Synthetic unit hydrographs explained
A unit hydrograph is a hydrograph for a given basin that is produced by a unit of rainfall (excess) depth. Since there are several possible durations for that unit of rainfall depth, 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 can be calculated.
(In practice, basin diffusion is commonly referred to as 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.
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. _{t}, and (2) a peak parameter C_{p}.
A larger C_{t} meant a greater basin lag and, consequently, greater diffusion.
A larger C_{p} meant a greater peak flow and, consequently, less diffusion.
In 1954, the USDA Natural Resources Conservation Service followed Snyder in developing
a synthetic unit hydrograph for agency use. _{bt}/t_{p} = 8/3.
For comparison, in the rational method, this ratio
is effectively 2.
Therefore, NRCS introduced some diffusion into their synthetic
unit hydrograph, but obviously 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 8/3 parameter will invariably overestimate the peak flows.
The U.S. Bureau of Reclamation has developed a series of synthetic unit hydrographs
applicable to regions within its jurisdiction. ^{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 regions of the Western United States.
The general dimensionless unit hydrograph (GDUH) is yet another way of formulating a synthetic
unit hydrograph. The method can be readily nondimensionalized, rendering it independent of the basin area and the unit hydrograph duration and, therefore, of global applicability. Once the two parameters, the Courant number C and the number N of linear reservoirs, are chosen, a dimensionless synthetic unit hydrograph can be calculated.
The method has considerable flexibility for simulating
a wide range of diffusion and associated
lag 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 time associated with the peak flow is 1-91.
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
Snyder, F. F. 1938. Synthetic Unit-Graphs. ^{1}Transactions, American Geophysical Union,
19, 447-454.
USDA Natural Resources Conservation Service. 1954, revised 1985. ^{2}National Engineering Handbook, Section 4: Hydrology,
Washington, D.C. (Republished as Part 630: Hydrology).
U.S. Bureau of Reclamation. 1987. ^{3}Design of Small Dams. 3rd edition, Denver, Colorado.
Ponce, V. M. 1989.
^{4}Engineering Hydrology, Principles and Practices. Prentice-Hall, Englewood Cliffs, New Jersey.
Ponce, V. M. 2009. A general dimensionless unit hydrograph.
^{5}
Ponce, V. M. 2009. Cascade and convolution: One and the same.
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