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There are a lot of variations of basic, first-order hydrology models to estimate runoff from rainfall with a few other parameters. From what I can tell, most very basic rainfall-runoff models use one of the following methods at their core: the SCS Curve Number method, the Rational method, and the Simple method. I'm trying to understand: how do these methods differ, and are there other methods used at the core of basic, first-order hydrology models?

From what I can tell, the SCS Curve Number method is only slightly different from the Rational method in that it uses a Curve Number (based on land use and soils) rather than a Runoff Coefficient (based on soil and basin slope). The two are both event-based models, at least in their initial design.

The Simple method appears to be a lot like the Rational method but the former is for estimating pollutant loading (using pollutant coefficients and runoff) while the latter is for estimating runoff (using runoff coefficients and rainfall). I could see the two being coupled, but they don't appear to have any redundancy in their use.

Considering the summary of my findings, can these methods be described together as "empirical models" given that they are all based on empirically derived coefficients (either Curve Number values, runoff coefficients, or pollutant coefficients)?

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  1. The models are similar in that they simplify the rainfall-runoff relationship into a few parameters, and essentially use some kind of first-order coefficient to partition rainfall into infiltration and runoff. The differences are mostly in what other parameters are brought in, such as initial abstraction in the SCS method (i.e. some capture of antecedent moisture conditions). You may wish to pick the method that best captures the information you wish to include in the calculation (or have available), such as drainage area. You can find more details about the implicit assumptiopns and ranges of applicability for each method (e.g. rational method).

  2. In terms of other methods, there are many methods that use some similar forms of soil moisture, soil saturation, etc. to estimate the rainfall-runoff partition. For example, take a look at the Infiltration section (4.2) of the Raven Hydrologic Modelling Framework manual v2.8.

  3. As to whether they are empirical, likely depends who you ask. Empiricism is likely more of a spectrum than a binary system. These are not simply linear regression equations and do capture some physics, although they are still clearly at least partially empirical since the coefficients are basically based on experiments to best fit results. I would likely describe them as empirical or semi-empirical, although I wouldn't spend too much time trying to split hairs for this question.

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    $\begingroup$ I would not hesitate to call these ones empirical. It is not a only question of parameters that are obtained empirically but how the law itself was obtained (i.e. on the basis of physical law or from experimental results). $\endgroup$ – Delforge Jul 2 '18 at 5:02

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