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Parameterizations in weather and climate models aim at representing the impact of non-resolved, small-scale processes. Standard closures use deterministic parameterizations with constant, but uncertain parameters. Uncertainty in model predictions is assessed using ensemble prediction systems, including strategies to effectively sample the space of uncertainty in the initial conditions, as well as stochastically disturbed but fixed parameterizations to account for model uncertainty.
Aforementioned approaches do not leave the deterministic model concept and ignore the interaction between the small-scale processes and the resolved dynamics. This might be very inaccurate particularly for highly non-linear systems. In contrast, stochastic parameterization schemes constitute a new type of parameterizations that regard the non-resolved processes as stochastic processes and that lead to a set of stochastic partial differential equations. The presentation will contrast the deterministic and stochastic approaches using simple examples. |
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