Advertisement

Environmental Processes

, Volume 6, Issue 1, pp 191–218 | Cite as

Wavelet-Exponential Smoothing: a New Hybrid Method for Suspended Sediment Load Modeling

  • Elnaz SharghiEmail author
  • Vahid Nourani
  • Hessam Najafi
  • Saeed Soleimani
Original Article
  • 47 Downloads

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.

Keywords

Suspended sediment load Artificial neural network Seasonality models Exponential smoothing methods Wavelet transform Time series decomposition 

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

Notes

References

  1. 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 34:175–199CrossRefGoogle Scholar
  2. 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 CrossRefGoogle Scholar
  3. Addison PS (2016) The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance. CRC Press, Boca RatonGoogle Scholar
  4. ASCE (2000) Artificial neural networks in hydrology. II: hydrologic applications. J Hydrol Eng 5:124–137CrossRefGoogle Scholar
  5. Asselman NEM (1995) The impact of climate change on suspended sediment transport in the river Rhine. In: Studies in Environmental Science. Elsevier, Amsterdam, pp 937–942Google Scholar
  6. 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 CrossRefGoogle Scholar
  7. Box GEP, Jenkins GM, Reinsel GC, Ljung GM (2015) Time Series Analysis: Forecasting and Control. Wiley, HobokenGoogle Scholar
  8. 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 CrossRefGoogle Scholar
  9. Chu C-W, Zhang GP (2003) A comparative study of linear and nonlinear models for aggregate retail sales forecasting. Int J Prod Econ 86:217–231CrossRefGoogle Scholar
  10. Cigizoglu HK (2002) Suspended sediment estimation and forecasting using artificial neural networks. Dev Water Sci 47:1645–1652Google Scholar
  11. 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 CrossRefGoogle Scholar
  12. Dawson CW, Wilby RL (2001) Hydrological modelling using artificial neural networks. Prog Phys Geogr 25:80–108.  https://doi.org/10.1177/030913330102500104 CrossRefGoogle Scholar
  13. 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 22:1034–1052CrossRefGoogle Scholar
  14. 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 CrossRefGoogle Scholar
  15. 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 CrossRefGoogle Scholar
  16. 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 29:148–158CrossRefGoogle Scholar
  17. Gardner ES (1985) Exponential smoothing: the state of the art. J Forecast 4:1–28.  https://doi.org/10.1002/for.3980040103 CrossRefGoogle Scholar
  18. 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 CrossRefGoogle Scholar
  19. 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 CrossRefGoogle Scholar
  20. Guttman NB (1989) Statistical descriptors of climate. Bull Am Meteorol Soc 70:602–607CrossRefGoogle Scholar
  21. 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 CrossRefGoogle Scholar
  22. 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 550:103–117CrossRefGoogle Scholar
  23. Holt CC (1957) Forecasting seasonals and trends by exponentially weighted moving averages. ONR Memorandum Int J Forecast 20:5–10CrossRefGoogle Scholar
  24. Hornik K, Stinchcombe M, White H (1989) Multilayer feedforward networks are universal approximators. Neural Netw 2:359–366CrossRefGoogle Scholar
  25. 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 CrossRefGoogle Scholar
  26. 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 CrossRefGoogle Scholar
  27. Hyndman R, Koehler AB, Ord JK, Snyder RD (2008) Forecasting with Exponential Smoothing: The State Space Approach. Springer Science & Business Media, BerlinCrossRefGoogle Scholar
  28. 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 CrossRefGoogle Scholar
  29. 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 CrossRefGoogle Scholar
  30. 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:W05407CrossRefGoogle Scholar
  31. 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):233–241CrossRefGoogle Scholar
  32. Machekposhti KH, Sedghi H, Telvari A, Babazadeh H (2017) Forecasting by stochastic models to inflow of Karkheh dam at Iran. Civil Eng J 3:340–350Google Scholar
  33. 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 CrossRefGoogle Scholar
  34. 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 CrossRefGoogle Scholar
  35. 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 CrossRefGoogle Scholar
  36. Moeeni H, Bonakdari H, Ebtehaj I (2017) Integrated SARIMA with neuro-fuzzy systems and neural networks for monthly inflow prediction. Water Resour Manag 31:2141–2156CrossRefGoogle Scholar
  37. 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 CrossRefGoogle Scholar
  38. Natrella M (2010) NIST/SEMATECH e-Handbook of Statistical Methods. NIST/SEMATECH. https://www.itl.nist.gov/div898/handbook. Accessed 04 Feb 2019
  39. 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 CrossRefGoogle Scholar
  40. 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 CrossRefGoogle Scholar
  41. 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 CrossRefGoogle Scholar
  42. Nourani V, Khanghah TR, Baghanam AH (2015) Application of entropy concept for input selection of wavelet-ANN based rainfall-runoff modeling. J Environ Inf 26:52–70Google Scholar
  43. 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
  44. 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 CrossRefGoogle Scholar
  45. 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) CrossRefGoogle Scholar
  46. 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 CrossRefGoogle Scholar
  47. Salas JD, Delleur JW, Yevjevich VM, Lane WL (1980) Applied Modeling of Hydrologic Time Series. Water Resources Publication, LittletonGoogle Scholar
  48. 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 CrossRefGoogle Scholar
  49. Sharghi E, Nourani V, Molajou A, Najafi H (2019) Conjunction of emotional ANN (EANN) and wavelet transform for rainfall-runoff modeling. J Hydroinf 21:136–152CrossRefGoogle Scholar
  50. 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 CrossRefGoogle Scholar
  51. 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 CrossRefGoogle Scholar
  52. 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 CrossRefGoogle Scholar
  53. Stellwagen E (2012) Exponential smoothing: the workhorse of business forecasting. Foresight 27:23–28Google Scholar
  54. 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 CrossRefGoogle Scholar
  55. Taghavifar H, Mardani A (2014) Application of artificial neural networks for the prediction of traction performance parameters. J Saudi Soc Agric Sci 13:35–43Google Scholar
  56. Tarar Z, Ahmad S, Ahmad I, Majid Z (2018) Detection of sediment trends using wavelet transforms in the upper Indus River. Water 10:918CrossRefGoogle Scholar
  57. 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 CrossRefGoogle Scholar
  58. Torrence C, Compo GP (1998) A practical guide to wavelet analysis. Bull Am Meteorol Soc 79:61–78CrossRefGoogle Scholar
  59. 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 CrossRefGoogle Scholar
  60. Weron R (2007) Modeling and forecasting electricity loads and prices: a statistical approach. Wiley, HobokenGoogle Scholar
  61. Winters PR (1960) Forecasting sales by exponentially weighted moving averages. Manag Sci 6:324–342CrossRefGoogle Scholar
  62. 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 CrossRefGoogle Scholar
  63. 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
  64. 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 CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Water Resources Engineering, Faculty of Civil EngineeringUniversity of TabrizTabrizIran

Personalised recommendations