Stream flow response to precipitation

One of the more central themes of watershed hydrology is understanding the mechanisms that control how runoff from a watershed in the form of stream flow will respond to a given precipitation event. In this module we will cover some of the basics of hydrograph separation, source water separation, and transfer function approaches to understanding the response of watersheds to precipitation (8:00 min).

Contents of this module

Generally speaking, the transfer function approaches to thinking about rainfall-runoff modeling require that the immediate response of the watershed (often called "event flow") be separated from the rest of the hydrograph. While Hewlett and Hibbert famously called this the most desperate technique in hydrology due to the lack of mechanistic theory and potential for subjective bias, hydrograph separation between base flow and event flow is still central to the more empirical transfer function approaches to predicting how a watershed will respond to precipitation (8:10 min).

Despite its potential flaws, the concept of separating base flow and event flow yield some useful indices that elegantly summarize a watershed's ability to buffer the influence of precipitation on runoff. Let's introduce the baseflow index and the runoff ratio for storms, which has a different interpretation from the runoff ratio for annual hydrographs (4:56 min)

The idea that precipitation is an input signal and runoff is an output signal leads to the application of signal processing theory to watersheds. Central to signal processing theory is the idea that the convolution of an input signal with a transfer function representing the storage capacity of a system will be able to predict the nature of the output signal from the system. The following introduces the transfer function approach to watershed hydrology and provides an example of its application in the form of the rational method (5:14 min).

The NRCS curve number method is, by far, the most widely applied approach to flood risk assessment from precipitation events, where more sophisticated hydrologic models or extensive meteorological data are not available. The approach is based on estimating a "curve number" for different areas of the landscape that ultimately represent the potential for that part of the landscape to store precipitation and thus buffer its immediate influence on runoff. While the approach is not academically satisfying in terms of understanding the fundamentals of how watersheds work, it is a good starting point to the logic behind tying distributed land management to landscape scale hydrologic behavior. Let's start by defining the underlying theory of the NRCS curve number method (15:50 min).

The best way to get a feel for the application of the NRCS curve number method is to work through an example. First you have to decide how much precipitation to apply to the watershed in question. In conservative risk assessments this is usually derived from a worst case scenario perspective (10:37 min).

The next step is to estimate a curve number for each of the different landscape covers. The curve number defines the inflection of the curve used to estimate how much precipitation is stored, where higher curve numbers lead to predictions of less storage and more immediate runoff response and lower curve numbers lead to predictions of more storage and less immediate runoff response (12:35 min).

The fundamental curve number method is used to predict the total volume of runoff in response to a total volume of precipitation, but simple assumptions about the shape of the storm response curve can be used to estimate the peak flow of the response (6:38 min).

The unit hydrograph approach is another empirical method to predicting runoff response based on a history of runoff responses measured for a given watershed. We will not cover it in detail here, but will describe the basic ideas of the approach (3:55 min).

Ultimately, transfer function approaches rely to some degree on empiricism and are not intended to represent the detailed mechanisms of watershed function. While they are extremely useful for making important immediate decisions about land use management in data-limited watersheds, they have their limits in advancing science and predicting water quality (2:57 min).

Another useful way to parse hydrographs is to use mixing models to infer how much of the runoff response is water coming directly from the precipitation versus how much of runoff response is water that was already in the watershed. This method of source water separation is much more conducive to thinking about watershed function than the more empirical approaches reviewed above (5:38 min).

Mixing models are a common method applied to many hydrological questions regarding the sources of water to a given control volume. Let's review the mass conservation equations used to derive a two-end-member mixing analysis useful for separating "old" and "new" water in runoff response during a precipitation event (6:29 min).

We can work an example of mixing model calculations to help solidify the concepts (6:07 min).

When mixing models are applied to storm hydrographs, many watersheds (especially those in wetter climates) will exhibit the property that much of runoff response to precipitation is "old" water. This implies that the response of the watershed to precipitation is as much (if not more) about the transfer of mechanical energy through the watershed as it is about the movement of water from precipitation to the outlet. Hence, my mantra that you must remember that energy is likely to move through hydrologic systems much faster than water (7:30 min).

End member mixing analyses (or EMMAs) are applied in many different hydrological contexts other than those reviewed above. It is worth reviewing the nature of the method more generally, since it is a method applicable to understanding the relative contributions of multiple sources to any water resource if end members with sufficiently different character can be identified (3:50 min).

Study guide

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Study guides are designed to summarize the vocabulary, concepts, and mathematics learned in this module.

Readings from Dingman (3rd ed)

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A list of associated readings from Physical Hydrology by S. Lawrence Dingman (3rd edition)

Slides used in videos

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Laboratory preparation materials for this module

Link to online laboratory preparation materials for the curve number method

Link to online laboratory preparation materials for hydrograph and source water separation

Detailed documentation on the curve number method from the National Engineering Handbook

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A (possibly dated) training document from the NRCS on the curve number method

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Links to other useful online materials

A good nontechnical description of "old" versus "new" water in stream flow response to precipitation

Another source water separation exercise based on isotopic data

Classic papers

Horton 1933 Eos article (Transactions of the American Geophysical Union) which is one of the original papers on watershed hydrology and the origin of the idea that infiltration capacity into soils is critical to predicting a watershed's response to precipitation

Classic Hewlett and Hibbert paper (1967 from the International Symposium on Forest Hydrology) on the "desperation" of hydrograph separation analysis.

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