In this paper, simple indicators of the propensity for sea water intrusion (SWI) to occur (referred to as "SWI vulnerability indicators") are devised. The analysis is based on an existing analytical solution for the steady-state position of a sharp fresh water-salt water interface. Interface characteristics, that is, the wedge toe location and sea water volume, are used in quantifying SWI in both confined and unconfined aquifers. Rates-of-change (partial derivatives of the analytical solution) in the wedge toe or sea water volume are used to quantify the aquifer vulnerability to various stress situations, including (1) sea-level rise; (2) change in recharge (e.g., due to climate change); and (3) change in seaward discharge. A selection of coastal aquifer cases is used to apply the SWI vulnerability indicators, and the proposed methodology produces interpretations of SWI vulnerability that are broadly consistent with more comprehensive investigations. Several inferences regarding SWI vulnerability arise from the analysis, including: (1) sea-level rise impacts are more extensive in aquifers with head-controlled rather than flux-controlled inland boundaries, whereas the opposite is true for recharge change impacts; (2) sea-level rise does not induce SWI in constant-discharge confined aquifers; (3) SWI vulnerability varies depending on the causal factor, and therefore vulnerability composites are needed that differentiate vulnerability to such threats as sea-level rise, climate change, and changes in seaward groundwater discharge. We contend that the approach is an improvement over existing methods for characterizing SWI vulnerability, because the method has theoretical underpinnings and yet calculations are simple, although the coastal aquifer conceptualization is highly idealized.
[1] A new analytical solution of the flow equation has been developed to estimate the time to reach a near-equilibrium state in mixed aquifers, i.e., having unconfined and confined portions, following a large hydraulic perturbation. Near-equilibrium is defined as the time for an initial aquifer perturbation to dissipate by an average 95% across the aquifer. The new solution has been obtained by solving the flow system of a simplified conceptual model of a mixed aquifer using Laplace transforms. The conceptual model is based on two assumptions: (1) the groundwater flow can be reduced to a horizontal 1-D problem and (2) the transmissivity, a function of the saturated thickness, is assumed constant on the unconfined portion. This new solution depends on the storativity of the unconfined portion, the lengths of the unconfined and confined portions and the transmissivity, assumed to be constant and equal in both portions of the mixed aquifer. This solution was then tested and validated against a numerical flow model, where the variations of the saturated thickness and therefore variations of the transmissivity were either ignored, or properly modeled. The agreement between the results from the new solution and those from the numerical model is good, validating the use of this new solution to estimate the time to reach near-equilibrium in mixed aquifers. This solution for mixed aquifers, as well as the solutions for a fully confined or fully unconfined aquifer, has been used to estimate the time to reach nearequilibrium in 13 large aquifers in the world. For those different aquifers, the time to reach near-equilibrium ranges between 0.7 kyr to 2.4 Â 10 7 kyr. These results suggest that the present hydraulic heads in these aquifers are typically a mixture of responses induced from current and past hydrologic conditions and thus climate conditions. For some aquifers, the modern hydraulic heads may in fact depend upon hydrologic conditions resulting from several past climate cycles.
[1] Water level rises associated with river flow events induce both pressure and solute movement into adjacent aquifers at vastly different rates. We present a simple analytical solution that relates the travel time and travel distance of solutes into an aquifer following river stage rise to aquifer properties. Combination with an existing solution for pressure propagation indicates that the ratio of solute to pressure travel times is proportional to the ratio of the volume of water stored in the aquifer before the river stage rise and the volume added by the stage rise and is independent of hydraulic conductivity. Two-dimensional numerical simulations of an aquifer slice perpendicular to a river demonstrate that the solutions are broadly applicable to variably saturated aquifers and partially penetrating rivers. The solutions remain applicable where river stage rise and fall occur, provided that regional hydraulic gradients are low and the duration of the river stage rise is less than pressure and solute travel times to the observation point in the aquifer. Consequently, the solutions provide new insight into the relationships between aquifer properties and distance and time of solute propagation and, in some cases, may be used to estimate system characteristics. Travel time metrics obtained for a flood event in the Cockburn River in eastern Australia using electrical conductivity measurements enabled estimates of aquifer properties and a lateral extent of river-aquifer mixing of 25 m. A detailed time series of any soluble tracer with distinctly different concentrations in river water and groundwater may be used.
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