One Problem: Two Methods? Factor Separation in the Atmospheric Sciences

Modeling the atmosphere necessarily involves properly representing the interactions of many factors. Because of these manifold interactions, Numerical Weather Prediction codes can become quite complex; consequently, properly sampling the codes is the only computationally tractable means of identifying an optimal configuration. Two sampling methods are currently available to attribute model response to particular factors: 1) the method of factor separation proposed by Stein and Alpert in current use in the atmospheric science community and 2) statistical design of experiments (DOE) in extensive use in other communities. We explore the mathematical connections between these two methods and demonstrate the differences using the shallow water equations.