Procedure of Thiessen mean rainfall

The Thiessen polygon method gives the mean rainfall by weighting each gauge by the area nearest to it.

Procedure

1. Draw the catchment boundary to scale and mark the positions of all rain gauges (inside, and a few just outside).
2. Join adjacent stations by straight lines to form a network of triangles (avoid very acute triangles).
3. Draw the perpendicular bisector of each side. The bisectors meet at the circumcentres of the triangles and form a polygon around each station.
4. Each polygon is the area closer to its station than to any other. Trim the polygons at the catchment boundary.
5. Measure the area $A_i$ of each polygon inside the catchment (planimeter, grid or coordinates).
6. Find the weight $W_i = A_i/A$, where $A = \sum A_i$ is the catchment area.
7. Mean rainfall:

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

        *1
       /|\
      / | \     perpendicular bisectors
   *2---+---*3   form polygons around
      \ | /     each station
        *4

Remarks

It is better than the arithmetic mean for uneven gauge spread, but it does not include orographic effects. The polygons must be redrawn when a gauge is added or fails.