COMPUTATION AF AVERAGE PRECIPITATION

LECTURE # 05

Compiled By: ENGR. MUHAMMAD WAQAS DEPT. OF CIVIL ENGINEERING

UCET, UNIVERSITY OF SARGODHA

AVERAGE PRECIPITATION OVER AN AREA

• Average precipitation is defined as the amount of rainfall that can be assumed uniform for the whole basin area.

• It can be obtained by adding the precipitation of all stations and dividing by the number of stations in the area or outside the area closer to the boundary.

Compiled By: ENGR. MUHAMMAD WAQAS DEPT. OF CIVIL ENGINEERING

UCET, UNIVERSITY OF SARGODHA

SIGNIFICANCE OF AVG. PRECIPITATION

• If average precipitation over an area is known, then it is very easy to compute the total volume of rainfall received by the area from nature.

Rainfall volume= Area x Avg. precipitation

Compiled By: ENGR. MUHAMMAD WAQAS DEPT. OF CIVIL ENGINEERING

UCET, UNIVERSITY OF SARGODHA

METHODS

The methods mostly used for calculating average precipitation over an area are:

1. Arithmetic mean method

2. Thiessen polygon method

3. Isohyetal method

Compiled By: ENGR. MUHAMMAD WAQAS DEPT. OF CIVIL ENGINEERING

UCET, UNIVERSITY OF SARGODHA

ARITHMETIC MEAN METHOD

• In this method the average precipitation over an area is the arithmetic average of the gauge precipitation values.

• We take data for only those stations which arewithin the boundary.

• This is the simplest method but can be applicable only for flat areas and not for the hilly areas i.e. this method is used when:1. Basin area is flat.2. All stations with in practical limits are uniformly distributed

over the area.3. The rainfall is also nearly uniformly distributed over the

area.

Compiled By: ENGR. MUHAMMAD WAQAS DEPT. OF CIVIL ENGINEERING

UCET, UNIVERSITY OF SARGODHA

ARITHMETIC MEAN METHOD

Compiled By: ENGR. MUHAMMAD WAQAS DEPT. OF CIVIL ENGINEERING

UCET, UNIVERSITY OF SARGODHA

Procedure:

• Note down the annual precipitation for all the gauging stations.

• Sum the mean annual precipitations of all of the gauging stations.

• Divide the sum by the total number of stations to get average precipitation for the whole basin area.

Compiled By: ENGR. MUHAMMAD WAQAS DEPT. OF CIVIL ENGINEERING

UCET, UNIVERSITY OF SARGODHA

Compiled By: ENGR. MUHAMMAD WAQAS DEPT. OF CIVIL ENGINEERING

UCET, UNIVERSITY OF SARGODHA

THIESSEN POLYGON METHOD

• The fundamental principle followed in thismethod consists of

“weighing the value of precipitation at each station by a suitable proportion of the basin area.”

Where:

Pavg = Average precipitation over an area

Pi = Mean precipitation for the ith polygon

Ai = Area of the ith polygon

Compiled By: ENGR. MUHAMMAD WAQAS DEPT. OF CIVIL ENGINEERING

UCET, UNIVERSITY OF SARGODHA

• The Thiessen polygon map for a typical watershed

Compiled By: ENGR. MUHAMMAD WAQAS DEPT. OF CIVIL ENGINEERING

UCET, UNIVERSITY OF SARGODHA

Procedure:• Select suitable and same scale for the both axes

depending upon the boundary limits for the catchment area.

• Plot catchment boundary and gauging stations locations.

• Plot polygons around each station by connecting closest stations by straight dash-lines and then drawing perpendicular bisectors to make the sides of the polygons.

• Determine area of each polygon by counting the numbers of squares.

• Compute product (PiAi) and sum up all the products.

Compiled By: ENGR. MUHAMMAD WAQAS DEPT. OF CIVIL ENGINEERING

UCET, UNIVERSITY OF SARGODHA

Thiessen Polygon Map For Annual Precipitation Over Pakistan

Compiled By: ENGR. MUHAMMAD WAQAS DEPT. OF CIVIL ENGINEERING

UCET, UNIVERSITY OF SARGODHA

Compiled By: ENGR. MUHAMMAD WAQAS DEPT. OF CIVIL ENGINEERING

UCET, UNIVERSITY OF SARGODHA

Compiled By: ENGR. MUHAMMAD WAQAS DEPT. OF CIVIL ENGINEERING

UCET, UNIVERSITY OF SARGODHA

Compiled By: ENGR. MUHAMMAD WAQAS DEPT. OF CIVIL ENGINEERING

UCET, UNIVERSITY OF SARGODHA

Compiled By: ENGR. MUHAMMAD WAQAS DEPT. OF CIVIL ENGINEERING

UCET, UNIVERSITY OF SARGODHA

Compiled By: ENGR. MUHAMMAD WAQAS DEPT. OF CIVIL ENGINEERING

UCET, UNIVERSITY OF SARGODHA

Compiled By: ENGR. MUHAMMAD WAQAS DEPT. OF CIVIL ENGINEERING

UCET, UNIVERSITY OF SARGODHA

Compiled By: ENGR. MUHAMMAD WAQAS DEPT. OF CIVIL ENGINEERING

UCET, UNIVERSITY OF SARGODHA

ISOHYETAL METHOD

• The most accurate method of averaging precipitation over an area is the isohyetalmethod.

• It is defined as the line representing the same amount of precipitation. In this method, area between two isohyets is determined. Weighted average for these isohyets is determined and then average precipitation for the whole basin area is computed. i.e:

Compiled By: ENGR. MUHAMMAD WAQAS DEPT. OF CIVIL ENGINEERING

UCET, UNIVERSITY OF SARGODHA

Procedure

• Select suitable and same scale for both X and Y axis.

• Plot catchments boundary and station locations.

• Maintain precipitation amount on each station.

• Select suitable counter interval and number of Isohyets.

• Draw Isohyets by linear interpolation between the stations.

• Compute product ( PiAi) and sum up all the products.

• Find average precipitation by the formula.

Compiled By: ENGR. MUHAMMAD WAQAS DEPT. OF CIVIL ENGINEERING

UCET, UNIVERSITY OF SARGODHA

May be written as:

Where:

• N = Number of strip / segment within catchment

• Pi = Mean annual precipitation for the i’thstrip.

• Ai = Area of the i’th strip

Compiled By: ENGR. MUHAMMAD WAQAS DEPT. OF CIVIL ENGINEERING

UCET, UNIVERSITY OF SARGODHA

Compiled By: ENGR. MUHAMMAD WAQAS DEPT. OF CIVIL ENGINEERING

UCET, UNIVERSITY OF SARGODHA

• The isohyets are draw on the topographic map by interpolating rainfall depths at given stations. Once isohyets are drawn, the area enclosed between consecutive isohyets is determined suitable &precise method. Calculations are given below:

Compiled By: ENGR. MUHAMMAD WAQAS DEPT. OF CIVIL ENGINEERING

UCET, UNIVERSITY OF SARGODHA

Lab # 05

• The names, locations by latitude and longitude and mean annual precipitations for certain weather stations within the catchment’s area are given below:

Estimate the average rain fall over basin area by using following three methods

1. Arithmetic Mean Method2. Thiessen Polygon Method3. Isohyetal Method

Compiled By: ENGR. MUHAMMAD WAQAS DEPT. OF CIVIL ENGINEERING

UCET, UNIVERSITY OF SARGODHA

Calculation Table For Theissen Polygon Method

Stations Mean annual

ppt “P” mm

Area “A”

Sq km

Pi x Ai

A 128.3 18.45

B 136.73 27.40

C 113.03 30.14

D 123.77 26.10

E 150.41 27.95

F 186.51 22.45

G 223.85 19.21

H 120.51 25.36

I 108.84 27.09

J 141.4 31.45

K 151.33 28.55

L 161.45 27.70

Compiled By: ENGR. MUHAMMAD WAQAS DEPT. OF CIVIL ENGINEERING

UCET, UNIVERSITY OF SARGODHA

The Thiessen Polygon map for a LAB#05:

Compiled By: ENGR. MUHAMMAD WAQAS DEPT. OF CIVIL ENGINEERING

UCET, UNIVERSITY OF SARGODHA

Calculation Table For Isohyetal Method

Stations Mean annual

ppt “P” mm

Area “A”

Sq km.

Pi x Ai

A 128.3 70.12

B 136.73 70.12

C 113.03 4.5

D 123.77 83.1

E 150.41 34.45

F 186.51 8.51

G 223.85 3.21

H 120.51 83.1

I 108.84 4.76

J 141.4 29.2

K 151.33 34.35

L 161.45 22.58

Compiled By: ENGR. MUHAMMAD WAQAS DEPT. OF CIVIL ENGINEERING

UCET, UNIVERSITY OF SARGODHA

• The isohyetal map for a LAB#05:

Compiled By: ENGR. MUHAMMAD WAQAS DEPT. OF CIVIL ENGINEERING

UCET, UNIVERSITY OF SARGODHA