Abstract
The Boussinesq equation permits, in principle, estimation of recharge for steady groundwater flow by taking derivatives of hydraulic head and transmissivity functions. The obstacles for doing this are as follows. Taking derivatives of the spatially-distributed data, even when they are known at every point, leads to numerical instability. Hydraulic heads are always measured with inaccuracies. Differentiating this “noisy” data leads to large errors in recharge estimation. It is shown that by using a special modification of the Boussinesq equation it is possible to overcome all three difficulties simultaneously. The methods of recharge estimation proposed are suitable for taking spatial derivatives from “noisy” measurements in other fields of Science and might be useful in Remote Sensing for edge enhancement.
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References
Aboufirassi, M, and M.A. Marino (1984). A geostatistically based approach to the identification of aquifer tramsmissivities in Yolo Basin, California. Math. Geology, Vol. 16, No. 2, pp. 125–137.
Allison, H.T. (1979). Inverse unstable problems and some of their applications. Math. Scientist, 4, pp. 9–30.
Allison, H. and Peck, A. (1985). Inverse problems for groundwater research. I.E. Aust. Hydrology and Water Resources Symposium, Sydney, pp. 20–24.
Courant, R. and Hilbert, D. (1966). Methods of Mathematical Physics, Vol.II, p. 792, Wiley, New York.
Dietrich, C.R., Anderssen, R.S. and Jakeman, A.J. (1986). Solving the inverse groundwater flow problem,in I.E. Aust. Hydrology and Water Resources Symposium, Brisbane, pp. 83–86.
Emsellem, Y., and G. de Marsily (1971). An automatic solution for the inverse problem, Water Res. Research, Vol. 7, No. 5, pp. 1264–1283.
Freeze, A.R. (1983). Regional groundwater analysis in surface and subsurface hydrology In Int. Conf. on Groundwater and Man, Sydney, pp.101–119.
Hall, E.L. (1979). Computer image processing and recognition. Acad. Press, New York, N.Y.
Hoerl, A.E. and R.W. Kennard (1970). Ridge regression: biased estimation for nonorthogonal problems. Technometrics, Vol. 12, No. 1, p. 55–67.
Hunt, B. (1983). Mathematical analysis of groundwater Resources. Butterworths, London.
Kalman, K.E. (1978). A retrospective after twenty years: from pure to applied. In Applications of Kalman Filter to Hydrology, ed. by C.L. Chiu, Pittsburgh, pp. 31–53.
Kisiel, C.C. and Duckstein, L. (1976). Ground-water Models, in Biswas, A.K. (ed.), Systems Approach to Water Management, McGraw-Hill, New York.
Levin, G.E. (1974). Use of functional analysis methods to input force reconstruction. Vibrotechnika, Acad. of Science Lit. SSR, No. 2 (23), pp. 161–173 (in Russian).
Peck, A.T., Johnston, C.D. and Williamson, D.R. (1981). Analysis of solute distributions in deeply weathered soils. In Agricultural Water Management, 4, Elsevier, Amsterdam, pp. 83–102.
Philip, T. (1975). Water movement in soil,in Heat and Mass Transfer in Biosphere, Scripta Book, Washington, pp. 30–45.
Phillips, D.L. (1962). A technique for the numerical solution of certain integral equations of the first kind. J. Assoc. Comput. Mach., 9, pp. 84–97.
Ross, B. (1975). A brief history and exposition of the fundamental theory of fractional calculus. In Lecture Notes in Mathematics, 457 ed. by Dold, A. and B. Eckmann, Springer-Verlag, Berlin. pp. 136.
Sharma, M.L. (1979). Evatranspiration and stream salinity as a consequence of land use change in south-western Australia. In H.T. Morel-Seytoux (ed.), Modelling Hydrologic Processes, Water Res. Publications, Colorado, USA, pp. 779–791.
Tikhonov, A.N. and V.Y. Arsenin (1977). Solutions of Ill-posed Problems. John Wiley & Sons, New York.
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© 1988 Springer Science+Business Media Dordrecht
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Allison, H. (1988). The Principles of Inverse Modelling for Estimation of Recharge from Hydraulic Head. In: Simmers, I. (eds) Estimation of Natural Groundwater Recharge. NATO ASI Series, vol 222. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7780-9_16
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DOI: https://doi.org/10.1007/978-94-015-7780-9_16
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-8444-6
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