Double-mass curves, with a section fitting curves to cyclic data

The double.-mass curve is used to check the consistency of many kinds of hydrologic data by comparing data for a single station with that of a pattern composed of the data from several other stations in the area The double-mass curve can be used to adjust inconsistent precipitation data.

The graph of the cumulative data of one variable versus the cumulative data of a related variable is a straight line so long as the relation between the variables is a fixed ratio. Breaks in the double-mass curve of such variables are caused by changes in the relation between the variables. These changes may be due to changes in the method of data collection or to physical changes that affect the relation.

Applications of the double-mass curve to precipitation, streamflow, and sediment data, and to precipitation-runoff relations are described. A statistical test for significance of an apparent break in the slope of the double-mass curve is described by an example. Poor correlation between the variables can prevent detection of inconsistencies in a record, but an increase in the length of record tends to offset the effect of poor correlation.

The residual-mass curve, which is a modification of the double-mass curve, magnifies imperceptible breaks in the double-mass curve for detailed study. Of the several methods of fitting a smooth curve to cyclic or periodic data, the moving-arc method and the double-integration method deserve greater use in hydrology. Both methods are described in this manual. The moving-arc method has general applicability, and the double integration method is useful in fitting a curve to cycles of sinusoidal form.