Double mass curve method for consistency

A double mass curve (DMC) checks the consistency of rainfall records of a station by comparing it with the average of a group of nearby, reliable stations. It detects changes caused by shifting of the gauge, change in exposure, observer or instrument.

Principle

For a consistent record, the cumulative rainfall at the test station is proportional to the cumulative average rainfall of the base stations, so the plot is a straight line. A break in slope shows that the regime of the test station has changed.

Procedure

1. Select 10 to 25 base stations of the same climate, with long, consistent records.
2. For each year, find the average annual rainfall of the base stations.
3. Compute the cumulative values of the test station ($\Sigma P_x$) and the base average ($\Sigma P_{av}$).
4. Plot $\Sigma P_x$ (ordinate) against $\Sigma P_{av}$ (abscissa).
5. If the points lie on one straight line, the record is consistent. If there is a break in slope, note the year of the break.

 SumPx
   |                . .
   |            .         <- later (recent) slope Mc
   |         .  <- break (change of regime)
   |      .
   |    .      <- earlier slope Ma
   |  .
   | .
   +------------------ Sum Pav

Correction

Records of the earlier (or doubtful) period are adjusted to the conditions of the recent period:

$$P_{cx} = P_x \times \frac{M_c}{M_a}$$

where $P_{cx}$ is the corrected rainfall, $P_x$ the original rainfall, $M_c$ the slope of the line to which the data is to be corrected (usually the recent period) and $M_a$ the slope of the line of the period being corrected.

The same technique is also used for checking consistency of runoff or other hydrologic records.