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
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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