Coupling Singular Spectrum Analysis with Least Square Support Vector Machine to Improve Accuracy of SPI Drought Forecasting

Abstract

The study proposed a Standardized Precipitation Index (SPI) drought forecasting model based on singular spectrum analysis (SSA) and single least square support vector machine (LSSVM) with a twofold investigation: (Beguería et al. Int J Climatol, 34(10): 3001–3023, 2014) the forecasting performance of the LSSVM-based model with or without coupling SSA and (Belayneh et al. J Hydrol, 508: 418–429, 2014) the model performances by using different inputs (i.e., antecedent SPIs and antecedent accumulated monthly rainfall) preprocessed by SSA. For the first part investigation, the LSSVM-based model using antecedent SPI as input (LSSVM1) and the LSSVM-based model coupling with SSA using antecedent SPI as input (SSA-LSSVM2) were developed. For the second part of investigation, the SSA-LSSVM-based model using antecedent accumulated monthly rainfall as input (SSA-LSSVM3) was developed and compared to SSA-LSSVM2. The drought indices (SPI3 and SPI6) were chosen as the outputs of the SPI drought forecasting models. The Tseng-Wen reservoir catchment in southern Taiwan was selected to test the aforementioned models. The results show that the forecasting performance of SSA-LSSVM2 is better than that of LSSVM1, which means the input data preprocessed by SSA can significantly increase the accuracy of the SPI drought forecasting. In addition, the performance comparison between SSA-LSSVM2 and SSA-LSSVM3 indicates that using antecedent accumulated monthly rainfalls (i.e., 3-month and 6-month accumulated rainfalls) as input of SSA-LSSVM3 are much better than using antecedent SPIs (i.e., SPI3 and SPI6) as input of SSA-LSSVM2. SSA-LSSVM3 is found to be the most appropriate model for SPI drought forecasting in the case study.

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Data Availability

The data and code that are available from the fist author (phambaoquoc@duytan.edu.vn) upon reasonable request.

References

  1. Beguería S, Vicente-Serrano SM, Reig F, Latorre B (2014) Standardized precipitation evapotranspiration index (SPEI) revisited: parameter fitting, evapotranspiration models, tools, datasets and drought monitoring. Int J Climatol 34(10):3001–3023

    Google Scholar 

  2. 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 models. J Hydrol 508:418–429

    Google Scholar 

  3. Bhagwat PP, Maity R (2012) Multistep-ahead river flow prediction using LS-SVR at daily scale. J Water Resource Prot 4(7):528–539

    Google Scholar 

  4. Bordi I, Sutera A (2007) Drought monitoring and forecasting at large scale, In Methods and tools for drought analysis and management (pp. 3–27). Springer, Dordrecht

    Google Scholar 

  5. Cancelliere A, Di Mauro G, Bonaccorso B, Rossi G (2007) Drought forecasting using the standardized precipitation index. Water Resour Manag 21(5):801–819

    Google Scholar 

  6. Chau KW, Wu CL (2010) A hybrid model coupled with singular spectrum analysis for daily rainfall prediction. J Hydroinformatics 12(4):458–473

  7. Chen ST, Kuo CC, Yu PS (2009) Historical trends and variability of meteorological droughts in Taiwan/Tendances historiques et variabilité des sécheresses météorologiques à Taiwan. Hydrol Sci J 54(3):430–441

    Google Scholar 

  8. Chiang JL, Tsai YS (2012). Reservoir drought prediction using support vector machines. In Applied Mechanics and Materials 145:455–459 Trans tech publications

  9. Chiang JL, Tsai YS (2013). Reservoir drought prediction using two-stage SVM. In Applied Mechanics and Materials 284:1473–1477 Trans tech publications

  10. Chou CM (2011) A threshold based wavelet denoising method for hydrological data modelling. Water Resour Manag 25(7):1809–1830

    Google Scholar 

  11. Choubin B, Malekian A, Golshan M (2016) Application of several data-driven techniques to predict a standardized precipitation index. Atmósfera 29(2):121–128

    Google Scholar 

  12. Djerbouai S, Souag-Gamane D (2016) Drought forecasting using neural networks, wavelet neural networks, and stochastic models: case of the Algerois Basin in North Algeria. Water Resour Manag 30(7):2445–2464

    Google Scholar 

  13. Guo X, Sun X, Ma J (2011) Prediction of daily crop reference evapotranspiration (ET0) values through a least-squares support vector machine model. Hydrol Res 42(4):268–274

    Google Scholar 

  14. Hassani H, Zhigljavsky A (2009) Singular spectrum analysis: methodology and application to economics data. J Syst Sci Complex 22(3):372–394

    Google Scholar 

  15. Heng S, Suetsugi T (2013) Coupling singular spectrum analysis with artificial neural network to improve accuracy of sediment load prediction. Journal of Water Resource and Protection 5(04):395–404

    Google Scholar 

  16. Hwang SH, Ham DH, Kim JH (2012) Forecasting performance of LS-SVM for nonlinear hydrological time series. KSCE J Civ Eng 16(5):870–882

    Google Scholar 

  17. Kalteh AM (2016) Improving forecasting accuracy of streamflow time series using least squares support vector machine coupled with data-preprocessing techniques. Water Resour Manag 30(2):747–766

    Google Scholar 

  18. Kalteh AM (2017) Enhanced monthly precipitation forecasting using artificial neural network and singular Spectrum analysis conjunction models. INAE Letters 2(3):73–81

    Google Scholar 

  19. Keshavarz M, Karami E, Vanclay F (2013) The social experience of drought in rural Iran. Land Use Policy 30(1):120–129

    Google Scholar 

  20. Khan M, Muhammad N, El-Shafie A (2018) Wavelet-ANN versus ANN-based model for hydrometeorological drought forecasting. Water 10(8):998

    Google Scholar 

  21. Khan MMH, Muhammad NS, El-Shafie A (2020) Wavelet based hybrid ANN-ARIMA models for meteorological drought forecasting. J Hydrol 590:125380

    Google Scholar 

  22. Kisi O (2013) Least squares support vector machine for modeling daily reference evapotranspiration. Irrig Sci 31(4):611–619

    Google Scholar 

  23. Kisi O (2015a) Pan evaporation modeling using least square support vector machine, multivariate adaptive regression splines and M5 model tree. J Hydrol 528:312–320

    Google Scholar 

  24. Kisi O (2015b) Streamflow forecasting and estimation using least square support vector regression and adaptive neuro-fuzzy embedded fuzzy c-means clustering. Water Resour Manag 29(14):5109–5127

    Google Scholar 

  25. Komasi M, Sharghi S, Safavi HR (2018) Wavelet and cuckoo search-support vector machine conjugation for drought forecasting using standardized precipitation index (case study: Urmia Lake, Iran). J Hydroinf 20(4):975–988

    Google Scholar 

  26. Kumar U, Jain VK (2010) Time series models (Grey-Markov, Grey model with rolling mechanism and singular spectrum analysis) to forecast energy consumption in India. Energy 35(4):1709–1716

    Google Scholar 

  27. McKee TB, Doesken NJ, Kleist J (1993a). The relationship of drought frequency and duration to time scales. In Proceedings of the 8th Conference on Applied Climatology (Vol. 17, no. 22, pp. 179-183). Boston, MA: American Meteorological Society

  28. McKee TB, Doesken NJ, Kleist J (1993b). The relationship of drought frequency and duration to time scales. In Proceedings of the 8th Conference on Applied Climatology 17(22):179–183). Boston, MA: American Meteorological Society

  29. Mellit A, Pavan AM, Benghanem M (2013) Least squares support vector machine for short-term prediction of meteorological time series. Theor Appl Climatol 111(1–2):297–307

    Google Scholar 

  30. Okkan U, Serbes ZA (2012) Rainfall–runoff modeling using least squares support vector machines. Environmetrics 23(6):549–564

    Google Scholar 

  31. Okkan U, Serbes ZA (2013) The combined use of wavelet transform and black box models in reservoir inflow modeling. Journal of Hydrology and Hydromechanics 61(2):112–119

    Google Scholar 

  32. Ouyang Q, Lu W (2018) Monthly rainfall forecasting using echo state networks coupled with data preprocessing methods. Water Resour Manag 32(2):659–674

    Google Scholar 

  33. Palmer WC (1965). Meteorological droughts. U.S. Department of Commerce weather bureau research paper 45, 58

  34. Pham QB, Yang TC, Kuo CM, Tseng HW, Yu PS (2019) Combing random Forest and Least Square support vector regression for improving extreme rainfall downscaling. Water 11(3):451

    Google Scholar 

  35. Samsudin R, Saad P, Shabri A (2011) River flow time series using least squares support vector machines. Hydrol Earth Syst Sci 15(6):1835–1852

    Google Scholar 

  36. Shabri A, Suhartono (2012) Streamflow forecasting using least-squares support vector machines. Hydrol Sci J 57(7):1275–1293

    Google Scholar 

  37. Sivapragasam C, Liong SY, Pasha MFK (2001) Rainfall and runoff forecasting with SSA–SVM approach. J Hydroinf 3(3):141–152

    Google Scholar 

  38. Soh YW, Koo CH, Huang YF, Fung KF (2018) Application of artificial intelligence models for the prediction of standardized precipitation evapotranspiration index (SPEI) at Langat River basin, Malaysia. Comput Electron Agric 144:164–173

    Google Scholar 

  39. Sun M, Li X (2017) Window length selection of singular spectrum analysis and application to precipitation time series. Global NEST J 19:306–317

    Google Scholar 

  40. Sun M, Li X, Kim G (2019) Precipitation analysis and forecasting using singular spectrum analysis with artificial neural networks. Clust Comput 22(5):12633–12640

  41. Suykens JA, De Brabanter J, Lukas L, Vandewalle J (2002) Weighted least squares support vector machines: robustness and sparse approximation. Neurocomputing 48(1–4):85–105

    Google Scholar 

  42. Tigkas D, Vangelis H, Tsakiris G (2020) Implementing crop evapotranspiration in RDI for farm-level drought evaluation and adaptation under climate change conditions. Water Resour Manag:1–15

  43. Tirivarombo S, Osupile D, Eliasson P (2018) Drought monitoring and analysis: standardised precipitation evapotranspiration index (SPEI) and standardised precipitation index (SPI). Physics and Chemistry of the Earth, Parts A/B/C 106:1–10

    Google Scholar 

  44. Tseng HW, Yang TC, Kuo CM, Yu PS (2012) Application of multi-site weather generators for investigating wet and dry spell lengths under climate change: a case study in southern Taiwan. Water Resour Manag 26(15):4311–4326

    Google Scholar 

  45. Unnikrishnan P, Jothiprakash V (2015) Extraction of nonlinear rainfall trends using singular spectrum analysis. J Hydrol Eng 20(12):05015007

    Google Scholar 

  46. Unnikrishnan P, Jothiprakash V (2018a) Daily rainfall forecasting for one year in a single run using singular spectrum analysis. J Hydrol 561:609–621

    Google Scholar 

  47. Unnikrishnan P, Jothiprakash V (2018b) Data-driven multi-time-step ahead daily rainfall forecasting using singular Spectrum analysis-based data pre-processing. J Hydroinf 20(3):645–667

    Google Scholar 

  48. Van Gestel T, Suykens JA, Baesens B, Viaene S, Vanthienen J, Dedene G et al (2004) Benchmarking least squares support vector machine classifiers. Mach Learn 54(1):5–32

    Google Scholar 

  49. Vitanov NK, Sakai K, Dimitrova ZI (2008) SSA, PCA, TDPSC, ACFA: useful combination of methods for analysis of short and nonstationary time series. Chaos, Solitons Fractals 37(1):187–202

    Google Scholar 

  50. Wang Y, Guo S, Chen H, Zhou Y (2014) Comparative study of monthly inflow prediction methods for the three gorges reservoir. Stoch Env Res Risk A 28(3):555–570

    Google Scholar 

  51. Wang Y, Guo S, Xiong L, Liu P, Liu D (2015) Daily runoff forecasting model based on ANN and data preprocessing techniques. Water 7(8):4144–4160

    Google Scholar 

  52. Wu CL, Chau KW (2011) Rainfall–runoff modeling using artificial neural network coupled with singular spectrum analysis. J Hydrol 399(3–4):394–409

    Google Scholar 

  53. Wu, Chau KW, Li YS (2009) Methods to improve neural network performance in daily flows prediction. J Hydrol 372(1–4):80–93

    Google Scholar 

  54. Wu CL, Chau KW, Fan C (2010) Prediction of rainfall time series using modular artificial neural networks coupled with data-preprocessing techniques. J Hydrol 389(1–2):146–167

    Google Scholar 

  55. Yang TC, Chen C, Kuo CM, Tseng HW, Yu PS (2012) Drought risk assessments of water resources systems under climate change: a case study in southern Taiwan. Hydrol Earth Syst Sci Discuss 9(11):12395–12433

    Google Scholar 

  56. Yu PS, Yang TC, Kuo CC (2006) Evaluating long-term trends in annual and seasonal precipitation in Taiwan. Water Resour Manag 20(6):1007–1023

    Google Scholar 

  57. Yu PS, Yang TC, Kuo CM, Tseng HW, Chen ST (2015) Climate change impacts on streamflow drought: a case study in Tseng-wen reservoir catchment in southern Taiwan. Climate 3(1):42–62

    Google Scholar 

  58. Zhang Q, Wang BD, He B, Peng Y, Ren ML (2011) Singular spectrum analysis and ARIMA hybrid model for annual runoff forecasting. Water Resour Manag 25(11):2683–2703

    Google Scholar 

  59. Zhang Y, Li W, Chen Q, Pu X, Xiang L (2017) Multi-models for SPI drought forecasting in the north of Haihe River basin, China. Stoch Env Res Risk A 31(10):2471–2481

    Google Scholar 

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Appendix

Appendix

Results of LSSVM1 without data pre-processing

Fig. 10
figure10

Observed vs. forecasted SPI3 values by LSSVM1 during the calibration and validation periods

Fig. 11
figure11

Scatter plots of observed vs. forecasted SPI3 values by LSSVM1 during the calibration and validation periods

Results of SSA-LSSVM hybrid models (SSA-LSSVM2 and SSA-LSSVM3)

Fig. 12
figure12

Observed vs. forecasted SPI3 values by SSA-LSSVM2 model during the calibration and validation periods

Fig. 13
figure13

Scatter plots of observed and forecasted SPI3 values by SSA-LSSVM2 model during the calibration and validation periods

Fig. 14
figure14

Observed vs. forecasted SPI3 values by SSA-LSSVM3 model during the calibration and validation periods

Fig. 15
figure15

Scatter plots of observed and forecasted SPI3 values by SSA-LSSVM3 model during the calibration and validation periods

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Pham, Q.B., Yang, TC., Kuo, CM. et al. Coupling Singular Spectrum Analysis with Least Square Support Vector Machine to Improve Accuracy of SPI Drought Forecasting. Water Resour Manage 35, 847–868 (2021). https://doi.org/10.1007/s11269-020-02746-7

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Keywords

  • Standardized precipitation index
  • Least square support vector machine
  • Drought forecasting
  • Singular spectrum analysis