This document discusses different methods for measuring and averaging rainfall over an area: - Rainfall is measured using rain gauges and expressed as depth over an area. - The arithmetic mean, Thiessen polygon, and isohyet methods are used to calculate average rainfall values from point measurements at rain gauge stations. - The Thiessen polygon method assigns influence areas to each station based on the location of stations, and weights each measurement by its influence area. - The isohyet method involves drawing lines of equal rainfall and calculating a weighted average based on the rainfall amounts and sizes of the areas between the lines.

1. Hydrology

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Measurement of
Rainfall

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Introduction
Rainfall is expressed in terms of the depth to which
rainwater would stand on an area, if all the rain were
collected on it.
Thus, 1cm of rainfall over a catchment area of 1km2
represents a volume of water equal to 104m3.

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Raingauge
The precipitation is collected and measured in a Raingauge.
In India, the raingauges commonly used are Symon’s gauge.

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Average Rainfall over an area
Arithmetic Mean Method
Thiessen Polygon Method
Isohytel Method
To convert the point rainfall values measured by various raingauge
stations into an average value over a catchment, following methods
are used.

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Arithmetic Mean
Method

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If there are small variations in the rainfall values measured by the
stations, this method can be used.
If P1, P2, . . . , Pn are the rainfall values obtained from n raingauge
stations within a catchment, then the average precipitation is given
by
1 2 1.....
n
i
n i
P
P P P
P
n n
  
 


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Thiessen Polygon
Method

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In this method, the rainfall recorded at each station is given a
weightage on the basis of an area closest to that station.
1. Draw the catchment area to a scale and mark the raingauge
stations on it.

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2. Join each station by straight line to create a triangulated
network.

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3. Draw perpendicular bisectors on each sides of each triangles.
Extend the bisectors to meet the other bisectors and the catchment
boundary.

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4. The polygons formed by the perpendicular bisectors (and part
of catchment boundary) are the influence areas of each stations.

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If there are n number of raingauge stations in and around the
catchment and if A1,A2, . . . ,An are the respective influence areas of
Thiessen Polygon, then the average rainfall is given by

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Example
Four raingauge stations are located in a catchment area,
approximated by a circle of radius 100km, as shown in the figure.
Annual precipitation recorded by these stations in the year 2003 are:
A(85cm), B(130cm), C(105cm), D(98cm).
Draw the Thiessen polygon and calculate the average annual
precipitation on the catchment in 2003.

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Solution

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Isohytel Method

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Introduction
Isohyet: An isohyet is a line joining points of equal rainfall
magnitude.
If P1, P2, . . . , Pn are the values of isohyets and if A1,A2, . . . ,An−1 are
the inter-isohyet area respectively, then the mean precipitation over
the catchment is given by

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Example
The isohyets due to a storm in a catchment were drawn and the
area of the catchment bounded by isohyets were tabulated as
below. Estimate the mean precipitation due to the storm.

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Solution

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Thank You