Ocean tide‐induced head fluctuations in wells

Abstract

Abstract. Wells in coastal aquifers can attenuate and delay aquifer hydraulic head fluctuations induced by ocean tides. To infer how the attenuation/delay depend on system dimensions and hydraulic properties, I solved a boundary value problem in which a well with storage fully penetrates a confined, coastal aquifer. The well-induced attenuation and delay are (1) maximum at the well and decrease to zero at the aquifer's horizontal periphery; (2) generally increasing functions of well radius, distance from seaward boundary, and tidal frequency; (3) decreasing functions of transmissivity; and (4) nearly independent of storativity for lesser radii and generally decreasing functions of storativity for greater radii. Approximations were developed for (1) a point in the aquifer, valid when the distance from the point to the well greatly exceeds the well radius, and (2) at the well, valid when the distance from the well to the seaward boundary greatly exceeds the radius. Hsieh et al. [1987] investigated the problem of estimating aquifer properties using observations of well response to the solid Earth tide (SET). Ritzi et al.[1991] examined the problem of estimating aquifer properties using observations of the combined well response to SET and atmospheric pressure variation (APV). Although both the SET and the OT are caused by periodic variations in tidal potential and hence occur at the same frequencies, they influence an aquifer through different mechanisms and thus lead to different hydraulic responses. In the case of SET, an aquifer responds to periodic variations in tidal potential by harmonically dilating/contracting. In a homogeneous and isotropic, horizontally infinite, confined aquifer where wells are absent the hydraulic response to this dilatation is a harmonic pressure head disturbance that is horizontally uniform. Hsieh et al. [1987] found that in the presence of a finite-diameter well the hydraulic response of such an aquifer to SET is azimuthally symmetric.In contrast, the OT is viewed as a forcing that occurs at or near the aquifer's seaward boundary. If the aquifer outcrops at the seaward boundary, so that it is in direct hydraulic communication with the ocean, then the forcing is hydraulic. If the aquifer extends under the ocean, so that the OT produces variations in loading, then the forcing is mechanical. In either case, the hydraulic response of the aquifer to the OT is a pressure head wave that is attenuated as it propagates landward. Owing to the presence of the seaward boundary, the hydraulic response is expected to be azimuthally asymmetric regardless of whether or not a well is present.Townley [1995] presents solutions to a number of boundary value problems involving periodic flow of groundwater in homogeneous, confined aquifers of finite length. All of the problems considered by Townley are either one-dimensional or two-dimensional and azimuthally symmetric.The objective of this analysis is to infer the effects of a fully penetrating finite-storage well on the periodic OT-induced head fluct...

Determining the hydraulic properties of coastal aquifer systems using groundwater response to tidal fluctuations: applicability and limitations

“…Both the transmissivity, T, and the storage coefficient, S can then be quantified as 6.018221 × 10 −2 m 2 /h (equal to1.44437304 m 2 /day) and 7.15 × 10 −7 , respectively. Since the effects of well storage (Depner 2000) and the sensitivity of changes in water level in the well depend on well radius, it is advisable to use a smallsized monitoring well.…”

Stochastic relationships for periodic responses in randomly heterogeneous aquifers

“…Observations of oscillating heads within an aquifer can provide information on aquifer diffusivity, thus yielding hydrogeological property estimates that are independent of conventional pumping tests and that apply at quite different temporal and spatial scales. The most common applications of the tidal method are to homogeneous systems, where a mean tidal response function parameterized by mean aquifer diffusivity is estimated and analytical solutions for these cases are well developed [ Townley , 1995; Depner , 2000]. In the last decade, a variety of tidal response solutions have been generated for heterogeneous systems, but these have usually applied to systems displaying deterministic macrostructures, such as aquifer layering [ Li et al , 2000; Li and Jiao , 2002] or subdomains in the horizontal [ Trefry , 1999].…”