On the use of exponential time integration methods in atmospheric models

Exponential integration methods offer a highly accurate approach to the time integration of large systems of differential equations. In recent years, they have attracted increased attention in a number of diverse fields due to advances in their computational efficiency. This has been as a result of the use of Krylov subspace methods for the approximation of the matrix exponentials which typically arise. In this work, we investigate the potential of exponential integration methods for use in atmospheric models. Two schemes are implemented in a shallow water model and tested against reference explicit and semi-implicit methods. In a number of experiments with standard test cases, the exponential methods are found to yield very accurate solutions with time-steps far longer than even the semi-implicit method allows. The relative efficiency of the exponential integrators, which depends mainly on the choice of the specific algorithm used for the calculation of the matrix exponent, is also discussed. The future work aimed at further improvements of the proposed methodology is outlined.