Implementation of the Kalman Filter for a Geostatistical Bivariate Spatiotemporal Estimation of Hydraulic Conductivity in Aquifers
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 represe...
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MDPI AG
2020-11-01
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| Series: | Water |
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| Online Access: | https://www.mdpi.com/2073-4441/12/11/3136 |
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| author | Hugo Enrique Júnez-Ferreira Julián González-Trinidad Carlos Alberto Júnez-Ferreira Cruz Octavio Robles Rovelo G.S. Herrera Edith Olmos-Trujillo Carlos Bautista-Capetillo Ada Rebeca Contreras Rodríguez Anuard Isaac Pacheco-Guerrero |
| author_facet | Hugo Enrique Júnez-Ferreira Julián González-Trinidad Carlos Alberto Júnez-Ferreira Cruz Octavio Robles Rovelo G.S. Herrera Edith Olmos-Trujillo Carlos Bautista-Capetillo Ada Rebeca Contreras Rodríguez Anuard Isaac Pacheco-Guerrero |
| author_sort | Hugo Enrique Júnez-Ferreira |
| collection | DOAJ |
| description | 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 m<sup>2</sup>/day<sup>2</sup> value for K for all the cases, however, the smallest number of cells with values above 2 m<sup>2</sup>/day<sup>2</sup> 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. |
| first_indexed | 2024-03-10T14:59:37Z |
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| id | doaj.art-2fc6fd1916a947eaa18cb54480acf39a |
| institution | Directory Open Access Journal |
| issn | 2073-4441 |
| language | English |
| last_indexed | 2024-03-10T14:59:37Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
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| series | Water |
| spelling | doaj.art-2fc6fd1916a947eaa18cb54480acf39a2023-11-20T20:17:56ZengMDPI AGWater2073-44412020-11-011211313610.3390/w12113136Implementation of the Kalman Filter for a Geostatistical Bivariate Spatiotemporal Estimation of Hydraulic Conductivity in AquifersHugo Enrique Júnez-Ferreira0Julián González-Trinidad1Carlos Alberto Júnez-Ferreira2Cruz Octavio Robles Rovelo3G.S. Herrera4Edith Olmos-Trujillo5Carlos Bautista-Capetillo6Ada Rebeca Contreras Rodríguez7Anuard Isaac Pacheco-Guerrero8Licenciatura en Ciencias y Tecnología del Agua y Doctorado en Ciencias de la Ingeniería, Universidad Autónoma de Zacatecas, Campus Siglo XXI, 98160 Zacatecas, MexicoLicenciatura en Ciencias y Tecnología del Agua y Doctorado en Ciencias de la Ingeniería, Universidad Autónoma de Zacatecas, Campus Siglo XXI, 98160 Zacatecas, MexicoFacultad de Ingeniería Civil, Universidad Michoacana de San Nicolás de Hidalgo, 58000 Morelia Michoacán, MexicoLicenciatura en Ciencias y Tecnología del Agua y Doctorado en Ciencias de la Ingeniería, Universidad Autónoma de Zacatecas, Campus Siglo XXI, 98160 Zacatecas, MexicoInstituto de Geofísica, Universidad Nacional Autónoma de México, Ciudad Universitaria, Delegación Coyoacán, 04510 Ciudad de México, MexicoDoctorado en Ciencias de la Ingeniería, Universidad Autónoma de Zacatecas, Campus Siglo XXI, 98160 Zacatecas, MexicoLicenciatura en Ciencias y Tecnología del Agua y Doctorado en Ciencias de la Ingeniería, Universidad Autónoma de Zacatecas, Campus Siglo XXI, 98160 Zacatecas, MexicoLicenciatura en Ciencias y Tecnología del Agua y Doctorado en Ciencias de la Ingeniería, Universidad Autónoma de Zacatecas, Campus Siglo XXI, 98160 Zacatecas, MexicoDoctorado en Ciencias de la Ingeniería, Universidad Autónoma de Zacatecas, Campus Siglo XXI, 98160 Zacatecas, MexicoThe 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 m<sup>2</sup>/day<sup>2</sup> value for K for all the cases, however, the smallest number of cells with values above 2 m<sup>2</sup>/day<sup>2</sup> 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.https://www.mdpi.com/2073-4441/12/11/3136hydraulic conductivitygroundwater numerical modellingbivariate spatiotemporal geostatisticsKalman filter |
| spellingShingle | Hugo Enrique Júnez-Ferreira Julián González-Trinidad Carlos Alberto Júnez-Ferreira Cruz Octavio Robles Rovelo G.S. Herrera Edith Olmos-Trujillo Carlos Bautista-Capetillo Ada Rebeca Contreras Rodríguez Anuard Isaac Pacheco-Guerrero Implementation of the Kalman Filter for a Geostatistical Bivariate Spatiotemporal Estimation of Hydraulic Conductivity in Aquifers Water hydraulic conductivity groundwater numerical modelling bivariate spatiotemporal geostatistics Kalman filter |
| title | Implementation of the Kalman Filter for a Geostatistical Bivariate Spatiotemporal Estimation of Hydraulic Conductivity in Aquifers |
| title_full | Implementation of the Kalman Filter for a Geostatistical Bivariate Spatiotemporal Estimation of Hydraulic Conductivity in Aquifers |
| title_fullStr | Implementation of the Kalman Filter for a Geostatistical Bivariate Spatiotemporal Estimation of Hydraulic Conductivity in Aquifers |
| title_full_unstemmed | Implementation of the Kalman Filter for a Geostatistical Bivariate Spatiotemporal Estimation of Hydraulic Conductivity in Aquifers |
| title_short | Implementation of the Kalman Filter for a Geostatistical Bivariate Spatiotemporal Estimation of Hydraulic Conductivity in Aquifers |
| title_sort | implementation of the kalman filter for a geostatistical bivariate spatiotemporal estimation of hydraulic conductivity in aquifers |
| topic | hydraulic conductivity groundwater numerical modelling bivariate spatiotemporal geostatistics Kalman filter |
| url | https://www.mdpi.com/2073-4441/12/11/3136 |
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