Implementation of the Kalman Filter for a Geostatistical Bivariate Spatiotemporal Estimation of Hydraulic Conductivity in Aquifers

Abstract

The estimation of the hydraulic parameters of an aquifer such as the hydraulic conductivity is somehow complicated due to its heterogeneity, on the other hand field and laboratory tests are both time consuming and costly. The use of geostatistical-based techniques for data assimilation could represent an alternative tool that allows the use of space-time aquifer behaviour to characterize hydraulic conductivity heterogeneity. In this paper, a spatiotemporal bivariate methodology was implemented combining historical hydraulic head data with hydraulic conductivity sparse data in order to obtain an estimate of the spatial distribution of the latter variable. This approach takes advantage of the correlation between the hydraulic conductivity (K) and the hydraulic head (H) behaviour through time. In order to evaluate this approach, a synthetic experiment was constructed through a transitory numerical flow-model that simulates hydraulic head values in a horizontally-heterogeneous aquifer. Geostatistical tools were used to describe the correlation between simulated spatiotemporal data of hydraulic head and the spatial distribution of the hydraulic conductivity in a group of model nodes. Subsequently, the Kalman filter was used to estimate the hydraulic conductivity values at nonsampled sites. The results showed acceptable differences between estimated and synthetic hydraulic conductivity data, with low estimate error variances (predominating the 1 m2/day2 value for K for all the cases, however, the smallest number of cells with values above 2 m2/day2 correspond to the bivariate spatiotemporal case) and the best agreement between the estimated errors and the selected model variance (SMSE values of 0.574 and 0.469) were found for the bivariate cases, which suggests that the implemented methodology could be used for reducing calibration efforts, particularly when the hydraulic parameters data are scarce.

About 3D Incompressible Flow Reconstruction from 2D Flow Field Measurements

“…Under the practical point of view, the model chosen for the random function is bound to be the space continuity of the sampled data set. The above representation has been applied to flow measurement [ 23 , 24 ], particularly to detect the third component of Table 2 . We can say that the approach adopted in this paper is correct, given the fact that the velocities represented in Figure 10 (+symbols) fall within the range of uncertainty designated in the paper.…”

Use of the Kalman Filter for the Interpretation of Aquifer Tests Including Model and Measurement Errors

“…However, simulated drawdowns and the Cooper-Jacob solution deviate significantly from the measurements for times greater than 500 min. For comparison purposes, in Table 3 are also presented the values for 𝑇 and 𝑆 reported in [27] obtained with traditional methods (Theis and Cooper-Jacob procedures) For comparison purposes, in Table 3 are also presented the values for T and S reported in [27] obtained with traditional methods (Theis and Cooper-Jacob procedures) and using an adaptative pumping test analysis based on the Kalman filter (the Şen procedure); the results of using the software AquiferWin32 version 4.00 [16] are also included. In Table 3, it can be observed that the values reported in [27] for T and S differ considerably from those found with the procedure proposed in this paper.…”

“…For comparison purposes, in Table 3 are also presented the values for 𝑇 and 𝑆 reported in [27] obtained with traditional methods (Theis and Cooper-Jacob procedures) For comparison purposes, in Table 3 are also presented the values for T and S reported in [27] obtained with traditional methods (Theis and Cooper-Jacob procedures) and using an adaptative pumping test analysis based on the Kalman filter (the Şen procedure); the results of using the software AquiferWin32 version 4.00 [16] are also included. In Table 3, it can be observed that the values reported in [27] for T and S differ considerably from those found with the procedure proposed in this paper. When the former parameters are used to obtain drawdowns with the Cooper-Jacob solution, significant differences are obtained with respect to the measurements, especially for larger times.…”

“…The Kalman filter has been used for data assimilation in hydrogeology in different applications, such as: the calibration of groundwater numerical flow models [22], the optimal design of monitoring networks [23][24][25], the estimation of hydrogeological variables [26,27], and the interpretation of aquifer tests [28,29]. Recent studies proposed the use of artificial neural networks to estimate hydrogeological variables [30].…”

Groundwater Characteristics Assessment in Kurdistan Region Provinces-iraq: A Review

“…Protection the groundwater quality is important, the major approach to the protection of groundwater is the monitoring and estimate of the chemical, physical and biological substances of it (Jang et al, 2013). Monitoring groundwater and collecting data from the process of monitoring provides an understanding of the situation of groundwater (Júnez-Ferreira & Herrera, 2013;Mogheir et al, 2006). An excellent monitoring scheme would suggest both accurate and sufficient groundwater property data as well as cost-effectively fair data (Baalousha, 2010).…”