Thiessen polygon method with rainfall data

a) Thiessen polygon method

The Thiessen polygon method gives the average rainfall by weighting each station's rainfall by the area it represents. It assumes the rainfall at any point equals that at the nearest gauge.

Procedure:

1. Plot all rain gauge stations (inside and near the catchment) on a map of the catchment.
2. Join adjacent stations by straight lines to form a network of triangles.
3. Draw perpendicular bisectors of each side; they meet to form a polygon around each station.
4. Measure (by planimeter or GIS) the area $A_i$ of each polygon inside the catchment boundary.
5. Compute:

$$\bar{P} = \frac{P_1A_1 + P_2A_2 + \dots + P_nA_n}{A_1 + A_2 + \dots + A_n} = \sum P_i\frac{A_i}{A}$$

   +-------+--------+
   |   A   |    B   |   * = rain gauge
   |   *   |    *   |   lines = perpendicular
   +---+---+----+---+   bisectors
       |  C *   |
       +--------+

Merits: allows for uneven gauge spacing. Demerits: ignores orographic effects; polygons must be redrawn when the network changes.

b) Numerical

$$\bar{P} = \frac{\sum P_iA_i}{\sum A_i} = \frac{33500}{450} = 74.44\ \text{mm}$$

Answer: Average rainfall over the catchment ≈ 74.4 mm.