Calculating Average Depth of Precipitation | Measuring the Average Depth of Rainfall: 3 Methods  | Estimation of the Average Depth of Rainfall

The information on the average depth of precipitation (or rainfall) over a specified area on either the storm basis or seasonal basis or annual basis is often required in several types of hydrologic problems. The depth of rainfall measured by a rain gauge is valid for that rain gauge station and in its immediate vicinity. Over a large area like watershed (or catchment) of a stream, there will be several such stations and the average depth of rainfall over the entire area can be estimated by one of the three methods:

A.    Arithmetic Mean Method

B.    Theissen Polygon Method

C.     Isohyetal Method

A.    Arithmetic Mean Method

This is the simplest method in which average depth of rainfall is obtained by obtaining the sum of the depths of rainfall (say P₁, P₂, P₃, P₄ .... P_n) measured at stations 1, 2, 3, ..... n and dividing the sum by the total number of stations i.e. n. Thus,

This method is suitable if the rain gauge stations are uniformly distributed over the entire area and the rainfall variation in the area is not large.

B.    Theissen Polygon Method

The Theissen polygon method takes into account the non-uniform distribution of the gauges by assigning a weightage factor for each rain gauge. In this method, the entire area is divided into number of triangular areas by joining adjacent rain gauge stations with straight lines, as shown in Fig. 1 (a and b). If a bisector is drawn on each of the lines joining adjacent rain gauge stations, there will be number of polygons and each polygon, within itself, will have only one rain gauge station. Assuming that rainfall P_i recorded at any station i is representative rainfall of the area Ai of the polygon i within which rain gauge station is located, the weighted average depth of rainfall P for the given area is given as

where, 

Here, A_i/A is termed the weightage factor for ith rain gauge.

Fig 1. Areal averaging of precipitation (a) rain gauge network, (b) Theissen polygon

This method is, obviously, better than the arithmetic mean method since it assigns some weightage to all rain gauge stations on area basis. Also, the rain gauge stations outside the catchment can also be used effectively. Once the weightage factors for all the rain gauge stations are computed, the calculation of the average rainfall depth P is relatively easy for a given network of stations.

While drawing Theissen polygons, one should first join all the outermost raingauge stations. Thereafter, the remaining stations should be connected suitably to form quadrilaterals.The shorter diagonals of all these quadrilaterals are, then, drawn. The sides of all these triangles are, then bisected and, thus, Theissen polygons for all raingauge stations are obtained.

C.     Isohyetal Method

An isohyet is a contour of equal rainfall. Knowing the depths of rainfall at each rain gauge station of an area and assuming linear variation of rainfall between any two adjacent stations, one can draw a smooth curve passing through all points indicating the same value of rainfall, Fig. 1 (c). The area between two adjacent isohyets is measured with the help of a planimeter.

The average depth of rainfall P for the entire area A is given as :

P = 1/A Σ [Area between two adjacent isohyets] × [mean of the two adjacent isohyet values]

Since this method considers actual spatial variation of rainfall, it is considered as the best method for computing average depth of rainfall.

Isohyetal

Example : The average depth of annual precipitation as obtained at the rain gauge stations for a specified area are as shown in Fig. 1 (a). The values are in cms. Determine the average depth of annual precipitation using (i) the arithmetic mean method, (ii) Theissen polygon method, and (iii) isohyetal method.

Solution: (i) Arithmetic mean method :

Using Eq. (2.2), the average depth of annual precipitation,

P =1/11 [20.3 + 88.1 + 60.9 + 54.7 + 48.1 + 45.6 + 60.0 + 84.0 + 93.2 + 140.6 + 154.0]

= 1/11 (849.5) = 77.23 cm.

 

(ii) Theissen polygons for the given problem have been shown in Fig. 1 (b). The computations for the average depth of annual precipitation are shown in the following

Table :

Average annual Precipitation for basin = ⨊ P_i A_i /⨊A_i = 87.97

(iii) Isohyetal method : Isohyets are shown in Fig. 1 (c). The computations for the average depth of annual precipitation are shown in the following Table 

Average annual precipitation for the basin = 151380/1944

= 77.92 cm

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