An introduction to variable-resolution modeling

It is commonly necessary in analysis and other activities involving models to work at two or more levels of resolution. Resolution is a relative concept, but at any given level one may think of increasing resolution (e.g., to gain greater insight about phenomenology) or decreasing resolution (e.g., to produce something more comprehensible and more appropriate for policy analysis or operational decision support). Sometimes one can calibrate lower-resolution models with higher-resolution models and, to some extent, vice versa. Ideally, models (or integrated models families) would be built from the outset with variable-resolution capability. Often, however, it is necessary to do cross-resolution work by linking existing models that were not designed to be connected. Although there are software techniques for connecting dissimilar models, these techniques do not guarantee that it is substantively meaningful to do so. Similarly, while many workers have found off-line methods for tuning one model of an alleged family to be at least somewhat consistent with another model of the family, the consistency is sometimes more apparent than real. To put it differently, taking existing models with varied resolutions and declaring them to constitute a hierarchical family is sometimes quite misleading because the models are not integrated nor can they be integrated readily. Further, even when means for relating the models sensibly have been developed (either off-line methods or model-connection methods), doing so may involve complex, tedious, error-prone, and expensive calibration efforts. This article describes building models with variable-resolution capability. It also describes generic substantive challenges in connecting models developed independently, and recommends that such model-connection activities be guided by design work to identify how the models would have been developed in the first place if their subsequent integration had been a goal. This approach can make it possible to connect the models usefully and comprehensively with one set of adaptations rather than a series of incremental patches. In other cases it may convince users to commission the building of a new variable-resolution model by demonstrating that the existing models will never work together well. The article also describes a particular design method called integrated hierarchical variable-resolution modeling, which is very helpful when it is feasible. It greatly clarifies relationships among levels of resolutions.