Average rainfall methods with merits and demerits

Rain gauges give point rainfall. The mean rainfall over a catchment due to a storm is found by three methods.

1. Arithmetic mean method

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

The simple average of the gauges inside the catchment. Used for flat areas with uniformly spread gauges and rainfall that varies little.

2. Thiessen polygon method

1. Plot the gauges on the catchment map and join adjacent gauges to form triangles.
2. Draw perpendicular bisectors of the sides; they form a polygon around each gauge.
3. Measure the area $A_i$ of each polygon inside the catchment.
4. Compute

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

3. Isohyetal method

1. Draw isohyets (lines of equal rainfall) by interpolating between gauge values.
2. Find the area $A_i$ between consecutive isohyets and the mean of their values $\bar P_i$.
3. Compute $\bar P = \sum A_i \bar P_i / \sum A_i$.

Merits and demerits

For hilly catchments such as those in Nepal, the isohyetal method is preferred if enough gauges exist; otherwise Thiessen is used.