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.