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A detailed search for the optimum values of the parameters of the Boughton model is described. The Simplex and Davidon optimization methods were used. Rapid initial reductions in the objective function were readily achieved, but the solutions approached several widely different apparent optima. Alternate use of different optimization methods and numerical and algebraic studies enabled considerable further progress to be made in the search. Much information was obtained on various aspects of parameter optimization. These include interdependence and indifference of parameters, the form of the response surface and the occurrence of discontinuities, the required length of the 'warm-up' period for different types of stores, and the effects of using different types of objective functidns. As typical stores were analyzed and the only basic assumption involved was that the data contained errors, the findings should apply to most watershed models. Two broad approaches have been used in assigning values to the parameters of mathematical rainfall-runoff models for application to given watersheds. In the first, values are estimated from available knowledge of processes or from measurements of physical properties of the watershed, it being assumed that the model realistically represents measurable physical processes. In the second approach, which is the subject of the study described herein, parameter values are found by a systematic optimization technique. The intention is to achieve the best possible reproduction of the observed runoff in terms of some chosen objective function.Many difficulties may be encountered in using optimization methods, and inspection of the results of most published studies of watershed models reveals the effects of these difficulties in that different sets of 'optimum' parameter values are derived from different sets of initial values of the parameters or from different sets of observed data for the given watershed. As a result, it is doubtful that truly optimum values have been obtained, and the significance of the fitted values is therefore open to question. Until greater confidence can be placed in the estimation of appropriate parameter values for particular watersheds, it is unlikely that the potential usefulness of watershed models will be fulfilled. In addition to the above difficulties in optimization, optimum values are thought by many workers to depend on the form of the objective function, which must be chosen subjectively.This study was initiated when the authors attempted to derive optimum values for the parameters of the Boughton model [Boughton, 1965[Boughton, , 1966 for a large number of small rural watersheds as part of a major Australian Water Resources Council research project [Snowy Mountains Engineering Corporation, 1971]. The intention was then to correlate the values with measurable watershed characteristics. Difficulties such as those described above were encountered in obtaining true optimum parameter values, and the objectives of the study were changed to a detailed inves...

The difference between the dissolved-solids concentration in base flow and in storm flow has often been used as the basis for separating components of flow. However, an analysis that explicitly relates the amount of time that runoff water has been in contact with watershed soils to the resulting dissolved-solids concentration shows that simple mass balance chemistry methods for hydrograph separation are misleading. Field studies of surface and subsurface storm flow, when coupled with laboratory determination of the relationship between contact time and dissolved solids content of a soil water mixture, guggest that the residence time of infiltrated water is as short as a few hours in the cases studied. In those cases, hydrograph separation methods based on the simple mass balance equation for the dissolved solids will yield considerable overestimates of the base flow component.

Flood runoff has been traced from seven inje.ction points to the outlet of a 96-acre watershed. Each radioactivity time record at the outlet provides a hydrograph of outflow of the labeled drop of water. The results yield direct information on the flood process of a type and accuracy not possible from conventional analysis of rainfall and runoff records. The relationships of travel time and average velocity with discharge are examined together with the variations of these relationships over the watershed. Average travel times are shown to be similar to the watershed lag. The nature of the nonlinearity of the flood runoff process is demonstrated. Although the process is grossly nonlinear at low flows, linearity is approximated at high flows. Spatial variations of travel time and hydrograph shape are shown to make contributions to nonlinearity that are additional to the lumped dependence on flood magnitude that is normally considered. Although time of travel is a basic characteristic and descrip-tor of the flood hydrograph, very little direct and quantitative information is available on values and variations of travel times of actual flood runoff for use in research on hydrograph behavior. Values are generally inferred from, or implicit in, measures of time differences between effective or excess rainfall and the resulting flood hydrograph or from assumed analytical functions used in representing or synthesizing the hydrograph. Unfortunately, such measures a re generally subject to considerable systematic and random errors or are of questionable validity. The true temporal and spatial distributions of rainfall and losses to storm runoff and hence of effective rainfall cannot be directly observed, the initial state of the watershed is only partially known, and doubtful separations of flow components are often involved. These uncertainties have resulted in doubt regarding trends in measures of travel time and consequently nonlinear behavior of flood runoff in many studies. Linsley [1967] has attributed much apparent nonlinearity to these uncertainties, while Amorocho [1967] and Eagleson et al. [1966] have suggested that they have been a major factor in the justification of the continued development of linear approximations for hydrograph analysis and synthesis.Tracing of flood runoff provides an alternative means of measuring travel times that is subject to much lower uncertainty. A direct measure is given, and travel times from different points on the watershed can be determined to investigate spatial variations, a result that is not generally available from other methods. Results can only be obtained over a long period of time, and the physical presence of the investigator is generally required on the watershed during floods. The technique is thus only useful for research and not for operational purposes, but it can provide valuable information to aid in the understanding of the flood runoff process and the assessment of the degree of nonlinearity involved. This information is of a type and accuracy that cannot be ...

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