On water vapor Jacobian in fast radiative transfer model

The Community Radiative Transfer Model (CRTM) is a powerful numerical software used for satellite data assimilation and remote sensing applications. Its accuracies in simulating satellite radiances and their gradients relative to water vapor (or Jacobians) are improved through this study when the CRTM includes additional gaseous absorbers. Three water vapor transmittance regression methods (labeled with A-C, respectively) are discussed that differ primarily in vertical coordinates and the application of constraints to smooth vertical structures of the regression coefficients. Method A computes optical depth profiles at fixed pressure levels, whereas method B computes the profiles at fixed levels of the integrated absorber amount. Method C is a derived version of method B with an addition that a polynomial function is applied to the regression coefficients to improve the water vapor Jacobians. The intercomparison focuses on the modeling of 22 sounding channels routinely used at numerical weather prediction (NWP) centers: 9 Atmospheric Infrared Radiance Sounder channels, 4 High-Resolution Infrared Sounder channels, 4 Advanced Microwave Sounding Unit-A channels, and 5 Microwave Humidity Sounder channels. An ensemble of 48 diverse atmosphere profiles at the University of Maryland at Baltimore County was used to test the results. The results were compiled for methods A and C for water vapor line absorption only while keeping the other components the same under the CRTM framework. The comparison quantities include the water vapor Jacobians, temperature Jacobians, and the forward top-of-the-atmosphere brightness temperature (BT). In the infrared, the forward models mean errors are very small (less than 0.03 K) compared to the line-by-line model. Temperature and water vapor Jacobian goodness-of-fit measure values are very small and sufficient for NWP application, except for some dry atmospheric profiles. For the cold and dry atmospheric profiles, method C can significantly improve the water vapor Jacobian profile and remove the unphysical kinks (oscillations) that appear in method A. The improved water vapor Jacobian profile results in the improved temperature Jacobian. For the microwave channels, the forward BTs show very small biases less than 0.1 K for all the channels, and the overall water vapor Jacobian using method A is better than those using method C, especially for warm and wet atmospheric profiles.