Computation of

Average Rainfall Over a Basin

Topics

Computation of average rainfall over a basin.

Discussion on various methods of average rainfall computation with examples

Presentation of Rainfall data.

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.

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.

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

in i

av

PP P P P

Pn n

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

in i

av

PP P P P

Pn n

mm 56.145

8.72

5

2.164.108.148.186.12

avP

Solution:

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 in n i

av nn

ii

PAPA P A P A P A

PA A A A

A

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 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.

Example: Using Thiesen Polygon Method, find average rainfall over a catchment. The data is:Rain Gauge Station A B C D EPolygon Area (km2) 40 45 38 30 43Precipitation (mm) 30.8 33.4 34.6 32.6 24.6

Solution:

mm 53.31

193

6.6085

A

PAPav

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

2av

P PA

PA

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:

Example: Using Isohyetal Method, find average rainfall over a catchment. The data is:Isohyetes (cm) 12 13 14 15 1617Area b/w Isohyetes (km2) 22 80 110 89 70Average Precipitation (cm) 12.5 13.5 14.5 15.5 16.5

cm 78.14371

5.5484A

2PP

AP

21

av

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.

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

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.

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.