Rainfall‐runoff regression with logarithmic transforms and zeros in the data

When some zeros occur in a data matrix to be used in a log‐log regression analysis, the data require the addition of a ‘small increment’ to make the transformation of the zeros feasible. If this increment is <1.0, the logarithm takes on negative values that, when they are squared, may have as much weight in the variance computations as the nonzero data, or more. The use of 1.0 as an increment is suggested, since log 1.0 = 0.0 and zero would have the desired weight of a null variate in both the variance computations and the regression relation. In a multilag rainfall‐runoff regression for the San Lorenzo River at Big Trees, California, increments of 1.0 added to all variates resulted in significant improvements in the standard error of estimate and the coefficient of multiple determination in comparison to results with an increment of 0.001 added to only the zero variates.