The watershed shown below (Figure 2) has four rain gages which record the follow

Question

The watershed shown below (Figure 2) has four rain gages which record the following cumulative rainfall for a 2-hr storm event: Compute the mean areal rainfall during the storm using the arithmetic mean method. Consider only the basin area in your calculation. From additional measurements it is determined that only 40% of the total precipitation contributes to stormflow runoff. In other words, the effective precipitation is 40% of the total precipitation. Based on this estimate, what is the effective precipitation for this storm (in cm)? The 1-hr unit hydrograph (i.e. corresponding to 1 cm of runoff) for this basin has been constructed from historical data and is tabulated below. Using the unit hydrograph approach, determine the peak flow and time-to-peak from the 2-hr storm in this problem. A bridge crossing the river is designed for a flood equal to 500 m^3s^-1. Based on your UH-based prediction, will the bridge be overtopped as a result of this storm? If you are not certain about your computations in part c) you may answer this question conceptually. List some of the potential factors that might contribute to your UH-derived prediction being different from observed runoff from this storm.

Explanation / Answer

In areas where more than one rain gauge is established, following methods may be employed to compute the average rainfall:

1)Arithmetic average method
2)Weighing mean method or Thiessen polygon method
3) Isohyetal method.

a) Arithmetic Average Method:--

This is the simplest method of computing the average rainfall over a basin. As the name suggests, the resu lt is obtained by the division of the sum of rain depths recorded at differe nt rain gauge stations of the basin by the number of the stations.

If the rain gauges are uniformly distributed over the area and the rainfall varies in a very regular manner, the results obtained by this method will be quite satisfactory and will not differ much than those obtained by other
methods. This method can be used for the storm rainfall, monthly or annual rainfall average computations.

p = 10.5 +11+7.6+3.9 /4

p = 33/4

p = 8.25 cm

b) if we consider the the total precipitation = 10.5+11+7.6+3.9 = 33 cm

given effective precipitation = 40%

33 * 40 / 100 = 13.2 cm

(c) Major factors affecting the Unit Hydrograph:--

Rainfall duration-

For a given rainfall duration, the peak and volume of the surface runoff are essentially proportional to the intensity of rainfall. Duration also has a direct proportional effect on the volume of runoff.
Rainfall uniformity-

The unit hydrograph concept assumes a uniform rainfall over the watershed. If this factor, which is also affected by the watershed size, is not maintained, unit hydrograph duration will be shorter or longer than required.
Watershed size-

Small basins behave differently from the large ones in terms of the relative importance of various phases of the runoff phenomenon. In small catchments the overland phase is predominant over the channel flow.
Runoff volume-

The unit hydrograph is defined in terms of the effective rainfall of a specified duration. Therefore the runoff volume is directly proportional to the effective rainfall volume and hence the unit hydrograph ordinates.

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