NUMERICAL MODELING: DIFFERENT STRATEGIES FOR DIFFERENT GOALS

When we think of numerical models, 'simulation models' often come to mind: The modeler strives to include as many of the processes operating the system of interest, and in a much detail, as is practical. The goal is to construct a "miniature" version of a particular location as realistically as possible, to maximize the quantitative accuracy of predictions such as "Variable A will equal Z at location X and time T."

However, numerical models can also help answer questions like "Why does this puzzling behavior occur?" The goal of explanation is often best pursued with 'exploratory' models (Murray 2002, 2003), in which a modeler leaves out as much as possible, to try to determine what processes are essential in causing the poorly understood phenomena. The modeler also seeks the simplest formal representations of the processes included, rather than the most numerically accurate ones, to examine the key aspects of the interactions and feedbacks involved; the simpler the model, the greater the potential for clear insights.

Simulation modelers often tend toward 'explicit numerical reductionism.'-directly representing interactions at scales as small as possible, parameterizing sub-grid-scale processes only when necessary. Exploratory modelers often employ a top-down strategy, endeavoring to represent only the effects that much smaller-scale processes have on the scale of interest. This approach allows investigation of the interactions between the emergent variables and structures that most directly explain many complex behaviors. As a caricature, we don't investigate water-wave phenomena by simulating molecular collisions.

In addition, exploring the key large-scale interactions that cause enigmatic phenomena bypasses the risk that small-scale model imperfections will cascade up through the scales, leading to unrealistic behaviors at the scale of interest. For this reason, it has been suggested recently that a top-down approach leads to models that are better able to make practically useful predictions. The strategies described here represent end members of modeling continua, and what blend of approaches leads to predictions most useful to science or society likely varies from case to case.

I will illustrate these points with the example of modeling Large-Scale Coastal Behavior (e.g. Ashton et al. 2001, 2003a,b).