Double mass curve, station X and 18 stations

A double mass curve plots the cumulative rainfall of station X against the cumulative average rainfall of the 18 base stations. A change in slope shows an inconsistency.

Step 1: Cumulative values

Step 2: Plot and slopes

Plotting cum. X (y-axis) against cum. base average (x-axis), the points follow one straight line up to 1959 and another, flatter line afterwards.

• Slope before the break (to 1959): $M_a = \dfrac{282.4}{223.3} = 1.265$
• Slope after the break (1960-1970): $M_c = \dfrac{272.1}{301.8} = 0.902$

The slopes differ, so the record of station X is not consistent. The change in regime occurred in 1960 (the break appears at the 1959-60 point).

Step 3: Adjust to the changed (present) regime

$$P_{cx} = P_x \times \frac{M_c}{M_a} = P_x \times \frac{0.902}{1.265} = 0.713\,P_x$$

Adjusted total for 1952-1959 $= 0.7129 \times 282.4 = 201.3$ cm; the total of 1960-1970 is unchanged $= 272.1$ cm.

$$\bar P_{1952-70} = \frac{201.3 + 272.1}{19} = 24.92\ \text{cm}$$

Answer: Record is inconsistent; change in regime in 1960; mean annual rainfall for 1952-1970 under the changed regime = 24.9 cm (compared with the unadjusted mean of 29.2 cm).