Contents preface (VII) introduction 1—37

2.3.5. Interpretation of Precipitation Data
Precipitation data must be checked for the continuity and consistency before they are analysed for any significant purpose. This is essential when it is suspected that the gauge site (or its surroundings) might have changed appreciably during the period for which the average is being computed.
2.3.5.1. Estimation of Missing Data
The continuity of a record of precipitation data may have been broken with missing data due to several reasons such as damage (or fault) in a rain gauge during a certain period. The missing data is estimated using the rainfall data of the neighbouring rain gauge stations. The missing annual precipitation P_x at a station x is related to the annual precipitation values, P₁, P₂, P₃ ...... P _m and normal annual precipitation, N₁, N₂, N₃ ...... N_m at the neighbouring M stations 1, 2, 3, ...... M respectively. The normal precipitation (for a particular duration) is the mean value of rainfall on a particular day or in a month or year over a specified 30-year period.

HYDROLOGY

51

The 30-year normals are computed every decade. The term normal annual precipitation at any station is, therefore, the mean of annual precipitations at that station based on 30-year record.

The missing annual precipitation P_x is simply given as

P =	1	(P		+ P + ..... P )	(2.7)
M	1
		x		2	m

if the normal annual precipitations at various stations are within about 10% of the normal annual precipitation at station x i.e., N_x. Otherwise, one uses the normal ratio method which gives

	N	x	L	P	P	P
Px =		M	1	+	2	+ ......	M
					NM
	^M N	N2	N2

O

P (2.8)

Q


This methods works well when the precipitation regimes of the neighbouring stations and the station x are similar (or almost the same).
Multiple linear regression (amongst precipitation data of M stations and the station x, excluding the unknown missing data of station x and the concurrent (or corresponding) data of the neighbouring M stations) will yield an equation of the form

	Px = a + b1P1 + b2P2 + ......	bmPm	(2.9)
in which,	a ≈ 0
and	bi ≈		Nx
MNi

The regression method allows for some weighting of the stations and adjusts, to some extent, for departures from the assumption of the normal ratio method.
2.3.5.2. Test for Cosistency of Precipitation Data
Changes in relevant conditions of a rain gauge (such as gauge location, exposure, instrumen-tation, or observation techniques and surroundings) may cause a relative change in the precipitation catchment of the rain gauge. The consistency of the precipitation data of such rain gauges needs to be examined. Double-mass analysis (5), also termed double-mass curve technique, compares the accumulated annual or seasonal precipitation at a given station with the concurrent accumulated values of mean precipitation for a group of the surrounding stations (i.e., base stations). Since the past response is to be related to the present conditions, the data (accumulated precipitation of the station x, i.e., ΣP_x and the accumulated values of the average of the group of the base stations, i.e., ΣP_av) are usually assembled in reverse chronological order. Values of ΣP_x are plotted against ΣP_av for the concurrent time periods, Fig. 2.8. A definite break in the slope of the resulting plot points to the inconsistency of the data indicating a change in the precipitation regime of the station x. The precipitation values at station x at and beyond the period of change is corrected using the relation,

^Pcx ^= ^Px	Sc	(2.10)
S
	a
where, Pcx = corrected value of precipitation at station x at any time t
Px = original recorded value of precipitation at station x at time	t.
Sc = corrected slope of the double-mass curve
Sa = original slope of the curve.

52 IRRIGATION AND WATER RESOURCES ENGINEERING

	2.4
	2.2
3cm	2.0	Break in the year 1993			1984
10			correction ratio =	Sc	=	c			1985
of	1.8		^Sa	a			1986
units	1.6								1987
in						1988
X
ΣP	1.4							1989		a
X,
							1990
	at
1.2
rainfall									c
						1991
1.0
annual					1992
0.8						1993
Accumulated				1994
	0.6		1995
		1996
	0.4	1997
		1998
	0.2	1999
	2000
	0	0.4	0.8	1.2	1.6	2.0	2.4	2.8
	0

3

Accumulated annual rainfall of 10 station mean Σ P_av in units of 10 cm

Fig. 2.8 Double-mass curve
Thus, the older records of station x have been corrected so as to be consistent with the new precipitation regime of the station x.