Average Depth of Precipitation Over an Area

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 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 .... Pn) 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.

2) 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 enitre 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 Pi 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-bar for the given area is given as

Here, Ai/ A is termed the weightage factor for i^th  rain gauge.

Fig. 1 Areal averaging of precipitation a) Rain gauge network, b) Theissen polygons, c) Isohyets

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-bar is relatively easy for a given network of stations.

While drawing Theissen polygons, one should first join all the outermost rain gauge 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 rain gauge stations are obtained.

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

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

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