Design Hydrographs in Small Watersheds from General Unit Hydrograph Model and NRCS-NOAA Rainfall Distributions

Abstract

It is time to shift our paradigm of small watershed design from a graphic (or tabular) to a theoretical method, because (1) the recent general unit hydrograph (UH) model can convert a design hyetograph to a design hydrograph simply, accurately, and theoretically; (2) the Natural Resources Conservation Service (NRCS) has recommended that the National Oceanic and Atmospheric Administration (NOAA) Atlas 14 rainfall data of depths and distributions at a specific site, which is often called the NRCS-NOAA rainfall distributions, should be used for small watershed design if runoff data are unavailable; and (3) in this paper, we have presented a design procedure that formulates design hydrographs from the NRCS-NOAA Atlas 14 rainfall distributions and the general UH model automatically, using the MATLAB convolution function. A literature review indicated that the current practice for design hydrographs in small watersheds from hyetographs is laborious because both hyetographs and UHs are discrete. By contrast, the theoretical general UH model can significantly simplify this process. In this research, we first found analytic design hydrographs from rectangular and triangular hyetographs, which were next used to validate the MATLAB convolution method. We then proposed a double exponential rainfall distribution for both asymmetric and symmetric hyetographs. After that, we modified the symmetric exponential distribution model to describe NRCS-NOAA Atlas 14 data for site-specific hyetographs, which are finally convolved with the general UH model for site-specific design hydrographs, using the MATLAB convolution function. It is noteworthy that the proposed method extends the classic rational method from the peak discharge to the whole hydrograph; and it is valid for both continuous and discrete hyetographs. Hence, it provides a powerful tool in urban development, agriculture land use, roadway planning, and airport construction; it can also be used to evaluate an existing drainage system under various meteorologic–hydrologic conditions. Finally, we expect that this research will shift our current design practice and university UH teaching from an empirical to a theoretical paradigm in the near future.