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Application of GIS in comparison study of annual rainfall mapping using ordinary Kriging and universal Kriging in Moulouya watershed ZEMZAMI M.* & BENAABIDATE L. Department of Earth Sciences, Faculty of Sciences and Techniques, University Mohammad Ben Abdellah, P.O. Box: 2202, 30000 Fez, Morocco, * [email protected] Abstract. Knowledge of spatial variation of rainfall is extremely an important information for hydrologists and meteorologists. This variation is highly dependents on meteorological conditions and relief. The use of geostatistical methods in the study of the space variation of annual rainfall led to understand and explain some aspect of this variation and to calculate values of rainfall in unmeasured regions to best cover the entire study area. The objective of the current paper is to find the best geostatistical model for mapping the space variation of annual rainfall in unmeasured areas using the ordinary kringing and to explain the cause of this 2 variation. Rainfall records of 65 raingauges are used in this study covering an area of about 5000km . The performance of models is investigated using the cross validation method. Two types of Kriging are used in this paper, including ordinary and universal Kriging. The corresponding experimental variograms are modeled using three mathematical models. Based on cross validation, we found that ordinary Kriging method with Gaussian model gives low RMS errors (Root mean square error). Keywords: geostatistical modeling, cross validation, semivariogram, Moulouya watershed 1. Introduction. The estimation of spatial variability of rainfall is a complex work because of the complex relationship relating rainfall to other factors. Indeed, topography and climatic conditions are the principal factors that control this variability and there relationship with spatial variability of rainfall is not very well known especially in mountainous areas [1] [8]. In this paper we used kriging interpolation technique to estimate the values of annual rainfall in the Moulouya watershed. Kriging geostatistical algorithms allow the construction of models of random distribution variables, which are used to infer of attribute’s values and to estimate the uncertainties associated to such values [2] [4]. This technique is widely and successfully used in the interpolation of climatic data such temperature and rainfall [1] [9] [7] [5]. 2. Study area. The Moulouya watershed (Figure 1) ,covers about 55 500 km2, is limited in the north by the Mediterranean Sea, in the east by Algeria, in the south by the Grand Atlas Mountains and in the west by the Middle Atlas and Rif mountains. From a hydrological point of view, the watershed is divided into 3 parts: upper, middle and low Moulouya. Moulouya watershed is characterized by an arid to semiarid climate. The annual average rainfall is approximately 245mm. It generally varies between 110mm and over 515mm. The lowest values are recorded at the Mid Moulouya while the highest values are recorded in the Beni Snassen Mountains, and the High and Middle Atlas. 3. Methodology. One of the powerful methods for modeling spatial information and derive more information from the limited data is kriging interpolation Fig. 1 The study area technique. Kriging is a geostatistical tool developed by Matheron [6] and named after the South African mining engineer, D.G. Krige. According to the original definition given by Matheron, Kriging is the probabilistic

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279 process of obtaining the best linear unbiased estimator of an unknown variable, "best" being taken in the sense of minimization of the resulting estimation variance [3]. The first step is to explore data, this allows us to become familiar with the data and inform the choice of the model. Then, the model can be stated. This last step included the selection of the shape of the deterministic trend for the expectation Z, the variogram and cross-validation if desired. This sub-step allows comparing the performance of different models and helps to select the one that could lead to better forecasts. Finally the interpolation is performed by Kriging. Here we used ordinary and universal Kriging to perform the interpolation. 4. Results and discussions. The map of figure 2 represents the output of the geostatistical methodology used in our study. Because of the high mountain barriers of the North West, the better-watered areas are the slopes of the Middle Atlas where rainfall can exceed 500 mm / year, while in the middle valley of the Moulouya, they barely reach 100 mm / year. The Eastern and Central Moulouya have the least rainfall values. Indeed these regions known a high evapotranspiration that exceed generally 1m/year. It is always higher than precipitation, and infiltration is not possible. The nature of impermeable soils and vegetation conditions accentuate this phenomenon. While the northern region is influenced by the sea which can limit the effect of the dry desert located at the northern boundary. Fig. 2 Map of estimated annual rainfall using ordinary kriging interpolation 5. Conclusion. The goal of this work is to estimate annual rainfall in unmeasured areas. The results obtained from this study are important for hydrologic models that need information about the distribution of hydrologic data in continuous domain. The interpolation is subject to underestimates and/or overestimates. Areas where gaugestations are few and widely scattered may produce misleading results. This problem is present in the central area where there is few gaugestations. Fortunately, the mountainous areas are best covered by the gaugestations, which reduces the prediction errors in these sensitive areas. Indeed, areas with high relief have a complicated relationship with precipitations and make the spatial interpolation misleading without a good spatial coverage. References. [1] Christel Prudhomme, Duncan W. Reed 1999. Mapping Extreme Rainfall In A Mountainous Region Using Geostatistical Techniques: A Case Study In Scotland. International Journal Of Climatology. 19: 1337–1356. [2] Deutsch, C.V. & Journel, A.G. 1998. GSLIB Geostatistical Software Library and User’s Guide. Oxford University Press, New York, 369p. [3] Dongxiang Jiang 1989. The application of Kriging technique to mathematical modeling of estuarine water quality.university of Newcastle Upon Tyne, department of civil engineering. Thesis L3465. p.19. [4] Goovaerts, P. 1997. Geostatistics for natural resources evaluation. Oxford University Press, New York, 481p. [5] Margaret R. Holdaway, 1996. spatial modeling and interpolation of monthly temperature using kriging. climat research. vol.6:215-225,1996. [6] Matheron, G. 1963. Principles of geostatistics. Economic Geol. 58:1246-1266. [7] Peter M. Atkinson. 1998. mapping precipitation in switzerland with ordinary and indicator kriging. journal of geographic information and decision analysis, vol.2, no 2, pp.65-76. [8] Tveito, O. E., and W. Schöner, 2002: Application of spatial interpolation of climatological and meteorological elements by the use of geographical information systems (GIS), met.no REPORT NO. 28/02 KLIMA. [9] X.Sun, M.J Manton and E.E Ebert.2003. regional rainfall estimation using double-kriging of raingauge and satellite observation. BMRC research report No.94. December 2003. bureauof meteorology research center, Australia.

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