Synthetic unit hydrographs explained

Victor M. Ponce

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1. Unit hydrographs

A unit hydrograph is a hydrograph for a given basin that is produced by a unit depth of effective rainfall (rainfall excess). There are several possible durations for that unit of rainfall depth; therefore, a given basin can have several unit hydrographs. Once a unit hydrograph has been determined for a given basin, say the X-hr unit hydrograph, other unit hydrographs for the same basin can be derived from this X-hr unit hydrograph following established procedures; either the method of superposition of the S-hydrograph method.

A unit hydrograph embodies the diffusion properties of a basin, that is, the unit hydrograph is the means by which basin diffusion may be calculated. (In practice, basin diffusion is commonly referred to as basin storage). Steeper basins have less diffusion; milder basins have more diffusion. The main parameter of the unit hydrograph is the basin lag; the longer the lag, the more the diffusion. The peak flow of the unit hydrograph is inversely related to the basin lag; the longer the lag, the lesser the peak flow, and vice versa.

Unit hydrographs can be derived from rainfall-runoff data. However, the procedure is time-consuming and it is limited to gaged basins, which are comparatively small in number.

2. Snyder's synthetic unit hydrograph

A synthetic unit hydrograph retains all the features of the unit hydrograph, but does not require rainfall-runoff data. A synthetic unit hydrograph is derived from theory and experience, and its purpose is to simulate basin diffusion by estimating the basin lag based on a certain formula or procedure.

The first synthetic unit hydrograph was developed by Snyder in 1938.1 In order to provide sufficient flexibility for simulating a wide range of diffusion amounts, Snyder devised two parameters: (1) a time parameter Ct, and (2) a peak parameter Cp. A larger Ct meant a greater basin lag and, consequently, greater diffusion. A larger Cp meant a greater peak flow and, consequently, less diffusion.

3. NRCS synthetic unit hydrograph

In 1954, the USDA Natural Resources Conservation Service followed Snyder in developing a synthetic unit hydrograph suited for agency use.2 Since NRCS applications typically involved smaller basins, that is, less than 10 square miles, they chose to set the peak parameter at a fixed ratio of triangular-time-base to time-to-peak Tbt/tp = 8/3. For comparison, in the rational method, this ratio is exactly 2, i.e., no diffusion. Therefore, NRCS introduced some diffusion into their synthetic unit hydrograph, but clearly not a lot. The diffusion is fixed by the 8/3 parameter, and it is certainly less than Snyder's, who unlike NRCS, could vary its diffusion, within certain limits.

The NRCS synthetic unit hydrograph is generally justified because the NRCS basins were typically relatively small, and small basins usually do not exhibit a great amount of diffusion. However, caution is advised when attempting to use the NRCS procedure for larger and/or milder basins. In this case, the use of the NRCS unit hydrograph will invariably result in overestimation of the peak flows.

4. USBR synthetic unit hydrograph

The U.S. Bureau of Reclamation has developed a series of synthetic unit hydrographs applicable to regions within its jurisdiction.3 These regions are: (1) Great Plains, (2) Rocky Mountains, (3) Southwestern Desert, Great Basin, and Colorado Plateau, (4) Sierra Nevada of California, (4) Coast and Cascade Ranges, and (6) Urban basins. The basin lag is directly proportional to the parameter C, which varies within and between the six regions. A smaller C means less diffusion; a larger C means more diffusion. Recommended C values vary from as low as 0.34-0.88 for urban basins, which are typically small, to 1.65-3.90 for the larger or more diffused basins of the Sierra Nevada of California.4

The USBR methodology reveals that the basins tend to vary widely in their diffusion properties. This confirms the wide range of basin scales and topographic features that characterizes the regions of the Western United States.

5. General Dimensionless Unit Hydrograph

The general dimensionless unit hydrograph (GDUH) is yet another way of formulating a synthetic unit hydrograph.5 The procedure is based on the cascade of linear reservoirs, a conceptual model which simulates basin response by routing watershed/basin flows through a series of linear reservoirs. The method has two parameters: the Courant number C and the number N of linear reservoirs.

The cascade of linear reservoirs may be readily nondimensionalized, leading to the GDUH (Ponce, 2010). The procedure renders the methodology independent of the basin area and unit hydrograph duration, confirming its global applicability. Once the two parameters, the Courant number and the number of linear reservoirs, are chosen, a unique synthetic general dimensionless unit hydrograph (GDUH) is obtained.

The method has considerable flexibility for simulating a wide range of diffusion effects. For parameter ranges 0.1 < C < 2, and 1 < N < 10, the range in dimensionless peak flow is 1.00 - 0.013, and the range of dimensionless peak flow time is 1 - 91.6 Rainfall-runoff data and/or experience are recommended in order to estimate the model parameters for specific applications.

6. Concluding remarks

The Snyder method is the precursor to all synthetic unit hydrographs. It is flexible and generally applicable to larger basins, in the hundreds to thousands of square miles. The NRCS method is simple, a de facto standard by way of practice, somewhat inflexible and applicable to smaller basins, in the tens of square miles or less. The NRCS method should be used with caution in larger and/or milder basins. The USBR method is applicable to the regions for which it was developed, with its focus in the Western United States. The method is flexible and applicable to basins both large and small, depending on the choice of parameters. The Generalized Dimensionless Unit Hydrograph (GDUH) has unlimited flexibility and it is of global applicability. The parameters C and N may be estimated from measured data or, alternatively, from experience with basins of similar geomorphologic and hydrologic characteristics.

1 Snyder, F. F. 1938. Synthetic Unit-Graphs. Transactions, American Geophysical Union, 19, 447-454.
2 USDA Natural Resources Conservation Service. 1954, revised 1985. National Engineering Handbook, Section 4: Hydrology, Washington, D.C. (Republished as Part 630: Hydrology).
3 U.S. Bureau of Reclamation. 1987. Design of Small Dams. 3rd edition, Denver, Colorado.
4 Ponce, V. M. 1989. Engineering Hydrology, Principles and Practices. Prentice-Hall, Englewood Cliffs, New Jersey.
5 Ponce, V. M. 2009. A general dimensionless unit hydrograph.
6 Ponce, V. M. 2009. Cascade and convolution: One and the same.
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