Mixed Parallel–Sequential-Split Schemes for Time-Stepping Multiple Physical Parameterizations

Abstract

Split schemes for time-stepping physical parameterizations in numerical weather prediction and climate models are investigated within the context of simplified model equations. A symmetrized-splitting technique is applied to various parameterized systems containing fast and slow physics processes. The physics processes are represented by time-dependent forcing terms and linear damping/oscillatory terms. Finite-difference schemes, obtained from the splitting procedures, are examined to determine their stability properties, degree of splitting error, and truncation error. This analysis provides insight into the advantages and disadvantages of different splitting procedures across a range of possible parameterization scenarios. Many schemes obtained via splitting have time-step-dependent splitting errors, which can lead to inaccurate solutions when fast processes are present and the time step is large. Some splitting combinations, however, are more useful than others. The symmetrized-splitting procedure considered in this paper can produce stable first- and second-order accurate schemes, which have either no significant splitting errors or acceptably small errors relative to a steady-state solution. The consequences of this analysis for physics coupling strategies in realistic numerical weather prediction and climate models are noted.