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Performance Comparison between Artificial Neural Networks and Geostatistics for estimating annual rainfall based on rain gage measurements 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. Interpolation in multidimensional space is one of the most important tasks that GIS can do. These systems propose many methods for interpolating geographic data including classical and newest techniques. In this work we explore the application of a specific class of artificial neural networks for spatial prediction of annual rainfall. The performance of this interpolation is compared with Kriging, which is one of the popular techniques for interpolating spatial data. The results show clearly that the two methods produce different pattern for the annual rainfall mapping. Neural networks produce much smother surface than Kriging. In term of performance expressed by the mean squared error function and despite that neural networks give small error surface than Kriging, but this difference is not important and can’t lead to significant conclusion. Keywords: artificial neural networks, GIS, Kriging. 1. Introduction. In this work we compare the capability of interpolation between a class of artificial neural networks and geostatistical modeling. This class of artificial neural networks derives their structure and interpretation from the theory of interpolation in multidimentional spaces, and have a mathematical foundation imbedded in regularization theory for solving ill-conditioned problems. Such networks, almost invariably, consists of three layers- a transparent input layer, a hidden layer with sufficiently large number of nodes, and an output layer [9]. In the other hand we have one of the powerful methods for modeling spatial information and derive more information from the limited data is kriging interpolation technique. Kriging is a geostatistical tool developed by Matheron [3] and named after the South African mining engineer, D.G. Krige. According to the original definition given by Matheron, Kriging is the probabilistic 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 [4]. 2. Problem description. The data of raingauges often suffers of a lack in measurement and also are typically sparse and of uneven density. So it is necessary to use an adequate mathematical model which describes well this variability and where the errors generated by the model are minimized. The mathematical interpolation of geographic information is a technique that interpolates the data at irregular points to regular grid covering the area of interest to obtain climatic information that is more continuous in space. Many studies exist on the issue of interpolating data from irregular points to a regular grid using different climate variables and different mathematical techniques [1], [2], [5], [6], [7], and [10]. In recent years these models have been implemented in GIS, with the aim of representing several environmental features, to aid interpretation and providing better understanding so more informed decisions can be made [8]. The goal of comparing several models and techniques is to determine the best way that generalizes best results in term of performance. Figure 1 and 2 give the output of the two approaches used in the current study.

Fig. 1 Annual rainfall interpolation based on artificial Neural Networks.

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Fig. 2 Annual rainfall interpolation based on artificial Kriging modeling. 3. Conclusion. Comparing results from both Neural Networks and Geostatistical modeling allows stating that traditional geostatistical modeling like Kriging visualizes the interpolant as a realization of a random field. However neural networks have their origine in the regression-based methods and are based on interpolation theory. Neural networks yields s much smoother representation of the annual rainfall surface compared to the one generated by geostatistical modeling. References [1] C. D. Lloyd, “Assessing the effect of integrating elevation data into the estimation of monthly precipitation in Great Britain”, Journal of Hydrology 308, 2005, pages 128 – 150. [2] C. L. Goodale, J. D. Aber and S.V. Ollinger, “Mapping monthly precipitation, temperature, and solar radiation for Ireland with polynomial regression and a digital elevation model”, Climate Research 10, 1998, pages 35 – 49. [3] G. Matheron, “Principles of geostatistics”, Economic Geol. 58:1246-1266, 1963 [4] J, Dongxiang,“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 (1989). [5] J. A Hevesi, J. D. Istok and A. L. Flint, “Precipitation estimation in mountainous terrain using multivariate geostatistics. Part І: Structural analysis”, Journal of Applied Meteorology 31, 1992, pages 661 – 676. [6] N. Hofstra, M. Haylock, M. New, P. Jones and C. Frei, “Comparison of six methods for the interpolation of daily European climate data”, Journal of Geophysical Research 113, 2008, D21110, doi: 10.1029/2008JD010100. [7] P. Goovaerts, ”Geostatistical approaches for incorporating elevation into the spatial interpolation of rainfall”, Journal of Hydrology 228, 2000, pages113 – 129. [8] R. M. Mendes and R. Lorandi, “Indicator Kriging Geostatistical Methodology Applied to Geotechnics Project Planning”, The Geological Society Of London. IAEG, 2006 page 527. [9] R. S. Govindaraju and B. Zhang ,’’Radial Basis Function networks’’ West Lafayette, IN 47906, USA, 200, pages 93-109. [10] S. M. Vicente-Serrano, M. A. Saz and J. M. Cuadrat, “Comparative analysis of interpolation methods in the middle Ebro valley (Spain): Application to annual precipitation and temperature”, Climate Research 24,2003, pages 161–180.

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