2.5.3. Combining Wavelet Analysis and Artificial Neural Networks

Wavelet transforms are mathematical tools that covert the one-dimensional time-domain signals into two-dimensional time-frequency-domain signals. The transformation separates significant changes in the time series in the form of high- and low-frequency signals. This property of wavelets is required for the identification of seasonality and hysteresis phenomenon in the data and helps ANNs to build a better relationship between inputs and sediment parameters. The level of transformation of signals depends on river properties, such as catchment, tributaries, lag-time, landslides, spatio-temporal sediment storage in tributaries, etc. Owing to the irregular and non-symmetric shape of the wavelets, their coupling with ANNs has been successful for filling missing sediment load data and for predictions in catchments where no land use/land cover changes occurred. There are many mother wavelets like Haar, Daubechies, or Coiflet. Application of the Daubechies wavelet using more than one decomposition level with a one-day lag-time has been proven more successful for the Upper Indus River [41]. We adopted the design of the WA-ANN model from [41], but extended the training period from 1969–2008 to 1969–2014.
