Friday Coffee with Doc Thompson

So this time, only a few more months passed before I revisited the corporate weblog. I guess that means I’m doing better, but it’s slow going. The holidays presented a lot of time away from the office. That’s my excuse and I’m going to stick to it.

In my previous posts I wrote a few basic things about hydrologic modeling. To date I described a general definition of a hydrologic model and presented some of the differences between continuous simulation and event-based models. This time I’d like to step back and bit with some general thoughts about modeling.

By their nature, models (regardless of what type) are a simplification of reality. They cannot include all elements of the physical systems they represent. This happens at three levels. The first is the formulation of the cause-effect relation. A wonderful example is the Green-Ampt infiltration function. The derivation of that governing equation, while based in the physics of variably-saturated porous media flow, derives from the assumption that water enters the soil as piston flow. That is, the wetting front advances vertically through the soil profile in a uniform, single direction. This assumption allows use of Darcy’s equation to derive the slope of the hydraulic grade line (same as the energy grade line in this application) so that the flux rate can be estimated. A parameter is included to represent initial soil wetness (effective saturation) as is one to indicate the capillary suction at the wetting front. These assumptions are substantial simplifications of the movement of water through an unsaturated soil profile.

As an aside, there was an excellent article by R.T. Clarke in 1973 in which definitions of components and approaches to modeling were presented. Clarke made a distinction between parameters (values held constant through an instance of a model application) and variables (quantities that vary during application of a model).

The second is the model representation in its parameter space. In general, watersheds are highly variable in terms of land cover, soil texture, surface slope, and so on. It is not physically possible to include all variations of these components in an application of a model. Therefore, representative values must be selected and the impact of the uncertainty of these estimates should be assessed as part of the analyst’s report. I should note that in my experience, the analysis of uncertainty is rarely done.

The third source of simplification is in the input variable or variables. For example, real floods results from real precipitation events. The latter rarely approximate the beautiful curvilinear representations of mass hyetographs. The are herky-jerky pulses of precipitation that occur over the course of the storm. Although it’s possible to model the structure of flood-producing rainfall events, a long history of simplification resulted in a comfort-level of engineers that this approximation of nature is reasonable.

All of this brings us to the assumption that our models represent reality. In truth, the representation is only approximate and depends heavily on the skill and experience of the analyst. The term for the attribution of truth to the approximations is reification. There is a illustrative entry on this concept in Wikipedia that is worth reading.

The bottom line is that models are only approximate representations of reality. To attribute anything more to values obtained from models is an error.