This study gives a phenomenologically based stochastic model of space -time rainfall. Specifically, two random variables on the spatial rainfall, e.g. the cumulative rainfall within a season and the maximum cumulative rainfall per rainfall event within a season are considered. An approach is given to determine the cumulative distribution function (c.d.f.) of the cumulative rainfall per event, based on a particular random structure of space -time rainfall. Then the first two moments of the cumulative seasonal rainfall are derived based on a stochastic dependence between the cumulative rainfall per event and the number of rainfall events within a season. This stochastic dependence is important in the context of the spatial rainfall process. A theorem is then proved on the rate of convergence of the exact c.d.f. of the seasonal cumulative rainfall up to the ith year, i > 1, to its limiting c.d.f. Use of the limiting c.d.f. of the maximum cumulative rainfall per rainfall event up to the ith year within a season is given in the context of determination of the 'design rainfall'. Such information is useful in the design of hydraulic structures. Special mathematical applications of the general theory are developed from a combination of empirical and phenomenological based assumptions. A numerical application of this approach is demonstrated on the Atterbury watershed in the Southwestern United States.

This item was digitized as part of the Million Books Project led by Carnegie Mellon University and supported by grants from the National Science Foundation (NSF). Cornell University coordinated the participation of land-grant and agricultural libraries in providing historical agricultural information for the digitization project; the University of Arizona Libraries, the College of Agriculture and Life Sciences, and the Office of Arid Lands Studies collaborated in the selection and provision of material for the digitization project.

Distributed rainfall-runoff models are gaining widespread acceptance; yet, a fundamental issue that must be addressed by all users of these models is definition of an acceptable level of watershed discretization (geometric model complexity). The level of geometric model complexity is a function of basin and climatic scales as well as the availability of input and verification data. Equilibrium discharge storage is employed to develop a quantitative methodology to define a level of geometric model complexity commensurate with a specified level of model performance. Equilibrium storage ratios are used to define the transition from overland to channel-dominated flow response. The methodology is tested on four subcatchments in the USDA-ARS Walnut Gulch Experimental Watershed in southeastern Arizona. The catchments cover a range of basins scales of over three orders of magnitude. This enabled a unique assessment of watershed response behavior as a function of basin scale. High quality, distributed, rainfall-runoff data were used to verify the model (KINEROSR). Excellent calibration and verification results provided confidence in subsequent model interpretations regarding watershed response behavior. An average elementary channel support area of roughly 15% of the total basin area is shown to provide a watershed discretization level that maintains model performance for basins ranging in size from 1.5 to 631 hectares. Detailed examination of infiltration, including the role and impacts of incorporating small-scale infiltration variability in a distribution sense, into KINEROSR, over a range of soils and climatic scales was also addressed. The impacts of infiltration and channel losses on runoff response increase with increasing watershed scale as the relative influence of storms is diminished in a semi-arid environment such as Walnut Gulch. In this semi-arid environment, characterized by ephemeral streams, watershed runoff response does not become more linear with increasing watershed scale but appears to become more nonlinear.

This study is concerned with design forecasting of storm hydrographs with emphasis on runoff volume and peak discharge. The objective of the study was to develop, calibrate and test a method for forecasting storm runoff from small semi-arid watersheds using an available prediction model. In order to turn the selected prediction model into a forecasting model an objective procedure in terms of an API-type model was developed for evaluating the soil moisture deficit in the upper soil layer at the beginning of each storm. Distinction was made between the physically-based parameters and the other fitting parameters. The rainfall excess calculation was computed by solving the Green and Ampt equation for unsteady rainfall conditions using the physically-based parameters. For the physically-based parameters a geographic information system was developed in order to account for the variability in time and space of the input data and the watershed characteristics and to coregister parameters on a common basis. The fitting parameters were used to calibrate the model on one subwatershed in the Walnut Gulch Experimental Watershed while the physically-based parameters remained constant. Two objective functions were selected for the optimization procedure. These functions expressed the goodness of fit between the calculated hydrograph volume and peak discharge and the observed volume and peak discharge. Linear relationships between the effective matric potential parameter and the two objective functions obtained from the sensitivity analyses made it possible to develop a bilinear interpolation algorithm to minimize, simultaneously, the difference between the calculated and observed volume and peak discharge. The prediction mode of the model was tested both on different storm events on the same subwatershed and on another subwatershed with satisfactory results. In the prediction mode the effective matric potential parameter was allowed to vary from storm to storm, however, in the forecasting mode these values were obtained from the API model. Relatively poor results were obtained in testing the forecasting mode on another subwatershed. These errors were able to be corrected by changing the channel losses fitting parameters.

The U.S. Geological Survey and the City of Tucson, Arizona, have been collecting rainfall and runoff data on several watersheds in the Tucson area for several years. Among the purposes of this project is to use the data to test rainfall-runoff models in an effort to find one to successfully simulate flood flows in Tucson. One such model, the Distributed Routing Rainfall-Runoff Model (DR3M), was tested using data collected on Rob Wash in Tucson. It was found DR3M performs about as well as it does in other parts of the United States, although it tends to underestimate flood flows for large storms and overestimate flows for smaller storms. Unique features with regard to the hydrology of urban Tucson require special attention when using DR3M; these features are associated with the nature of dry washes and summer rainfall in Tucson. Experience indicates DR3M is not truly a deterministic model.

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Distributed Rainfall-Runoff models are gaining widespread acceptance; yet, a fundamental issue that must be addressed by all users of these models is definition of an acceptable level of watershed discretization (geometric model complexity). The level of geometric model complexity is a function of basin and climatic scales as well as the availability of input and verification data. Equilibrium discharge storage is employed to develop a quantitative methodology to define a level of geometric model complexity commensurate with a specified level of model performance. Equilibrium storage ratios are used to define the transition from overland to channel -dominated flow response. The methodology is tested on four subcatchments in the USDA -ARS Walnut Gulch Experimental Watershed in Southeastern Arizona. The catchments cover a range of basins scales of over three orders of magnitude. This enabled a unique assessment of watershed response behavior as a function of basin scale. High quality, distributed, rainfall -runoff data was used to verify the model (KINEROSR). Excellent calibration and verification results provided confidence in subsequent model interpretations regarding watershed response behavior. An average elementary channel support area of roughly 15% of the total basin area is shown to provide a watershed discretization level that maintains model performance for basins ranging in size from 1.5 to 631 hectares. Detailed examination of infiltration, including the role and impacts of incorporating small scale infiltration variability in a distribution sense, into KINEROSR, over a range of soils and climatic scales was also addressed. The impacts of infiltration and channel losses on runoff response increase with increasing watershed scale as the relative influence of storms is diminished in a semiarid environment such as Walnut Gulch. In this semiarid environment, characterized by ephemeral streams, watershed runoff response does not become more linear with increasing watershed scale but appears to become more nonlinear.