A three‐dimensional stochastic analysis of the contaminant transport problem is developed in the spirit of Naff (1990). The new derivation is more general and simpler than previous analysis. The fast Fourier transformation is used extensively to obtain numerical estimates of the mean concentration and various spatial moments. Data from both the Borden and Cape Cod experiments are used to test the methodology. Results are comparable to results obtained by other methods, and to the experiments themselves.

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A two‐level point stochastic model for the rainfall occurrences at a given rainfall station is constructed in the time dimension. The model is a cluster process of the Neyman‐Scott type. The model has the rainfall‐generating mechanisms as its primary level and the rainfalls that are generated by these mechanisms as the secondary level. It uses infinite superposition of rainfalls and has a very flexible dependence structure. The model is fitted to daily rainfall sequences in Indiana after these are stationarized by a transformation. The fit of the model is then tested in terms of its correlation and marginal probability characteristics. The present form of the Neyman‐Scott cluster model is time homogeneous. Therefore the Neyman‐Scott process, as presented in this paper, may be of practical use only for modeling the stationary rainfall occurrences.

Stochastic linear models are fitted to hydrologic data for two main reasons: to enable forecasts of the data one or more time periods ahead and to enable the generation of sequences of synthetic data. These techniques are of considerable importance to the design and operation of water resource systems. Short sequences of data lead to uncertainties in the estimation of model parameters and to doubts about the appropriateness of particular time series models. A premium is placed on models that are economical in terms of the number of parameters required. One such family of models is multiplicative seasonal autoregressive integrated moving average (Arima) models that have been described by G. E. P. Box and G. M. Jenkins. In this paper we illustrate the process of identifying the particular member of the family that fits logarithms of monthly flows, estimating the parameters, and checking the fit. The seasonal Arima model accounts for the seasonal variability in the monthly means but not the seasonal variability of the monthly standard deviations: for this reason its value is limited. The forecasting of flows one or more months ahead is described with an example.

Abstract. A Monte Carlo simulation of flow and transport is employed to study tracer migration in porous media with evolving scales of heterogeneity (fractal media). Transport is studied with both conservative and reactive chemicals in media that possess physical as well as chemical heterogeneity. Linear kinetic equations are assumed to relate the sorbed phase and the aqueous phase concentrations. The fluctuating log conductivity possesses the power law spectrum of a fractional Brownian motion (fBm). Chemical heterogeneity is represented as spatially varying reaction rates that also are assumed to obey fBm statistics and may be correlated to the conductivity field. The model is based on a finite difference approximation to the flow problem and a random walk particle-tracking approach for solving the solute transport equation. The model is used to make comparisons with the nonlocal transport equations recently developed by Deng et al. [1993], and Hu et al. [1995, 1997]. The results presented herein support these nonlocal models for a wide range of heterogeneous systems. However, the infinite integral scale associated with the fractal conductivity has a significant effect on the prediction of the nonlocal theories. This suggests that integral scale should play a role in stochastic Eulerian perturbation theories. The importance of the local-scale dispersion depends to a great extent on the magnitude of the local dispersivities. The effect of neglecting local dispersion decreases with the decrease in local dispersivity.

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A model of the dynamic contributing area during a storm is formulated in terms of the history of precipitation in excess of B horizon permeability. The spatial dynamic contributing area along the main stream is obtaihed under the assumptions that the velocity of flow along the stream network is uniform, the drainage density is a constant within a given watershed, and the first-order streams are uniformly distributed in the basin. The runoff from the dynamic contributing area is then routed through the synthesized stream network to obtain the direct runoff at the basin outlet by making use of a method based on the linearized Saint Yenant equations. The model has been tested in several watersheds in the central United States. INTRODUCTION SYNTHESIS OF THE STREAM NETWORKMany hydrologic phenomena and transport processes occurring in a watershed are associated with rainfall-runoff transfer. Erosion, sedimentation, and transport of plant nutrients, pesticides, and pollutants are examples of phenomena closely associated with the rainfall-runoff process. Hydrologic models of runoff cycles are thus needed not only to simulate water transport in the watershed but also to promote the understanding and simulation of the transport processes of these other conservative substances. In order to trace properly the substances transported, the hydrologic model must indicate where the runoff is likely to originate and how it reaches the stream. Cahill et al. [1974], in tracing the dynamics of phosphorus in a small river system, and Huff and Kruger [1967], in tracing radioactive aerosols from precipitation to water supplies, indicate these requirements.In their classical role, hydrologic models of the runoff cycle have been used to obtain the runoff information necessary to determine the location and size of hydraulic structures. Such models did not require specific information regarding the source of the runoff. More recently, these models have also served to study alternate solutions to water resources developments and associated environmental, economic, and social impacts. Simulation of environmental effects, in particular, requires specific information on the origin and path of the runoff. Lumped deterministic and stochastic systems, which have been successfully used in many hydrologic analyses, do not describe the transport of water irlSide the catchment. Spatially distributed deterministic models would seem ideally suited for describing the internal flows within a watershed. Their analyses require very laborious discretization and tabtl!ation of all the necessary physical and topographical properties of all the infinitesimal areas forming the watershed. Complete simulation of all the combinations of overland flows and of the flows in all the ramifichtions of the stream network is extremely complex, and the necessary data are generally unavailable and too expensive to obtain, except for a few experimental watersheds. An intermediate approach is proposed in this paper. It is based on a syn[hesis of the stream network and on the w...