Methods of average rainfall over catchment

Rainfall measured at a gauge is point rainfall. To find the average depth over a catchment, three methods are used.

1. Arithmetic mean method

The average of rainfall of all gauges in the area:

$$\bar P = \frac{P_1 + P_2 + \dots + P_n}{n}$$

Suitable for flat areas with uniform gauge distribution and little variation of rainfall. It is simple but ignores the position of gauges and topography.

2. Thiessen polygon method

Gauge stations are joined to form triangles, perpendicular bisectors of the sides are drawn, and the polygon around each station is the area closest to it. Each gauge is weighted by its polygon area:

$$\bar P = \frac{\sum A_i P_i}{\sum A_i}$$

It considers non-uniform gauge density and is more accurate than the arithmetic mean. It does not account for orographic effects, and the polygons must be redrawn if a gauge is added or fails.

3. Isohyetal method

Isohyets (lines of equal rainfall) are drawn using gauge values. The average rainfall between two successive isohyets is taken as their mean, and weighted by the area between them:

$$\bar P = \frac{\sum A_i \dfrac{P_i + P_{i+1}}{2}}{\sum A_i}$$

It is the most accurate, particularly for hilly regions, as it accounts for topography and storm pattern, but requires many gauges and judgement.

   15 cm   10 cm   5 cm   (isohyets)
   ( (  ( o ) ) )    A1, A2, A3 = inter-isohyet areas