Accurate and Efficient Numerical Simulation of Land Models Using SUMMA With SUNDIALS

Numerical simulation of land models without error control can be highly inaccurate. We present the incorporation of the Suite of Nonlinear and Differential-Algebraic Equation Solvers (SUNDIALS) package to solve the equations that simulate thermodynamics and hydrologic processes in the Structure for Unifying Multiple Modeling Alternatives (SUMMA) land model. The algorithmic features of SUNDIALS, such as error estimation and adaptive order and step-size control, result in a SUMMA-SUNDIALS model that delivers substantially improved accuracy and relative computational efficiency compared to integration with the previous SUMMA model, which uses the low-order backward Euler method with no rigorous error control. The results are demonstrated through simulations over the North American continent with more than 500,000 spatial elements. Compared to the previous SUMMA model, we find that the simulations produced by the SUMMA-SUNDIALS model are orders of magnitude closer to converged solutions for the same computational cost. Being able to efficiently perform more reliable simulations makes the SUMMA-SUNDIALS model a powerful tool for improving our understanding of the terrestrial component of the Earth System.