Time-series modelling of harmful cyanobacteria blooms by convolutional neural networks and wavelet generated time-frequency images of environmental driving variables.

Early warning systems for harmful cyanobacterial blooms (HCBs) that enable precautional control measures within water bodies and in water works are largely based on inferential time-series modelling. Among deep learning techniques, convolutional neural networks (CNNs) are widely applied for recognition of pictorial, acoustic and thermal images. Time-frequency images of environmental drivers generated by wavelets may provide crucial signals for modelling of HCBs to be recognized by CNNs. This study applies CNNs for time-series modelling of HCBs of Microcystis sp. in four South Korean rivers between 2016 and 2022 by means of time-frequency images of environmental drivers within the lead time of HCBs. After estimating the cardinal dates of beginning, peak, and ending of HCBs, wavelet analysis identified key drivers by phase analysis and generated time-frequency images of the drivers within the cardinal dates for 3, 4 and 5 years. Performances of CNNs were compared in terms of four determinants of input images: methods of estimating critical timings, the number of segments, time-series continuity, and image size. The resulting CNNs predicted high or low intensities of HCBs with a mean accuracy of 97.79 ± 0.06% and F1-score 97.49 ± 0.06% for training dataset, and a mean accuracy of 95.01 ± 0.06% and F1-score 93.30 ± 0.07% for testing dataset. Predictions of Microcystis abundances by CNNs achieved a mean MSE of 2.58 ± 2.46 and a mean R of 0.78 ± 0.20 for training, and a mean MSE of 2.76 ± 2.42 and a mean R of 0.55 ± 0.20 for testing dataset. Precipitation and discharge appeared to be the best performing drivers for qualitative and quantitative predictions of HCBs pointing at the nonstationary nature of river habitats. This study highlights the opportunities of time-series modelling by CNNs driven by wavelet generated time-frequency images of key environmental variables for forecasting of HCBs.