Lloyd R. Townley

Surface water‐groundwater interaction near shallow circular lakes: Flow geometry in three dimensions

Steady flow regimes for three-dimensional lake-aquifer systems are studied via idealized mathematical models that are extensions of earlier simplified vertical section models of interaction between shallow lakes and underlying aquifers. The present models apply to a shallow circular lake at the surface of a rectangular aquifer of finite depth, yielding a truly three-dimensional representation of the resulting flow system. Flux boundary conditions are applied at the ends of the aquifer, with net vertical recharge or evapotranspiration at the water table. The lake is defined by a region with constant head. By determining and visualizing solutions to the discretized saturated flow equations, a range of possible flow regimes is identified, and their topological properties are studied. Tools for analyzing flow regimes are described, including a method for locating and mapping three-dimensional dividing surfaces within steady flow fields. Results show strong similarities between two- and three-dimensional systems, including a large number of flow-through, recharge, and discharge regimes and reverse flow cells. Flow lines calculated on a vertical plane through the middle of a lake resemble but are not identical to two-dimensional streamlines for a range of aquifer flow and recharge conditions. Estimates of the widths and depths of capture and release zones for various lake-aquifer geometries are asymptotic to earlier results for two-dimensional systems. Numerical predictions are compared with analytical results for certain limiting flow regimes.

Definition of a capture zone for shallow water table lakes

Abstract Lake-aquifer interaction is studied with the aim of developing simple relationships between easily measurable geometrical and aquifer parameters and the bulk behaviour of the flow system. Attention is focused on shallow flow-through lakes which receive groundwater along the up-gradient shoreline and discharge lake water along the down-gradient shoreline. Although the flow system is physically three-dimensional, two idealised two-dimensional geometries, in plan and in vertical section, are studied in detail. The resulting potential flow problems are solved using a boundary integral approach, based on a Greens function chosen to satisfy desired homogeneous boundary conditions on a semi-infinite strip. Results are presented for circular and elliptical lakes in plan and for lakes so shallow that they are adequately represented in vertical section by a line at the surface. The size of an upstream capture zone, in which all groundwater flow eventually passes through the body of the lake, is defined in terms of the size of the lake, inter-lake spacing, aquifer saturated thickness, an anisotropy ratio and the ratio of downstream to upstream hydraulic gradients. Even in cases where the net groundwater inflow to a lake is zero, it is shown that a substantial throughflow can occur.

Influence of regional setting on the interaction between shallow lakes and aquifers

[1]xa0Interaction between surface water and groundwater depends on the position of a lake within the regional flow system. The approach in this paper is to nest a local-scale two-dimensional (2-D) lake aquifer model within a 1-D regional aquifer model to examine the effect of the regional setting on surface water–groundwater interaction. This extends previous steady state flow modeling, which is presented in earlier publications. The results indicate that the type of regional setting and position of the lake within that setting impose constraints on the near field flow geometry. Only nine of 39 previously identified flow regimes are possible in the regional flow system considered. Flow-through lakes are dominant and can occur anywhere within the regional flow. Recharge and discharge lakes are more likely to occur near the groundwater divide where regional hydraulic gradients are flattest and can be counteracted by local forcing in and near the lake.

Nonlinear, discrete flood event models, 3. Analysis of prediction uncertainty

Abstract This series of papers consists of three parts. Part 1 ∗ described and illustrated the application of maximum a posteriori (MAP) estimation to nonlinear, discrete flood event models. Part 2 ∗∗ dealt with the application of measures of statistical nonlinearity to model and rainfall-runoff data set combinations. The present paper (Part 3) is concerned with the assessment of the precision of model predictions. The use of first-order, second-order and Monte Carlo analyses to evaluate the prediction uncertainty caused by errors in model parameter estimates is described. A case study is presented to demonstrate the utility of prediction uncertainty analysis.

Nonlinear, discrete flood event models, 1. Bayesian estimation of parameters

Abstract In this paper (Part 1), a Bayesian procedure for parameter estimation is applied to discrete flood event models. The essence of the procedure is the minimisation of a sum of squares function for models in which the computed peak discharge is nonlinear in terms of the parameters. This objective function is dependent on the observed and computed peak discharges for several storms on the catchment, information on the structure of observation error, and prior information on parameter values. The posterior covariance matrix gives a measure of the precision of the estimated parameters. The procedure is demonstrated using rainfall and runoff data from seven Australian catchments. It is concluded that the procedure is a powerful alternative to conventional parameter estimation techniques in situations where a number of floods are available for parameter estimation. Parts 2 and 3 ∗ will discuss the application of statistical nonlinearity measures and prediction uncertainty analysis to calibrated flood models.

Second Order Effects of Uncertain Transmissivities on Predictions of Piezometric Heads

Finite element techniques are frequently used for deterministic analysis of steady state two-dimensional aquifer flow. When the spatial distribution of transmissivities is uncertain, however, the usual solution for piezometric heads is only correct to first order. Using a Taylor series expansion, it is shown that the mean distribution of heads consists of the usual solution plus a second order correction. Numerical results are presented which show agreement between Monte Carlo solutions and the second order Taylor series solutions for expected heads. An efficient procedure is described which avoids the explicit evaluation of the extremely large second derivative matrix.

Estimation of boundary values and identification of boundary type for numerical models of aquifer flow

Inverse methods which focus on aquifer properties implicitly assume that boundary conditions are known with certainty and can therefore lead to biased results. An inverse procedure is described which allows the simultaneous estimation of not only spatially varying aquifer storage coefficients and transmissivities, but also model parameters which represent both boundary type and boundary values. The weighted least-squares procedure is based on either Bayesian or maximum likelihood arguments and requires both measurements of transient piezometric heads and prior information on all model parameters. Prior estimates and their covariance can be nonconditioned (e.g. a stationary mean and covariance structure) or conditioned on direct measurements (e.g. a kriged transmissivity field with its estimation covariance). Hypothetical examples are presented using an unsteady finite element model. In some cases, with weak prior information on the boundary type, it is possible to distinguish between prescribed head, prescribed flux and mixed boundaries. Simultaneous estimates of aquifer properties and boundary values are always possible, although their accuracy depends on the relative magnitudes of model sensitivities and prior information.