Double mass curve, station X and 25 stations, 1941-1976

The double mass curve plots cumulative X against cumulative base-station average. A single straight line means consistent data.

(i) Cumulative values and consistency

Plotting cum. X against cum. base average shows a straight line up to 1952 and a flatter straight line afterwards.

• Slope up to 1952: $M_a = \dfrac{1654}{1419} = 1.1656$
• Slope after 1952: $M_c = \dfrac{2299}{2718} = 0.8458$

The slope changes, so the data of station X are not consistent.

(ii) Change in regime

The break occurs at the 1952 point, so the regime changed after 1952 (the changed conditions apply from 1953). (The 1954 value of 97 is taken as printed.)

(iii) Mean annual rainfall of X (36 years)

• Without adjustment: $\bar P = \dfrac{3953}{36} = 109.8$ cm
• With adjustment to the present site (recent regime), the 1941-1952 data are corrected by $M_c/M_a = 0.8458/1.1656 = 0.7257$. Corrected total for 1941-52 $= 1200.3$ cm; total for 1953-76 $= 2299$ cm.

$$\bar P_{adj} = \frac{1200.3 + 2299}{36} = 97.2\ \text{cm}$$

(iv) Adjusted annual rainfall for the affected period (1941-1952)

$$P_{cx} = P_x \times 0.7257$$

Answer: Inconsistent; change in regime after 1952; mean = 109.8 cm (unadjusted) and 97.2 cm (adjusted); adjusted values for 1941-52 are listed above (factor 0.726).