Calculation of the temporal gravity variation from spatially variable water storage change in soils and aquifers

Silvia Leiriao, Xin He, Lars Christiansen, Ole Baltazar Andersen, Peter Bauer-Gottwein

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    Total water storage change in the subsurface is a key component of the global, regional and local water balances. It is partly responsible for temporal variations of the earth's gravity field in the micro-Gal (1 mu Gal = 10(-8) m s(-2)) range. Measurements of temporal gravity variations can thus be used to determine the water storage change in the hydrological system. A numerical method for the calculation of temporal gravity changes from the output of hydrological models is developed. Gravity changes due to incremental prismatic mass storage in the hydrological model cells are determined to give an accurate 3D gravity effect. The method is implemented in MATLAB and can be used jointly with any hydrological simulation tool. The method is composed of three components: the prism formula, the MacMillan formula and the point-mass approximation. With increasing normalized distance between the storage prism and the measurement location the algorithm switches first from the prism equation to the MacMillan formula and finally to the simple point-mass approximation. The method was used to calculate the gravity signal produced by an aquifer pump test. Results are in excellent agreement with the direct numerical integration of the Theis well solution and the semi-analytical results presented in [Damiata, B.N., and Lee, T.-C., 2006. Simulated gravitational response to hydraulic testing of unconfined aquifers. journal of Hydrology 318, 348-359]. However, the presented method can be used to forward calculate hydrology-induced temporal variations in gravity from any hydrological model, provided earth curvature effects can be neglected. The method allows for the routine assimilation of ground-based gravity data into hydrological models.
    Original languageEnglish
    JournalJournal of Hydrology
    Issue number3-4
    Pages (from-to)302-309
    Publication statusPublished - 2009


    • Model calibration
    • Time-lapse gravity
    • GRACE
    • Hydrological modelling
    • Aquifer pump test


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