A synthetic unit hydrograph (SUH) is a widely used tool in hydrology for estimating the design flood hydrograph, especially for catchments where detailed information about observed rainfall and resulting flood hydrographs is scarce or unavailable. It is derived using empirical equations of regional validity that relate salient hydrograph characteristics to the basin characteristics.
Purpose and Derivation: When observed discharge and concurrent rainfall data are not available for deriving a unit hydrograph (UH) directly, SUHs are developed using basin characteristics. The process generally involves:
- Deriving representative unit hydrographs from gauged catchments in a region where data is available.
- Establishing relationships between defined parameters of these unit hydrographs and the physical characteristics of their respective catchments.
- Applying these established relationships to estimate the parameters of a unit hydrograph for ungauged catchments, for which only topographic map characteristics can be determined.
For this purpose, countries like India are divided into hydro-meteorologically homogeneous sub-zones, and specific Flood Estimation Reports (FER) are published by organizations like the Central Water Commission (CWC).
Catchment Characteristics Used for SUH Derivation: The physiographic parameters of a catchment that are typically used to derive a synthetic unit hydrograph include:
- Catchment area (A).
- Length of longest main stream along the river course in km (L).
- Length of the longest main stream from a point opposite to the centroid of the catchment area to the gauging site along the main stream in Km (Lc).
- Equivalent stream slope in m/km (S).
Underlying Principles and Limitations of Unit Hydrograph Theory (which apply to SUHs): A unit hydrograph, in general, represents the direct runoff hydrograph resulting from one unit of effective rainfall (typically 1 mm or 1 cm) uniformly distributed over the basin at a uniform rate during a specified unit duration. The theory relies on several key assumptions:
- Uniform distribution of effective rainfall over the basin.
- Uniform rate of effective rainfall during the unit time.
- Constant base or time duration of the direct runoff hydrograph.
- Principle of linearity, superposition, and proportionality: Ordinates of the direct runoff hydrograph are directly proportional to the total amount of direct runoff.
- Principle of time invariance: For a given basin, the direct runoff hydrograph from a specific effective rainfall pattern will always be the same, irrespective of when it occurs.
However, these ideal conditions are rarely perfectly met in natural settings. The unit hydrograph theory is not applicable to runoff originating from snow or ice, nor to conditions where the duration of effective rainfall is greater than the time of concentration. Also, the reliability of the method diminishes for very large catchments, generally exceeding about 5000 Sq.km, because uniformly distributed storms are rare over such large areas. For larger basins, it is recommended to divide them into sub-basins and develop individual unit hydrographs, combining them using flood routing procedures.
Application: Once a synthetic unit hydrograph is derived, it can be used in convolution with rainfall excess hyetographs (rainfall intensity vs. time) to compute the design flood hydrograph. This allows for a realistic determination of the moderating effect as the flood passes through a reservoir or river reach. Examples include the estimation of Probable Maximum Flood (PMF) hydrographs for dams like Dam A and Dam B, where regional Flood Estimation Reports were used to derive the synthetic unit hydrograph parameters. The critically sequenced effective rainfall is then convoluted with the unit hydrograph ordinates to obtain the PMF hydrograph, with base flows added to get the total design flood.
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