Algal bloom forecasting with time-frequency analysis: A hybrid deep learning approach.

The rapid emergence of deep learning long-short-term-memory (LSTM) technique presents a promising solution to algal bloom forecasting. However, the discontinuous and non-stationary processes within algal dynamics still largely limit the functions of LSTMs. To overcome this challenge, an advanced time-frequency wavelet analysis (WA) technique was introduced to enhance the prediction accuracy of LSTMs. Herein, the novel hybrid approach (named WLSTM) successfully decreased the algal forecasting inaccuracy of classic LSTMs by 41% ± 8% in Lake Mendota (Wisconsin, USA), with powerful one-step-ahead predictions at hourly, daily, and monthly time resolutions (R2 = 0.976, 0.878, and 0.814, respectively). In addition, the WLSTM outperformed the other two widely used algal forecasting approaches - deep neural network (DNN), and autoregressive-integrated-moving-average (ARIMA) model, represented by average 72% and 85% decrease in root-mean-square-error, respectively. Furthermore, the WLSTM was implemented in an experimentally fertilized lake (Lake Tuesday, Michigan) for a multi-step forecasting examination. It satisfactorily forecasted the algal fluctuations involving substantial peak and extreme values (average R2 > 0.900) and presented accurate judgment outcomes to their bloom levels with high accuracy > 95% on average. This work highlighted the utility of deep learning approaches in effective early-warning for algal blooms, and demonstrated an important direction for improving the adaptability of conventional deep learning approaches to the aquatic problems.