Integration of Rosenbrock-type solvers into CAM4-Chem and evaluation of its performance in the perspectives of science and computation

In this study, the perennial problem of overestimation of ozone concentration from the global chemistry-climate model (CAM4-Chem [Community Earth System Model with chemistry activated]) is investigated in the sense of numerics and computation. The high-order Rosenbrock-type solvers are implemented into CAM4-Chem, motivated by its higher order accuracy and better computational efficiency. The results are evaluated by comparing to the observation data and the ROS-2 [second-order Rosenbrock] solver can reduce the positive bias of ozone concentration horizontally and vertically at most regions. The largest reduce occurs at the mid-latitudes of north hemisphere where the bias is generally high, and the summertime when the photochemical reaction is most active. In addition, the ROS-2 solver can achieve ~2x speed-up compared to the original IMP [first-order implicit] solver. This improvement is mainly due to the reuse of the Jacobian matrix and LU [lower upper] factorization during its two-stage calculation. In order to gain further speed-up, we port the ROS-2 solver to the GPU [graphics processing unit] and compare the performance with CPU. The speed-up of the GPU version with the optimized configuration reaches a factor of ~11.7× for the computation alone and ~3.82× considering the data movement between CPU and GPU. The computational time of the GPU version increases more slowly than the CPU version as a function of the number of loop iterations, which makes the GPU version more attractive for a massive computation. Moreover, under the stochastic perturbation of initial input, we find the ROS-3 [third-order Rosenbrock] solver yields better convergence property than the ROS-2 and IMP solver. However, the ROS-3 solver generally provides a further overestimation of ozone concentration when it is implemented into CAM4-Chem. This is due to the fact that more frequent time step refinements are involved by the ROS-3 solver, which also makes the ROS-3 solver less computationally efficient than the IMP and ROS-2 solvers. We also investigate the effect of grid resolution and it shows that the fine resolution can provide relatively better pattern correlation than the coarse resolution, given the same chemical solver.