Abstract
Rainfall modeling is one of the major component process in the meteorological engineering. Hence, exploring an advance and reliable intelligent model for its forecasting is essential for water resources engineering. In this current research, novel integrative intelligence model coupled with phase space reconstruction is proposed to forecast monthly rainfall in Chhattisgarh State, India. The proposed model is a hybridization of support vector machine (SVM) model with firefly optimization algorithm (FFA). The modeling is undertaken based on three stages starting with configuring the delay time and embedding dimension using mutual information and false nearest neighbors to determine the input matrix of the forecasting model. In the second stage, the firefly optimizer is employed to tune the SVM model. Finally, the hybrid model is conducted to forecast the monthly time scale rainfall time series. Monthly time scale rainfall data for sixteen raingauge stations over a century (1901–2002) are utilized and tested. A validation of the capacity of the suggested model is carried out by comparing the accuracy results with classical SVM and hybrid SVM-FFA “without mutual information analysis” models. The three predictive models are trained using 75% of available data set and tested the remaining 25% dataset. The model’s results were statistically verified using mean absolute error and best-good-fitness measurements in addition to Taylor diagram visualization. In conclusion, the proposed model was significantly improved the forecasting accuracy of the modeling. Also, it was exhibited a very robust intelligent model that can be applied for the Indian regional zone for monthly rainfall forecasting.
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References
Abarbanel H, Brown R, Kadtke JB (1990) Prediction in chaotic nonlinear systems: Methods for time series with broadband Fourier spectra
Abrahart RJ, Anctil F, Coulibaly P, Dawson CW, Mount NJ, See LM, Wilby RL (2012) Two decades of anarchy? Emerging themes and outstanding challenges for neural network river forecasting. Prog Phys Geogr 36(4):480–513
Al-Shammari ET, Mohammadi K, Keivani A et al (2016) Prediction of daily dewpoint temperature using a model combining the support vector machine with firefly algorithm. J Irrig Drain Eng. https://doi.org/10.1061/(ASCE)IR.1943-4774.0001015
Bao Y, Hu Z, Xiong T (2013) A PSO and pattern search based memetic algorithm for SVMs parameters optimization. Neurocomputing 117:98–106. https://doi.org/10.1016/j.neucom.2013.01.027
Baydaroǧlu Ö, Koçak K (2014) SVR-based prediction of evaporation combined with chaotic approach. J Hydrol 508:356–363. https://doi.org/10.1016/j.jhydrol.2013.11.008
Bhatia N, Author C (2010) Survey of nearest neighbor techniques. (IJCSIS) Int J Comput Sci Inf Secur 8:302–305. https://doi.org/10.1016/j.pmcj.2015.02.001
Ch S, Sohani SK, Kumar D et al (2014) A support vector machine-firefly algorithm based forecasting model to determine malaria transmission. Neurocomputing 129:279–288. https://doi.org/10.1016/j.neucom.2013.09.030
Chai T, Draxler RR (2014) Root mean square error (RMSE) or mean absolute error (MAE)? -arguments against avoiding RMSE in the literature. Geosci Model Dev 7:1247–1250. https://doi.org/10.5194/gmd-7-1247-2014
Cover T, Hart P (1967) Nearest neighbor pattern classification. IEEE Trans Inf Theory 13:21–27. https://doi.org/10.1109/TIT.1967.1053964
Danandeh Mehr A, Nourani V, Karimi Khosrowshahi V, Ghorbani MA (2018) A hybrid support vector regression–firefly model for monthly rainfall forecasting. Int J Environ Sci Technol. https://doi.org/10.1007/s13762-018-1674-2
Delafrouz H, Ghaheri A, Ghorbani MA (2017) A novel hybrid neural network based on phase space reconstruction technique for daily river flow prediction. Soft Comput. https://doi.org/10.1007/s00500-016-2480-8
Fahimi F, Yaseen ZM, El-shafie A (2016) Application of soft computing based hybrid models in hydrological variables modeling: a comprehensive review. Theor Appl Climatol 1–29. https://doi.org/10.1007/s00704-016-1735-8
Fraser A, Swinney H (1986) Independent coordinates for strange attractors from mutual information
Ghorbani MA, Deo RC, Yaseen ZM et al (2017) Pan evaporation prediction using a hybrid multilayer perceptron-firefly algorithm (MLP-FFA) model: case study in North Iran. Theor Appl Climatol. https://doi.org/10.1007/s00704-017-2244-0
Ghosh A, Dehuri S (2004) Evolutionary algorithms for multi-criterion optimization: a survey. Int J Comput Inf Sci 2:38–57
Gocic M, Shamshirband S, Razak Z et al (2016) Long-term precipitation analysis and estimation of precipitation concentration index using three support vector machine methods. Adv Meteorol. https://doi.org/10.1155/2016/7912357
Gwenzi W, Nyamadzawo G (2014) Hydrological impacts of urbanization and urban roof water harvesting in water-limited catchments: a review. Environ Process 1:573–593. https://doi.org/10.1007/s40710-014-0037-3
Hegger R, Kantz H (1999) Improved false nearest neighbor method to detect determinism in time series data. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 60:4970–4973. https://doi.org/10.1103/PhysRevE.60.4970
Heo KY, Ha KJ, Yun KS, Lee SS, Kim HJ, Wang B (2014) Methods for uncertainty assessment of climate models and model predictions over East Asia. Int J Climatol 34(2):377–390
Huang SC, Hsieh CH (2012) Wavelet-based relevance vector regression model coupled with phase space reconstruction for exchange rate forecasting. Int J Innov Comput Inf Control 8:1917–1930
Kennel MB, Brown R, Abarbanel H DI (1992) Determining embedding dimension for phase- space reconstruction using a geometrical construction
Kumar D, Gautam AK, Palmate SS, et al (2016) Evaluation of TRMM multi-satellite precipitation analysis (TMPA) against terrestrial measurement over a humid sub-tropical basin, India. Theor Appl Climatol 1–17
Li B, Li J, Tang K, Yao X (2015) Many-objective evolutionary algorithms. ACM Comput Surv 48:1–35. https://doi.org/10.1145/2792984
Lukasik S, Zak S (2009) Firefly algorithm for continuous constrained optimization tasks. Firefly Algorithm Contin Constrained Optim Tasks 5796:97–106. https://doi.org/10.1007/978-3-642-04441-0_8
Moghaddam TB, Soltani M, Shahraki HS et al (2016) The use of SVM-FFA in estimating fatigue life of polyethylene terephthalate modified asphalt mixtures. Meas J Int Meas Confed 90:526–533. https://doi.org/10.1016/j.measurement.2016.05.004
Nagy HM, Watanabe K, Hirano M (2002) Prediction of sediment load concentration in rivers using artificial neural network model. J Hydraul Eng 128:588–595. https://doi.org/10.1061/(ASCE)0733-9429(2002)128:6(588)
Nash JE, Sutcliffe JV (1970) River flow forecasting through conceptual models part I - a discussion of principles. J Hydrol 10:282–290. https://doi.org/10.1016/0022-1694(70)90255-6
Nourani V, Hosseini Baghanam A, Adamowski J, Kisi O (2014) Applications of hybrid wavelet–artificial intelligence models in hydrology: a review. J Hydrol 514:358–377. https://doi.org/10.1016/j.jhydrol.2014.03.057
Pahasa J, Ngamroo I (2011) A heuristic training-based least squares support vector machines for power system stabilization by SMES. Expert Syst Appl 38:13987–13993
Raghavendra S, Deka PC (2014) Support vector machine applications in the field of hydrology: a review. Appl Soft Comput J 19:372–386. https://doi.org/10.1016/j.asoc.2014.02.002
Shamshirband S, Mohammadi K, Tong CW et al (2016) A hybrid SVM-FFA method for prediction of monthly mean global solar radiation. Theor Appl Climatol 125:53–65. https://doi.org/10.1007/s00704-015-1482-2
Sivakumar B (2002) A phase-space reconstruction approach to prediction of suspended sediment concentration in rivers. J Hydrol 258:149–162. https://doi.org/10.1016/S0022-1694(01)00573-X
Sivakumar B, Berndtsson R, Persson M (2001) Monthly runoff prediction using phase space reconstruction. Hydrol Sci J 46:377–387. https://doi.org/10.1080/02626660109492833
Tabari H, Kisi O, Ezani A, Hosseinzadeh Talaee P (2012) SVM, ANFIS, regression and climate based models for reference evapotranspiration modeling using limited climatic data in a semi-arid highland environment. J Hydrol 444–445:78–89. https://doi.org/10.1016/j.jhydrol.2012.04.007
Taylor KE (2001) Summarizing multiple aspects of model performance in a single diagram. J Geophys Res Atmos 106:7183–7192. https://doi.org/10.1029/2000JD900719
Vapnik V (1995a) The nature of statistical learning theory. Springer-Verlag New York, Inc., New York
Vapnik V (1995b) The Nature of statistical Learning Theory
Vignesh R, Jothiprakash V, Sivakumar B (2015) Streamflow variability and classification using false nearest neighbor method. J Hydrol 531:706–715. https://doi.org/10.1016/j.jhydrol.2015.10.056
Willmott CJ (1981) On the validation of models. Phys Geogr 2:184–194
Wu J, Liu M, Jin L (2010) A hybrid support vector regression approach for rainfall forecasting using particle swarm optimization and projection pursuit technology. Int J Comput Intell Appl 09:87–104. https://doi.org/10.1142/S1469026810002793
Yang X-S (2010) Firefly algorithm, stochastic test functions and design optimization. Int J Bio-inspired Comput 2(2):78–84. https://doi.org/10.1504/IJBIC.2010.032124
Yaseen ZM, El-shafie A, Jaafar O et al (2015) Artificial intelligence based models for stream-flow forecasting: 2000–2015. J Hydrol 530:829–844. https://doi.org/10.1016/j.jhydrol.2015.10.038
Yaseen ZM, Jaafar O, Deo RC et al (2016) Stream-flow forecasting using extreme learning machines: a case study in a semi-arid region in Iraq. J Hydrol. https://doi.org/10.1016/j.jhydrol.2016.09.035
Yoon H, Jun SC, Hyun Y, Bae GO, Lee KK (2011) A comparative study of artificial neural networks and support vector machines for predicting groundwater levels in a coastal aquifer. J Hydrol 396(1-2):128–138
Zhang Y, Lu J, Meng Y et al (2012) Wind power short-term forecasting based on empirical mode decomposition and chaotic phase space reconstruction. Autom Electr Power Syst 36:24–28
Zhao G, Zhai J, Tian P, et al (2017) Variations in extreme precipitation on the Loess Plateau using a high-resolution dataset and their linkages with atmospheric circulation indices
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Tao, H., Sulaiman, S.O., Yaseen, Z.M. et al. What Is the Potential of Integrating Phase Space Reconstruction with SVM-FFA Data-Intelligence Model? Application of Rainfall Forecasting over Regional Scale. Water Resour Manage 32, 3935–3959 (2018). https://doi.org/10.1007/s11269-018-2028-z
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DOI: https://doi.org/10.1007/s11269-018-2028-z