# 4A Description

Calculating transmittances, jacobians, radiances and fluxes for a given input of atmospheric and surface conditions is known as forward modelling. Basically, both research and operational studies require fast, accurate and tractable forward models.

Applications of fast forward models include:

- the simulation of high spectral resolution radiances and study of their sensitivity to surface and atmospheric variables to interface NWP models.
- the selection of the best possible spectral intervals for the retrieval of atmospheric and surface parameters,
- the investigation of the dynamic range of variation of radiances received at the satellite as a function of spectral and atmospheric variables,
- modelling of the Earth radiation budget, simulations of atmospheric cooling rates and radiative forcing
- the generation of observations to be used in simulation studies (retrievals, validation processes, direct assimilations, etc.),

For many years, several generations of forward models have been derived which have become more and more accurate and efficient through the exploitation of new mathematical techniques, the development of new approximation in the models to save computational time, the provision of better spectroscopic data and the availability of faster and faster computer systems.

The 4A line-by-line model to calculate forward radiative transfer is an advanced version of the nominal line-by-line STRANSAC. Both of them rely upon the information contained in the GEISA spectroscopic database.

Since 4A saves all the characteristics of a genuine line-by-line code, any kind of apparatus function may be used at the time of the convolution. 4A is and has been used for many different applications including low and high resolution spectra of the earth atmosphere (not only HIRS but also AVHRR, METEOSAT, AIRS, IASI, …,) and spectra of planetary atmospheres (e.g. within the frame of the VOYAGER mission to giant planets).

Our models have a long history of validation in the international radiative transfer community.

Most of the validation results have been extensively discussed in a number of intercomparison exercises and in particular during the ITRA (Intercomparison of Transmittance and Radiance Algorithms) working groups – 1983, 1985, 1988, 1991 of the International Radiation Commission.(see e.g. Chédin et al., 1988) and during the ICRCCM (Intercomparison of Radiation Codes in Climate Models ) campaigns (see e.g. F. Luther et al. 1988).

More recent (between years 2000 and 2003) validation campaigns have been considered to evaluate the performances of the 4A model: results are given in (Soden et al., Garand et al., Tjemkes et al.). Furthermore, specific to IASI, validation campaigns based on airborne observations have been used to evaluate the 4A model ( R. Knuteson , private communication from Un. Wisconsin (2000) ; J. Taylor within the frame of the VIRTEM project (2000)).

Our models are regularly updated and refined in connection with the new generation of spectrometers or interferometers launched on research or operational satellite platforms.

### The 4A – Automatized Atmospheric Absorption Atlas – : a brief description

Briefly, 4A is a compressed look-up table of optical depths. The concept was described in Scott N.A. and Chédin A. (J.Appl.Meteor, Vol 20, 801-812, 1981).

STRANSAC – the LMD genuine line-by-line and layer-by-layer model (Scott, 1974 and later on Tournier et al., 1995) – is used to compute the atlases of optical depths :

- for 12 nominal atmospheres (12 temperature profiles 7K distant)
- for each absorbing gas (reference concentration profiles)
- for a set of 40 pressure levels (between surface and top of the atmosphere; 40 is the current default but not mandatory)
- at, at least, a fraction of half width spacing (adaptable, through atmospheric layers “spectral representation step”)

4A is separated into 15 cm^{-1} blocks, leading to several thousands (15 cm^{-1} / representation step) by 480 (40 layers times 12 temperatures) matrices for each gas and each 15 cm^{-1} region. Each matrix is compressed in wavenumber/layer/temperature and wavenumber/layer/gas space and only the significant values are kept. Values (in transmittance units) too close to zero or too close to one are kept and treated separately in order to be reintroduced and taken into account in case of high values of viewing angles or absorber amounts.

The resulting compressed matrices are stored.

To do a calculation, the compressed matrix is:

- uncompressed (in addition, “zero” and “one” are reintroduced)
- interpolated:
- to the correct temperature for each layer (interpolation between two adjacent temperature profiles)
- to the correct pressure levels (the nominal 40 pressure levels are not mandatory)
- scaled to the correct absorber amount and secant (all gases may be considered as “variable” with respect to the altitude)

Absorption from each individual gas is added up and a radiance calculation, as well as transmittance and jacobian calculations (these latter are optional), are performed.

Starting from these high spectral resolution optical depths ,transmittance profiles, Jacobian profiles, brightness temperatures are generated using an appropriate “spectral integration step” combined with a relevant convolution step to take into account the various instrument functions.

Some important 4A attributes are as follows.

- c-correction of Voigt profiles (Perrin et al, 1989)
- Continuum updates H
_{2}O (Clough et al., 1989), N_{2}(Lafferty et al, 1996), O_{2}(Thibault et al,1997) - Update of GEISA spectroscopic parameters (Jacquinet-Husson et al, 1999, 2003)
- Partition Function used for the temperature dependence of the line intensities (Gamache et al., 2000)
- Effects of line coupling (Rodrigues, 1998 )

4A is maintained at LMD which includes introducing all the newly derived parameters for spectroscopy, for line-coupling or for continua, for aerosols and CFCs, …, as far as they have been validated. The current version is referred to as 4A-2000.