The SUMMA-SUNDIALS Earth System Model

The next generation of Earth System models promisesunprecedented predictive power through the application of improvedphysical representations, data collection, and high-performancecomputing. A key component to the accuracy, efficiency, and robustnessof the Earth System simulations is the time integration ofdifferential equations describing the physical processes. Manyexisting Earth System models are simulated using low-order,constant-stepsize time-integration methods with no error control,opening them up to being inaccurate, inefficient, or require aninfeasible amount of manual tweaking when run over multipleheterogeneous domains or scales. We have implemented the variable-stepize, variable-order differentialequation solver SUNDIALS as the time integrator within the Structurefor Unifying Multiple Modelling Alternatives (SUMMA) modelframework. The model equations in SUMMA were modified and augmented toexpress conservation of mass and enthalpy. Water and energy balanceerrors were tracked and kept below a strict tolerance. The resultingSUMMA-SUNDIALS software was successfully run in a fully automatedfashion to simulate hydrological processes on the North Americancontinent, sub-divided into over 500,000 catchments. We compared the performance of SUMMA-SUNDIALS with a version (calledSUMMA-BE) that used the backward Euler method with a fixed stepsize asthe time-integration method. We find that SUMMA-BE required two ordersof magnitude more CPU time to produce solutions of comparable accuracyto SUMMA-SUNDIALS. Solutions obtained with SUMMA-BE in a similar orshorter amount of CPU time than SUMMA-SUNDIALS often contained largediscrepancies. We conclude that sufficient accuracy, efficiency, and robustness ofnext-generation Earth System model simulations can realistically onlybe obtained through the use of adaptive solvers. Furthermore, wesuggest simulations produced with low-order, constant-stepsizesolvers deserve more scrutiny in terms of their accuracy.