Estimation of the Average Depth of Rainfall

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 following methods:

1. 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……………..nth and dividing the sum by 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.

2. Theissen Polygon Method:

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. 2.8 (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 A_i of the polygon i within which rain gauge station is located, their average depth of rainfall P is given as

3. 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. 2.8(c). The area between two adjacent isohyets is measured with the help of planimeter.

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

P = 1/A ∑ Area between two adjacent isohyets x mean of the two adjacent isohyet values … (2.3)

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

Example 2.1:

Figure 2.8(a) shows annual rainfall in centimeters at the corresponding rain gauge stations of a watershed.

Determine the average depth of annual precipitation using:

(i) The arithmetic mean method,

(ii) Theissen polygon method, and

(iii) Isohyetal method.

(i) Arithmetic Mean Method:

Using Eq. 2.1, the average depth of annual precipitation,

= 44.535 cm

(ii) Theissen Polygon Method:

Theisson polygons for the given problem have been shown in Fig. 2.8(b) after making suitable adjustments. The calculations for the average depth of annual precipitation are shown in Table 2.1.

(iii) Isohyetal Method:

The isohyetes have been drawn as shown in Fig. 2.8(c). The calculations for the average depth of annual precipitation are shown in Table 2.2.