This document discusses different methods for computing average rainfall over a basin including arithmetic average, Thiessen polygon, and isohyetal methods. It provides examples of calculating average rainfall using each method. It also discusses presenting rainfall data through mass curves and hyetographs. The arithmetic average method simply takes the mean of recorded rainfall values at stations. Thiessen polygon method weights values based on each station's representative area. Isohyetal mapping involves contouring equal rainfall and calculating weighted averages between contours.

2. HYDROLOGY
Second Term, Final Year
B.E. Civil Engineering

3. Topics
Computation of average rainfall over a
basin.
Discussion on various methods of
average rainfall computation with
examples
Presentation of Rainfall data.

4. Computation of
Average Rainfall Over a Basin

5. Computation of average rainfall over a
basin.
In order to compute the average rainfall over a basin or
catchment area, the rainfall is measured at a number of rain-
gauge stations suitably located in the area.
The no. of rain-gauge stations depends upon the area and
distribution of rainfall.
If a basin or catchment area contains more than one rain-gauge
station, the computation of average rainfall may be done by the
following methods:
Arithmetic average method.
Thiessen polygon method.
Isohytel method.

6. 1.Arithmetic average method.
 Simplest method of estimating average rain fall.
 Average rainfall is calculated by arithmetic average of
recorded rainfall @ various stations.
 If P1, P2, P3…..Pn are the rainfall values measured@ n
gauge stations, we have
Advantages: suitable method when rainfall is uniform.
1 2 3 1......
n
i
n i
av
P
P P P P
P
n n
=+ + + +
= =
∑

7. Example: Using Arithmetic Average Method, find average rainfall
over a catchment. The rain gage data is: 12.6, 18.8, 14.8, 10.4 and
16.2 mm.
1 2 3 1......
n
i
n i
av
P
P P P P
P
n n
=+ + + +
= =
∑
mm56.14
5
8.72
5
2.164.108.148.186.12
==
++++
=avP
Solution:

8. 2.Thiessen polygon method.
 This method is a more common method of weighing the rain-
gauge observation according to the area.
 Also called Weighted Mean Method.
 Accurate than arithmetic average method.
 Average rainfall can be computed by the following expression.
Advantages: This method is based on assumption that a rain-
gauge station best represents the area which is close to it.
1 1 2 2 3 3 1
1 2 3
1
( )
......
....
n
i i
n n i
av n
n
i
i
PA
P A P A P A P A
P
A A A A
A
=
=
+ + + +
= =
+ + + +
∑
∑

9. Procedure: 1. Join the adjacent rain-gauge
stations.
2. Construct the perpendicular
bisectors of each of these lines.
3. The polygon formed by the
perpendicular bisectors around a
station encloses an area
encloses an area which is every
where closer to that station than
to any other station.
4. Find the area of each of these
polygons, shown hatched in the
figure.
5. Compute the average
precipitation using the given
formula.

10. Example: Using Thiesen Polygon Method, find average rainfall
over a catchment. The data is:
Rain Gauge Station A B C D E
Polygon Area (km2
) 40 45 38 30 43
Precipitation (mm) 30.8 33.4 34.6 32.6 24.6
Solution:
( )
mm53.31
193
6.6085
==
×
=
∑
∑
A
PA
Pav

11. 3.Isohytel method.
 An isohyet is a line, on a rainfall map of the basin, joining
places of equal rainfall readings.
 An isohyetal map showing contours of equal rainfall
presents a more accurate picture of the rainfall distribution
over the basin.
 Average rainfall can be computed by the following
expression.
 Advantages: The isohytel method is the most elaborate
and accurate than other methods.
1 2
2
av
P P
A
P
A
 + 
 ÷ 
  =
∑
∑

12. 1. From the rainfall values
recorded at various rain-
gauge stations, prepare the
isohyetal map.
2. Measure the areas enclosed
between successive isohyets
with the help of planimeter.
3. Multiply each of these areas
by the average rainfall
between the isohyets.
4. Compute the average rainfall
applying the given formula.
Procedure:

13. Example: Using Isohyetal Method, find average rainfall over a
catchment. The data is:
Isohyetes (cm) 12 13 14 15 16 17
Area b/w Isohyetes (km2
) 22 80 110 89 70
Average Precipitation (cm) 12.5 13.5 14.5 15.5 16.5
cm78.14
371
5.5484
A
2
PP
A
P
21
av
==





 +
=
∑
∑

14. Problem:
Find the mean precipitation for the area sketched in figure by
Thiessen’s method. The area is composed of a square plus an
equilateral triangular plot of side 4 kms. Rainfall readings in cms at
the various stations are also given in figure.

15. Presentation of rainfall data
A few commonly used methods of presentation of
rainfall data which have been found to be useful in
interpretation and analysis of such data are:
1.Mass curve of Rainfall
2.Hyetograph

16. 1.Mass curve of Rainfall
 If the total accumulated precipitation is plotted
against time, the curve obtained is known as Mass
curve of Rainfall/Storm.
 The curve rises steeply in the beginning and then
tends to become constant.
 Mass curve of rainfall are very useful in extracting the
information on the duration and the magnitude of
storm.
 Also, intensities at various time intervals in a storm
can be obtained.

17. 2.Hyetograph.
It can be defined as a plot of intensity of rainfall (cm/hr) against
the time interval, represented as a bar chart.
The area under hyetograph represents the total precipitation
received in that period.
This chart is very useful in representing the characteristics of
storm, and is particularly important in developing the design
storms to predict extreme floods.
The time interval used depends on the purpose; in urban-
drainage problems, small durations are used, while in flood flow
computations in larger catchments, the intervals are of about 6
hr.