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The graphics processing units (GPUs) are becoming a compelling acceleration strategy for geoscience numerical model due to their powerful computing performance. In this study, AMD's heterogeneous compute interface for portability (HIP) was implemented to port the GPU acceleration version of the Piecewise Parabolic Method (PPM) solver (GPU-HADVPPM) from the NVIDIA GPUs to China' s domestically GPU-like accelerators as GPU-HADVPPM4HIP, and further introduced the multi-level hybrid parallelism scheme to improve the total computational performance of the HIP version of CAMx (CAMx-HIP) model on the China' s domestically heterogeneous cluster. The experimental results show that the acceleration effect of GPU-HADVPPM on the different GPU accelerator is more obvious when the computing scale is larger and the maximum speedup of GPU-HADVPPM on the domestic GPU-like accelerator is 28.9 times. The hybrid parallelism with a message passing interface (MPI) and HIP enables achieve up to 17.2 times speedup when configure 32 CPU cores and GPU-like accelerators on the domestic heterogeneous cluster. And the OpenMP technology is introduced to further reduce the computation time of CAMx-HIP model by 1.9 times. More importantly, by comparing the simulation results of GPU-HADVPPM on NVIDIA GPUs and domestic GPU-like accelerators, it is found that the simulation results of GPU-HADVPPM on domestic GPU-like accelerators have less difference than the NVIDIA GPUs, and the reason for this difference may be related to the fact that the NVIDIA GPU sacrifices part of the accuracy for improved computing performance. All in all, the domestic GPU-like accelerators are more accuracy for scientific computing in the field of geoscience numerical models. Furthermore, we also exhibit that the data transfer efficiency between CPU and GPU has an important impact on heterogeneous computing, and point out that optimizing the data transfer efficiency between CPU and GPU is one of the important directions to improve the computing efficiency of geoscience numerical models in heterogeneous clusters in the future. [ABSTRACT FROM AUTHOR]