Prediction of commonly used drought indices using support vector regression powered by chaotic approach


  • Ozlem Baydaroglu Yesilkoy Altınbaş University, School of Engineering and Natural Sciences, Department of Civil Engineering, İstanbul/Turkey
  • Kasım Koçak İstanbul Technical University, Faculty of Aeronautics and Astronautics, Department of Meteorological Engineering, İstanbul/Turkey
  • Levent Şaylan İstanbul Technical University, Faculty of Aeronautics and Astronautics, Department of Meteorological Engineering, İstanbul/Turkey



Drought indices, prediction, phase space reconstruction, machine learning


An effective water resources management requires accurate predictions of possible risks. Drought is one of the most devastating phenomena that has a certain risk of occurrence. Understanding the variability of the drought indices is of great importance in determining the spatiotemporal behavior of the drought phenomenon. Moreover, determination of the variability and short-term prediction of the drought indices enables us to take necessary steps in hydrological and agricultural issues. In this study, drought indices have been predicted via Support Vector Regression, SVR. This method originated from a linear regression method in a high dimensional feature space. SVR necessitates a special input matrix. In this study, this matrix has been constructed on the basis of Chaotic Approach, CA. Commonly used drought indices are used in the prediction stage. These indices consist of monthly Palmer Drought Severity Index, PDSI, Palmer Hydrological Drought Index, PHDI, Palmer Z-Index, ZNDX, Modified Palmer Drought Severity Index, PMDI, and Standard Precipitation Index, SPI. One-step ahead prediction has been realized for a 36-month period. Most results show that predictions of the drought indices using SVR are quite promising.


Alley, W. M. (1984). The Palmer Drought Severity Index: Limitations and Assumptions. Journal of Climate and Applied Meteorology 23:1100–1109. doi: 10.1175/1520-0450(1984)023< 1100:TPDSIL>2.0.CO;2
American Meteorological Society, (1997) Meteorological Drought-Policy statement. Bulletin of the American Meteorological Society 78: 847-849.
Arya, S., Mount, D. M., (1993). Approximate nearest neighbor searching. Proc. 4th Ann. ACM-SIAM Symposium on Discrete Algorithms (SODA'93) 271-280.
Arya, S., Mount, D.M., Netanyahu, N. S., Silverman, R., Wu, A. Y., (1998). An optimal algorithm for approximate nearest neighbor searching fixed dimensions. Journal of the ACM 45 891-923. doi: 10.1145/293347.293348
Baydaroğlu, Ö., Koçak, K., (2014). SVR-based prediction of evaporation combined with chaotic approach. Journal of Hydrology 508 356-363. doi: 10.1016/j.hydrol.2013.11.008
Baydaroğlu, Ö., Koçak, K., Duran, K. (2017). River flow prediction using hybrid models of support vector regression with the wavelet transform, singular spectrum analysis and chaotic approach. Meteorology and Atmospheric Physics 1-11. doi: 10.1007/s00703-017-0518-9
Belayneh, A., Adamowski, J., Khalil, B., Ozga-Zielinski, B., (2014). Long-term SPI Drought forecasting in the Awash River Basin in Ethiopia using wavelet neural network and wavelet support vector regression model. Journal of Hydrology 508 418-429. doi: 10.1016/ j.hydrol.2013.10.052
Cao, L., (1997). Practical method for determining the minimum embedding dimension of a scalar time series. Physica D: Nonlinear Phenomena 110 1 pp. 43-50. doi: 10.1016/S0167-2789 (97)00118-8
Cortes, C., Vapnik, V., (1995). Support vector networks. Machine Learning vol. 20 pp. 273-297. doi: 10.1007/BF00994018
Cutore, P., Di Mauro, G., Cancelliere, A., (2009). Forecasting Palmer Index using neural networks and climate indexes. Journal of Hyrologic Engineering Vol. 14 No.6. doi: 10.1061/(ASCE)HE.1943-5584.0000028#sthash.7USLO2fJ.dpuf
De Martino, G., Fontana, N., Marini, G., Singh, V. P., (2013). Variability and trend in seasonal precipitation in the continental United States. Journal of Hyrologic Engineering Vol. 18 No.6. doi: 10.1061/(ASCE)HE.1943-5584.0000677
Dougherty, J., Kohavi, R., Sahami, M., (1995). Supervised and unsupervised discretization of continuous features. In International Conference on Machine Learning. doi: 10.1016/B978-1-55860-377-6.50032-3
Fraser, A. M., Swinney, H. L., (1986). Independent coordinates for strange attractors from mutual information. Phys. Rev. A Vol. 33 Number 2. doi: 10.1103/PhysRevA.33.1134
Granata, F., Gargano, R., De Marinis, G., (2016). Support vector regression for rainfall-runoff modeling in urban drainage: A comparison with the epa’s storm water management model. Water 8(3) 69. doi: 10.3390/w8030069
Grassberger, P., Procaccia, I., (1983). Estimation of the Kolmogorov entropy from a chaotic signal. Physical Review A 28(4): 2591-2593. doi: 10.1103/PhysRevA.28.2591
Heddinghaus, T. R., Sabol, P., (1991). A review of the Palmer Drought Severity Index and where do we go from here? In Proc. 7th Conf. on Applied Climatology pp. 242–246. American Meteorological Society Boston.
Karl, T. R., Knight, R. W., (1985). Atlas of Monthly Palmer Hydrological Drought Indices (1931–1983) for the Contiguous United States. Historical Climatology Series 3–7 National Climatic Data Center Asheville North Carolina.
Kennel, M. B., Brown, R., Abarbanel, H. D. I., (1992). Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys. Rev. A 45 3403-3411. doi: 10.1103/PhysRevA.45.3403
Kim, H. S., Eykholt, R., Salas, J. D., (1999). Nonlinear dynamics, delay times and embedding windows. Physica D 127 48-60. doi: 10.1016/S0167-2789(98)00240-1
Koçak, K., Şaylan, L., Eitzinger, J., (2004). Nonlinear prediction of near-surface temperature via univariate and multivariate time series embedding. Ecological Modelling 1-7. doi: 10.1016/S0304-3800(03)00249-7
Li, P. C., Xu, S. H., (2005). Support vector machine and kernel function characteristic analysis in pattern recognition. Computer Engineering and Design vol. 26 pp. 302-304.
Liong, S., Sivapragasam, C., (2002). Flood stage forecasting with support vector machines. Journal of the American Water Resources Association Vol.38 No.1. doi: 10.1111/j.1752-1688.2002.tb01544.x
Liu, X., Ren, L., Yuan, F., Yang, B., (2009). Meteorological drought forecasting using Markov Chain Model. 2009 International Conference on Environmental Science and Information Application Technology. doi: 10.1109/ESIAT.2009.19
McKee, T. B., Doesken, N. J., Kleist, J., (1993). The Relationship of Drought Frequency and Duration to Time Scales. Proceedings of the Eighth Conference on Applied Climatology American Meteorological Society: Boston: 179–184.
Mehta, V. M., Wang, H., Mendoza, K., Rosenberg, N. J., (2014). Predictability and prediction of decadal hydrological cycles: A case study in Southern Africa. Weather and Climate Extremes 3 47-53. doi: 10.1016/j.wace.2014.04.002
Meyer, P. E., (2008). Information-Theoretic Variable Selection and Network Inference from Microarray Data. PhD thesis of the Universite Libre de Bruxelles.
Mishra, A. K., Özger, M., Singh, V. P., (2009). An entropy-based investigation into the variability of precipitation. Journal of Hydrology 370 139-154. doi: 10.1016/j.hydrol. 2009.03.006
Ortiz-Garcia, E. G., Salcedo-Sanz, S., Perez-Bellido, A. M., Portilla-Figueraz, J. A., Prieto, L. (2010). Prediction on hourly O3 concentrations using support vector regression algorithms. Atmospheric Environment 44 4481-4488. doi: 10.1016/j.atmosenv.2010.07.024
Packard, N. H., Crutchfield, J. P., Farmer, J. D., Shaw, R. S., (1980). Geometry from a time series. Physical Review Letters 45 (9). doi: 10.1103/PhyRevLett.45.712
Palit, S. K., Mukherjee, S., Bhattacharya, D. K., (2013). A high dimensional delay selection for the reconstruction of proper phase space with cross auto-correlation. Neurocomputing 113 49-57. doi: 10.1016/j.neucom.2013.01.034
Palmer, W. C., (1965). Meteorological Drought. Res. Paper No.45 58pp. Dept. of Commerce Washington D.C.
Porporato, A., Ridolfi, L., (1997). Nonlinear Analysis of near-wall turbulence time series. Applied Scientific Research 57: 235-261. doi: 10.1007/BF02506062
Santamaria-Bonfil, G., Reyes-Ballesteros, A., Gershenson, C., (2016). Wind speed forecasting for wind farms: A method based on support vector regression. Renewable Energy 85 790-809. doi: 10.1016/j.renene.2015.07.004
Shannon, C. E., (1948). A mathematical theory of communication. Bell Syst. Tech. J. 27 379–423. doi: 10.1002/j.1538-7305.1948.tb00917.x
Stefannson, A., Koncar, N., Jones, A. J., (1997). A note on the Gamma Test. Neural Computing and Applications 5:131-133. doi: 10.1007/BF01413858
Takens, F., (1981). Detecting strange attractors in turbulence. In: Rand, DA Young, LS (Eds.) Lecture Notes in Math. Springer-verlag pp. 366-381.
Vapnik, V., Lerner, A., (1963). Pattern recognition using generalized portrait method. Automation and Remote Control 24: 774-780.
Vapnik, V., Chervonenkis, A., (1964). A note on one class of perceptrons. Automation and Remote Control vol. 25.
Vapnik, V. N., (1995). The nature of statistical learning theory. Springer New York.
Vapnik, V. N., (1999). An overview of statistical learning theory. Neural Networks IEEE Transactions on Vol.10 No.5 988-999. doi: 10.1109/72.788640
Wilhite, D. A., Glantz, M. H., (1985). Understanding the drought phenomenon: The role of definitions. Water International 10 (3): 111–120. doi: 10.1080/02508068508686328
Yang, Y., Webb, G. I., (2003). Discretization for naive-bayes learning: managing discretization bias and variance. Technical Report 2003/131 School of Computer Science and Software Engineering Monash University. doi: 10.1007/s10994-008-5083-5
Yu, P., Chen, S., Chang, I., (2006). Support vector regression for real time flood stage forecasting. Journal of Hydrology 328 704-716. doi: 10.1016/j.jhydrol.2006.01.021
Yu, X., Liong, S., (2007). Forecasting of hydrologic time series with ridge regression in feauture space. Journal of Hydrology 332 290-302.
Zhao, C., Ding, Y., Ye, B., Yao, S., Zhao, Q., Wang, Z., Wang, Y., (2011). An analyses of long term precipitation variability based on entropy over Xinjiang, Northwestern China. Hydrology and Earth System Sciences Discussions 8 2975-2999. (accessed in May, 2014)




How to Cite

Baydaroglu Yesilkoy, O., Koçak, K., & Şaylan, L. (2021). Prediction of commonly used drought indices using support vector regression powered by chaotic approach. Italian Journal of Agrometeorology, (2), 65-76.