Satellite data assimilation in numerical weather prediction models. Part I: Forward radiative transfer and Jacobian modeling in cloudy atmospheres

Satellite data assimilation requires rapid and accurate radiative transfer and radiance gradient models. For a vertically stratified scattering and emitting atmosphere, the vector discrete-ordinate radiative transfer model (VDISORT) was developed to derive all Stokes radiance components at the top of the atmosphere. This study further enhances the VDISORT to compute the radiance gradients or Jacobians. The band matrix used in the VDISORT is simplified and confined along the diagonal direction so that the Jacobians relative to atmospheric and surface parameters are directly derived from its analytic solutions. The radiances and Jacobians at various wavelengths from the VDISORT are compared against those from other techniques that have been benchmarked before. It is shown that the present method is accurate and computationally efficient. In the VDISORT, both emissivity vector and reflectivity matrix are integrated as part of the radiance and Jacobian calculations. In this study, only the emissivity models at microwave frequencies are tested and implemented for VDISORT applications. Over oceans, a full polarimetric emissivity model is utilized. The cutoff wavenumber separating the large-scale waves from the small-scale waves is derived from an ocean wave spectrum model. Over land, a microwave emissivity model previously developed is used to compute various emissivity spectra.