Tide‐induced head fluctuations in coastal aquifers of variable thickness

Abstract

In this work, a new analytical solution to describe tide‐induced head fluctuations in aquifers of variable thickness is presented. The proposed model assumes a finite and confined aquifer with a thickness that increases or decreases quadratically with the distance to the coast. A closed‐form analytical solution is obtained by solving a boundary‐value problem with both a separation of variables method and a change of variables method. This solution is a generalization of the solution obtained by Cuello et al., Hydrogeological Journal, 2017, 25, 1509–1515. The analytical solution is expressed in terms of the wedging parameter, a parameter that depends on the length and thicknesses at the coast and at the inland edge of the aquifer. Positive values of the wedging parameter describe aquifers with increasing thickness towards land and negative values describe aquifers with a decreasing thickness in the inland direction. The comparison of the new solution and the solution for a finite aquifer with constant thickness indicates that the sign of the wedging parameter enhances or decreases the amplitude of the tide‐induced signal. However, the differences in time‐lag between both solutions are negligible near the coast. The slope factor, which quantifies the inconsistencies between aquifer diffusivities estimated from attenuation and time‐lag data, is computed and analysed. Near the coast, slope factor values greater than one are obtained for negative wedging parameters while slope factor values less than one are obtained for positive wedging parameters. The analysis of the new solution also indicates that more reliable estimates of the hydraulic diffusivity can be obtained from time‐lag data.

Technical note: Displacement variance of a solute particle in heterogeneous confined aquifers with random aquifer thickness fields

“…stochastic analysis of solute transport in heterogeneous porous formations has focused on relating the spatial variability of the hydraulic conductivity field to that of the flow velocity field, and thus to the spatial variability of the displacement of a solute particle. However, natural aquifers at regional scales often exhibit nonuniform aquifer thickness (e.g., Masterson et al, 2013;Zamrsky et al, 2018;DeSimone et al, 2020), and spatial variability in the aquifer thickness field has also been shown to have an important influence on flow field variability (e.g., Hantush, 1962;Cuello and Guarracino, 2020;Chang et al, 2021). Thus, the underlying motivation for this work is to provide an analytical stochastic method for improved quantification of the variability of solution displacement at the regional scale in heterogeneous aquifers under more realistic field conditions, i.e., taking into account the effects not only of the spatial variation of the hydraulic conductivity field but also of the thickness field of the confined aquifer.…”

Modelado y análisis de la marea inducida en acuíferos costeros del río de la Plata

“…Analíticas so de Hidrogeología (Cuello y Guarracino, 2018), y la segunda solución está en proceso de revisión en Hydrological Processes (Cuello y Guarracino, 2020).…”

“…Comparando las estimaciones de difusividad hidráulica realizadas mediante atenuación y desfasaje y la difusividad hidráulica verdadera, se pudo concluir que los datos de desfasaje proveen mejores estimaciones de difusividad hidráulica que los datos de atenuación. La segunda solución analítica y su correspondiente análisis se encuentra en revisión en la revista " Hydrological Processes" (Cuello y Guarracino, 2020). Finalmente, se utilizaron las conclusiones surgidas en el estudio de las soluciones analíticas derivadas para analizar los valores del factor de heterogeneidad calculados en el Capítulo 4, infiriendo posibles acuñamientos de los acuíferos.…”