CALCULATION OF NONLINEAR CONFIDENCE AND PREDICTION INTERVALS FOR GROUND-WATER FLOW MODELS.

ABSTRACT: A method is derived to efficiently compute nonlinear confidence and prediction intervals on any function of parameters derived as output from a mathematical model of a physical system. The method is applied to the problem of obtaining confidence and prediction intervals for manually-calibrated ground-water flow models. To obtain confidence and prediction intervals resulting from uncertainties in parameters, the calibrated model and information on extreme ranges and ordering of the model parameters within one or more independent groups are required. If random errors in the dependent variable are present in addition to uncertainties in parameters, then calculation of prediction intervals also requires information on the extreme range of error expected. A simple Monte Carlo method is used to compute the quantiles necessary to establish probability levels for the confidence and prediction intervals. Application of the method to a hypothetical example showed that includsion of random errors in the dependent variable in addition to uncertainties in parameters can considerably widen the prediction intervals.

[1]  George F. Pinder,et al.  Simulation of groundwater flow and mass transport under uncertainty , 1977 .

[2]  J. C. Ramírez,et al.  Estimation of aquifer parameters under transient and steady-state conditions , 1984 .

[3]  Allan L. Gutjahr,et al.  Stochastic analysis of spatial variability in subsurface flows: 1. Comparison of one‐ and three‐dimensional flows , 1978 .

[4]  Richard L. Cooley,et al.  Nonlinear‐regression groundwater flow modeling of a deep regional aquifer system , 1986 .

[5]  P. Kitanidis,et al.  An Application of the Geostatistical Approach to the Inverse Problem in Two-Dimensional Groundwater Modeling , 1984 .

[6]  L. Townley,et al.  Computationally Efficient Algorithms for Parameter Estimation and Uncertainty Propagation in Numerical Models of Groundwater Flow , 1985 .

[7]  B. Sagar,et al.  Galerkin Finite Element Procedure for analyzing flow through random media , 1978 .

[8]  Gedeon Dagan,et al.  Models of groundwater flow in statistically homogeneous porous formations , 1979 .

[9]  M. S. Hantush,et al.  Growth and Decay of Groundwater-Mounds in Response to Uniform Percolation , 1967 .

[10]  G. Dagan.  Stochastic modeling of groundwater flow by unconditional and conditional probabilities: 1. Conditional simulation and the direct problem , 1982 .

[11]  B. Troutman.  Errors and Parameter Estimation in Precipitation‐Runoff Modeling: 1. Theory , 1985 .

[12]  S. P. Neuman,et al.  Statistical Characterization of Aquifer Heterogeneities: An Overview , 1982 .

[13]  Ali H. Dogru,et al.  Confidence Limits on the Parameters and Predictions of Slightly Compressible, Single-Phase Reservoirs , 1977 .

[14]  R. L. Cooley.  Some new procedures for numerical solution of variably saturated flow problems , 1983 .

[15]  R. Freeze.  A stochastic‐conceptual analysis of one‐dimensional groundwater flow in nonuniform homogeneous media , 1975 .

[16]  C. V. Theis.  The relation between the lowering of the Piezometric surface and the rate and duration of discharge of a well using ground‐water storage , 1935 .

[17]  Allan L. Gutjahr,et al.  Stochastic analysis of spatial variability in two‐dimensional steady groundwater flow assuming stationary and nonstationary heads , 1982 .

[18]  R. W. Andrews,et al.  Sensitivity Analysis for Steady State Groundwater Flow Using Adjoint Operators , 1985 .

[19]  Richard L. Cooley,et al.  A method of estimating parameters and assessing reliability for models of steady state Groundwater flow: 2. Application of statistical analysis , 1979 .

[20]  Michael D. Dettinger,et al.  First order analysis of uncertainty in numerical models of groundwater flow part: 1. Mathematical development , 1981 .

[21]  R. Allan Freeze,et al.  Stochastic analysis of steady state groundwater flow in a bounded domain: 2. Two‐dimensional simulations , 1979 .

[22]  Robert B. Schnabel,et al.  Computational experience with confidence intervals for nonlinear least squares , 1986 .

[23]  Gerald J. Lieberman,et al.  Prediction Regions for Several Predictions from a Single Regression Line , 1961 .

[24]  R. L. Naff,et al.  STOCHASTIC ANALYSIS OF THREE-DIMENSIONAL FLOW IN A BOUNDED DOMAIN. , 1986 .

[25]  Analysis of mass transport with uncertain physical parameters , 1979 .

[26]  Brent M. Troutman,et al.  Errors and Parameter Estimation in Precipitation‐Runoff Modeling: 2. Case Study , 1985 .

[27]  W. R. Buckland,et al.  Distributions in Statistics: Continuous Multivariate Distributions , 1974 .

[28]  J. P. Delhomme,et al.  Spatial variability and uncertainty in groundwater flow parameters: A geostatistical approach , 1979 .