Current SW scheme in the JMA-GSM is based on the delta-Eddington two-stream approximation method (referred to as δ2S) (Joseph et al. 1976) for computation of radiative transfer with absorption and scattering processes. This method is computationally efficient for both clear-sky and cloudy-sky conditions, and is widely used in SW schemes of global atmospheric models. However, the two-stream approximation may cause large computational errors in calculation of shortwave fluxes and heating rates under cloudy-sky conditions, depending on the optical depth of cloud layer and the solar zenith angle. Therefore, there is a need for higher-order approximation method utilized in SW scheme of the model. Under this background, δ4S was tested in the JMA-GSM SW scheme in order to confirm its accuracy and impact on the radiative calculation, compared with the currently used δ2S.
The accuracy of δ4S is examined by idealized single column model (SCM) experiments. The results of experiments, with using δ4S and δ2S, are compared with those of the delta-32-stream discrete ordinate method (Stamnes et al.1988) as a reference. In the high-cloud case with thin cloud lying around 250-hPa height, negative errors for downward flux at the surface and positive errors for upward flux at the top of the atmosphere are confirmed by using current SW scheme (δ2S). These errors are reduced by applying δ4S which is able to calculate multiple scattering processes more accurately, especially in the optically thin cloud case where the calculated radiation field significantly differs from δ2S. In the low-cloud case with thick cloud around 850-hPa height, δ4S and δ2S have comparable computational accuracy of the SW fluxes, whereas have large difference for the shortwave heating rate. Current SW scheme has negative (positive) shortwave heating errors at the cloud top (base) possibly because δ2S tend to underestimate absorption due to thick clouds. This implies that absorption of the downward SW flux weakens in the upper part of the cloud layer and therefore more energy is absorbed in the lower part of the cloud layer. The δ4S can successfully reduce these errors. From these experiments, increase of computational time for SW calculation by using δ4S is estimated about roughly five times as large as the current SW scheme.
The δ4S is under implementation to JMA-GSM, and some impacts on the forecasted radiation field and the model atmosphere will also be shown.