The groundwater flow equation governing the elevation (h) of the steady-state phreatic surface in a sloping aquifer fed by constant recharge over a bi-circular sector is rhh'- r2Bh' + Pr2 - PR2 = 0, where r is the radial coordinate, P is a constant involving recharge and aquifer properties, and B is the slope of the aquifer-bedrock boundary. The derived flow equation describes radially convergent flow through a sloping aquifer that discharges to a water body of fixed head. One important simplification is that in which the width of the bi-circular sector is constant, and the draining land becomes a rectangular aquifer. The bi-circular sector and rectangular-strip groundwater flow problems are solved in terms of implicit equations. The solutions for the steady-state phreatic surfaces depend on the ratio of recharge to hydraulic conductivity, the slope of the aquifer-bedrock, and the downstream constant-head boundary. Computational examples illustrate the application ofthe solution. Copyright © 2006 IAHS Press.

Theoretical principles of sustainable aquifer management are laid out in this work. The premise of our treatment is that groundwater is a renewable, although exhaustible, natural resource. The theory of this work is aimed at aquifers with a relatively homogeneous recharge that can be approximated by a logistic growth function. Sustainable aquifer exploitation occurs when the rate of ground-water extraction is equal to or less than the natural rate of groundwater replenishment for any level of aquifer storage. There can be many levels of sustainable aquifer exploitation depending on the level of aquifer storage, but there may be only one that maximizes economic returns under a variety of economic and aquifer conditions. Different strategies for sustainable exploitation are derived depending on whether or not the analysis considers tradeoffs among: (i) current and future exploitation; (ii) constant and dynamic aquifer storage conditions; and (iii) regulated and unregulated aquifer exploitation. Key factors affecting sustainable exploitation strategies include: (1) the market price of groundwater; (2) the cost of groundwater extraction; (3) the aquifer storage and natural replenishment characteristics; (4) institutional and environmental regulations on groundwater extraction; and (5) the real discount rate. An example of sustainable groundwater exploitation in Santa Barbara, California, illustrates the methods of this article. © 2001, Taylor & Francis Group, LLC.

Theoretical principles of sustainable aquifer management are laid out in this work. The premise of our treatment is that groundwater is a renewable, although depletable, natural resource. The theory of this work is aimed at aquifers with a relatively homogeneous recharge that can be approximated by a logistic growth function. Sustainable aquifer exploitation occurs when the rate of groundwater extraction is equal to or less than the natural rate of groundwater replenishment for any level of aquifer storage. There can be many levels of sustainable aquifer exploitation depending on the level of aquifer storage, but there may be only one which maximizes economic returns under a variety of economic and aquifer conditions. Different strategies for sustainable exploitation are derived depending on whether or not the analysis considers tradeoffs among (i) current and future exploitation, (ii) constant and dynamic aquifer storage conditions, and (iii) regulated and unregulated aquifer exploitation. Key factors affecting sustainable exploitation strategies include (1) the market price of groundwater; (2) the cost of groundwater extraction; (3) the aquifer storage and natural replenishment characteristics; (4) institutional and environmental regulations on groundwater extraction; and (5) the real discount rate. An example of sustainable groundwater exploitation in Santa Barbara, California, illustrates the methods of this paper. © 2001 Elsevier Science Ltd. All rights reserved.

The probability density function (p.d.f.) of the ratio of two correlated gamma variables is derived and used to fit aquatic microbial-density data. The ratio p.d.f. is tackled by first taking the Fourier transform of a generalized Kibble-Gaver, unsymmetrical, characteristic function (c.f.) to obtain the corresponding bivariate p.d.f. of two correlated gamma variables with different shape and scale parameters. The ratio p.d.f. follows by weighted integration of the bivariate p.d.f. The derivation of the gamma bivariate and ratio p.d.f.s relies on the use of weighted Laguerre-Charlier polynomials that lead to p.d.f.s amenable to computation. The bivariate gamma p.d.f. and the ratio p.d.f. of correlated gamma variables are useful statistical tools in the analysis of skewed water-resources data. Computational examples illustrate the calculation of bivariate p.d.f.s for positive and negative correlation and the fitting of the ratio p.d.f. to correlated bacterial densities in stream water. © 2004 Elsevier Ltd. All rights reserved.

Starting with a stochastic differential equation with random coefficients describing steady-stale flow, the effective hydraulic conductivity of 1-, 2-, and 3-dimensional aquifers is derived. The natural logarithm of hydraulic conductivity (lnK) is assumed to be heterogeneous, with a spatial trend, and Isotropic. The effective conductivity relates the mean specific discharge in an aquifer to the mean hydraulic gradient, thus its importance in predicting Darcian discharge when field data represent mean or average values of conductivity or hydraulic head. Effective conductivity results are presented in exact form in terms of elementary functions after the introduction of special sets of coordinate transformations in two and three dimensions. It was determined that in one, two, and three dimensions, for the type of aquifer heterogeneity considered, the effective hydraulic conductivity depends on: (i) the angle between ihe gradient of the trend of lnK and the mean hydraulic gradient (which is zero in the one-dimensional situation): (2) (inversely) on the product of the magnitude of the trend gradient of lnK, b, and the correlation scale of InK, λ; and (3) (proportionally) on the variance of lnK, σ12. The product bλ plays a central role in the stability of the results for effective hydraulic conductivity. 1996 International Association for Mathematical Geology.

Tree‐ring reconstructions of centuries‐long streamflows in four river basins of western United States were used to assess the severity, frequency and distribution of duration of droughts in the basins, and the probability of extreme drought in well‐populated areas of California and Arizona. Our results show (i) greater long‐drought threat than that inferred from historical streamflow records; (ii) weak statistical dependence of streamflows across the river basins; and (iii) significant probability of droughts in individual river basins. Copyright 1992 by the American Geophysical Union.