Abstract
In this study, four conventional and a newly proposed method of wavelet-exponential smoothing (WES) - with two presented scenarios (WES1 and WES2) – are employed to estimate daily and monthly suspended sediment load (SSL) in two rivers (Lighvanchai river in Iran and Upper Rio Grande in the USA), which have different hydro-geomorphological characteristics of the related watersheds. In the proposed WES method, first, wavelet transform (WT) is applied to the original observed time series to decompose them into approximation and detailed subseries to separate different components of time series. For the first scenario (WES1), only two time series, i.e., an approximation and a detail time series are utilized as inputs of model, whereas for the second scenario (WES2), all subseries are separately fed into different exponential smoothing (ES) models. The results revealed that for both rivers, the proposed WES2 and wavelet based artificial neural network (WANN) models could lead to superior performance in comparison to the autoregressive integrated moving average (ARIMA), seasonal ARIMA (SARIMA), ES ad-hoc and artificial neural network (ANN). The WES2 method could enhance the overall performance of SSL forecasting both in daily and monthly modeling of the case studies regarding Nash-Sutcliffe (E) efficiency criteria, respectively up to 13%, 42% and 87%, 116% in daily and monthly scales for SSL modeling of the Lighvanchai and Upper Rio Grande Rivers. As a result, combining WT with ES method and ANN led to more accurate modeling.
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Abbreviations
- ACF:
-
Auto Correlation Function
- AI:
-
Artificial Intelligence
- AIC:
-
Akaike Information Criterion
- ANN:
-
Artificial Neural Network
- ARIMA:
-
Auto Regressive Integrated Moving Average
- CC:
-
Correlation Coefficient
- db4:
-
Daubechies order 4 wavelet
- DEM:
-
Digital Elevation Model
- DLMs:
-
Deep Learning Models
- E:
-
Nash-Sutcliffe
- EP:
-
Nash-Sutcliffe for peak values
- ELM:
-
Extreme Learning Machine
- ES:
-
Exponential Smoothing
- FFBP:
-
Feed Forward Back Propagation
- HW:
-
Holt-Winters
- IWPC:
-
Iran Water & Power Resources Development Co
- LSSVM:
-
Least Squares Support Vector Machine
- MARE:
-
Mean Absolute Relative Error
- MI:
-
Mutual Information
- MSRE:
-
Mean Squared Relative Error
- RMSE:
-
Root Mean Square Error
- RF:
-
Random Forest
- SARIMA:
-
Seasonal Auto Regressive Integrated Moving Average
- SSL:
-
Suspended Sediment Load
- SVM:
-
Support Vector Machine
- USGS:
-
United States Geological Survey
- WANN:
-
Wavelet–artificial neural network
- WES:
-
Wavelet-Exponential Smoothing
- WT:
-
Wavelet Transform
References
Abbaszadeh P, Alipour A, Asadi S (2018) Development of a coupled wavelet transform and evolutionary Levenberg-Marquardt neural networks for hydrological process modeling. Comput Intell 34:175–199
Adamowski J, Fung Chan H, Prasher SO, Ozga-Zielinski B, Sliusarieva A (2012) Comparison of multiple linear and nonlinear regression, autoregressive integrated moving average, artificial neural network, and wavelet artificial neural network methods for urban water demand forecasting in Montreal, Canada. Water Resour Res 48:W01528. https://doi.org/10.1029/2010WR009945
Addison PS (2016) The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance. CRC Press, Boca Raton
ASCE (2000) Artificial neural networks in hydrology. II: hydrologic applications. J Hydrol Eng 5:124–137
Asselman NEM (1995) The impact of climate change on suspended sediment transport in the river Rhine. In: Studies in Environmental Science. Elsevier, Amsterdam, pp 937–942
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 networks and wavelet support vector regression models. J Hydrol 508:418–429. https://doi.org/10.1016/j.jhydrol.2013.10.052
Box GEP, Jenkins GM, Reinsel GC, Ljung GM (2015) Time Series Analysis: Forecasting and Control. Wiley, Hoboken
Caiado J (2010) Performance of combined double seasonal univariate time series models for forecasting water demand. J Hydrol Eng 15:215–222. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000182
Chu C-W, Zhang GP (2003) A comparative study of linear and nonlinear models for aggregate retail sales forecasting. Int J Prod Econ 86:217–231
Cigizoglu HK (2002) Suspended sediment estimation and forecasting using artificial neural networks. Dev Water Sci 47:1645–1652
Cigizoglu HK (2004) Estimation and forecasting of daily suspended sediment data by multi-layer perceptrons. Adv Water Resour 27:185–195. https://doi.org/10.1016/j.advwatres.2003.10.003
Dawson CW, Wilby RL (2001) Hydrological modelling using artificial neural networks. Prog Phys Geogr 25:80–108. https://doi.org/10.1177/030913330102500104
Dawson CW, Abrahart RJ, See LM (2007) HydroTest: a web-based toolbox of evaluation metrics for the standardised assessment of hydrological forecasts. Environ Model Softw 22:1034–1052
Dehghani M, Saghafian B, Nasiri Saleh F, Farokhnia A, Noori R (2014) Uncertainty analysis of streamflow drought forecast using artificial neural networks and Monte-Carlo simulation. Int J Climatol 34:1169–1180. https://doi.org/10.1002/joc.3754
Foufoula-Georgiou E, Kumar P (1994) Wavelet analysis and its applications. Wavelets Geophys 4:373. https://doi.org/10.1016/B978-0-08-052087-2.50022-0
Ganju NK, Schoellhamer DH (2009) Calibration of an estuarine sediment transport model to sediment fluxes as an intermediate step for simulation of geomorphic evolution. Cont Shelf Res 29:148–158
Gardner ES (1985) Exponential smoothing: the state of the art. J Forecast 4:1–28. https://doi.org/10.1002/for.3980040103
Gardner ES (2006) Exponential smoothing: the state of the art-part II. Int J Forecast 22:637–666. https://doi.org/10.1016/j.ijforecast.2006.03.005
Garg N, Sharma MK, Parmar KS, Soni K, Singh RK, Maji S (2016) Comparison of ARIMA and ANN approaches in time-series predictions of traffic noise. Noise Control Eng J 64:522–531. https://doi.org/10.3397/1/376398
Guttman NB (1989) Statistical descriptors of climate. Bull Am Meteorol Soc 70:602–607
Heng S, Suetsugi T (2013) Using artificial neural network to estimate sediment load in ungauged catchments of the Tonle Sap River basin, Cambodia. J Water Resour Prot 05:111–123. https://doi.org/10.4236/jwarp.2013.52013
Himanshu SK, Pandey A, Yadav B (2017) Assessing the applicability of TMPA-3B42V7 precipitation dataset in wavelet-support vector machine approach for suspended sediment load prediction. J Hydrol 550:103–117
Holt CC (1957) Forecasting seasonals and trends by exponentially weighted moving averages. ONR Memorandum Int J Forecast 20:5–10
Hornik K, Stinchcombe M, White H (1989) Multilayer feedforward networks are universal approximators. Neural Netw 2:359–366
Hyndman R, Khandakar Y (2008) Automatic time series forecasting: the forecast package for R. J Stat Softw 27:1–22. https://doi.org/10.18637/jss.v027.i03
Hyndman R, Koehler AB, Snyder RD, Grose S (2002) A state space framework for automatic forecasting using exponential smoothing methods. Int J Forecast 18:439–454. https://doi.org/10.1016/S0169-2070(01)00110-8
Hyndman R, Koehler AB, Ord JK, Snyder RD (2008) Forecasting with Exponential Smoothing: The State Space Approach. Springer Science & Business Media, Berlin
Kaffas K, Hrissanthou V (2015) Estimate of continuous sediment graphs in a basin, using a composite mathematical model. Environ Process 2:361–378. https://doi.org/10.1007/s40710-015-0069-3
Kisi O, Zounemat-Kermani M (2016) Suspended sediment modeling using neuro-fuzzy embedded fuzzy c-means clustering technique. Water Resour Manag 30:3979–3994. https://doi.org/10.1007/s11269-016-1405-8
Kwon H, Lall U, Khalil AF (2007) Stochastic simulation model for nonstationary time series using an autoregressive wavelet decomposition: applications to rainfall and temperature. Water Resour Res 43:W05407
Legates DR, McCabe GJ Jr (1999) Evaluating the use of goodness-of-fit measures in hydrologic and hydroclimatic model validation. Water Resour Res 35(1):233–241
Machekposhti KH, Sedghi H, Telvari A, Babazadeh H (2017) Forecasting by stochastic models to inflow of Karkheh dam at Iran. Civil Eng J 3:340–350
Machekposhti KH, Sedghi H, Telvari A, Babazadeh H (2018) Modeling climate variables of rivers basin using time series analysis (case study: Karkheh River basin at Iran). Civ Eng J 4:78. https://doi.org/10.28991/cej-030970
McCormick GP (1969) Communications to the editor—exponential forecasting: some new variations. Manag Sci 15:311–320. https://doi.org/10.1287/mnsc.15.5.311
Melesse AM, Ahmad S, Mcclain ME, Wang X, Lim YH (2011) Suspended sediment load prediction of river systems: an artificial neural network approach. Agric Water Manag 98:855–866. https://doi.org/10.1016/j.agwat.2010.12.012
Moeeni H, Bonakdari H, Ebtehaj I (2017) Integrated SARIMA with neuro-fuzzy systems and neural networks for monthly inflow prediction. Water Resour Manag 31:2141–2156
Mustafa MR, Rezaur RB, Saiedi S, Isa MH (2012) River suspended sediment prediction using various multilayer perceptron neural network training algorithms-a case study in Malaysia. Water Resour Manag 26:1879–1897. https://doi.org/10.1007/s11269-012-9992-5
Natrella M (2010) NIST/SEMATECH e-Handbook of Statistical Methods. NIST/SEMATECH. https://www.itl.nist.gov/div898/handbook. Accessed 04 Feb 2019
Noori R, Deng Z, Kiaghadi A, Kachoosangi FT (2016) How reliable are ANN, ANFIS, and SVM techniques for predicting longitudinal dispersion coefficient in natural rivers? J Hydraul Eng 142:04015039. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001062
Nourani V, Kisi O, Komasi M (2011) Two hybrid artificial intelligence approaches for modeling rainfall-runoff process. J Hydrol 402:41–59. https://doi.org/10.1016/j.jhydrol.2011.03.002
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
Nourani V, Khanghah TR, Baghanam AH (2015) Application of entropy concept for input selection of wavelet-ANN based rainfall-runoff modeling. J Environ Inf 26:52–70
NRCS (2002) Rapid Watershed Assessment, Upper Rio Grande Watershed. United States Department of Agriculture. https://www.nrcs.usda.gov/Internet/FSE_DOCUMENTS/nrcs144p2_068015.pdf. Accessed 04 Feb 2019
Partal T, Cigizoglu HK (2008) Estimation and forecasting of daily suspended sediment data using wavelet–neural networks. J Hydrol 358:317–331. https://doi.org/10.1016/j.jhydrol.2008.06.013
Pulido-Calvo I, Roldán J, López-Luque R, Gutiérrez-Estrada JC (2003) Demand forecasting for irrigation water distribution systems. J Irrig Drain Eng 129:422–431. https://doi.org/10.1061/(ASCE)0733-9437(2003)129:6(422)
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
Salas JD, Delleur JW, Yevjevich VM, Lane WL (1980) Applied Modeling of Hydrologic Time Series. Water Resources Publication, Littleton
Sharghi E, Nourani V, Najafi H, Molajou A (2018) Emotional ANN (EANN) and wavelet-ANN (WANN) approaches for markovian and seasonal based modeling of rainfall-runoff process. Water Resour Manag 32:3441–3456. https://doi.org/10.1007/s11269-018-2000-y
Sharghi E, Nourani V, Molajou A, Najafi H (2019) Conjunction of emotional ANN (EANN) and wavelet transform for rainfall-runoff modeling. J Hydroinf 21:136–152
Shiri J, Kisi O (2010) Short-term and long-term streamflow forecasting using a wavelet and neuro-fuzzy conjunction model. J Hydrol 394:486–493. https://doi.org/10.1016/j.jhydrol.2010.10.008
Singer MB, Dunne T (2001) Identifying eroding and depositional reaches of valley by analysis of suspended sediment transport in the Sacramento River, California. Water Resour Res 37:3371–3381. https://doi.org/10.1029/2001WR000457
Soni K, Parmar KS, Agrawal S (2017) Modeling of air pollution in residential and industrial sites by integrating statistical and Daubechies wavelet (level 5) analysis. Model Earth Syst Environ 3:1187–1198. https://doi.org/10.1007/s40808-017-0366-0
Stellwagen E (2012) Exponential smoothing: the workhorse of business forecasting. Foresight 27:23–28
Sudheer G, Suseelatha A (2015) Short term load forecasting using wavelet transform combined with Holt-Winters and weighted nearest neighbor models. Int J Electr Power Energy Syst 64:340–346. https://doi.org/10.1016/j.ijepes.2014.07.043
Taghavifar H, Mardani A (2014) Application of artificial neural networks for the prediction of traction performance parameters. J Saudi Soc Agric Sci 13:35–43
Tarar Z, Ahmad S, Ahmad I, Majid Z (2018) Detection of sediment trends using wavelet transforms in the upper Indus River. Water 10:918
Taylor JW (2003) Exponential smoothing with a damped multiplicative trend. Int J Forecast 19:715–725. https://doi.org/10.1016/S0169-2070(03)00003-7
Torrence C, Compo GP (1998) A practical guide to wavelet analysis. Bull Am Meteorol Soc 79:61–78
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 476:433–441. https://doi.org/10.1016/j.jhydrol.2012.11.017
Weron R (2007) Modeling and forecasting electricity loads and prices: a statistical approach. Wiley, Hoboken
Winters PR (1960) Forecasting sales by exponentially weighted moving averages. Manag Sci 6:324–342
Xia X, Dong J, Wang M, Xie H, Xia N, Li H, Zhang X, Mou X, Wen J, Bao Y (2016) Effect of water-sediment regulation of the Xiaolangdi reservoir on the concentrations, characteristics, and fluxes of suspended sediment and organic carbon in the Yellow River. Sci Total Environ 571:487–497. https://doi.org/10.1016/j.scitotenv.2016.07.015
Zhang G, Eddy Patuwo B, Hu MY (1998) Forecasting with artificial neural networks: The state of the art. Int J Forecast. https://doi.org/10.1016/S0169-2070(97)00044-7
Zhu YM, Lu XX, Zhou Y (2007) Suspended sediment flux modeling with artificial neural network: an example of the Longchuanjiang River in the upper Yangtze catchment, China. Geomorphology 84:111–125. https://doi.org/10.1016/j.geomorph.2006.07.010
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Sharghi, E., Nourani, V., Najafi, H. et al. Wavelet-Exponential Smoothing: a New Hybrid Method for Suspended Sediment Load Modeling. Environ. Process. 6, 191–218 (2019). https://doi.org/10.1007/s40710-019-00363-0
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DOI: https://doi.org/10.1007/s40710-019-00363-0