Gage ConsistencyEstimating missing data is one problem that hydrologists need to address. A

second problem occurs when the catch at rain gauges is inconsistent over a period of time and adjustment of the measured data is necessary to provide a consistent record.

Double Mass Curve analysis is a technique commonly employed to detect changes in data-collection procedures or conditions at a given location. The changes may result from changes in instrumentation, changes in observation procedures or changes in gauge location or surrounding conditions. A double mass curve is a plot of the accumulation of the observed element over time for one location ( test station) versus the accumulation over time for a reference location (base station). The mass curve is approximately a straight line if the variations at both test and base stations are quite consistent. Any break point in the curve suggests a possible change at the test station in relation to the base station. If a change in slope is evident, then the record needs to be adjusted, with either the early or later period of record adjusted.

The first step is to form the double mass curve and compute the slopes are as follows:

i) Add the annual precipitation of base stations. ii) Cummulate the sums of Step 1. iii) Cummulate the annual precipitation for station X.iv) Plot graph accumulated annual precipitation Station X versus

accumulated precipitation of Base stations and compute the slope Mo

and Ma.

Mo = P o

P and

Ma = P a

Pv) Adjust the measured precipitation of gauge X using the general equation:

Pa = Po Ma

Mo

where Pa = adjusted precipitation value at station X Po = original precipitation value at Station X Ma = adjusted slope Mo = original slope

PPox

Pax Ma

Mo

EXAMPLE 2.5Measured annual precipitation gauge for five stations (A, B, C, D and E) from 1926 until 1942 are given below. After 5 years, gauge A was relocated at a new location due to changes in land use that make it impractical to maintain the gauge at the old location. You are required to adjust the record for the period from 1926 to 1930 using the records at gauges B, C, D and E.

YEAR Annual precipitation (mm) Total Cummulative precipitation

(mm)A B C D E B+C+D+E A B+C+D+E

1926 32.9 39.8 45.7 30.7 37.4 153.6 33 1541927 28.1 39.6 38.5 41.0 30.9 150 61 3041928 33.5 42.0 48.3 40.4 42.0 172.7 95 4761929 29.6 41.4 34.6 32.5 39.9 148.4 124 6251930 23.8 31.6 45.1 36.7 36.3 149.7 148 7741931 58.4 56.5 53.3 62.4 36.6 208.8 206 9831932 46.3 48.1 40.1 47.9 38.6 174.7 253 11581933 30.8 39.9 29.6 32.7 26.9 129.1 283 1287

Acc

umul

ated

tota

l pre

cipi

tatio

n at

Sta

tion

X

Accumulated precipitation of base stations

1934 46.8 45.4 41.7 36.1 32.4 155.6 330 14431935 38.1 44.9 48.1 30.7 41.6 165.3 368 16081936 40.8 32.6 39.5 35.4 31.3 138.8 411 17471937 37.9 45.9 44.1 39.2 44.1 173.3 449 19201938 50.7 46.1 38.9 43.3 50.6 178.9 499 20991939 46.9 49.8 41.6 49.9 41.1 182.4 546 22811940 50.5 47.3 49.7 47.9 39.0 183.9 597 24651941 34.4 37.1 31.9 32.2 34.5 135.7 631 26011942 47.6 45.9 38.2 52.4 47.3 183.8 679 2785

P nb = P x Ma

Mo

i) P1926 = 32.9 0.26 iii) P1928 = (33.5) (1.37) 0.19 P1928 = 45.90 mm P1926 = 32.9 (1.37) P1926 = 45 mm

ii) P1927 = 28.1 (1.37) iv) P1929 = (29.6) (1.37) P1927 = 38.5 mm P1929 = 40.55 mm