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Precipitation Modeling by Polyhedral RCMARS and Comparison with MARS and CMARS

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Abstract

Climate change is becoming an ever important issue due to the possibility that it may result in extreme weather events such as floods or droughts. Consequently, precipitation forecasting has similarly gained in significance as it is a useful tool in meeting the increasing need for the efficient management of water resources as well as in preventing disasters before they happen. In the literature, there are various statistical and computational methods used for this purpose, including linear and nonlinear regression, kriging, time series models, neural networks, and multivariate adaptive regression splines (MARS). Among them, MARS stands out as the better performing precipitation modeling method. In this article, we used a recently developed method called robust conic mars (RCMARS), based on MARS (also on CMARS), to forecast precipitation owing to its ability to model complex uncertain data. In CMARS, which was developed as a powerful alternative to MARS, the model complexity is penalized in the form of Tikhonov regularization and studied as a conic quadratic programming. In RCMARS, on the other hand, CMARS is refined further by including the existence of uncertainty in the future scenarios and robustifying it with a robust optimization technique. To evaluate the performance of the RCMARS method, it was applied to build a precipitation model constructed as an early warning system for the continental Central Anatolia Region of Turkey, where drought has been a recurrent phenomenon for the last few decades. Furthermore, the performance of the RCMARS precipitation model was also compared to that of MARS and CMARS. The results indicated that RCMARS builds more accurate, precise, and stable precipitation models compared to those of MARS and CMARS. In addition to these advantageous features of the RCMARS precipitation model, it also provided a good fit to the data. As a result, we propose its use in precipitation forecasting for the region studied.

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Acknowledgments

The authors would like to thank the NINLIL research group (http://www.stat.metu.edu.tr/research-projects/ninlil) for providing us with the precipitation data. The authors also would like to thank Gary Conlan (School of Foreign Languages, METU, Turkey) for assessment of the language qualification of our manuscript.

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Authors and Affiliations

  1. Institute of Mathematics, Middle East Technical University, 06800, Ankara, Turkey

    Ayşe Özmen, İnci Batmaz & Gerhard-Wilhelm Weber

  2. Department of Statistics, Middle East Technical University, 06800, Ankara, Turkey

    İnci Batmaz

  3. Faculty of Economics, Business and Law University of Siegen, Siegen, Germany

    Gerhard-Wilhelm Weber

  4. School of Science, Information Technology and Engineering, University of Ballarat, Ballarat, Australia

    Gerhard-Wilhelm Weber

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  1. Ayşe Özmen
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Correspondence to İnci Batmaz.

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Özmen, A., Batmaz, İ. & Weber, GW. Precipitation Modeling by Polyhedral RCMARS and Comparison with MARS and CMARS. Environ Model Assess 19, 425–435 (2014). https://doi.org/10.1007/s10666-014-9404-8

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  • DOI: https://doi.org/10.1007/s10666-014-9404-8

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