# Friday Coffee with Doc Thompson

I will be another of the webloggers here on the R.O. Anderson Engineering website. This is also my first entry (here), although I have ten-years of experience writing weblog essays (on my personal site).

This morning, I think I’ll define what is meant by a “hydrologic model.” It is a term that is used a great deal when talking about flood-related hydrology. It is often used in discussions with lay-people who don’t have a scientific background.

A model is a representation of a cause-effect relation. In the context of hydrology, the cause is incoming precipitation and the effect is flow from the watershed. When the flow exceeds the capacity of the channel, flooding occurs. So, a hydrologic model is a representation of the precipitation-runoff process. The form of the model can vary from a simple non-linear equation to a complex set of partial differential equations (trust me, that’s complex). Those are mathematical models of the precipitation-runoff process. A physical model could be constructed, but such models are used only for research and not practice.

So, a hydrologic model is a mathematical model that takes incoming precipitation (measured or assumed) and converts it to runoff (discharge from the watershed).
There are a number of subprocesses active in the conversion, each of which are generally represented by a submodel (or process model). In general terms, incoming precipitation is subject to interception (trapped by vegetation), infiltration (into the soil), and depression storage (small pools or puddles on the landscape surface). In a hydrologic model, then, each of these processes is represented by one or more equations. Each of these equations has parameters (set values that determine the relations between variables) that must be estimated.

Each of these parameters is subject to uncertainty. If there are no data for calibration (adjusting the parameters to reproduce known results), then the parameters are just estimates and the uncertainty is greater. Although the uncertainty is not necessarily additive, it does accumulate. Therefore, the greater number of parameters (the more complex the hydrologic model), the greater the uncertainty in the result.

This is the reason hydrology is sometimes called a “voodoo” science. Hydrologists are often required to make estimates of parameter values so that estimates of flow can be developed for design and analysis. It is a reason why different hydrologists can arrive at different results. Even so, both estimates might be reasonable because of the uncertainty in all of the parts of the process.

It is sometimes said “If you ask five hydrologists for an estimate of the discharge from a watershed, you’ll get five different answers.” This is true. It is also true that all of them can be reasonable estimates and none of them might be incorrect. This is the reason I became a hydrologist — a great deal of judgment is required and working out the uncertainties is fascinating. This is also one of the reasons I prefer to have measurements of some kind to assist in reducing the uncertainty.

So, a hydrologic model is a mathematical model that relates incoming precipitation (measured or assumed) to discharge from a watershed. The form and complexity of hydrologic models vary considerably. Measurement of one or more parameters used in the model is important for reducing the uncertainty in the results. But, that is a topic for another coffee.

See you next time…