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Open Access Publications from the University of California

Scholarly Works (34 results)

  • Article
Technical Completion Reports (1995)

A methodology for the restoration and cleanup of existing subsurface contaminated sites and for the containment of pollutants is developed. The remediation problem is posed as an optimization model where the rates and locations of pumping and injections are to be determined given the characteristics and extent of the contamination plume. The solution of the remediation problem is based on the econometric method of feedback control coupled with ground water flow and transport simulations. For site characterization and monitoring of the contaminant distribution and extent, an optimal sampling methodology is presented. The sampling design is based on geostatistical methods and yields optimal estimation of the subsurface parameters and pollutant concentrations, therefore providing informed decision-making for ground water remediation and contaminant removal. The remediation plan is optimized so as to lower the contamination level to a pre-specified level by the end of the remediation period while minimizing the cost of pumping and treatment The objective function of the optimal feedback control model consists of a successive minimization of a weighted sum of squared deviations of the achieved cleanup level at each stage from the desired target level of ground water quality.

    Cover page: Optimal Well Network Design for Subsurface Remediation and Pollutant Containment
    • Article
    Technical Completion Reports (1983)

    This report presents a methodology to obtain optimal reservoir operation policies for a large-scale reservoir system. The model maximizes the system annual energy generation while satisfying constraints imposed on the operation of the reservoir network. The model incorporates the stochasticity of river flows and keeps future operating schedules up-to-date with the actual realization of those random variables. It yields medium-term (one-year ahead) optimal release policies that allow the planning of activities within the current water year, with the possibility of updating preplanned activities to account for uncertain events that affect the state of the system. The solution approach is a sequential dynamic decomposition algorithm that keeps computational requirements and dimensionality problems at low levels. The model is applied to a nine-reservoir portion of the California Central Valley Project and the results are compared with those from conventional operation methods currently in use, showing that the use of the model can improve the levels of energy production (about 30 percent increase) while the optimal release policies meet satisfactorily all other functions of the reservoir system. Sensitivity analysis is conducted to assess the optimality of the solutions and several alternative formulations of the model are developed and tested, the results showing the robustness of the optimal policies to the choice of model.

      Cover page: Optimal Operation of a Multiple Reservoir System
      • Article
      • Peer Reviewed
      UC Santa Barbara Previously Published Works (1988)
      A statistical method for deriving frequency distribution functions of minima of streamflows is presented. An innovative feature of the proposed methodology is that it does not require the specification of a parent distribution for streamflows, i.e., it is distribution free. The only assumption necessary is that the realizations of streamflows be independent, identically distributed random variables. The validity of this assumption is established with a nonparametric test. The main use of the methodology developed herein is in estimating small quantiles of the flow distribution for water supply planning and low-flow investigations. An example is included to illustrate the applicability of the approach, using a record of annual flows. © ASCE.
        Cover page: Fitting Minima of Flows Via Maximum Likelihood
        • Article
        • Peer Reviewed
        UC Santa Barbara Previously Published Works (1992)
          Cover page: Closure to Recurrence Interval of Geophysical Events by Hugo A. Loaiciga and Miguel A. Marino MayJune, 1991, Vol. 117, No. 3
          • Article
          • Peer Reviewed
          UC Santa Barbara Previously Published Works (1990)
          In the stochastic analysis of steady aquifer flow, the log hydraulic conductivity is the random “input” and the piezometric potential is the random “output.” Their joint behavior is governed by a differential equation that, in view of the random nature of its dependent (piezometric potential) and independent (log hydraulic conductivity) variables, represents a stochastic differential equation. The analysis of the distributional properties of the piezometric potential field involves the product of the gradients of log hydraulic conductivity and of the piezometric potential. Previous research in this field assumes that such product of gradients is small in some sense. This paper derives a closed‐form expression for the standard deviation, and hence the order of magnitude, of the product of the random gradients of log hydraulic conductivity and of piezometric potential. It was found in this research that for statistically homogeneous log hydraulic conductivity fields (1) the product of the random gradients may or may not have a zero mean, depending on whether the specific discharge is a constant or a random quantity, respectively; (2) under joint normality of the log hydraulic conductivity and the piezometric potential fields, their random gradients are statistically independent if the specific discharge is constant but are dependent when the specific discharge is random; (3) the standard deviation of the product of random gradients is proportional to the variance of log‐hydraulic conductivity times a term involving three quantities: the covariance of the piezometric potential, the covariance of the log hydraulic conductivity, and the cross covariance of the latter two fields; (4) a necessary and sufficient condition for the smallness of the product of random gradients is that the second derivatives of the covariance of the log hydraulic conductivity, the covariance of the piezometric potential, and the cross covariance of the latter two random fields be finite and that the variance of log hydraulic conductivity be much less than one. This paper also reviews some fundamental principles on the stochastic analysis of random fields and their importance to the modeling of log hydraulic conductivity fields and to the analysis of subsurface flow. Specifically, the paper highlights the role of Gaussian distributional assumptions in deriving key results of stochastic groundwater flow via perturbation analysis. Copyright 1990 by the American Geophysical Union.
            Cover page: Error Analysis and Stochastic Differentiability in Subsurface Flow Modeling
            • Article
            • Peer Reviewed
            UC Santa Barbara Previously Published Works (1987)
            This work deals with a theoretical analysis of parameter uncertainty in groundwater management models. The importance of adopting classical, Bayesian, or deterministic distribution assumptions on parameters is examined from a mathematical standpoint. In the classical case, the parameters (e.g., hydraulic conductivities or storativities) are assumed fixed (i.e., nonrandom) but unknown. The Bayesian assumption considers the parameters as random entities with some probability distribution. The deterministic case, also called certainty equivalence, assumes that the parameters are fixed and known. Previous work on the inverse problem has emphasized the numerical solution for parameter estimates with the subsequent aim to use them in the simulation of field variables. In this paper, the role of parameter uncertainty (measured by their statistical variability) in groundwater management decisions is investigated. It is shown that the classical, Bayesian, and deterministic assumptions lead to analytically different management solutions. Numerically, the difference between such solutions depends upon the covariance of the parameter estimates. The theoretical analyses of this work show the importance of specifying the proper distributional assumption on groundwater parameters, as well as the need for using efficient and statistically consistent methods to solve the inverse problem. The distributional assumptions on groundwater parameters and the covariance of their sample estimators are shown to be the dominant parameter uncertainty factors affecting groundwater management solutions. An example illustrates the conceptual findings of this work. Copyright 1987 by the American Geophysical Union.
              Cover page: Parameter estimation in groundwater: Classical, Bayesian, and deterministic assumptions and their impact on management policies
              • Article
              • Peer Reviewed
              UC Santa Barbara Previously Published Works (1987)
              ABSTRACT: This paper presents criteria for establishing the identification status of the inverse problem for confined aquifer flow. Three linear estimation methods (ordinary least squares, two‐stage least squares, and three‐stage least squares) and one nonlinear method (maximum likelihood) are used to estimate the matrices of parameters embedded in the partial differential equation characterizing confined flow. Computational experience indicates several advantages of maximum likelihood over the linear methods. Copyright © 1987, Wiley Blackwell. All rights reserved
                Cover page: SIMULTANEOUS EQUATION SYSTEMS: A CONSISTENT ESTIMATOR FOR UNKNOWN PARAMETERS IN CONFINED AQUIFERS1
                • Article
                • Peer Reviewed
                UC Santa Barbara Previously Published Works (1986)
                The planning of reservoir operation presents decision makers with a trade‐off between competing functions, which are energy production and flood control in this study. To optimally resolve the trade‐off between maximization of energy revenues and minimization of downstream losses, the interaction between the expected value and variance of revenues (accruing from the reservoir operation) is included in a stochastic daily reservoir operation planning model. By parametrically varying the expected value and variance of the objective function, the risk‐averse nature of decision makers is incorporated, resulting in a range of feasible alternative policies that reflect the decision maker's attitude toward revenue maximization and poor performance of the reservoir operation. Copyright 1986 by the American Geophysical Union.
                  Cover page: Risk Analysis for Reservoir Operation
                  • Article
                  • Peer Reviewed
                  UC Santa Barbara Previously Published Works (1986)
                  Joint estimation of transmissivity (T) and storativity (S) in a confined aquifer is done via maximum likelihood (ML). The differential equation of groundwater flow is discretized by the finite-element method, leading to equation ψφ{symbol}t+Γxt=ut. Elements of matrices ψ and Γ, as well as estimated covariance matrix of noise term ut, are functions of T and S. By minimizing the negative loglikelihood function corresponding to discretized groundwater flow equation with respect to T and S, ML estimators are obtained. The ML approach is found to yield accurate estimates of T and S (within 9 and 10% of their actual values, respectively) and showed quadratic convergence in Newton's search technique. Prediction of aquifer response, using ML estimators, results in estimated piezometric heads accurate to ±0.5 m from their actual, exact values. Statistical properties of ML estimators are derived and some basic results for statistical inference are given. © 1986 Plenum Publishing Corporation.
                    Cover page: On solution of the inverse problem for confined aquifer flow via maximum likelihood
                    • Article
                    • Peer Reviewed
                    UC Santa Barbara Previously Published Works (1987)
                    The contributions of this work are twofold. First, a methodology for estimating the elements of parameter matrices in the governing equation of flow in a confined aquifer is developed. The estimation techniques for the distributed‐parameter inverse problem pertain to linear least squares and generalized least squares methods. The linear relationship among the known heads and unknown parameters of the flow equation provides the background for developing criteria for determining the identifiability status of unknown parameters. Under conditions of exact or overidentification it is possible to develop statistically consistent parameter estimators and their asymptotic distributions. The estimation techniques, namely, two‐stage least squares and three stage least squares, are applied to a specific groundwater inverse problem and compared between themselves and with an ordinary least squares estimator. The three‐stage estimator provides the closer approximation to the actual parameter values, but it also shows relatively large standard errors as compared to the ordinary and two‐stage estimators. The estimation techniques provide the parameter matrices required to simulate the unsteady groundwater flow equation. Second, a nonlinear maximum likelihood estimation approach to the inverse problem is presented. The statistical properties of maximum likelihood estimators are derived, and a procedure to construct confidence intervals and do hypothesis testing is given. The relative merits of the linear and maximum likelihood estimators are analyzed. Other topics relevant to the identification and estimation methodologies, i.e., a continuous‐time solution to the flow equation, coping with noise‐corrupted head measurements, and extension of the developed theory to nonlinear cases are also discussed. A simulation study is used to evaluate the methods developed in this study. Copyright 1987 by the American Geophysical Union.
                      Cover page: The inverse problem for confined aquifer flow: Identification and estimation with extensions
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