Existing goodness of fit indices are inadequate for comparing model-generated hydrographs with measured hydrographs. The Pearson product-moment correlation coefficient, which is the most frequently used index of regeneration, is inadequate because it is insensitive to differences in the size of the two hydrographs. A better coefficient of regeneration is obtained if Pearson's coefficient is adjusted by using a ratio of the standard deviations of the two hydrographs being compared. The resulting index is numerically the same as the regression of the hydrograph with the smaller variance on the hydrograph having the larger variance. Examples are used to illustrate the superiority of the modified correlation index.

The techniques of multivariate analysis are proposed for certain hydrologic applications where multiple regression produces unsatisfactory results. Equations evaluated by the method of least squares in multiple regression predict the dependent variable with minimum least‐square error. This paper offers no suggestions concerning the use of multiple regression for this desired end result. Regression has also been used in hydrologic applications in which the numerical structure of the solution was of primary importance. The desired end result of this application is a reasonable numerical evaluation of the assumed model of the particular hydrologic processes under study. Multiple regression may produce unsatisfactory results in applications of the second kind. Comparative results of multiple regression and multivariate analysis for three applications are presented in this paper. First, the simple two‐variable relationship is presented. Second, the improvement in establishing a relationship between rainfall and runoff is shown. Multivariate analysis produces a logical equation; multiple regression does not. Third, an application is shown in which the convergence to solution in the iterative technique of nonlinear least squares is improved.

No abstract

A mathematical model has been developed describing the rate and quantity of runoff water from separate rainfall events on a watershed and the rate and quantity of sediment and pesticides transported. The runoff water is calculated by convolving an areacharacteristic and variable state function to produce a variable response function which is then convolved with a computed effective rain. Rill and interrill erosion are conceptually distinguished which allows similar partitioning of associated pesticides. The sediment contribution from interrill erosion is a function of rainfall intensity and soil susceptibility to erosion. The rill erosion is a function of water runoff and the rate of change of water runoff. The concentrations of pesticides in the runoff are functions of the amount of runoff, the sediment concentrations derived from rill and interrill erosion, and the pesticide concentrations in the respective runofferosion zones. Experience with the model in simulating the water, sediment, and pesticide runoff from an upland Piedmont plain watershed for four summer storms is related. Excellent simulations were obtained. Additional Index Words: erosion, sediment, water quality.

No abstract