Lesson 8 Consistency of Rainfall Record

Precipitation puts water in the watershed. Precipitation measurements help determine water availability for evaporation and streamflow, and the risk of forest fires, landslides, and soil erosion. Precipitation is liquid (rain) or frozen (sleet, hail, graupel, snow) water or a combination of both falling from the sky. Measurement of the accumulation and disappearance of frozen precipitation on the ground is discussed in the following subsection. Precipitation is measured as depth of water that would accumulate on a horizontal surface. Typical recorded values for precipitation are the daily, monthly, and annual totals (depth of water in millimeters), as well as storm total, maximum intensity (millimeters per minute or per hour), and duration (hours). Precipitation is measured at a point using a manual or automatic recording gauge and over an area using meteorological radar (e.g., Doppler) or satellite images. Measurement of rainfall with a gauge is less prone to error than the measurement of solid precipitation because it is less susceptible to the influence of wind on “catch” by gauges. Some gauges are suitable only for measuring rainfall, and others are used only for solid precipitation. Very few can measure both forms reliably. Precipitation is usually not uniform in spatial distribution, intensity, or duration within a storm. Wind flow interacting with watershed topography also affects the distribution of precipitation. The standard technique for measuring rainfall is a plastic or metal cylinder with a sharp edge and funnel-like cover to minimize evaporation. 

Rainfall is measured to the nearest 0.2 mm; an accumulation of less than this is called a “trace.” If these gauges are not measured daily, then a small amount of mineral oil or kerosene is added after each measurement to cover the surface of the water and reduce evaporative loss. 
The depth of fluid is measured with a ruler. Precipitation intensity or amount can be measured automatically using weighing gauges or tipping buckets. The latter method is usually restricted to rainfall measurement. The tipping bucket gauge has a pair of buckets that pivot under a funnel such that when one bucket fills with about 0.25 mm of rain, it tips, discharging its contents and bringing the other bucket under the funnel. Tipping activates a switch that sends a pulse to the recording device. The weighing gauges can have a clock-driven chart to record weight or send an electronic signal to a data logger from a pressure transducer. Weighing gauges used to measure snow, contain antifreeze to melt the snow.
 Many studies require long term rainfall data, therefore, a test must be conducted to check homogeneity or self consistency of the rainfall record.  This is necessary because over a period of time, it may happen that there be a some obstructions (trees, buildings) may have emerged after the installation of gage or its location might have changed or observational procedure might have changed.  The inconsistency of rainfall record can be checked by graphical or statistical methods including double mass curve, the von Neumann ratio test, cumulative deviation, run test.  Double mass curve method described below is one of the most common and widely accepted methods for checking the consistency of rainfall record.
 
8.1             Double-mass Curve
This method is based on the assumption that the mean accumulated precipitation for a large group of stations is not significantly affected by a change or changes in individual stations.  If we plot the mean accumulated precipitation for several stations against the accumulated precipitation of the record for the station that needs to be adjusted, any change in slope will indicate a “break” in the station record.  This is shown by point B in the Fig. for the year 1974.
 
If the slope of the line AB (year 1970-74 in the example) is a and of the line AC (1974-85 in example fig.) is b, the adjustment of the inconsistent data is made by the ration of the slope of two line segments.  Two ways of adjustments are possible.
1.     The dataadjusted to reflect the conditions that existed prior to the indicated break.  This is done by multiplying each recent precipitation value after break point B of station X (being tested) by the ratio a/b.
2.     The data are adjusted toreflect recent conditions following the break.  This is achieved by multiplying each value of the precipitation before the break by the ratio b/a.  Adjustment of this type is generally made.
 
This is essentially a simple graphical method but statistical concepts and tests can be also utilized. Let us assume that we wish to check whether the data y1, y2 ,..., yN (N= sample size) are consistent data or not. For this purpose we will use another data set N x1, x2... xN, which is known to be reliable. The latter data set could be data measured at another gage or more generally the average of the data records available at several sites located in the same region as the suspected gage y. We will define the cumulative partial sums as 
 St(Y)=St-1 (Y) + Yt                         , t = 1,2,…,N 
 St(X) = St-1 (X) +Xt   , t = 1,2,…,N
 
in which   . Thus we have two sequences of partial sums, namely:   and  . The double mass plot is constructed as shown in the sketch below.  
81
Fig. 8.1(a)                                         Fig. 8.1(b)
Fig.8.1. (Source:Singh,1994)
 
Figure 1(a) reflects the inconsistency in the data while Fig.1(b) reflects that series yt has a pattern consistent with that of series xt. Referring to Fig.1(a) the point where the slope changes from s1 to s2 marks the time where the inconsistency occurs. Therefore part of the record of y must be adjusted. Which part of the record must be adjusted (before the break point or after) depends on the particular case. For example, if the inconsistency in y has occurred because the gage was moved from the original location to another location (the current location), then it is logical to adjust the record before the break point. 
 
8.2            Limitations and Cautions
It is possible that an apparent change in slope is noticed because of a natural variation in the data which is not associated with changes in gage location, gage environment or observation procedure.  In the case of doubt, a test of hypothesis should be performed by the Fisher distribution on two data sets (before and after the break) to check whether the data are homogeneous and the break is purely by chance.
 If the fewer than 10 stations are grouped together to check the consistency of a station, the record of each station should be tested by double mass analysis for consistency by plotting it against the group of all other stations, and those records that are inconsistent should be eliminated from the group.
 This method should seldom be used in mountainous areas.  Furthermore, it is also not suitable for adjusting daily or storm precipitation.
 
Example
Test the consistency of the 22 years of data of the annual precipitation measuredat stationA. Rainfall data for station A as well as the averageannual rainfall measured for a group of eight neighboring stations  located in a meteorologicallyhomogeneous region are given below as follows:

Sl. No.

Year

Annual Rainfall of Station A

Average Annual Rainfall (AAR) of 8 Station Group

(mm)

(mm)

1

1946

177

143

2

1947

144

132

3

1948

178

146

4

1949

162

147

5

1950

194

161

6

1951

168

155

7

1952

196

152

8

1953

144

117

9

1954

150

130

10

1955

130

190

11

1956

141

170

12

1957

160

190

13

1958

155

166

14

1959

140

150

15

1960

120

125

16

1961

148

140

17

1962

142

163

18

1963

140

145

19

1964

130

143

20

1965

137

135

21

1966

130

150

22

1967

163

165


 
a)     In what year is a change in regime indicated?
b)    Adjust the record data at a station A and determine the mean annual precipitation. 

Col 3

Col 4

Col 5

Col 6

Sl. No.

Year

Annual Rainfall of Station A

Average Annual Rainfall (AAR) of 8 Station groups

Cumulative Station A rainfall

Cumulative  of 8 Station A.A.R.

Correction factor

Adjusted rainfall at station A

(mm)

(mm)

(mm)

(mm)

1

1946

177

143

177

143

1.18

140.8471

2

1947

144

132

321

275

114.5875

3

1948

178

146

499

421

141.6428

4

1949

162

147

661

568

128.9109

5

1950

194

161

855

729

154.3748

6

1951

168

155

1023

884

133.6854

7

1952

196

152

1219

1036

155.9663

8

1953

144

117

1363

1153

114.5875

9

1954

150

130

1513

1283

119.3619

10

1955

130

190

1643

1473

0.94

196

11

1956

141

170

1784

1643

141

12

1957

160

190

1944

1833

158

13

1958

155

166

2099

1999

145

14

1959

140

150

2239

2149

132

15

1960

120

125

2359

2274

95

16

1961

148

140

2507

2414

148

17

1962

142

163

2649

2577

142

18

1963

140

145

2789

2722

140

19

1964

130

143

2919

2865

130

20

1965

137

135

3056

3000

137

21

1966

130

150

3186

3150

130

22

1967

163

165

3349

3315

163

139.134


Correction factor:
(0.935/1.175)= 0.7957= 0.796 or 0.8

Mean Annual Precipitation
139.134

82 
 
  
References
  • Singh, V. P. (1994). Elementary Hydrology. Prentice Hall of India Private Limited,180-181.

 Suggested Reading
  • Subramanya, K. (1994). Engineering Hydrology.Third edition, Tata McGraw Hill, New Delhi.

Last modified: Saturday, 15 March 2014, 6:18 AM