Document Type : Research Article

Authors

1 Ferdowsi University of Mashhad

2 Shahid Beheshti University

Abstract

 
Introduction: Drought is a very complex natural phenomenon which changes with time and space. Spatial and temporal variations of drought are analyzed separately. Geostatistical methods can be used for spatiotemporal analyses to find related spatial and temporal pattern changes. These methods, which use the spatio-temporal data, considering the spatial position of the data relative to each other, also take into account their temporal dependence. If needed, they can estimate values of their variable at any location and any time. Moreover, the drought spatial variations in the studied region can be drawn at every desired period. On the other hand, it is expected that intervening of the time dimension in the equations of these methods, as compared to the purely spatial methods, provide more precision in estimating the values of drought indices, which is studied in this research.
Materials and Methods: Monthly rainfall data of 48 stations in the northeast of Iran for the period of 1981-2012 were used in this study. The SPI drought index is calculated for the 12-month time scale. Data were divided into two groups of training data from 1981-2011 and experimental data of 2012. After analyzing the data regarding their stationarity and isotropic assumptions, the spatiotemporal data were formed and their spatiotemporal empirical variogram was drawn. Furthermore, the purely spatial and temporal variograms for the zero space and time steps were also drawn. Then, four models of the spatiotemporal variogram functions were applied on the training data. The performance of these models was tested and compared by estimating the parameters of the model based on the Square Error (MSE). Moreover, three-dimensional fitted variograms were drawn for different models. Mean The best spatiotemporal variogram model was selected by comparing the models prediction with experimental data using the Mean Square Prediction Error (MSPE). Using spatiotemporal kriging method, the predicted values of experimental data were interpolated ​​and that of the observed values ​​were interpolated by kriging method. Cross validation on experimental data was also performed using RMSE, MAE, ME and COR. Then spatiotemporal and purely spatial variogram models were investigated and compared.
Results and Discussion: The results showed that the 12-month SPI index had no spatial trend but had a decreasing trend against the time. Hence, a simple regression equation was used for fitting the trend of the data. After detrending the data, the SPI index values were considered as the dependent variable, while the time was taken as the independent variable. On the other hand, drawing the variogram in different directions (0°, 45°, 90°, and 135°) had no significant effect relative to each other, and the hypothesis of isotropic state was accepted. The plots of purely spatial and temporal variograms showed that the spherical variogram for space and the linear variogram for the time would have the best fitting. The empirical 3-D and 2-D spatiotemporal variograms of the training data were plotted. The empirical 3-D variogram showed that the data had reached to its temporal sill in a 1-year time lag, and had reached to its spatial sill, in about 25-kilometers, which are in conformity with the purely spatial and temporal variograms. The comparison of different variogram functions showed that the MSE values of the separable, metric, product-sum and sum-metric models were 0.00139, 0.00295, 0.00111, and 0.00112, respectively, the last two of which had fewer errors. Drawing the spatiotemporal variogram of these functions showed that the spatiotemporal variogram of product-sum and sum-metric models have more similarity to the sample one. Regarding the selection of the best model, the MSPE statistics of the product-sum and sum-metric models were 0.281 and 0.389, respectively. Therefore, the product-sum model could be selected as the best model. The least rate of errors was found in the exponential variogram model for space, and in the linear variogram for the time. The parameters of the nugget effect, partial sill and range for the spatial variogram would be 0.00, 0.063, and 5.78, and for the temporal variogram would be 0.00, 0.635, and 1.044, respectively. After predicting values of 12-month SPI in 2012 by the product-sum variogram model and adding the values of the trend, they were interpolated by using the spatiotemporal kriging, and the observed values were interpolated by the use of kriging. The obtained plot from the predicted values had great similarity with that of the observed values, which indicates the appropriate capability of the model in predicting the unobserved values. The cross-validation of different spatiotemporal and the spatial models with 25 and 47 neighborhoods showed that the performance of the models had no significant differences relative to each other, and they also had no better performance relative to the purely spatial model.
Conclusion: The results of this study showed that the product-sum model had a better performance among different spatiotemporal variogram models in predicting the 12-month SPI values of 2012. However, the performances of different spatiotemporal models were quite close to each other. There is no significant difference that could be observed between spatiotemporal and purely spatial models. Also, it is proposed to use the dynamic spatiotemporal models and the results to be compared with the classical models.

Keywords

1-Ahmed S.O., Mazloum R., and Abou-Ali H. 2018. Spatiotemporal interpolation of air pollutants in the Greater Cairo and the Delta, Egypt. Environmental Research 160: 27–34.
2-Akbarzadeh M., and Ghahraman B. 2013. A combined strategy of entropy and spatio-temporal kriging in determining optimal network for groundwater quality monitoring of Mashhad basin. Journal of Water and Soil 27(3): 613-629. (In Persian with English abstract)
3-Ashgar Toosi, Sh., and Alizadeh A. 2005. Monitoring and forecasting droughts in eastern Iran. Journal of Drought and Agricultural Drought 16: 1-16. (In Persian)
4-Ansari H., and Davari K. 2007. Dry period zoning using standardized precipitation index in GIS environment (Case study: Khorasan Province). Journal of Geographical Researches 60: 97-108. (In Persian)
5-Bonaccorso B., Bordi I., Cancelliere A., Rossi G., and Sutera A. 2003. Spatial variability of drought: An analysis of the SPI in Sicily. Water Resources Management 17(4): 273–296.
6-Bordi I., Fraedrich K., Jiang J.-M., and Sutera A. 2004. Spatio-temporal variability of dry and wet periods in eastern China. Theoretical and Applied Climatology 79(1–2): 81–91.
7-De Cesare L., Myers D.E., and Posa D. 1997. Spatial temporal modeling of SO2 in the Milan district. In: Baafi, E.Y., Scho6eld, N.A. (Eds.), Geostatistics Wollongong ’96, Vol. 2. Kluwer Academic Publishers, Dordrecht, pp. 1031–1042.
8-De Cesare L., Myers D.E., and Posa D. 2001a. Estimating and modelling space–time correlation structures. Statistics and Probability Letters 51(1): 9–14.
9-De Cesare L., Myers D.E., and Posa D. 2001b. Product–sum covariance for space–time modeling: an environmental application. Environmetrics 12: 1–23.
10- De Iaco S., Myers D.E., and Posa D. 2001. Space-time analysis using a general product-sum model. Statistics and Probability Letters 52(1): 21–28.
11-De Iaco S., Myers D.E., and Posa D. 2002a. Space-time variograms and a functional form for total air pollution measurements. Computational Statistics and Data Analysis 41(2): 311–328.
12-Dimitrakopoulos R., and Luo X. 1994. Spatiotemporal modeling: covariances and ordinary kriging System. In R. Dimitrakopoulos (ed), Geostatistics for the Next Century. Kluwer Academic Publisher, Dordrecht. P. 88–93.
13-Dracup J.A., Lee K.S., and Paulson E.G. 1980. On the definition of droughts. Water Resources Research 16(2): 297–302.
14-Gneiting T. 2002. Nonseparable, stationary covariance functions for space–time data. American Statistical Association 97(458): 590–600.
15-Gocic M., and Trajkovic S. 2014. Spatiotemporal characteristics of drought in Serbia. Hydrology 510: 110–123.
16-Gräler B., Rehr M., Gerharz L., and Pebesma E. 2013. Spatio-temporal analysis and interpolation of PM10 measurements in Europe for 2009. ETC/ACM Technical paper 2012/8, March 2013.
17-Gräler B., Pebesma E., and Heuvelink G. 2016. Spatio-Temporal Interpolation using gstat. Available at Web site https://cran.r-project.org/web/packages/gstat/vignettes/spatio-temporal-kriging.pdf.
18-Hasanalizadeh N., Mosaedi A., Zahiri A.R., and Hosseinalizadeh M. 2015. Modeling spatio-temporal variation of monthly precipitation (Case study: Golestan province). Journal of Water and Soil Conservation 22(1): 251-269. (In Persian with English abstract)
19-Hengl T., Heuvelink G.B.M., Tadić M., and Pebesma E.J. 2012. Spatio-temporal prediction of daily temperatures using time-series of MODIS LST images. Theoretical and Applied Climatology 107(1–2): 265–277.
20-Heuvelink G.B.M., Griffith D.A. 2010. Space-time geostatistics for geography: A case study of radiation monitoring across parts of Germany. Geographical Analysis 42(2): 161–179.
21-Hu D., Shu H., Hu H., and Xu J. 2017. Spatiotemporal regression Kriging to predict precipitation using time-series MODIS data. Cluster Computing 20(1): 347–357.
22-Karamooz M., and Araghi nejhad Sh. 2010. Advanced Hydrology. Publication of Amirkabir University of Technology(polytechniques), Tehran. (In Persian)
23-Kim D.W., Byun H.R., and Choi K.S. 2009. Evaluation, modification, and application of the Effective Drought Index to 200-Year drought climatology of Seoul, Korea. Hydrology 378(1–2): 1–12.
24-Kilibarda M., Hengl T., Heuvelink G.B.M., Gräler B., Pebesma E., Perčec Tadić, M., and Bajat B. 2014. Spatio-temporal interpolation of daily temperatures for global land areas at 1 km resolution. Geophysical Research: Atmospheres 119(5): 2294–2313.
25-Komuscu A.U. 1999. Using the SPI to Analyze Spatial and Temporal Patterns of Drought in Turkey Using the SPI to Analyze Spatial and Temporal Patterns of Drought in Turkey. Drought Network News 11(1): 6–13.
26-LLoyd-Hughes B., Saunders M.A. 2002. A drought climatology for Europe. Climatology 22(13): 1571–1592
27-Lorenzo-Lacruz J., and Moran-Tejeda E. 2016. Spatio-temporal patterns of meteorological droughts in the Balearic Islands (Spain). Cuadernos de Investigacion Geografica 42(1): 49-66.
28-Mckee T.B., Doesken N.J., and Kleist J. 1993. The relationship of drought frequency and duration to time scales. In 8’th Conference on Applied Climatology , Anaheim, California, 17-22 January 1993, p. 17–22.
29-Montero J., Fernandez-Aviles G., and Mateu J. 2015. Spatial and Spatio-Temporal Geostatistics Modeling and Kriging. John Wiley & Sons, Ltd, Chichester, UK.
30-Oh S.B., Byun H.R., and Kim D.W. 2014. Spatiotemporal characteristics of regional drought occurrence in East Asia. Theoretical and Applied Climatology 117(1): 89–101.
31-Potop V., Boroneanţ C., Možný M., Štěpanek P., and Skalak P. 2014. Observed spatiotemporal characteristics of drought on various time scales over the Czech Republic. Theoretical and Applied Climatology 115(3–4): 563–581.
32-Raziei T., Saghafian B., Paulo A.A., Pereira L.S., and Bordi I. 2009. Spatial patterns and temporal variability of drought in Western Iran. Water Resources Management 23(3): 439–455.
33-Rivaz F., Mohammadzadeh M., and Jafari Khaledi M. 2007. Emperical Bayesian prediction for spatio-temporal data under a separable model. Journal of Statistical Science 1(1): 45-59. (In Persian)
34-Rivaz F., M. Mohammadzadeh M., and Jafari Khaledi M. 2011. Spatio-temporal modeling and prediction of CO concentrations in Tehran city, Applied Statistics 38(9): 1995–2007.
35-Rodriguez‐Iturbe I., and Mejia J.M. 1974. The design of rainfall networks in time and space. Water Resources Research 10(4): 713–728.
36-Shadeed S. 2013. Spatio-temporal Drought Analysis in Arid and Semi-arid Regions: A Case Study from Palestine. Arabian Journal for Science and Engineering 38(9): 2303–2313.
37-Snepvangers J.J.J.C., Heuvelink G.B.M., and Huisman J.A. 2003. Soil water content interpolation using spatio-temporal kriging with external drift. Geoderma 112(3–4): 253–271.
38-Vicente-Serrano S.M., Gonzalez-Hidalgo J.C., De Luis M., and Raventos J. 2004. Drought patterns in the Mediterranean area: The Valencia region (eastern Spain). Climate Research 26(1): 5–15.
39-Wilhite D.A. 2000. Drought as a natural hazard: Concepts and definitions. In: Wilhite D (ed) Drought: A Global Assessment, Vol 1. Routledge publishers, London. pp. 3–18.
40-Wilhite D.A., and Glantz M.H. 1985. Understanding: the Drought Phenomenon: The Role of Definitions. Water International 10(3): 111–120.
41-Zamani R., Akhonali A.M., Solaimani K., Ansari A., and Allahbakhshian P. 2012. Application of geostatistics in zone classification of drought severities (Case study: Fars province). Journal of Watershed Management Research 6: 15-29. (In Persian with English abstract)
42-Zhang Q., Sun P., Li J., Singh V.P., and Liu J. 2015. Spatiotemporal properties of droughts and related impacts on agriculture in Xinjiang, China. Climatology 35(7): 1254-1266.
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