## 1. Introduction

[2] Fast radiative transfer (RT) models are now an integral component of any numerical weather prediction (NWP) model assimilating satellite radiances or using radiances for model validation purposes. Given the significant impacts of radiances in NWP model forecasts [*Andersson et al.*, 1994; *English et al.*, 2000] it is important that we strive to develop fast RT models which achieve the required level of accuracy while at the same time having error characteristics which are well understood. In this way the impact of the satellite radiances on the NWP analyses can be optimized. Ideally the errors in the RT forward model used for assimilation should be small relative to the instrument noise and uncorrelated. Fast RT models are also important for providing retrievals of the atmospheric state for climate data sets and providing simulated satellite data sets from NWP model fields. For both assimilation and retrieval applications it is important to emphasize that it is not only the forward model calculations (i.e., top of atmosphere radiances computed from a given atmospheric state) which are significant but also the gradients of the RT model radiances with respect to the profile variables strictly referred to as the Jacobian (but see later) and defined as

where ** y** is the vector of channel radiances (2378 for Atmospheric Infrared Sounder (AIRS)),

**is the vector of atmospheric state variables (typically dimensions of number of levels × number of active gases plus a few surface variables which for this study came to ∼310) and**

*X***H**is the Jacobian matrix with dimensions of

**by**

*y***. It is the Jacobian which allows increments in “radiance space” to be mapped back into increments in model state variables, assuming linearity about the model state**

*X***, thereby bringing the NWP model state closer to the radiance observations.**

*X*[3] Several years ago comparisons of radiative transfer (RT) models for ATOVS (Advanced TIROS Operational Vertical Sounder) infrared and microwave channels were made [*Soden et al.*, 2000; *Garand et al.*, 2001] that helped to better define the radiative transfer modeling errors for ATOVS. More recently, with the advent of high spectral resolution infrared sounders, e.g., Atmospheric Infrared Sounder (AIRS) and Infrared Atmospheric Sounding Interferometer (IASI), enhanced versions of the fast ATOVS radiative transfer models have evolved to include simulations of these sounders. The success of the AIRS spectrometer in providing very stable high spectral resolution top of atmosphere infrared radiances has provided an impetus to improve and assess the RT modeling for atmospheric sounding applications in the thermal infrared. A recent study by *Tjemkes et al.* [2003] comparing line-by-line RT models for IASI simulations has also helped quantify the errors in the line-by-line models.

[4] This AIRS radiative transfer model comparison was proposed at the first workshop for Soundings from High Spectral Resolution Observations at Madison, Wisconsin in May 2003, and was undertaken under the auspices of the International TOVS Working Group. The aims of the intercomparison were defined to be (1) to compare the forward model calculations for all AIRS channels for a set of diverse atmospheric profiles and one tropical Pacific profile coincident with AIRS data; (2) to compare the profile transmittances for a representative subset of 20 channels; and (3) to compare temperature, water vapor and ozone Jacobians from each model for these 20 channels. The results from this study would then allow the error characteristics of AIRS fast RT models to be better estimated for retrieval and data assimilation applications and to compare them with the AIRS instrument noise. In the process of this comparison exercise, several models had problems identified in their implementation as a result of the comparison and they were able to be corrected before the final analysis was undertaken.

[5] The paper is structured as follows: section 2 describes the models submitted, section 3 the details of the comparison process, section 4 the results for the forward model comparisons, section 5 the results for the transmittances and Jacobians, and section 6 summarises the conclusions of the intercomparison and identifies areas requiring further study.