Is There a Role for Statistical Design of Experiments in Numerical Weather Prediction?

Numerical Weather Prediction (NWP) is the science of forecasting weather or climatic conditions based on past and present observations using computational methods applied to mathematical representations of the atmosphere. Temporally, weather forecasts range from a few hours to a several days in the future, while climate forecasts range from several months to years (or decades) into the future. Spatially, forecasts can cover small scale, highly resolved “local” weather conditions over small domains to large scale global weather features and climatic patterns.

The foundation of NWP is the conservation of mass, heat, momentum, and water vapor, along with other gaseous and aerosol materials over a region of interest called the domain (Pielke 2002; Warner 2011). The conservation equations are nonlinear, partial-differential equations that are nearly impossible to solve analytically except in a few ideal cases. Practical solution approaches for these equations employ numerical methods to obtain approximate forecasts for a domain represented by a finite and generally regular set of discrete “grid points”. Discretizing the domain means that atmospheric processes occuring at sub-grid scales cannot be resolved by the modeled physics; however, these unresolved effects must be accounted for to maintain conservation. Such accounting is done via parameterizations that address physical effects (terrain, land use, turbulence, moisture, etc.) which occur at sub-grid scales. Depending on which parts of the atmosphere researchers consider, there are a number of parametric approaches to model these physical effects. It is difficult to efficiently explore how these parameterizations interact over a domain to produce a forecast; however, we require this knowledge to conduct trade-off studies and inform the selection of parameterization schemes to make the NWP robust for a variety of applications.

Statistical design of experiments, a technique applied successfully in other areas to large scale simulation models, shows promise in assisting in a structured exploration of these parameterized processes in NWP codes. In this paper, we develop an extended problem definition; we present a method for developing a design matrix suitable for that problem; and, we illustrate how to apply that design to study the role parameterizations play in a relevant forecast metric of interest.