On the Relation Between Model Parameters and Forecast Parameters

It is well-known that varying model parameters in a NWP model can affect multiple forecast parameters; but exactly how, is difficult to assess. The difficulty arises because of the nonlinearities and interactions inherent in the model. In other words, a change in a single model parameter can affect a number of forecast parameters, and the affect itself depends on the values of all the other model parameters. Here, it is shown that by casting the question in a statistical setting, it is possible to capture the nontrivial relationship between model parameters and forecast parameters. Specifically, it is shown that a “forward” statistical model can display how forecast parameters vary in response to changes in model parameters. Similarly, an “inverse” statistical model, mapping forecast parameters to model parameters, can point to specific values of the latter, given desired values for the former. An operational model (COAMPS R ©)1 is utilized to motivate the idea, but the approach is fully illustrated on the Lorenz model. It is shown that some natural forecast parameters in these models are indeed related to model parameters in a manner suggesting a deterministic underlying relation. Multivariate statistical models are then developed to capture that relationship. The utility of the statistical models is shown by deriving results which would not be evident without the statistical models. ∗http://www.faculty.washington.edu/marzban COAMPS is a registered trademark of the Naval Research Laboratory.