Abstract
Drought forecasting plays a vital role in managing drought and reducing its effects on agricultural systems and water resources. In the present study, three machine learning models including Gaussian Process Regression (GPR), Cascade Neural Network (Cascade-NN), and Multilayer Perceptron (MLP) neural network and their combination with the discrete wavelet transform were used to forecast Multi-scalar Standardized Precipitation Evapotranspiration Index (SPEI) (SPEI3, SPEI12, and SPEI24) 1 to 6 months ahead. It was done in Synoptic Station of Zanjan in Iran. Those meteorological data that was collected during 57 years (1961–2017) was used. The data related to the early 38 years (67%) was considered as train data, and the data related to the last 19 years (33%) was considered as test data. The results that have been obtained from this study showed that models based on wavelet have caused a high improvement in model performance in case of anticipating multi-scalar SPEI. Comparing different mother wavelets (db4, db8, sym8, coif5, and dmey) proved the dmey wavelet’s superiority. Also, a comparison of wavelet-GPR, wavelet-MLP, and wavelet-Cascade-NN models showed that in most cases, the GPR-based model could provide better results in forecasting. By increasing the forecasting interval from 1 to 6 months ahead, the accuracy of the model decreased. In the SPEI3 index, the R2 (determination coefficient) value decreased from 0.992 in the 1-month ahead forecast to 0.797 in the 6 months ahead forecast. In the SPEI12 index, the R2 value decreased from 0.996 in the 1 month ahead forecast to 0.940 in 6 months ahead forecast, and in the SPEI24 index, R2 values decreased from 0.993 in the 1 month ahead forecast to 0.962 in 6 months ahead forecast.
Similar content being viewed by others
Data availability
The dataset used in this research is available upon reasonable request from the corresponding author.
Code availability
The codes used in this research are available upon reasonable request from the corresponding author.
References
Abramowitz M, Stegun IA (1965) Handbook of mathematical functions: with formulas, graphs, and mathematical tables vol 55. Courier Corporation
Abujazar MSS, Fatihah S, Ibrahim IA, Kabeel AE, Sharil S (2018) Productivity modelling of a developed inclined stepped solar still system based on actual performance and using a cascaded forward neural network model. J Clean Prod 170:147–159. https://doi.org/10.1016/j.jclepro.2017.09.092
Adamowski J, Chan HF (2011) A wavelet neural network conjunction model for groundwater level forecasting. J Hydrol 407(1–4):28–40
Ahmed NK, Atiya AF, Gayar NE, El-Shishiny H (2010) An empirical comparison of machine learning models for time series forecasting. Economet Rev 29:594–621
Akbari M, Salmasi F, Arvanaghi H, Karbasi M, Farsadizadeh D (2019) Application of Gaussian process regression model to predict discharge coefficient of gated piano key weir. Water Resour Manage 33:3929–3947. https://doi.org/10.1007/s11269-019-02343-3
Alexander AA, Thampi SG, N RC (2018) Development of hybrid wavelet-ANN model for hourly flood stage forecasting. ISH Journal of Hydraulic Engineering 24:266–274 https://doi.org/10.1080/09715010.2017.1422192
Bacanli UG, Firat M, Dikbas F (2009) Adaptive neuro-fuzzy inference system for drought forecasting. Stoch Env Res Risk Assess 23:1143–1154. https://doi.org/10.1007/s00477-008-0288-5
Bazi Y, Alajlan N, Melgani F, AlHichri H, Yager RR (2014) Robust estimation of water chlorophyll concentrations with Gaussian process regression and IOWA aggregation operators. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing 7:3019–3028. https://doi.org/10.1109/JSTARS.2014.2327003
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. https://doi.org/10.1016/j.jhydrol.2013.10.052
Belayneh A, Adamowski J, Khalil B, Quilty J (2016) Coupling machine learning methods with wavelet transforms and the bootstrap and boosting ensemble approaches for drought prediction. Atmos Res 172–173:37–47. https://doi.org/10.1016/j.atmosres.2015.12.017
Beyaztas U, Yaseen ZM (2019) Drought interval simulation using functional data analysis. Journal of Hydrology 579:124141
Blenkinsop S, Fowler HJ (2007) Changes in drought frequency, severity and duration for the British Isles projected by the PRUDENCE regional climate models. Journal of Hydrology 342:50–71. https://doi.org/10.1016/j.jhydrol.2007.05.003
Bryant E (2004) Natural Hazards. 2 edn. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511811845
Danandeh Mehr A, Kahya E, Özger M (2014) A gene–wavelet model for long lead time drought forecasting. Journal of Hydrology 517:691–699. https://doi.org/10.1016/j.jhydrol.2014.06.012
Deo RC, Kisi O, Singh VP (2017) Drought forecasting in eastern Australia using multivariate adaptive regression spline, least square support vector machine and M5Tree model. Atmospheric Research 184:149–175. https://doi.org/10.1016/j.atmosres.2016.10.004
Deo RC, Tiwari MK, Adamowski JF, Quilty JM (2017) Forecasting effective drought index using a wavelet extreme learning machine (W-ELM) model Stochastic. Environmental Research and Risk Assessment 31:1211–1240. https://doi.org/10.1007/s00477-016-1265-z
Dharma S, Hassan MH, Ong HC, Sebayang AH, Silitonga AS, Kusumo F, Milano J (2017) Experimental study and prediction of the performance and exhaust emissions of mixed Jatropha curcas-Ceiba pentandra biodiesel blends in diesel engine using artificial neural networks. J Clean Prod 164:618–633. https://doi.org/10.1016/j.jclepro.2017.06.065
Dubrovsky M, Svoboda MD, Trnka M, Hayes MJ, Wilhite DA, Zalud Z, Hlavinka P (2009) Application of relative drought indices in assessing climate-change impacts on drought conditions in Czechia. Theoret Appl Climatol 96:155–171. https://doi.org/10.1007/s00704-008-0020-x
Ebrahimi H, Rajaee T (2017) Simulation of groundwater level variations using wavelet combined with neural network, linear regression and support vector machine. Global and Planetary Change 148:181–191. https://doi.org/10.1016/j.gloplacha.2016.11.014
Firat M, Güngör M (2007) River flow estimation using adaptive neuro fuzzy inference system. Math Comput Simul 75:87–96. https://doi.org/10.1016/j.matcom.2006.09.003
Gorgij AD, Kisi O, Moghaddam AA (2016) Groundwater budget forecasting, using hybrid wavelet-ANN-GP modelling: a case study of Azarshahr Plain, East Azerbaijan, Iran Hydrology Research:nh2016202
Grbić R, Kurtagić D, Slišković D (2013) Stream water temperature prediction based on Gaussian process regression. Expert Syst Appl 40:7407–7414. https://doi.org/10.1016/j.eswa.2013.06.077
Hargreaves GH, Samani ZA (1985) Reference crop evapotranspiration from temperature. Appl Eng Agric 1:96–99
Haykin SS, Haykin SS, Haykin SS, Haykin SS (2009) Neural networks and learning machines vol 3. Pearson Upper Saddle River, NJ, USA
He Z, Wen X, Liu H, Du J (2014) A comparative study of artificial neural network, adaptive neuro fuzzy inference system and support vector machine for forecasting river flow in the semi-arid mountain region. Journal of Hydrology 509:379–386. https://doi.org/10.1016/j.jhydrol.2013.11.054
Hoolohan V, Tomlin AS, Cockerill T (2018) Improved near surface wind speed predictions using Gaussian process regression combined with numerical weather predictions and observed meteorological data. Renewable Energy 126:1043–1054
Jäkel F, Schölkopf B, Wichmann FA (2007) A tutorial on kernel methods for categorization. J Math Psychol 51:343–358. https://doi.org/10.1016/j.jmp.2007.06.002
Jalalkamali A, Moradi M, Moradi N (2015) Application of several artificial intelligence models and ARIMAX model for forecasting drought using the Standardized Precipitation Index. Int J Environ Sci Technol 12:1201–1210. https://doi.org/10.1007/s13762-014-0717-6
Karbasi M (2018) Forecasting of multi-step ahead reference evapotranspiration using wavelet-Gaussian process regression model. Water Resources Management 32:1035–1052
Khan M, Muhammad N, El-Shafie A (2018) Wavelet-ANN versus ANN-based model for hydrometeorological drought forecasting. Water 10:998. https://doi.org/10.3390/w10080998
Khan MMH, Muhammad NS, El-Shafie A (2020) Wavelet based hybrid ANN-ARIMA models for meteorological drought forecasting. J Hydrol 590:125380. https://doi.org/10.1016/j.jhydrol.2020.125380
Khatib T, Mohamed A, Sopian K, Mahmoud M (2012) Assessment of artificial neural networks for hourly solar radiation prediction International journal of Photoenergy 2012
Kim T-W, Valdés JB (2003) Non-linear model for drought forecasting based on a conjunction of wavelet transforms and neural networks. J Hydrol Eng 8:319–328
Kisi O, Docheshmeh Gorgij A, Zounemat-Kermani M, Mahdavi-Meymand A, Kim S (2019) Drought forecasting using novel heuristic methods in a semi-arid environment. J Hydrol 578:124053. https://doi.org/10.1016/j.jhydrol.2019.124053
Kopsiaftis G, Protopapadakis E, Voulodimos A, Doulamis N, Mantoglou A (2019) Gaussian process regression tuned by Bayesian optimization for seawater intrusion prediction. Comput Intell Neurosci 2019:2859429. https://doi.org/10.1155/2019/2859429
Li G, Shi J (2010) On comparing three artificial neural networks for wind speed forecasting. Appl Energy 87:2313–2320. https://doi.org/10.1016/j.apenergy.2009.12.013
Li Z, Hong X, Hao K, Chen L, Huang B (2020) Gaussian process regression with heteroscedastic noises — a machine-learning predictive variance approach. Chemical Engineering Research and Design 157:162–173. https://doi.org/10.1016/j.cherd.2020.02.033
Liu Q-J, Shi Z-H, Fang N-F, Zhu H-D, Ai L (2013) Modeling the daily suspended sediment concentration in a hyperconcentrated river on the Loess Plateau, China, using the Wavelet–ANN approach. Geomorphology 186:181–190. https://doi.org/10.1016/j.geomorph.2013.01.012
Maheswaran R, Khosa R (2012) Comparative study of different wavelets for hydrologic forecasting. Comput Geosci 46:284–295
Malik A, Kumar A, Kisi O, Khan N, Salih SQ, Yaseen ZM (2021a) Analysis of dry and wet climate characteristics at Uttarakhand (India) using effective drought index. Nat Hazards 105(2):1643–1662. https://doi.org/10.1007/s11069-020-04370-5
Malik A, Kumar A, Salih SQ, Kim S, Kim NW, Yaseen ZM, Singh VP (2020) Drought index prediction using advanced fuzzy logic model: regional case study over Kumaon in India Plos one 15:e0233280
Malik A, Tikhamarine Y, Sammen SS, Abba SI, Shahid S (2021a) Prediction of meteorological drought by using hybrid support vector regression optimized with HHO versus PSO algorithms Environmental Science and Pollution Research:1–20
Malik A, Tikhamarine Y, Souag-Gamane D, Rai P, Sammen SS, Kisi O (2021c) Support vector regression integrated with novel meta-heuristic algorithms for meteorological drought prediction. Meteorol Atmos Phys. https://doi.org/10.1007/s00703-021-00787-0
Mehr AD (2018) Month ahead rainfall forecasting using gene expression programming. American Journal of Earth and Environmental Sciences 1:63–70
Mishra AK, Desai VR (2006) Drought forecasting using feed-forward recursive neural network. Ecol Model 198:127–138. https://doi.org/10.1016/j.ecolmodel.2006.04.017
Mishra AK, Desai VR, Singh VP (2007) Drought forecasting using a hybrid stochastic and neural network model. J Hydrol Eng 12:626–638. https://doi.org/10.1061/(ASCE)1084-0699(2007)12:6(626)
Mishra AK, Singh VP (2011) Drought modeling – a review. Journal of Hydrology 403:157–175. https://doi.org/10.1016/j.jhydrol.2011.03.049
Mishra N, Kushwaha A (2019) Rainfall prediction using Gaussian process regression classifier International Journal of Advanced Research in Computer Engineering & Technology (IJARCET) 8
Mohanty S, Jha MK, Raul SK, Panda RK, Sudheer KP (2015) Using artificial neural network approach for simultaneous forecasting of weekly groundwater levels at multiple sites. Water Resour Manage 29:5521–5532. https://doi.org/10.1007/s11269-015-1132-6
Mokhtarzad M, Eskandari F, Jamshidi Vanjani N, Arabasadi A (2017) Drought forecasting by ANN, ANFIS, and SVM and comparison of the models. Environmental Earth Sciences 76:729. https://doi.org/10.1007/s12665-017-7064-0
Moosavi V, Vafakhah M, Shirmohammadi B, Behnia N (2013) A wavelet-ANFIS hybrid model for groundwater level forecasting for different prediction periods. Water Resour Manage 27:1301–1321. https://doi.org/10.1007/s11269-012-0239-2
Nabaei S, Sharafati A, Yaseen ZM, Shahid S (2019) Copula based assessment of meteorological drought characteristics: regional investigation of Iran. Agric for Meteorol 276:107611. https://doi.org/10.1016/j.agrformet.2019.06.010
Özger M, Mishra AK, Singh VP (2012) Long lead time drought forecasting using a wavelet and fuzzy logic combination model: a case study in Texas. J Hydrometeorol 13:284–297
Pal M, Deswal S (2010) Modelling pile capacity using Gaussian process regression. Comput Geotech 37:942–947. https://doi.org/10.1016/j.compgeo.2010.07.012
Partal T, Cigizoglu HK (2008) Estimation and forecasting of daily suspended sediment data using wavelet–neural networks. Journal of Hydrology 358:317–331. https://doi.org/10.1016/j.jhydrol.2008.06.013
Polikar R (1996) Fundamental concept and an oveview of the wavelet theory wavelet tutorial. Rowan University. College of engineering web Servers. Glassboro, NJ
Pramanik N, Panda RK, Singh A (2011) Daily river flow forecasting using wavelet ANN hybrid models. J Hydroinf 13:49–63
Raghavendra NS, Deka PC (2016) Multistep ahead groundwater level time-series forecasting using gaussian process regression and ANFIS. In: Chaki R, Cortesi A, Saeed K, Chaki N (eds) Advanced Computing and Systems for Security: Volume 2. Springer India, New Delhi, pp 289–302. doi:https://doi.org/10.1007/978-81-322-2653-6_19
Rajaee T, Nourani V, Zounemat-Kermani M, Kisi O (2011) River suspended sediment load prediction: application of ANN and wavelet conjunction model. J Hydrol Eng 16:613–627. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000347
Rasmussen C, Williams C (2006) Gaussian processes for machine learning Cambridge:715–719
Rezaeianzadeh M, Stein A, Cox JP (2016) Drought Forecasting using Markov Chain Model and Artificial Neural Networks. Water Resour Manage 30:2245–2259. https://doi.org/10.1007/s11269-016-1283-0
Roushangar K, Garekhani S, Alizadeh F (2016) Forecasting daily seepage discharge of an earth dam using wavelet–mutual information–Gaussian process. Regression Approaches Geotechnical and Geological Engineering 34:1313–1326. https://doi.org/10.1007/s10706-016-0044-4
Saeid M, Vladimir SKB (2007) Drought forecasting using artificial neural networks and time series of drought indices. International Journal of Climatology 27:2103–2111. https://doi.org/10.1002/joc.1498
Sattari MT, Falsafian K, Irvem A, S S, Qasem SN (2020) Potential of kernel and tree-based machine-learning models for estimating missing data of rainfall. Engineering Applications of Computational Fluid Mechanics 14:1078–1094. https://doi.org/10.1080/19942060.2020.1803971
Schulz E, Speekenbrink M, Krause A (2018) A tutorial on Gaussian process regression: modelling, exploring, and exploiting functions. Journal of Mathematical Psychology 85:1–16. https://doi.org/10.1016/j.jmp.2018.03.001
Shabani S, Samadianfard S, Sattari MT, Mosavi A, Shamshirband S, Kmet T, Várkonyi-Kóczy AR (2020) Modeling pan evaporation using Gaussian process regression K-nearest neighbors random forest and Support Vector machines; comparative analysis. Atmosphere 11:66
Shoaib M, Shamseldin AY, Melville BW, Khan MM (2015) Runoff forecasting using hybrid Wavelet Gene Expression Programming (WGEP) approach. Journal of Hydrology 527:326–344. https://doi.org/10.1016/j.jhydrol.2015.04.072
Sifuzzaman M, Islam M, Ali M (2009) Application of wavelet transform and its advantages compared to Fourier transform
Sihag P, Esmaeilbeiki F, Singh B, Pandhiani SM (2020a) Model-based soil temperature estimation using climatic parameters: the case of Azerbaijan Province. Iran Geology, Ecology, and Landscapes 4:203–215. https://doi.org/10.1080/24749508.2019.1610841
Sihag P, Singh B, Sepah Vand A, Mehdipour V (2020b) Modeling the infiltration process with soft computing techniques ISH. J Hydraul Eng 26:138–152. https://doi.org/10.1080/09715010.2018.1464408
Sihag P, Tiwari NK, Ranjan S (2017) Modelling of infiltration of sandy soil using Gaussian process regression. Modeling Earth Systems and Environment 3:1091–1100. https://doi.org/10.1007/s40808-017-0357-1
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. Computers and Electronics in Agriculture 144:164–173. https://doi.org/10.1016/j.compag.2017.12.002
Solomatine DP, Xue Y (2004) M5 model trees and neural networks: application to flood forecasting in the upper reach of the Huai River in China. Journal of Hydrologic Engineering 9:491–501. https://doi.org/10.1061/(ASCE)1084-0699(2004)9:6(491)
Sun AY, Wang D, Xu X (2014) Monthly streamflow forecasting using Gaussian process regression. J Hydrol 511:72–81. https://doi.org/10.1016/j.jhydrol.2014.01.023
Verrelst J, Rivera JP, Gitelson A, Delegido J, Moreno J, Camps-Valls G (2016) Spectral band selection for vegetation properties retrieval using Gaussian processes regression. Int J Appl Earth Obs Geoinf 52:554–567. https://doi.org/10.1016/j.jag.2016.07.016
Vicente-Serrano SM, Beguería S, López-Moreno JI (2010) A multiscalar drought index sensitive to global warming: the standardized precipitation evapotranspiration index. J Clim 23:1696–1718. https://doi.org/10.1175/2009jcli2909.1
Wang J, Hu J (2015) A robust combination approach for short-term wind speed forecasting and analysis–Combination of the ARIMA (autoregressive integrated moving average), ELM (extreme learning machinE), SVM (support vector machine) and LSSVM (least square SVM) forecasts using a GPR (Gaussian process regression) model. Energy 93:41-56
Wilhite DA (2000) Drought as a natural hazard: concepts and definitions
Yaseen ZM, Sihag P, Yusuf B, Al‐Janabi AMS (2020) Modelling infiltration rates in permeable stormwater channels using soft computing techniques Irrigation and Drainage
Yoon H, Hyun Y, Ha K, Lee K-K, Kim G-B (2016) A method to improve the stability and accuracy of ANN- and SVM-based time series models for long-term groundwater level predictions. Comput Geosci 90:144–155. https://doi.org/10.1016/j.cageo.2016.03.002
Zeng J, Jamei M, Nait Amar M, Hasanipanah M, Bayat P (2021) A novel solution for simulating air overpressure resulting from blasting using an efficient cascaded forward neural network. Engineering with Computers. https://doi.org/10.1007/s00366-021-01381-z
Acknowledgements
The authors acknowledge Iran metrology organization for providing meteorological data of Zanjan Synoptic Station
Author information
Authors and Affiliations
Contributions
Masoud Karbasi: conceptualization, methodology, writing original draft, software, supervision; Maryam Karbasi: software, methodology; Mehdi Jamei: methodology, writing original draft, software, editing; Anurag Malik: methodology, editing; Hazi Mohammad Azamathulla: methodology, writing original draft, editing.
Corresponding author
Ethics declarations
Ethics approval
Not applicable.
Consent to participate
Not applicable.
Consent for publication
Not applicable.
Conflict of interest
The authors declare no competing interests.
Additional information
Publisher's note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Karbasi, M., Karbasi, M., Jamei, M. et al. Development of a new wavelet-based hybrid model to forecast multi-scalar SPEI drought index (case study: Zanjan city, Iran). Theor Appl Climatol 147, 499–522 (2022). https://doi.org/10.1007/s00704-021-03825-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00704-021-03825-4