Spatiotemporal estimation of hydraulic head using a single spatiotemporal random function model
DOI:
https://doi.org/10.24850/j-tyca-2010-02-06Keywords:
single spatio-temporal model, geostatistics, hydraulic head estimationAbstract
This paper presents a geostatistical method for performing estimates using space-time kriging which is applied for the estimation of the water level of the Queretaro-Obrajuelo aquifer in the 1981-2004 period. The estimates obtained by this method for the years 1993, 1995 and 1999 are compared with ordinary kriging and cokriging using cross validation. The average mean error (ME) for the three chosen years was lowest for ordinary kriging (-0.23), the average mean squared error (MSE) is the lowest in the case of the space-time method (224.29) and the value of the average squared mean standard error (SMSE) is better for the method of cokriging (0.95), because the SMSE values are close to unity. The SMSE for the space-time method is 0.8 when considering all the times, but it decreases in particular for the selected years. The results of the estimated variances are always smaller using the space-time method, because it uses more information to get the estimate. Also, it is possible to make estimates in the whole space for all times. Therefore, it was concluded that the tool is powerful, since it considers all available information to produce the estimates.
References
AHMED, S. and DE MARSILY, G. Comparison of geostatistical methods for estimating transmissivity using data on transmissivity and specific capacity. Water Resources Research. Vol. 23, no. 9, 1987, pp. 1717-1737. DOI: 10.1029/WR023i009p01717
ANGELINI, P. Correlation and spectral analysis of two hydrogeological systems in central Italy. Hydrological Sciences Journal. Vol. 42, no. 3, 1997, pp. 425-438. DOI: 10.1080/02626669709492038
ASCE. Review of geostatistics in geohydrology I: Basic concepts. Journal of Hydraulic Engineering. Vol. 116, no. 5, 1992a, pp. 612-632. DOI: 10.1061/(ASCE)0733-9429(1990)116:5(612)
ASCE. Review of geostatistics in geohydrology II: Aplications. Journal of Hydraulic Engineering. Vol. 116, no. 5, 1992b, pp. 633-658. DOI: 10.1061/(ASCE)0733-9429(1990)116:5(633)
ASLI, M. and MARCOTTE, D. Comparison of approaches to spatial estimation in a bivariate context. Mathematical Geology. Vol. 27, no. 5, 1995, pp. 641-658. DOI: 10.1007/BF02093905
BILONICK, R.A. and NICHOLS, D.G. Temporal variations in acid precipitation over New York State What the 1965-1979 USGS data reveal. Atmospheric Environment. Vol. 17, no. 6, 1983, pp. 1063-1072. DOI: 10.1016/0004-6981(83)90329-3
BILONICK, R.A. Risk qualifies maps of hydrogen ion concentration for the New York State area for 1966-1978. Atmospheric Environment. Vol. 17, no. 12, 1983, pp. 2513-2524. DOI: 10.1016/0004-6981(83)90077-X
BILONICK, R.A. Monthly hydrogen ion depositation maps for the northeastern U.S. from July 1982 to September 1984. Atmospheric Environment. Vol. 22, no. 9, 1988, pp. 1909-1924. DOI: 10.1016/0004-6981(88)90080-7
BOGAERT, P. and CHRISTAKOS, G., Sapatiotemporal analysis and processing of thermometric data over Belgium. Journal of Geophysical Research. Vol. 102, no. 22, 25, 1997, pp. 831-846. DOI: 10.1029/97JD01809
CAMERON, K. and HUNTER, P. Optimization of LTM networks using GTS: statistical approaches to spatial and temporal redundancy, Air Force Center for Environmental Excellence, Brooks AFB, TX, [en línea] Disponible para World Wide Web: http://www.afcee.brooks.af.mil/products/rpol/docs/GTSOptPaper.pdf, acceso libre [consulta, agosto de 2006]. DOI: 10.1061/40856(200)146
CHRISTAKOS, G. Modern Spatiotemporal Geostatistics. New York: Oxford University Press, 2000, 288 pp.
COMEGNA, V. and BASILE, A. Temporal stability of spatial patterns of soil water storage in a cultivated Vesuvian soil. Geoderma. Vol. 62, 1994, pp. 299-310. DOI: 10.1016/0016-7061(94)90042-6
DE CESARE, L., MYERS, D.E. and POSA, D. Estimating and modeling space-time correlation structures. Statistics & Probability Letteres. Vol. 51, 2001, pp. 9-14. DOI: 10.1016/S0167-7152(00)00131-0
DE CESARE, L., MYERS, D.E. and POSA, D. FORTRAN Programs for space-time modeling. Computers Geosciences. Vol. 28, 2002, pp. 205-212. DOI: 10.1016/S0098-3004(01)00040-1
DE IACO, S., MYERS D.E. and POSA, D. Space-time analysis using a general product-sum model. Statistics & Probability Letters. Vol. 52, 2001, pp. 21-28. DOI: 10.1016/S0167-7152(00)00200-5
DELHOMME, J.P. Kriging in the hydrosciences. Advances in Water Resources. Vol. 1, no. 5, 1978, pp. 251-266. DOI: 10.1016/0309-1708(78)90039-8
DEUTSCH, C.V. and JOURNEL, A.G. GSLIB Geostatistical software library and User's guide. Applied geostatistics series. Second edition. New York: Oxford University Press, 1998, 369 pp.
DIMITRAKOPOULOS, R. and LUO, X. Spatiotemporal modeling: covariances and ordinary kriging systems. Dimitrakopoulos, R. (editor). Geostatistics for the next century. Dordrecht: Kluwer Academic Publ., 1994, pp. 88-93. DOI: 10.1007/978-94-011-0824-9_11
GAMBOLATI, G. and GALEATI, G. Comment on analysis of non intrinsic spatial variability by residual kriging whit application to regional groundwater levels by Neuman, S.P. and Jacobson, E.A. Mathematical Geology. Vol. 19, no. 3, 1987, pp. 249-257. DOI: 10.1007/BF00897750
GAMBOLATI, G. and VOLPI, G. Groundwater contour mapping in Venice by stochastic interpolators. Water Resources Research. Vol. 15, no. 2, 1979a, pp. 281-290. DOI: 10.1029/WR015i002p00281
GAMBOLATI, G. and VOLPI, G. A conceptual deterministic analysis of the kriging technique in hidrology. Water Resources Research. Vol. 15, no. 3, 1979b, pp. 625-629. DOI: 10.1029/WR015i003p00625
GARDNER, B. and SULLIVAN, P. Spatial and temporal stream temperature prediction: modeling nonstationary temporal covariance structures. Water Resources Research. Vol. 40, 2004, W01102. DOI: 10.1029/2003WR002511
GUYSA. Estudio de simulación hidrodinámica y diseño óptimo de la red de observación en los acuíferos de Aguascalientes y Querétaro. Tomo III. Querétaro: Comisión Nacional del Agua, Gerencia de Aguas Subterráneas, Geofísica de Exploraciones Guysa, S.A. de C.V. GAS-008-PR-96, 1996.
HEVESI, J.A., ISTOK, J.D. and FLINT A.L. Precipitation estimation in mountainous terrain using multivariate geostatistics. Part I: Structural analysis. Journal of Applied Meteorology. Vol. 31, 1992a, pp. 661-676. DOI: 10.1175/1520-0450(1992)031<0661:PEIMTU>2.0.CO;2
HEVESI, J.A., ISTOK, J.D. and FLINT, A.L. Precipitation estimation in mountainous terrain using multivariate geostatistics. Part II: Isohyetal maps. Journal of Applied Meteorology. Vol. 31, 1992b, pp. 677-688. DOI: 10.1175/1520-0450(1992)031<0677:PEIMTU>2.0.CO;2
IBAÑEZ, G.M.V. Modelos estadísticos espacio-temporales en perimetría. Tesis doctoral. Castellón de la Plana, España: Departamento de Matemáticas, Escuela Superior de Tecnología y Ciencias Experimentales, Universitat Jaume, 2003, 322 pp.
JOURNEL, A.G. and ROSSI, M.E. When do we need a trend model in kriging. Mathematical Geology. Vol. 21, no. 7, 1989, pp. 715-740. DOI: 10.1007/BF00893318
KNOTTERS, M. and BIERKENS, M.F.P. Predicting water table depths in space and time using a regionalized time series model. Geoderma. Vol. 103, 2001, pp. 51-77. DOI: 10.1016/S0016-7061(01)00069-6
KYRIAKIDIS, P.C. and JOURNEL, A.G. Geostatistical space-time models: A review. Mathematical Geology. Vol. 31, no. 6, 1999, pp. 651-684. DOI: 10.1023/A:1007528426688
KYRIAKIDIS, P.C. and JOURNEL, A.G. Stochastic modeling of atmospheric pollution: a spatial time-series framework. Part I: methodology. Atmospheric Environment. Vol. 35, 2001a, pp. 2331-2337. DOI: 10.1016/S1352-2310(00)00541-0
KYRIAKIDIS, P.C. and JOURNEL, A.G., Stochastic modeling of atmospheric pollution: a spatial time-series framework. Part II: application to monitoring monthly sulfate deposition over Europe. Atmospheric Environment. Vol. 35, 2001b, pp. 2339-2348. DOI: 10.1016/S1352-2310(00)00540-9
LAROCQUE, M., MANGIN, A., RAZACK, M. and BANTON, O. Contribution of correlation and spectral analyses to the regional study of a large karst aquifer (Charente, France). Journal of Hydrology. Vol. 205, 1998, pp. 217-231. DOI: 10.1016/S0022-1694(97)00155-8
LEE, J.Y. and LEE, K. Use of hydrologic time series data for identification of recharge mechanism in a fractured bedrock aquifer system. Journal of Hydrology. Vol. 229, 2000, pp. 190-201. DOI: 10.1016/S0022-1694(00)00158-X
MENDOZA, C.E.Y. y HERERA, G. Estimación multivariada para determinar la carga hidráulica en el acuífero Querétaro-Obrajuelo. Ingeniería hidráulica en México. Vol. XXII, núm. 1, enero-marzo de 2007, pp. 63-79.
MENDOZA, C.E.Y. Análisis de alternativas para la estimación de la carga hidráulica utilizando métodos geoestadísticos en espacio y espacio-tiempo. Tesis doctoral. México, D.F.: Universidad Nacional Autónoma de México, 2008, 253 pp.
MYERS, D.E. and JUORNEL, A.G. Variograms whit zonal anisotropies and noninvertible kriging sytems. Mathematical Geology. Vol. 22, no. 7, 1990, pp. 779-785. DOI: 10.1007/BF00890662
PAPRITZ, A. and FLÜHLER, H. Temporal change of spatially autocorrelated soil properties: optimal estimation by cokriging. Geoderma. Vol. 62, 1994, pp. 29-43. DOI: 10.1016/0016-7061(94)90026-4
ROUHANI, S. Comparative study of ground water mapping techniques. Journal of Ground Water. Vol. 24, no. 2, 1986, pp. 207-216. DOI: 10.1111/j.1745-6584.1986.tb00996.x
ROUHANI, S. and HALL, T. Space-time kriging of groundwater data. Armstrong, M. (editor). Geostatistics. Vol. 2. Dordrecht: Kluwer Academic Publ., 1989, pp. 639-650. DOI: 10.1007/978-94-015-6844-9_50
ROUHANI, S. and MYERS D.E. Problems in space-time kriging of geohydrological data. Mathematical Geology, Vol. 22, no. 5, 1990, pp. 611-623. DOI: 10.1007/BF00890508
ROUHANI, S. and WACKERNAGEL, H. Multivariate geostatistical approach to space-time data analysis. Water Resources Research. Vol. 26, no. 4, 1990, pp. 585-591. DOI: 10.1029/WR026i004p00585
ROUHANI, S., EBRAHIMPOUR, M.R., YAQUB, I. and GIANELLA, E. Multivariate geostatistical trend detection and network evaluation of space-time acid deposition data I. Methodology. Atmospheric Environment. Vol. 14, 1992, pp. 2603-2614. DOI: 10.1016/0960-1686(92)90112-X
SAMPER, J. y CARRERA, J. Geoestadística. Aplicaciones a la hidrología subterránea. Barcelona: CIMNE, 1990, 481 pp.
SIMUTA, C.R. Modelo en elemento finito para el flujo del acuífero del valle de Querétaro. Tesis de maestría. México, D.F.: Universidad Nacional Autónoma de México, 2005.
SOLOW, A.R. and GORELICK, S.M. Estimating monthly streamflow values by cokriging. Mathematical Geology. Vol. 18, no. 8, 1986, pp. 785-809. DOI: 10.1007/BF00899744
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2010 Tecnología y ciencias del agua
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
By Instituto Mexicano de Tecnología del Agua is distributed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. Based on a work at https://www.revistatyca.org.mx/. Permissions beyond what is covered by this license can be found in Editorial Policy.
