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# DERIVATION OF UNIT HYDROGRAPHS

### DERIVATION OF UNIT HYDROGRAPHS

1. From a study of continuously gauged stream runoff, a number of isolated storm hydrographs caused by short spells of rainfall excess, each of approximately the same duration (0.9 to 1.1D h), are selected.

2. The base flow is separated for each of these surface runoff hydrographs.

3. To determine the depth of ER, evaluate the area under DRH and divide the volume of direct runoff obtained by the catchment area.

4. To obtain the ordinates of the unit hydrograph, divide the ordinates of the various DRHs by their respective ER values.

The flood hydrographs included in the analysis should have the following desirable characteristics in relation to the storms that caused them:

1. The storms should be isolated storms that occur one at a time.

2. Rainfall should be fairly consistent over the course of the event and cover the entire catchment area.

3. Rainfall duration should be 1/5 to 1/3 of the basin lag.

4. The selected storm’s rainfall excess should be significant (A range of ER values of 1.0 to 4.0 cm is preferred)

• As previously noted, a number of unit hydrographs of a certain duration are calculated and shown.

• The numerous unit hydrographs created will not be exactly equal due to regional and temporal variances in rainfall and storm deviations from the assumptions in the unit hydrograph theory.

• In general, the mean of these curves is used as the unit hydrograph for the watershed for the given duration.

The time to peaks and the average of peak flows are computed first.

• Then, using eye judgement, a mean curve of best fit is drawn across the averaged peak to close on an averaged base length.

• The DRH volume is calculated, and any deviations from unity are adjusted by modifying the peak value.

• Note – In the plot of the unit hydrograph, it is common to draw the averaged ERH of unit depth to highlight the type and length of rainfall that created the unit hydrograph.

Figure 1: Average unit hydrograph derivation

• During the duration D hours of a unit hydrograph, it is believed that the rainfall excess occurs uniformly across the catchment.

• For a unit hydrograph, an optimal period is one in which modest variations in rainfall intensity have no major impact on runoff.

• The unit hydrograph should not last more than 1/5 to 1/3 of the basin lag.

• For catchments greater than 250 square kilometres, a 6 hour period is sufficient.

Unit Hydrograph from a Complex Storm

When simple isolated storms are unavailable, data from complex storms with a lengthy duration must be used to calculate the unit hydrograph.

• The challenge is to break down a composite flood hydrograph into its constituent DRHs and base flow.• It is expected that a common unit hydrograph of adequate duration exists.

• This is the inverse problem of flood hydrograph derivation.• Consider a rainfall excess consisting of three consecutive D-hour periods with ER values of

• A composite DRH is obtained after base flow separation of the composite flood hydrograph. At a time interval of D hours, draw the ordinates of the composite DRH.

Let the ordinates of unit hydrographs be determined at various time intervals 1D, 2D, 3D, etc. from the commencement of the ERH.clip image004 and the composite DRH’s ordinate complex storm’s unit hydrograph

Figure: A complex storm’s unit hydrograph

• The worth ofcan be deduced from the preceding

• This method’s disadvantage is that errors propagate and grow as the computation progresses.