Improving Short-term Streamflow Forecasting with Wavelet Transforms: A Large Sample Evaluation

Abstract

Accurate streamflow forecasting is instrumental to water management, including flood preparation and drought monitoring. The past two decades have seen a steady rise in the application of machine learning (ML) models to streamflow forecasting, given their ability to model highly nonlinear relationships, moderate data requirements, and accuracy. Successful application of ML to streamflow forecasting requires the modeler to select appropriate features (e.g., precipitation and air temperature) to use in an ML model. Since the original features can be insufficient, adding new features derived from existing ones, also known as feature engineering, is often needed to improve the accuracy of streamflow forecasts. Wavelet transforms (WTs) have become promising feature engineering methods for streamflow forecasting since they can decompose time series (e.g., precipitation) into multiple sub series (coefficients). Each set of coefficients captures changes across different timescales (e.g., monthly, seasonal), allowing for the variance of the original time series to be associated with specific timescales. The different coefficients extracted by WTs are then used as features in an ML model, often improving the accuracy of streamflow forecasts compared to using the original features alone. Furthermore, different wavelet filters can capture different behaviours of a given time series (e.g., trends, short-term transients), making some more suitable for different applications (e.g., streamflow forecasting) than others. This leaves the modeler with the task of finding the right wavelet filter(s) for their application.

Despite many existing studies coupling WTs and ML for streamflow forecasting, none have explored a large hydro-climatically diverse sample of catchments to evaluate the impact of WTs on streamflow forecasting performance. Due to the small number of catchments included in existing streamflow forecasting studies using WT-based ML models, it is not clear how the performance of the adopted models generalizes to catchments with different characteristics. In addition, approximately 90% of studies using WTs for hydrological forecasting misuse WTs. The most common issue is not taking proper precautions to address look-ahead bias (i.e., the use of ‘future data’), invalidating the forecasts for real-world applications.

Thus, this thesis seeks to address the abovementioned gaps in the literature by undertaking a large sample case study involving 620 catchments across the contiguous United States, using best practices for WT-based streamflow forecasting at the daily timescale. The WT-generated features are used in long short-term memory networks (LSTMs) to produce streamflow forecasts. LSTMs are selected due to their exceptional streamflow forecasting performance compared to other commonly adopted models, as noted in the literature. In total, three LSTM configurations are considered: baseline LSTM (B LSTM), wavelet LSTM (W-LSTM), and grid search LSTM (GS-LSTM). In the first configuration, a baseline LSTM model is developed for each catchment. In the second configuration, 33 different wavelet filters are used to engineer features based on several hydro-meteorological features (e.g., precipitation and air temperature), resulting in 33 different W-LSTM models for each catchment. For each catchment, the 33 different W-LSTM models are compared to the B-LSTM model to evaluate the impact of WTs on streamflow forecasting performance. In the third configuration, the B-LSTM models undergo hyper-parameter selection using grid search. This setup is used to test whether grid search has a greater impact on streamflow forecasting performance than WTs. All configurations are applied to one- and three-day-ahead streamflow forecasting.

For the one-day-ahead forecast horizon, W-LSTM improves upon B-LSTM performance in 97% of catchments and improves upon GS-LSTM in 50% of catchments. For a forecast horizon of three days ahead, W-LSTM improves upon B-LSTM performance in 97% of catchments and improves upon GS LSTM in 41% of catchments. When considering only catchments where the B-LSTM model meets a minimum performance threshold (i.e., out-of-sample Nash-Sutcliffe Efficiency, OOS NSE, greater than 0.4), then for a forecast horizon of one day ahead, W-LSTM improves upon GS-LSTM in 60% of catchments, while for a forecast horizon of three days ahead, W-LSTM improves upon GS-LSTM in 70% of catchments.

Certain wavelet filters perform better than others. For instance, the W-LSTM using the Morris Minimum Bandwidth 4.2 filter outperforms B-LSTM in over 50% of catchments (where B-LSTM has an OOS NSE greater than 0.4) for both forecast horizons.

Overall, WTs provide the greatest improvement to forecasting performance (for both one and three day(s) ahead forecast horizons) in the D (snowy climates) and B (dry climates) Koppen classification regions. This finding presents a clear direction for researchers and practitioners when deciding whether WTs will benefit their streamflow forecasting models in their regions.

This thesis is the first to use a large sample of catchments to demonstrate that WTs are useful for improving ML-based streamflow forecasts. These models can be used for reservoir management, early flood warning systems, irrigation, navigation, and many other water management applications.

Future work can explore the combined optimization of wavelet filters and LSTM hyper-parameters to improve further upon the performance of the models reported in this thesis. Another worthwhile endeavor is to focus on modifications to the LSTM, such as quantile loss functions, Monte Carlo dropout connections, conformal prediction, and/or Bayesian methods to generate probabilistic forecasts enabling risk-based solutions to water management problems.