Two-dimensional physical-based inversion of confined and unconfined aquifers under unknown boundary conditions |
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| Institution: | 1. Department of Agricultural and Forest Sciences (SAF), Università degli Studi di Palermo, Italy;2. Department of Civil, Environmental, Aerospace, Material Engineering (DICAM), Università degli Studi di Palermo, Italy;1. Consiglio Nazionale delle Ricerche, Istituto di Ricerca Sulle Acque, Via Salaria km 29.300, 00015 Monterotondo, RM, Italy;2. Dipartimento DICATAM, Università degli Studi di Brescia, Via Branze 43, 25123 Brescia, Italy;3. Consiglio Nazionale delle Ricerche, Istituto di Ricerca Sulle Acque, UOS Brugherio, Via del Mulino, 19, 20861 Brugherio, MB, Italy;1. Earth Sciences and Engineering, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia;2. Subsurface and Groundwater Systems, Deltares, Princetonlaan 6, 3584 CB Utrecht, The Netherlands;3. Applied Mathematics and Computational Sciences, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia;1. Department of Earth and Planetary Sciences, University of Tennessee, Knoxville, TN, USA;2. Chemical and Engineering Materials Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA;3. Department of Biosystems Engineering and Soil Science, University of Tennessee, Knoxville, TN, USA;4. Department of Geosciences, Texas Tech University, Lubbock, TX, USA;5. Environmental Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA |
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| Abstract: | An inverse method is developed to simultaneously estimate multiple hydraulic conductivities, source/sink strengths, and boundary conditions, for two-dimensional confined and unconfined aquifers under non-pumping or pumping conditions. The method incorporates noisy observed data (hydraulic heads, groundwater fluxes, or well rates) at measurement locations. With a set of hybrid formulations, given sufficient measurement data, the method yields well-posed systems of equations that can be solved efficiently via nonlinear optimization. The solution is stable when measurement errors are increased. The method is successfully tested on problems with regular and irregular geometries, different heterogeneity patterns and variances (maximum Kmax/Kmin tested is 10,000), and error magnitudes. Under non-pumping conditions, when error-free observed data are used, the estimated conductivities and recharge rates are accurate within 8% of the true values. When data contain increasing errors, the estimated parameters become less accurate, as expected. For problems where the underlying parameter variation is unknown, equivalent conductivities and average recharge rates can be estimated. Under pumping (and/or injection) conditions, a hybrid formulation is developed to address these local source/sink effects, while different types of boundary conditions can also exert significant influences on drawdowns. Local grid refinement near wells is not needed to obtain accurate results, thus inversion is successful with coarse inverse grids, leading to high computation efficiency. Furthermore, flux measurements are not needed for the inversion to succeed; data requirement of the method is thus not much different from that of interpreting classic well tests. Finally, inversion accuracy is not sensitive to the degree of nonlinearity of the flow equations. Performance of the inverse method for confined and unconfined aquifer problems is similar in terms of the accuracy of the estimated parameters, the recovered head fields, and the solver speed. |
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| Keywords: | Aquifer calibration Inverse method Hydraulic conductivity Recharge rate Structure error Equivalent parameter |
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