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A Monte Carlo approach for improved estimation of groundwater level spatial variability in poorly gauged basins

Varouchakis Emmanouil, Christopoulos Dionysios

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Summary

Groundwater level is an important source of information in hydrologicalmodelling. In many aquifers the boreholes monitored are scarce and/orsparse in space. In both cases, geostatistical methods can help tovisualize the free surface of an aquifer, whereas the use of auxiliaryinformation improves the accuracy of level estimates and maximizes theinformation gain for the quantification of groundwater level spatialvariability. In addition, they allow the exploitation of datasets thatcannot otherwise be efficiently used in catchment models. In thispresentation, we demonstrate an approach for incorporating auxiliaryinformation in interpolation approaches using a specific case study. Inparticular, the study area is located on the island of Crete (Greece).The available data consist of 70 hydraulic head measurements for the wetperiod of the hydrological year 2002-2003, the average pumping rates atthe 70 wells, and 10 piezometer readings measured in the precedinghydrological year. We present a groundwater level trend model based onthe generalized Thiem's equation for multiple wells. We use the driftterm to incorporate secondary information in Residual Kriging (RK)(Varouchakis and Hristopulos 2013). The residuals are then interpolatedusing Ordinary Kriging and then are added to the drift model. Thiem'sequation describes the relationship between the steady-state radialinflow into a pumping well and the drawdown. The generalized form of theequation includes the influence of a number of pumping wells. Itincorporates the estimated hydraulic head, the initial hydraulic headbefore abstraction, the number of wells, the pumping rate, the distanceof the estimation point from each well, and the well's radius ofinfluence. We assume that the initial hydraulic head follows a lineartrend, which we model based on the preceding hydrological yearmeasurements. The hydraulic conductivity in the study basin variesbetween 0.0014 and 0.00014 m/s according to geological estimates. Sincepumping tests are not available, we determine the radius of influenceusing an empirical equation (Bear 1979) that involves the drawdown atthe well face, the hydraulic conductivity around the pumping well, andthe initial saturated thickness. Since the local variation of thedrawdown and the hydraulic conductivity is not known, we use uniformvalues based on the Monte Carlo analysis below. The initial saturatedthickness for all 70 wells is assumed to follow a linear trend estimatedfrom the 10 piezometer readings and from the geological cross-sectionsavailable for the basin. Using linear regression analysis of the meanannual groundwater level, we estimate the rate of mean annual leveldecrease at 1.85 m/yr, with the 95% confidence interval at [1.60-2.10]m/yr. The optimal hydraulic conductivity over the drawdown and thehydraulic conductivity parameter space is determined by means of MonteCarlo sensitivity analysis and leave-one-out cross validation that focuson the reproduction of the measured head values. The removed head valuesduring the validation procedure are estimated using RK. The meanabsolute error (MAE) is used as the criterion of optimal performance.The hydraulic head trend function is estimated for each combination ofthe hydraulic conductivity and the drawdown. The residuals are modeledusing several semivariogram models for each realization of the hydraulicconductivity and the drawdown tested. The Monte Carlo simulations showthat the MAE is primarily sensitive to the variation of the hydraulicconductivity and less to the drawdown. The minimum MAE is obtained for ahydraulic conductivity of 0.00015 m/s and a drawdown equal to 1.85 m.The recently proposed Spartan semivariogram models for the residualsprovide the most accurate estimates. Based on the above procedure, therange of the radius of influence is determined between 105 m and 160 m.The approach described above improves the MAE by 14% and the RMSE by 10%compared to similar approaches studied herein i.e. RK with a DigitalElevation Model of the area and the distance of the estimation pointfrom the temporary river crossing the basin. Bear, J., 1979. Hydraulicsof groundwater. New York: McGraw-Hill. Varouchakis, E. A. andHristopulos, D. T. 2013. Improvement of groundwater level prediction insparsely gauged basins using physical laws and local geographic featuresas auxiliary variables. Advances in Water Resources, 52, 34-49.

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