Discrete Ordinate Adding Method (DOAM), a new solver for Advanced Radiative transfer Modeling System (ARMS)

Satellite data assimilation requires a computationally fast and accurate radiative transfer model. Currently, three fast models are commonly used in the Numerical Weather Prediction models (NWP) for satellite data assimilation, including Radiative Transfer for TIROS Operational Vertical Sounder (RTTOV), Community Radiative Transfer Model (CRTM), and Advanced Radiative transfer Modeling System (ARMS). ARMS was initiated in 2018 and is now becoming the third pillar supporting many users in NWP and remote sensing fields. Its radiative transfer solvers (e.g. Doubling Adding method) is inherited from CRTM. In this study, we propose a Discrete Ordinate Adding Method (DOAM) to solve the radiative transfer equation including both solar and thermal source terms. In order to accelerate the DOAM computation, the single scattering approximation is used in the layer with an optical depth less than 10^-8 or a single scattering albedo less than 10^-10. From principles of invariance, the adding method is then applied to link the radiances between the layers. The accuracy of DOAM is evaluated through four benchmark cases. It is shown that the difference between DOAM and DIScrete Ordinate Radiative Transfer (DISORT) decreases with an increase of stream number. The relative bias of the 4-stream DOAM ranges from -5.03 % to 5.92 % in the triple layers of a visible wavelength case, while the maximum bias of the 8-stream DOAM is only about 1 %. The biases can be significantly reduced by the single scattering correction. Comparing to the visible case, the accuracy of the 4-stream DOAM is much higher in the thermal case with a maximum bias -1.69 %. Similar results are also shown in two multiple-layer cases. In the MacBook Pro (15-inch, 2018) laptop, the 2-stream DOAM only takes 1.68 seconds for calculating azimuthally independent radiance of 3000 profiles in the hyper-spectral oxygen A-band (wavelength ranges from 0.757 µm to 0.775 µm), while the 4-stream DOAM takes 4.06 seconds and the 16-stream DOAM takes 45.93 seconds. The time of the 2-, 4- and 16- stream DOAM are 0.86 seconds, 1.09 seconds and 4.34 seconds for calculating azimuthally averaged radiance. DISORT with 16 streams takes 1521.56 seconds and 127.64 seconds under the same condition. As a new solver, DOAM has been integrated into ARMS and is used to simulate the brightness temperatures at MicroWave Humidity Sounder (MWHS) as well as MicroWave Radiation Imager (MWRI) frequencies. The simulations by DOAM are compared to those by Doubling Adding method and accuracy of both solvers shows a general agreement. All the results show that the DOAM is accurate and computational efficient for applications in NWP data assimilation and satellite remote sensing.