Abstract
Skilful short-term streamflow forecasting is a challenging task, but useful for addressing a variety of issues associated with water resources planning and management. This study investigates the performance of four popular models for short-term streamflow forecasting, with particular emphasis on the combination of each model with wavelet transform (WT). The autoregressive (AR) model, autoregressive moving average (ARMA) model, artificial neural network (ANN) model, and linear regression (LR) model are used as the base models, and WT-AR, WT-ARMA, WT-ANN, and WT-LR models are used as the composite or hybrid models. These eight models are applied for short-term forecasting of daily streamflow time series in two different river basins in China. Streamflow data from two stations (Yingluoxia and Zhamashike) in the Heihe River basin of North China and two stations (Wuzhou and Longchuan) in the Pearl River basin of South China are considered, and forecasts are made 1-day, 2-day, and 3-day ahead. The accuracy of the models is evaluated using three widely used performance measures: root mean square error, mean absolute error, and correlation coefficient (R). The performances of the eight models are compared, and the influencing role of the wavelet transform in the hybrid models is discussed. The results suggest that the WT-ANN and ANN models are more suitable for the northern basin but perform poorly for the southern basin, while the WT-ARMA model is more suitable for the southern basin. The results also suggest that the wavelet-based hybrid models are better than the single models particularly for longer lead times, offering gradual improvement with increasing lead time. Therefore, the wavelet-based models are especially useful for areas that suffer from frequent natural disasters, fragile ecological environment, and poor self-regulations.
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References
Adamowski JF (2008) Development of a short-term river flood forecasting method for snowmelt driven floods based on wavelet and cross-wavelet analysis. J Hydrol 353(3):247–266
Adamowski J, Chan HF (2011) A wavelet neural network conjunction model for groundwater level forecasting. J Hydrol 407(1):28–40
Agarwal A, Maheswaran R, Sehgal V, Khosa R, Sivakumar B, Bernhofer C (2016) Hydrologic regionalization using wavelet-based entropy method. J Hydrol 538:22–32
Alexander AA, Thampi SG, Chithra NR (2018) Development of hybrid wavelet-ANN model for hourly flood stage forecasting. ISH J Hydraul Eng 9:1–9
Altunkaynak A, Nigussie TA (2015) Prediction of daily rainfall by a hybrid wavelet-season-neuro technique. J Hydrol 529:287–301
Baareh AKM, Sheta AF, Khnaifes KA (2006) Forecasting river flow in the USA: a comparison between auto-regression and neural network non-parametric models. WSEAS 2(10):7–12
Box GEP, Jenkins G (1976) Time series analysis, forecasting and control. Holden-Day, San Francisco
Carlson RF, Watts DG, Maccormick AJA (1970) Application of linear random models to four annual streamflow series. Water Resour Res 6(4):1070–1078
Delleur JW, Kavvas ML (1978) Stochastic models for monthly rainfall forecasting and synthetic generation. J Appl Meteorol 17(10):1528–1536
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
Hamburg M (1970) Statistical analysis for decision marking. Harcourt, Brace & World, Inc., San Diego, p 817
Hipel KW, Mcleod AI, Lennox WC (1977) Advances in Box–Jenkins modeling: 1 Model construction. Water Resour Res 13(3):567–575
Karthikeyan L, Kumar DN (2013) Predictability of nonstationary time series using wavelet and EMD based ARMA models. J Hydrol 502(2):103–119
Karunanithi N (1994) Neural networks for river flow prediction. J Comput Civil Eng 8(2):201–220
Kisi O (2003) River flow modeling using artificial neural networks. J Hydraul Eng 9(1):60–63
Kisi O (2010) Wavelet regression model for short-term streamflow forecasting. J Hydrol 389(3):344–353
Kisi O (2015) 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
Kucuk M, Agiralioglu N (2006) Wavelet regression technique for streamflow prediction. J Appl Stat 33(9):18
Kuligowski RJ, Barros AP (1998) Experiments in short-term precipitation forecasting using artificial neural networks. Mon Weather Rev 126(2):470–482
Kumar P, Foufoula-Georgiou E (1993) A multicomponent decomposition of spatial rainfall fields: 1. Segregation of large- and small-scale features using wavelet transforms. Water Resour Res 29(8):2515–2532
Kuo JT, Sun YH (1996) An ARMA-type section model for average 10-day streamflow synthesis. Water Resour Manag 10(5):333–354
Labat D (2010a) Cross wavelet analyses of annual continental freshwater discharge and selected climate indices. J Hydrol 385:269–278
Labat D (2010b) Wavelet analyses in hydrology. In: Sivakumar B, Berndtsson R (eds) Advances in data-based approaches for hydrologic modeling and forecasting. World Scientific Publishing Company, Singapore, pp 371–410
Labat D, Ababou R, Mangin A (2000) Rainfall-runoff relations for karstic springs. Part II: continuous wavelet and discrete orthogonal multiresolution analysis. J Hydrol 238:149–178
Li X, Sha J, Li YM, Wang ZL (2017) Comparison of hybrid models for daily streamflow prediction in a forested basin. J Hydroinform 20(1):191–205
Lin JY, Cheng CT, Chau KW (2006) Using support vector machines for long-term discharge prediction. Hydrol Sci J 51(4):599–612
Maier HR, Dandy GC (1997) The use of artificial neural networks for the prediction of water quality parameters. Water Resour Res 32(32):1013–1022
Mallat SG (1989) A theory for multi resolution signal decomposition: the wavelet representation. IEEE Trans Pattern Anal 11(7):674–693
Mcdonald J (1979) A time series approach to forecasting Australian total live-births. Demography 16(4):575–601
Mohammadi K, Eslami HR, Dardashti SD (2005) Comparison of regression, ARIMA and ANN models for reservoir inflow forecasting using snowmelt equivalent (a case study of Karaj). J Agric Sci Technol 1–2:17–30
Moss ME, Bryson MC (1974) Autocorrelation structure of monthly streamflows. Water Resour Res 10(4):737–744
Nanda T, Sahoo B, Beria H, Chatterjee C (2016) A wavelet-based non-linear autoregressive with exogenous inputs (WNARX) dynamic neural network model for real-time flood forecasting using satellite-based rainfall products. J Hydrol 539:57–73
Niu J, Sivakumar B (2013) Scale-dependent synthetic streamflow generation using a continuous wavelet transform. J Hydrol 496:71–78
Niu J, Chen J, Wang KY, Sivakumar B (2017) Multi-scale streamflow variability responses to precipitation over the headwater catchments in southern China. J Hydrol 551:14–28
Ozger M (2009) Comparison of fuzzy inference systems for streamflow prediction. Int Assoc Sci Hydrol 54(2):13
Parmar KS, Bhardwaj R (2015) River water prediction modeling using neural networks, fuzzy and wavelet coupled model. Water Resour Manag 29(1):17–33
Quimpo RG (1967) Stochastic model of daily river flow sequences. Hydrology paper 18, Colorado State University, Fort Collins, Colorado
Rakhshandehroo G, Akbari H, Igder MA, Ostadzadeh E (2017) Long term groundwater level forecasting in shallow and deep wells using wavelet neural networks trained by improved harmony search algorithm. J Hydrol Eng 23(2):04017058
Rathinasamy M, Adamowski J, Khosa R (2013) Multiscale streamflow forecasting using a new Bayesian model average based ensemble multi-wavelet Volterra nonlinear method. J Hydrol 507:186–200
Rathinasamy M, Khosa R, Adamowski J et al (2014) Wavelet-based multiscale performance analysis: an approach to assess and improve hydrological models. Water Resour Res 50(12):9721–9737
Ravansalar M, Rajaee T, Kisi O (2017) Wavelet-linear genetic programming: a new approach for modeling monthly streamflow. J Hydrol 549:461–475
Salas JD, Obeysekera JTB (1982) ARMA model identification of hydrologic time series. Water Resour Res 18(4):1011–1021
Salas JD, Delleur JR, Yevjevich VM, Lane WL (1995) Applied modeling of hydrologic time series. Water Resources Publications, Littleton
Shafaei M, Kisi O (2017) Predicting river daily flow using wavelet-artificial neural networks based on regression analyses in comparison with artificial neural networks and support vector machine models. Neural Comput Appl 28:15–28
Shoaib M, Shamseldin AY, Melville BW, Khan MM (2015) Runoff forecasting using hybrid wavelet gene expression programming (WGEP) approach. J Hydrol 527:326–344
Sivakumar B (2017) Chaos in hydrology: bridging determinism and stochasticity. Springer, Dordrecht, p 394
Sivakumar B, Berndtsson R (2010) Advances in data-based approaches for hydrologic modeling and forecasting. World Scientific Publishing Company, Singapore
Sudheer C, Maheswaran R, Panigrahi B, Mathur S (2014) A hybrid SVM-PSO model for forecasting monthly streamflow. Neural Comput Appl 24(6):1381–1389
Tang ZY, Dealmeida C, Fishwick PA (1991) Time series forecasting using neural networks versus Box–Jenkins methodology. Simulation 57(5):303–310
Tantanee S, Patamatammakul S, Oki T, Sriboonlue V, Prempree T (2005) Coupled wavelet-autoregressive model for annual rainfall prediction. J Environ Hydrol 13:124–146
Tao PC, Delleur JW (1976) Seasonal and nonseasonal ARMA models in hydrology. J Hydraul Div 102(10):1541–1559
Thomas HA, Fiering MB (1962) Mathematical synthesis of streamflow sequence for the analysis of river basins by simulation. In: Mass A et al (eds) Design of water resource systems. Harvard University Press, Cambridge, pp 459–493
Tiwari MK, Chatterjee C (2010) Development of an accurate and reliable hourly flood forecasting model using wavelet–bootstrap–ANN (WBANN) hybrid approach. J Hydrol (Amsterdam) 394(3–4):458–470
Tokar AS, Markus M (2000) Precipitation-runoff modeling using artificial neural networks and conceptual models. J Hydrol Eng 5(2):156–161
Valencia D, Schaake JC (1973) Disaggregation processes in stochastic hydrology. Water Resour Res 9(3):580–585
Valipour M (2012) Number of required observation data for rainfall forecasting according to the climate conditions. Am J Sci Res 74:79–86
Valipour M, Banihabib ME, Behbahani SMR (2013) Comparison of the ARMA, ARIMA, and the autoregressive artificial neural network models in forecasting the monthly inflow of Dez dam reservoir. J Hydrol 476(476):433–441
Wang GS, Barber ME, Chen SL, Wu JQ (2014) SWAT modeling with uncertainty and cluster analyses of tillage impacts on hydrological processes. Stoch Environ Res Risk Assess 28(2):225–238
Wu JS, Han J, Annambhotla S, Bryant S (2005) Artificial neural networks for forecasting watershed runoff and stream flows. J Hydrol Eng 10(3):216–222
Wu YP, Liu SG, Yan WD, **a JZ, **ang WH, Wang KL, Luo Q, Fu W, Yuan WP (2016) Climate change and consequences on the water cycle in the humid **angjiang River Basin, China. Stoch Environ Res Risk Assess 30:225–235
Zealand CM, Burn DH, Simonovic SP (1999) Short term streamflow forecasting using artificial neural networks. J Hydrol 214(1–4):32–48
Zhou J, Peng T, Zhang C, Sun N (2018) Data pre-analysis and ensemble of various artificial neural networks for monthly streamflow forecasting. Water 10(5):628
Zounemat-Kermani M, Kisi O, Rajaee T (2013) Performance of radial basis and LM-feed forward artificial neural networks for predicting daily watershed runoff. Appl Soft Comput 13(12):4633–4644
Acknowledgements
The authors are grateful for the financial support provided by the National Natural Science Foundation of China (51679233) and the National Key Research and Development Plan of China (2016YFC0400207). Many thanks to two anonymous reviewers and associate editor, for the valuable comments and suggestions, which helped improve an earlier version of this manuscript.
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Sun, Y., Niu, J. & Sivakumar, B. A comparative study of models for short-term streamflow forecasting with emphasis on wavelet-based approach. Stoch Environ Res Risk Assess 33, 1875–1891 (2019). https://doi.org/10.1007/s00477-019-01734-7
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DOI: https://doi.org/10.1007/s00477-019-01734-7