# A Novel GPU-Based Acceleration Algorithm for a Longwave Radiative Transfer Model
## 1 Introduction  
The radiative process, one of the important atmospheric physics processes, is often used for calculating atmospheric radiative fluxes and heating rates [1]. To simulate the radiative process, several radiative transfer models were developed, such as the line-by-line radiative transfer model (LBRTM) [2], and the rapid radiative transfer model (RRTM) [3]. The RRTM that is a validated model computing longwave and shortwave radiative fluxes and heating rates, uses the correlated-k method to provide the required accuracy and computing efficiency [4], but it still demands enormous computing resources for long-term climatic simulation. To address this issue, as an accelerated version of RRTM, the rapid radiative transfer model for general circulation models (RRTMG) provides improved efficiency with minimal loss of accuracy for atmospheric general circulation models (GCMs) [5]. As a coupled climate system model comprising eight separate component models and one central coupler, the Chinese Academy of Sciences-Earth System Model (CAS-ESM) [6,7] was developed by the Institute of Atmospheric Physics (IAP) of Chinese Academy of Sciences (CAS). As the atmospheric component model of the CAS-ESM, the IAP Atmospheric General Circulation Model Version 4.0 (IAP AGCM4.0) [8,9] used the RRTMG as its radiative parameterization scheme. Radiative transfer is relatively time-consuming [10; 11]. The RRTMG improves the computing efficiency of radiative transfer, but it is still so computationally expensive that it cannot be performed with shorter time steps or finer grid resolutions in operational models [12]. To greatly improve the computational performance, it is beneficial to use high-performance computing (HPC) technology to accelerate the RRTMG. At present, HPC is widely employed in earth climate system models [13; 14; 15]. With the rapid development of HPC technology, due to the features of multithreaded many-core processor, high parallelism, high memory bandwidth, and low cost, the modern graphics processing unit (GPU) has substantially outpaced its central processing unit (CPU) counterparts in dealing with data- and computing-intensive problems [16; 17; 18; 19]. Currently, increasing numbers of atmospheric applications were accelerated by the GPUs [20; 21]. For example, the WSM5 microphysics scheme from the Weather Research and Forecasting (WRF) model obtained a 206\(\times\) speedup on a GPU [22]. In view of the booming GPU capability, our previous study used a GPU for accelerating the RRTMG longwave radiation scheme (RRTMG_LW). In this study, the GPU-based acceleration algorithms with one-dimensional (1D) and two-dimensional (2D) domain decompositions for the RRTMG_LW were proposed [23]. However, the RRTMG_LW did not achieve an excellent speedup on a GPU. Therefore, the present paper focuses on the implementation of better GPU-based accelerating methods for the RRTMG_LW. To further accelerate the RRTMG_LW in the CAS-ESM, a GPU-based acceleration algorithm in the _g-point_ dimension is proposed. The proposed algorithm enables massively parallel calculation of the RRTMG_LW in the _g-point_ dimension. Then, an optimized version of the RRTMG_LW is built by successfully adopting GPU technology, resulting in G-RRTMG_LW. The experimental results demonstrated that the G-RRTMG_LW on one K40 GPU obtained a 30.98\(\times\) speedup. The main contributions of this study are as follows:  
1. To further accelerate the RRTMG_LW with a massively parallel computing technology, a GPU-based accelerating algorithm in the _g-point_ dimension is proposed. The aim is to explore the parallelization of the RRTMG_LW in the _g-point_ dimension. The proposed algorithm adapts well to the advances in multi-threading computing technology of GPUs and can be generalized to accelerate the RRTMG shortwave radiation scheme (RRTMG_SW). 2. The G-RRTMG_LW was implemented in CUDA (NVIDIA's Compute Unified Device Architecture) Fortran and shows excellent computational capability.