# Using a GPU to Accelerate a Longwave Radiative Transfer Model with Efficient CUDA-Based Methods
## 3 Model Description and Experiment Platform  
### RRTMG Radiation Scheme  
The RRTM is not fast enough for GCMs. To improve its computational efficiency without significantly degrading its accuracy, the RRTM was modified to produce the RRTMG [33; 34]. The RRTMG and the RRTM have the same basic physics and absorption coefficients, but there are several modifications in the RRTMG [35]. (1) The total number of quadrature points (\(g\) points) in the RRTMG_LW is 140, while it is 256 in the RRTM_LW. In the shortwave, the number of \(g\) points is reduced from 224 in the RRTM shortwave radiation scheme (RRTM_SW) to 112 in the RRTMG_SW. (2) The RRTMG_LW includes McICA (Monte-Carlo Independent Column Approximation) capability to represent sub-grid cloud variability with random, maximum-random, and maximum options for cloud overlap [36]; the RRTM_LW does not have the McICA, but it does include representations for random and maximum-random cloud overlap. (3) The RRTMG_LW performs radiative transfer only for a single (diffusivity) angle (angle = 53 deg, secant angle = 1.66) and varies this angle to improve accuracy in profiles with high water; the RRTM_LW can use multiple angles for radiative transfer. (4) The RRTMG_LW coding has been reformatted to use many Fortran 90 features. (5) The RRTMG_LW includes aerosol absorption capability. (6) The RRTMG_LW can be used as a callable subroutine and can be adapted for use within global or regional models. (7) The RRTMG_LW can optionally read the required input data either from a netCDF file or from the original RRTM_LW source data statements. (8) The RRTMG_LW can provide the change in upward flux with respect to surface temperature, dF/dT, and by layer for total sky and clear sky. The further description on \(g\) points in the RRTM or RRTMG is as follows. The RRTM uses the correlated k-distribution method to calculate the broadband radiative fluxes. In this method, the radiative spectrum is first divided into bands. Because of the rapid variation of absorption lines within the bands of gas molecules, the values of the absorption intensities within each band are further binned into a cumulative distribution function of the intensities. This distribution function is then discretized by using \(g\) intervals for integration within each band to obtain the band radiative fluxes, which are further integrated across the bands to obtain the total radiative flux to calculate atmospheric radiative heating or cooling. The \(g\) points are the discretized absorption intensities within each band. RRTM_LW has 16 bands and 256 \(g\) points. RRTM_SW has 16 bands and 224 \(g\) points. To speed up the calculations for climate and weather models, the spectral resolutions of RRTM_LW and RRTM_SW are further coarsened for applications in GCMs as RRTMG_LW and RRTMG_SW. RRTMG_LW has 16 bands and 140 \(g\) points. RRTMG_SW has 16 bands and 112 \(g\) points [35]. The spectrally averaged outgoing radiance from an atmospheric layer is calculated according to the following formula:  
\[I_{v}(\mu)=\frac{1}{v_{2}-v_{1}}\int_{v_{1}}^{v_{2}}dv\left\{I_{0}(v)+\int_{T_ {v}}^{1}[B(v,\theta(T_{v}^{\prime}))-I_{0}(v)]dT^{\prime}\right\}, \tag{1}\]  
where \(v\) is the wavenumber; \(\theta\) is temperature; \(\mu\) is the zenith direction cosine; \(v_{1}\) and \(v_{2}\) are the beginning and ending wavenumbers of the spectral interval, repectively; \(I_{0}\) is the radiance incoming to the layer; \(B(v,\theta)\) is the Planck function at \(v\) and \(\theta\); \(T_{v}\) is the transmittance for the layer optical path; and \(T_{v}^{\prime}\) is the transmittance at a point along the optical path in the layer.