The Impact of Noisy Physics on the Stability and Accuracy of Physics–Dynamics Coupling

The coupling of the dynamical core of a numerical weather prediction model to the physical parameterizations is an important component of model design. This coupling between the physics and the dynamics is explored here from the perspective of stochastic differential equations (SDEs). It will be shown that the basic properties of the impact of noisy physics on the stability and accuracy of common numerical methods may be obtained through the application of the basic principles of SDEs. A conceptual model setting is used that allows the study of the impact of noise whose character may be tuned to be either very red (smooth) or white (noisy). The change in the stability and accuracy of common numerical methods as the character of the noise changes is then studied. Distinct differences are found between the ability of multistage (Runge–Kutta) schemes as compared with multistep (Adams–Bashforth/leapfrog) schemes to handle noise of various characters. These differences will be shown to be attributable to the basic philosophy used to design the scheme. Additional experiments using the decentering of the noisy physics will also be shown to lead to strong sensitivity to the quality of the noise. As an example, the authors find the novel result that noise of a diffusive character may lead to instability when the scheme is decentered toward greater implicitness. These results are confirmed in a nonlinear shear layer simulation using a subgrid-scale mixing parameterization. This subgrid-scale mixing parameterization is modified stochastically and shown to reproduce the basic principles found here, including the notion that decentering toward implicitness may lead to instability.