# Using a GPU to Accelerate a Longwave Radiative Transfer Model with Efficient CUDA-Based Methods
## 1 Introduction  
With the rapid development of computer technology, high-performance computing (HPC) is employed in a wide range of real-world applications [1; 2; 3]. Earth system models (ESMs) have a large amount of calculation and high resolution, so HPC is widely used to accelerate their computing and simulation [4]. In the past few years, the modern graphics processing unit (GPU), which combines features of high parallelism, multi-threaded multicore processor, high-memory bandwidth, general-purpose computing, low cost, and compact size far beyond a graphics engine, has substantially outpaced its central processing unit (CPU) counterparts in dealing with data-intensive, computing-intensive, and time-intensive problems [5; 6; 7; 8; 9]. In the era of pursuing green computing, the booming GPU capability has attracted more and more scientists and engineers to use GPUs instead of CPUs to accelerate climate system models or ESMs [10; 11]. Due to the advent of NVIDIA's Compute Unified Device Architecture (CUDA) [12], GPU support has been added to many scientific and engineering applications. At present, CUDA, a general-purpose parallel computing architecture, supports many high-level languages, such as C/C++ and Fortran. An atmospheric general circulation model (GCM) usually consists of dynamical core and physics processes. As one of the important atmospheric physics processes, the radiative process is used to calculate atmospheric radiative fluxes and heating rates [13]. To simulate the radiative process, many radiative parameterization schemes and radiative transfer models have been developed, such as the line-by-line radiative transfer model (LBLRTM) [14; 15]. As the foundational model for all radiation development, the LBLRTM is an accurate, efficient, and highly flexible model for calculating spectral transmittance and radiance, but it still demands enormous computing resources for long-term climatic simulation [16]. To address this issue, several rapid radiative models with fast calculations of radiative flux and heating rates have already appeared, such as the rapid radiative transfer model (RRTM) [17]. As a validated model computing long-wave and shortwave radiative fluxes and heating rates, RRTM uses the correlated-k method to provide the required accuracy and computing efficiency [18]. Moreover, the rapid radiative transfer model for general circulation models (RRTMG), an accelerated version of RRTM, provides improved efficiency with minimal loss of accuracy for GCM applications [19; 20]. The Chinese Academy of Sciences-Earth System Model (CAS-ESM) [21; 22; 23], developed by the Institute of Atmospheric Physics (IAP) of the Chinese Academy of Sciences, is a coupled climate system model that is composed of eight separate component models and one central coupler. In the current version of the CAS-ESM, the atmospheric model is the IAP Atmospheric General Circulation Model Version 4.0 (IAP AGCM4.0) [24; 25]. This version uses the RRTMG as its radiative parameterization scheme. Although the RRTMG is more efficient, it is still computationally expensive, so it cannot be performed with finer grid resolutions and shorter time steps in operational models [26]. Many studies show that radiative transfer is relatively time-consuming, taking up to 30-50 percent of the total computing time in numerical weather and climate simulations [27; 28]. To address this issue, it is beneficial to use GPU technology to accelerate the RRTMG in order to greatly improve its computational performance. Therefore, this study focused on the implementation of sophisticated accelerating methods for the RRTMG long-wave radiation scheme (RRTMG_LW) on a GPU. The remainder of this paper is organized as follows. Section 2 presents representative approaches that aim to improve computational efficiency of the RRTM or the RRTMG. Section 3 introduces the RRTMG_LW model and the GPU environment.