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Atmospheric processes with smaller spatial scales are often associated with shorter time scales. This provides a possible explanation for the observation that parameterized sub-scale processes in models often appear noisy. The noisy processes are challenging for time stepping, since naive application of traditional time-stepping methods can lead to degradation in the accuracy or even the stability of a numerical simulation. While shorter step sizes and advanced time stepping methods can help, the associated computational costs can be very high. An alternative approach to addressing the challenge could be to describe the impact of fast processes with a “mean effect” and a “noise effect”. We will use a simple but relevant model to demonstrate that the stochastic approach can provide substantially increased accuracy for large step sizes. We will also point out the theoretical connection between this approach and the concept of parameterization, and discuss our plan to further explore the approach to for more complex problems with closer links to the sub-grid-scale processes in E3SM.
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