O3, N2O, CO, CH4, HNO3, SO2, NH3, OCS, CF4. Apart from these species whose concentration can be varied, hence retrieved, σ-IASI also considers a set of fixed species that are considered in the construction of the forward model. The set includes the major species N2 and O2, which are taken into account through their collision-induced continuum. In addition, σ-IASI can consider other trace gases, such as NO, NO2, OH, HCl, H2CO, HCN, CH3Cl, and C2H2. The reference vertical profiles of these molecules are fixed according to the US Standard atmosphere model [Anderson, 1986]. Fixed gases include also heavy molecules whose radiative effect is modeled through cross-sections. They are CCl4, CFC-11, CFC-12 and HCFC-22. For these heavy molecules, we use the original cross-sections from HITRAN2008, meaning that their spectral optical depth is not converted to the look-up table. As for other gases, their vertical mixing ratio is modeled according to [Anderson, 1986] and scaled for column abundance consistently with the most recent World Data Center for Greenhouse Gases report (WDCGG).

In its most recent version, new input species have been added explicitly to the state vector of σ-IASI. This could possibly be done also for the mixing ratio profiles HCl, H2S, C2H2, C2H4, and HCN. These species can thus be easily included in the retrieved state vector of the inverse scheme, δ-IASI [Carissimo et al. 2005].

Although initially developed for IASI, σ-IASI is presently a generic radiative transfer model, which is well suited for nadir viewing satellite and aircraft infrared sensors with spectral sampling intervals in the range of 0.1-2 cm-1. It covers the spectral range between 5 and 2760 cm-1 [Serio et al. 2008].

The software was developed in Fortran and tested to run on Linux platforms and MS Windows. In its latest version [Liuzzi et al., 2017] the model can deal with clouds and aerosol. Clouds and aerosols are specified with their own profile and transmittance calculations are performed at the level of the single layers, the same as for gas species.

Multiple scattering of clouds and particles is dealt with by a scaling scheme following [Chou et al., 1999], where particle scattering contribution is accounted for by replacing the optical depth with an apparent optical depth for extinction. Recently, thanks to a collaboration with UniBO (Department of Physics and Astronomy, University of Bologna) supported by a program of the Italian Space Agency, a new and accurate parametrization [Martinazzo et al. 2021] dealt with clouds and aerosol optical parameters as a function of their a) concentration; b) effective radii. Thanks to this original parameterization, the current version of σ-IASI is the only fast-forward model capable of computing analytical Jacobian derivatives with respect to ice and water content concentrations and respect to the effective radius. Thus, the new σ-IASI model yields for retrieving cloud microphysical properties.

The code is very fast and the computation of one single spectrum takes less than 0.5 s on an Intel Core i7-412HQ CPU @2.30 GHz.

The current version performs analytical derivatives of radiative transfer equation with respect the following parameters:

• Atmospheric Temperature

• Surface Emissivity

• Surface Temperature

• H2O, HDO, CO2, O3, N2O, CO, CH4, HNO3, SO2, NH3, OCS, and CF4 Atmospheric profiles

• liquid and ice water cloud concentration profiles

• liquid and ice water effective radii profiles

• H2O self continuum coefficients

• H2O foreign continuum coefficients

• CO2 foreign continuum coefficients.

It is available here doi:10.5281/zenodo.8152674.