The community radiative transfer model (CRTM) has been implemented for clear and cloudy satellite radiance simulations in the National Oceanic and Atmospheric Administration (NOAA) National Centers for Environmental Prediction (NCEP) Gridpoint Statistical Interpolation data assimilation system for global and regional forecasting as well as reanalysis for climate studies. Clear-sky satellite radiances are successfully assimilated, while cloudy radiances need to be assimilated for improving precipitation and severe weather forecasting. However, cloud radiance calculations are much slower than the calculations for clear-sky radiance, and exceed our computational capacity for weather forecasting. In order to make cloud radiance assimilation affordable, cloud optical parameters at the band central wavelength are used in the CRTM (OPTRAN-CRTM) where the optical transmittance (OPTRAN) band model is applied. The approximation implies that only one radiative transfer solution for each band (i.e., channel) is needed, instead of typically more than 10,000 solutions that are required for a detailed line-by-line radiative transfer model (LBLRTM). This paper investigated the accuracy of the approximation and helps us to understand the error source. Two NOAA operational sensors, High Resolution Infrared Radiation Sounder/3 (HIRS/3) and Advanced Microwave Sounding Unit (AMSU), have been chosen for this investigation with both clear and cloudy cases. By comparing the CRTM cloud radiance calculations with the LBLRTM simulations, we found that the CRTM cloud radiance model can achieve accuracy better than 0.4 K for the IR sensor and 0.1 K for the microwave sensor. The results suggest that the CRTM cloud radiance calculations may be adequate to the operational satellite radiance assimilation for numerical forecast model. The accuracy using OPTRAN is much better than using the scaling method (SCALING-CRTM). In clear-sky applications, the scaling of the optical depth derived at nadir for brightness temperature calculation at the other direction may result in an error up to about 7 K for some HIRS/3 channels. Under cloudy conditions, SCALING-CRTM may result in an error of about 3.5 K.
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