Parameter estimation using groundwater age and head data, Cape Cod, Massachusetts

Abstract

A practical inversion procedure is used to parametrize an unconfined aquifer on Cape Cod, Massachusetts, using groundwater age and hydraulic head data. The inversion resulted in estimates of the recharge flux, homogeneous but anisotropic hydraulic conductivity, porosity, boundary hydraulic heads, and the aquifer thickness. The range of estimated values agreed well with independent measurements at the site. By themselves hydraulic heads are sensitive to the ratio of recharge flux to hydraulic conductivity. The age data are sensitive to the ratio of recharge to porosity. Together, age and head data provide a constraint on both boundary values and material properties. However, a sensitivity analysis shows that porosity, hydraulic conductivity, and recharge are all correlated, and thus a unique inverse solution requires an independent constraint on one of these parameters. Simulations also show that groundwater ages at a given point on a streamline are sensitive to the recharge flux at the point where the streamline begins at the water table. This implies that a vertical profile of age data will be sensitive to the upstream recharge flux, suggesting that spatial patterns in recharge can be estimated using vertical profiles from multilevel monitoring wells. Because measurements of groundwater age can be made in many shallow aquifers, this approach may be applicable to other sites. PORTNIAGUINE

Estimate of recharge from radiocarbon dating of groundwater and numerical flow and transport modeling

“…Hence uncertainties in porosity result in nonunique estimates of recharge and hydraulic conductivity. The highly correlated problem of K and R is transformed to highly correlated parameter sets of K, R, and F/e [Portniaguine and Solomon, 1998]. However, porosities of sediments or sedimentary rocks are typically less variable than recharge in semiarid and arid regions or hydraulic conductivity.…”

Dating of ‘young’ groundwaters using environmental tracers: advantages, applications, and research needs

“…From a formal inversion point of view, it has been shown [87] that recharge, hydraulic conductivity, and porosity are correlated and hence a unique calibration of these parameters is only possible if one of the three is independently measured. This situation is amplified when multiple scales of porosity exist such as fracture porosity versus matrix porosity (see the discussion of matrix diffusion below).…”

Notes on Groundwater Age in Forward and Inverse Modeling

“…Later Weissmann et al (2002) modeled the distribution of ground water ages indicated by chlorofluorocarbons in a heterogeneous aquifer using particle tracing and echoed the need for the complete groundwater age distribution. In aquifer characterization by inverse problem solution, some early uses of groundwater age in analogy to tracer concentration data appears in Reilly et al (1994), Sheets et al (1998), and Portniaguine and Solomon (1998), and such coupled inverses are now common (e.g., Reynolds and Marimuthu 2007).…”

“…tritium/helium, 36 Cl/Cl, 14 C/C) and their history of decay in subsurface can serve as proxy for some measure of groundwater age. Such observation data have been used in the same way to help in estimation of aquifer properties (Reilly et al 1994;Sheets et al 1998;Portniaguine and Solomon 1998;Zhu 2000;Weissmann et al 2002;Reynolds and Marimuthu 2007). In the inverse study presented here, we apply modeling of both flow and transport in an idealized 2-D problem in the forward sense to solve simultaneously the steady-state piezometric head and mean age distributions, the filtered output of which is used as input to an indirect inversion scheme to calibrate some of the parameters involved.…”