The numerical implementation of land models: Problem formulation and laugh tests

Abstract The intent of this paper is to encourage improved numerical implementation land models. Our contributions in are two-fold. First, we present a unified framework formulate and implement model equations. We separate the representation physical processes from their solution, enabling use established robust methods solve Second, introduce set synthetic test cases (the laugh tests) evaluate include storage transmission water soils, lateral sub-surface flow, coupled hydrological thermodynamic snow, cryosuction soil. consider as “laugh tests” for models because they provide most rudimentary capabilities. tests presented all solved with Structure Unifying Multiple Modeling Alternatives (SUMMA) implemented using SUite Nonlinear DIfferential/Algebraic equation Solvers (SUNDIALS). simulations SUMMA/SUNDIALS compared against (1) solutions other documented peer-reviewed literature; (2) analytical solutions; (3) observations made laboratory experiments. In cases, similar benchmarks, building confidence implementation. posit that some may have difficulty solving these benchmark problems. Dedicating more effort critical order build