hydrology

Density of Precipitation gauge network

• Number of rain gauges in a catchment area depends on following parameters

1. topography 2. financial constraints 3. level of development 4. climate

Dense network is required for thunder stormsSparse network is required for level terrain10% of the rain gauges should be recording type

Density of Precipitation gauge network (WMO)

• 1. For flat temperate regions 600-900 sq km• 2. For mountainous regions temperate climate

100-250 sq. km• 3. For small mountainous islands - irregular

precipitation 25 sq. km• 4. For arid and polar zones 1500-10000 sq km

Density of Precipitation gauge networkBureau of Indian Standards

• In plains: 520 sq. km • elevation >= 1000 m : 260-390 sq. km • In hilly areas with heavy rainfall: (130 sq. km)

Determining adequacy of rain gauge stations

• Optimal number of raingauge stations N

• Cv is coefficient of variation

• ε is maximum error in percent of estimate of average rainfall

2

vCN

100vC

P

Determining adequacy of rain gauge stations

• Standard deviation σ

• Mean precipitation

2

1

1

n

ii

P P

n

1

1 n

ii

P Pn

We will do some example problems

• The average depth of annual precipitation as obtained at the rain gauge stations for a specified area are as shown in Fig. 1. The values are in cms. Determine the average depth of annual precipitation using (i) the arithmetic mean method, (ii) Theissen polygon method, and (iii) isohyetal method.

Arithmetic mean method

• Figure 1

Arithmetic mean method

Stations Rainfall (cm)1 20.32 88.13 60.94 54.75 48.16 45.67 608 849 93.2

10 140.611 154

Thiessen polygon method

Thiessen polygon method

StationsRainfall, Pi

(cm)Area of each polygon ,Ai (km2)

Weightage factor, wi =Ai/At

Precipitation * weightage factor (Pi

*wi

1 20.3 22 0.011 0.232 88.1 0 0.000 0.003 60.9 0 0.000 0.004 54.7 0 0.000 0.005 48.1 62 0.032 1.536 45.6 373 0.192 8.757 60 338 0.174 10.438 84 373 0.192 16.129 93.2 286 0.147 13.71

10 140.6 236 0.121 17.0711 154 254 0.131 20.12

total catchment area 1944 1 87.96

Isohyetal method

Isohyetal method

IsohyetsAverage rainfall (Pi), cm

Area between Isohyets (Ai), km2 Pi*Ai

20-30 25 96 240030-60 45 600 2700060-90 75 610 4575090-120 105 360 37800120-150 135 238 32130150-170 160 40 6400

Toal area, km2 = 1944 151480

average rainfall, cm 77.92

Adequacy of rain gauge stations

• A catchment has nine rain gauge stations. The annual rainfall recorded by these gauges in a given year are as listed in following Table. What should be the minimum number of the raingauges in the catchment for estimating the mean rainfall with an error of less than 7% ?

Adequacy of rain gauge stationsmaximum error permitted 7 percent

Raingauge stations

Annual rainfall, Pi (cm) Pi-average P (cm) (Pi-average P)2

1 80.8 -29.4 864.362 87.6 -22.6 510.763 102 -8.2 67.244 160.8 50.6 2560.365 120.4 10.2 104.046 110.8 0.6 0.367 142.3 32.1 1030.418 98.5 -11.7 136.899 88.6 -21.6 466.56

Total 991.8 5740.98Average P, cm 110.2 std sqroot(5741/8) 26.788477

Cv 100*26.78/110.2 24.3089628number of rain gauges required (24.30/7)2 12.0597076