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• W2064016711 abstract "[1] Mao et al. [2011] use numerical modeling to investigate sources of water contributing to s-shaped curves often seen when plotting, on logarithmic scale versus time, drawdown created by pumping water at constant rate from an unconfined aquifer. The relative contributions of three sources (compaction of aquifer material and expansion of water in the saturated zone, drainage from material that initially overlies a horizontal water table or zero-pressure isobar, and drainage from desaturated material behind the falling water table) are identified by studying the space-time evolution of temporal changes in volumetric storage. Mao et al. consider both uniform and randomly nonuniform aquifers but we restrict our comments to the former. The uniform case is analyzed by simulating flow at a particular rate to a line sink that penetrates a particular lower portion of an aquifer, with the water table at a particular elevation, having a particular thickness, and saturated-unsaturated hydraulic properties. This single simulation is supplemented by a few column simulations with fixed saturated properties, a narrow range of unsaturated parameters with water table either within or at the top of the column, and a constant-strength sink at the bottom. Based on these simulations, Mao et al. conclude that transitions from one water release mechanism to another during vertical flow are the causes of s-shaped time-drawdown variations in unconfined aquifers, these curves are affected to a greater degree by moisture retention than by relative hydraulic characteristics, and the popular terms “delayed yield” and “delayed water table response” fail to elucidate these phenomena, and so are therefore misleading. [2] We believe that it is dangerous to draw such general conclusions on the basis of limited numerical experiments. Mao et al. [2011] do not cite, and must thus have been unaware of, more recent analytical and numerical work by Mishra and Neuman [2010, 2011] which does not support their conclusions. We see little purpose in debating the merits and demerits of earlier related work by our group given that this latest work supersedes it. In particular, specific yield and unsaturated flow parameter values inferred with our recent model from pumping tests at Cape Cod and Borden were found to be supported by independent field and laboratory measurements. [3] The analytical solutions of Mishra and Neuman [2010, 2011] are similar to an earlier analytical solution by Tartakovsky and Neuman [2007] in that all adopt a linearization originally introduced by Kroszynski and Dagan [1975]. The linearization allows solving the saturated and unsaturated flow equations inside their original domains using the initial (static) distribution of variables in the unsaturated zone. In discussing the work of Tartakovsky and Neuman [2007], Mao et al. [2011] state incorrectly that it ignores unsaturated flow induced by lowering the water table and it assumes that unsaturated hydraulic conductivity and moisture capacity vary with elevation, not with pressure head. In fact, the analytical solutions predict a gradual fall of the water table with consequent unsaturated flow in the drained zone above it. They likewise predict a gradual drop in pressure heads in the original unsaturated zone above the initial water table, coupled with corresponding changes in material properties and fluxes. The reader can easily verify this by examining space-time variations in dimensionless drawdown depicted along vertical cross-sections in Figure 7 of Tartakovsky and Neuman [2007] and Figure 10 of Mishra and Neuman [2010]. Translating these drawdowns into pressure heads would reveal that they become more negative with time in the original vadose zone above the initial horizontal water table, and switch sign from positive to negative in a newly formed zone of desaturation contained between the original water table and its newly computed position below. The newly computed negative pressure heads above the falling zero-pressure isobar (water table) can be translated into water contents, or saturations, and corresponding unsaturated material properties according to equations (1) and (2) of Mishra and Neuman [2010]. The reader can verify that the linearization is accurate by glancing at Figures 11 and 12 of Mishra and Neuman [2010] and Figures 7–9 of Mishra and Neuman [2011] in which they are compared, successfully, with those of three-dimensional numerical simulations both below and above the water table. These numerical simulations use the popular van Genuchten [1980]-Mualem [1976] constitutive model of unsaturated hydraulic properties, not an exponential model as do Mao et al. [2011]. [4] That a transition from compression-dominated (artesian) to gravity-dominated drainage at [Neuman, 1972, 1974, 1975] and above [Tartakovsky and Neuman, 2007; Mishra and Neuman, 2010, 2011] the water is responsible for the s-shaped inflection (as well as other behaviors) of saturated-zone time-drawdown curves in unconfined aquifers is not new. Furthermore, it is incorrect to associate this transition exclusively with vertical flow, as do Mao et al. [2011]: flow at all stages of pumping, both above and below the water table, takes place in both horizontal and vertical directions as evidenced by Figure 7 of Tartakovsky and Neuman [2007] and Figure 10 of Mishra and Neuman [2010]. Similar to earlier work by Nwankwor et al. [1984], the one-dimensional column simulations of Mao et al. [2011] do not capture horizontal components of flow caused by pumping, conveying the inaccurate impression that s-shaped behavior is exclusively a vertical flow phenomenon. [5] Considering that gravity drainage is delayed in time relative to the artesian effect we, contrary to Mao et al. [2011], see nothing misleading about the popular terms “delayed yield,” “delayed gravity response,” and “delayed water table response;” the second term is particularly unambiguous about what transpires when an unconfined aquifer is pumped. [6] We disagree with Mao et al. [2011] that drawdown in an unconfined aquifer is always affected to a greater degree by moisture retention than by relative hydraulic characteristics of the material. As illustrated clearly by Figures 2 and 3 and 6 and 7 of Mishra and Neuman [2010], the relative degrees to which these characteristics affect time-drawdown behaviors (whether s-shaped or otherwise) in the saturated and the unsaturated zones, respectively, vary with these and other properties and parameters of the aquifer and the pumping regime. [7] We agree with Mao et al. [2011] that the analytical solution of groundwater flow problems entails mathematical approximations that are often more restrictive than those required for numerical simulation. We, however, believe that “where analytical solutions are applicable … they offer a number of advantages: having a dimensionless form, which renders the solution general rather than site specific; revealing dimensionless groups of parameters and space-time coordinates that control system behavior, which may otherwise (and in fact often do) remain unidentified; obviating the need to construct numerical grids and to compute results across the entire grid at all times of interest; and generally, rendering parameter estimation easier, more stable, and computationally efficient” [Li and Neuman, 2007, p. 673]. Analytical and numerical methods of investigation should be considered complementary and, where possible, pursed in tandem. [8] We also agree with Mao et al. [2011] on the need to better understand the effect of heterogeneity on aquifer responses to pumping. We believe, however, that simplified solutions which treat aquifers as uniform will continue to be useful in practice for many years to come. [9] This research was supported in part through a contract between the University of Arizona and Vanderbilt University under the Consortium of Risk Evaluation with Stakeholder Participation (CRESP) III, funded by the U.S. Department of Energy." @default.
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• W2064016711 date "2012-02-01" @default.
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• W2064016711 title "Comments on “A revisit of drawdown behavior during pumping in unconfined aquifers” by D. Mao, L. Wan, T.-C. J. Yeh, C.-H. Lee, K.-C. Hsu, J.-C. Wen, and W. Lu" @default.
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