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Article

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

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Licenciatura en Ciencias y Tecnología del Agua y Doctorado en Ciencias de la Ingeniería, Universidad Autónoma de Zacatecas, Campus Siglo XXI, 98160 Zacatecas, Mexico
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Facultad de Ingeniería Civil, Universidad Michoacana de San Nicolás de Hidalgo, 58000 Morelia Michoacán, Mexico
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Instituto de Geofísica, Universidad Nacional Autónoma de México, Ciudad Universitaria, Delegación Coyoacán, 04510 Ciudad de México, Mexico
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Doctorado en Ciencias de la Ingeniería, Universidad Autónoma de Zacatecas, Campus Siglo XXI, 98160 Zacatecas, Mexico
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Authors to whom correspondence should be addressed.
Water 2020, 12(11), 3136; https://doi.org/10.3390/w12113136
Received: 18 September 2020 / Revised: 22 October 2020 / Accepted: 30 October 2020 / Published: 9 November 2020
(This article belongs to the Section Hydrology and Hydrogeology)
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. View Full-Text
Keywords: hydraulic conductivity; groundwater numerical modelling; bivariate spatiotemporal geostatistics; Kalman filter hydraulic conductivity; groundwater numerical modelling; bivariate spatiotemporal geostatistics; Kalman filter
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MDPI and ACS Style

Júnez-Ferreira, H.E.; González-Trinidad, J.; Júnez-Ferreira, C.A.; Robles Rovelo, C.O.; Herrera, G.S.; Olmos-Trujillo, E.; Bautista-Capetillo, C.; Contreras Rodríguez, A.R.; Pacheco-Guerrero, A.I. Implementation of the Kalman Filter for a Geostatistical Bivariate Spatiotemporal Estimation of Hydraulic Conductivity in Aquifers. Water 2020, 12, 3136. https://doi.org/10.3390/w12113136

AMA Style

Júnez-Ferreira HE, González-Trinidad J, Júnez-Ferreira CA, Robles Rovelo CO, Herrera GS, Olmos-Trujillo E, Bautista-Capetillo C, Contreras Rodríguez AR, Pacheco-Guerrero AI. Implementation of the Kalman Filter for a Geostatistical Bivariate Spatiotemporal Estimation of Hydraulic Conductivity in Aquifers. Water. 2020; 12(11):3136. https://doi.org/10.3390/w12113136

Chicago/Turabian Style

Júnez-Ferreira, Hugo E.; González-Trinidad, Julián; Júnez-Ferreira, Carlos A.; Robles Rovelo, Cruz O.; Herrera, G.S.; Olmos-Trujillo, Edith; Bautista-Capetillo, Carlos; Contreras Rodríguez, Ada R.; Pacheco-Guerrero, Anuard I. 2020. "Implementation of the Kalman Filter for a Geostatistical Bivariate Spatiotemporal Estimation of Hydraulic Conductivity in Aquifers" Water 12, no. 11: 3136. https://doi.org/10.3390/w12113136

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