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


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.


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



Auto Correlation Function


Artificial Intelligence


Akaike Information Criterion


Artificial Neural Network


Auto Regressive Integrated Moving Average


Correlation Coefficient


Daubechies order 4 wavelet


Digital Elevation Model


Deep Learning Models




Nash-Sutcliffe for peak values


Extreme Learning Machine


Exponential Smoothing


Feed Forward Back Propagation




Iran Water & Power Resources Development Co


Least Squares Support Vector Machine


Mean Absolute Relative Error


Mutual Information


Mean Squared Relative Error


Root Mean Square Error


Random Forest


Seasonal Auto Regressive Integrated Moving Average


Suspended Sediment Load


Support Vector Machine


United States Geological Survey


Wavelet–artificial neural network


Wavelet-Exponential Smoothing


Wavelet Transform



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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

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

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