I am interested to find weighted average rainfall of the three stations given in attached figure for the given 598 Sq Km catchment area. Gauge 2 is within the catchment and gauge 1 and 3 are outside the catchment.
I would like to know how to apply Thiessen formula?
Hi Sultan, you may want to determine if any similarities in rainfall amount is due to proximity or due to differences in elevation (as Horvath has suggested). It appears that gauge 3 is nearer to the base of the hills/mountains and, depending on prevailing wind direction, may experience higher precipitation. If there are more stations in the region, consider applying statistical model like the generalized additive model (R is an option to implement GAM), and inputting elevation, distance to coast, wind direction, etc. Then use results from GAM to predict rainfall between and around the stations. This is not an easy solution because rain is event driven, so you would need data going back a number of years. A Thiessen model may not be appropriate with just 3 stations - while it is theoretically possible to estimate between gauges, extrapolating beyond the gauges would lead to unsubstantiated values.
you should draw Thiessen polygon for all three stations by ArcGIS software. Then you should calculate shared area between the polygon of each station and the basin, which is the effective weight (wi) of each station on the rainfall of the basin. finally, you can calculate weighted average of the stations as follows:
(wi*p1+w2*p2+w3*p3)/(w1+w2+w3)
pi: rainfall of the station i
w1+w2+w3= area of the basin
The calculation of the shared area (wi) is also possible by the use of ArcGIS.
One option is to use TdhGIS, which is free software obtainable at tdhgis.com, to generate contours lines from the rain gauge data. Thiessen polygons themselves will just provide an area for each gauge but TdhGIS uses thiessen polygons to calculate the weighted average points that define the contour lines.