Contents preface (VII) introduction 1—37

2.3.4. Precipitation Gauge Network

The spatial variability of the precipitation, nature of the terrain and the intended uses of the precipitation data govern the density (i.e., the catchment area per rain gauge) of the precipitation

HYDROLOGY

49

gauge (or rain gauge) network. Obviously, the density should be as large as possible depending upon the economic and other considerations such as topography, accessibility etc. The World Meteorological Organisation (WMO) recommends the following ideal densities (acceptable values given in brackets) of the precipitation gauge network (3):

1. 
   For flat regions of temperate, mediterranean, and tropical zones, 600 to 900 sq. km (900–3000 sq. km) per station.
   

2. 
   For mountainous regions of temperate, mediterranean, and tropical zones, 100 to 250 sq. km (250 to 1000 sq. km) per station.
   

3. 
   For small mountainous islands with irregular precipitation, 25 sq. km per station.
   

4. 
   For arid and polar zones, 1500 to 10,000 sq. km per station.
   

At least ten per cent of rain gauge stations should be equipped with self-recording gauges to know the intensities of rainfall. The Bureau of Indian Standards (4) recommends the following densities for the precipitation gauge network:

1. 
   In plains: 520 sq. km per station;
   

2. 
   In regions of average elevation of 1000 m: 260 to 390 sq. km per station; and
   

3. 
   In predominantly hilly areas with heavy rainfall: 130 sq. km per station.
   

For an existing network of raingauge stations, one may need to know the adequacy of the raingauge stations and, therefore, the optimal number of raingauge stations N required for a desired accuracy (or maximum error in per cent, ε) in the estimation of the mean rainfall. The optimal number of raingauge stations N is given as

F C_v I ²

N = ^{G J} (2.5)

H ε K
Here, C_v = the coefficient of variation of the rainfall values at the existing m stations (in per cent) and is calculated as (Eq. 2.1))

3. 
   ₌ ^{100 × σ} m− 1
   
   5. 
      _P
      

								m
	^σm–1			∑ (Pi − P)^2
in which,		= standard deviation =			i		(2.6)
									m − 1
	P	i	= precipitation measured at i^th station
							F		I
						1		m
						∑i
and	P	= mean precipitation =			G			^Pi J
						m H			K

For calculating N, ε is usually taken as 10%. Obviously, the number N would increase with the decrease in allowable error, ε.
Example 2.2 A catchment has eight rain gauge stations. The annual rainfall recorded by these gauges in a given year are as listed in column 2 of the following Table.

50	IRRIGATION AND WATER RESOURCES ENGINEERING
	Table for computation of (P –		)^2	(Example 2.2)
	P
		i
										–		)^2
Rain Gauge	Annual Rainfall (cm)		P –	P		(P	i	P
					i
A	80.8				– 32.1	1030.41
B	87.6				– 25.3	640.09
C	102.0				– 10.9	118.81
D	160.8				47.9		2294.41
E	120.4				7.5		56.25
F	110.8				– 2.1			4.41
G	142.3				29.4		864.36
H	98.5				– 14.4	207.36
Total	903.2				0.0		5216.10

What should be the minimum number of the raingauges in the catchment for estimating the mean rainfall with an error of less than 7% ?

1

m

1

8

Solution: Mean rainfall,

=

∑ Pi =

∑ Pi =

903.2

= 112.9 cm

P

^m i = 1

^8 i = 1

8

Values of P –

P

and (P –

P

)^2

are as in cols. (3) and (4) of the Table.

i

i

Σ(P − P)^2

1

^σm–1 ^=

i

=

(5216.10)

= 27.298

m − 1

7

C =

100 ×

^σ m−1

= 100 × 27.298 = 24.18

v

P

112.9

Therefore, the number of raingauges for errors of less than 7% in estimation of the mean annual rainfall

F	Cv I ^2	F	24.18I ^2
= G	J	= G	J
H	ε K	H	7 K

= 11.93, say 12.
Hence, four additional raingauges are required in the catchment.