عنوان مقاله [English]
The water resources are limited and the groundwater levels decrease due to water abuse. This causes the lack of water problem in some regions of Iran. Therefore the hydrological and statistical methods needed for prediction of the water levels at a given location, region or times. The groundwater levels are variables changing by space and time, and their data can be considered as a spatial-temporal data set. Modeling of the correlation structures of such data is a major tool, for the prediction of unknown water level at some specified locations and times. This correlation structure is specified by fitting suitable variogram or covariogrammodels to the data. In this article some nonseparable covariance models were briefly reviewed. Then the spatial-temporal variogram of underground water levels were estimated as product and sum-product models. Finally the underground water levels of Birjand region was predicted using the universal kriging and give the contour map at the selected time. Moreover the prediction precision of different models were compared numerically.
1- Einon, B.P., and Switzer, P. (1983). “The variability of rainfall acidity.” Canadian J. of statistics, 11, 11-24.
2- Guttorp, P., Meiring, W., and Sampson, P. (1994). “A space-time analysis of ground level ozone data.” J. of Environmentrics, 5, 241-254.
3- Wikle, C.K., Milliff, R.F., Nychka, D., and Berliner, L.M. (2001). “Spatio-temporal hierarchical bayesian modeling, tropical ocean surface winds.” J. of the American Statistical Association, 96, 382-397.
4- Banerjcee, S., Carlin, B.P., and Gelfand, A.E. (2004). Hierarchical modeling and analysis for spatial data, Boca Raton, F1: Capman and Hall/ CRC, Florida.
5- Rivaz, F., Mohamadzadeh, M., and Jafari Khaledi, M. (2007). “Empirical bayes prediction for space-time data under separable model.” J. of Statistical Sciences, 1, 45-60. (In Persian)
6- Etminan, J. (2005). “Using kriging In hydrogeology studies.” M.Sc. Dissertation, Birjand University. (In Persian)
7- Shafeie, A. (2007). “Spatial-temporal prediction of groundwater level in Birjand region.” M.Sc. Dissertation, Birjand University. (In Persian)
8- Rezapour Tabari, M.M., Ebadi, T., and Maknoon, R. (2010). “Development of a smart model for groundwater level prediction based on aquifer dynamic conditions.” J. of Water and Wastewater, 76, 70-80. (In Persian)
9- Soltani Gerdefaramarzy, S., and Abedi Koupai, J. (2010). “Quantification of groundwater recharge in the karvan aquifier in Esfahan (Iran) using the CRD model.” J. of Water and Wastewater, 76, 92-97. (In Persian)
10- Cressie, N. (1993). Statistics for spatial data, John Wiley and Sons Pub., New York.
11- Kolvos, A., Christakos, G., Hristopulos, D.T., and Serre, M.L. (2004). “Methods for generating nonseparable spatio-temporal covariance models with potential environmental applications advance in water resources.” J. of Advance in Water Resources, 27, 815-830.
12- De Csare, L., Myers, D.E., and Posa, D. (1997). “Spatial-temporal modeling of SO2 in the Milan district.” Baafi, E.Y., and Schofield, N.A. (Eds.). Geostatistics Wolongong, kluwer Academic Pub., Dordrecht.
13- Chunsheng, M.A. (2003). “Spatio-temporal stationary covariance models.” J. of Multivariate Analysis, 86, 97-107.
14- Rouhani, S., and Hall, J. (1989). “Space-time kriging of groundwater data, in Armstrong, M. (ed.) Geostatistics.” J. of Kluwer Academic Publication, 2, 639-651.
15- Myers, D.E., and Journel, A.G. (1990). “Variograms with zonal anisotropies and noninvertible kriging systems.” J. of Mathematical Geology, 22, 758-779.
16- De Cesare, L., Myers, D.E., and Posa, D. (2001). “Estimating and modeling space-time correlation structures.” J. of Statistical and Probability Letters, 51, 9-14.
17- De Iaco, S., Myers, D.E., and Posa, D. (2001). “Space-ttime analysis using a general product-sum model.” J. of Statistical and Probability Letters, 52, 21-28.
18- Sadeghian, A. (2009). “Estimation of spatial-temporal covariogram.” M.Sc. Dissertation, Birjand University, Birjand. (In Persian)
19- Nhu, D.L., and zideck, J.V. (2006). Statistical analysis of environmental space-time procees, Springer Pub., USA.