What does the complexity of physics parameterization mean, since no parameterization can be exact?

A numerical weather prediction (NWP) model is a computer program that follows a numerical recipe to discretize the governing equations of atmospheric dynamics for numerical solutions.  The center of these governing equations is the Navier-Stokes (NS) equations of fluid motion.  The closure paradox theorem (Guermond et al., 2004, J. Math. Fluid Mech.) for the numerically discretized (i.e., filtered) NS equations states that discretization (i.e., filtering) and exact subgrid closure are mutually exclusive in practice.  To feasibly solve the discretized NS equations, the subgrid closure must be inexact.  All physics parameterization schemes in an NWP model serve as a closure for the discretized governing equations of atmospheric dynamics.  Even though these schemes vary in complexity, the closure paradox theorem implies that none of them can be exact if the objective is to efficiently produce useful forecasts at the NWP model's grid resolution.  Therefore, empirical adjustment, i.e., constraining its behavior using available observations, is inevitable for any physics parameterization scheme to be feasibly used in an NWP model.

In this presentation, we will use the land-surface parameterization scheme as an example to discuss what the complexity of a physics parameterization scheme actually means, since it cannot be exact.  We will argue that the choice of complexity in a scheme is a trade-off between realism and simplicity.  We will show that a simple land-surface scheme may meet performance constraints with modest observational requirements and is computationally inexpensive enough to be practically useful.  In contrast, a more complex land-surface scheme with sounder physical foundations will yield forecasts that are acceptably more accurate only if enough observations are available to constrain its behavior.  When there are insufficient observations to constrain the complex scheme, the simple scheme should be used so that the scheme's behavior can be effectively constrained using available observations.