Combining physical-based model and machine learning to forecast chlorophyll-a concentration in freshwater lakes

Increasing algal blooms in freshwater lakes have become a serious challenge facing the world. Short-term forecast of chlorophyll-a concentration (Chla) is essential for providing early warnings and taking action to mitigate the risks of algal blooms in freshwater lakes. At present, a variety of data-driven models and physical-based models have been developed for Chla forecast, yet how to effectively combine multiple models for improving the forecast accuracy remains largely unknown. Here we developed an effective model by combining a physical-based model and machine learning algorithms (long short-term memory, LSTM; random forest, RF; support vector machine, SVM) to forecast the Chla in a freshwater lake, and a Bayesian model averaging (BMA) ensemble forecasting method was further proposed to improve the accuracy and reliability of the forecast results. We found that, with the increase of time steps of advance forecast from 1-day to 7-day, the forecast accuracy as measured by R² of the machine learning algorithms is decreased from 0.95 to 0.68. The combination of physical-based modeling with LSTM had great capability in short-term forecast of Chla, owing to the fact that the physical-based model can provide high-frequency Chla data and LSTM is skilled at forecasting in the sequence. This is also evidenced by the weights in the BMA method. The proposed BMA short-term ensemble forecasting results had the robust performance when compared to each individual machine learning forecast model for the 7-day advance forecast, with the largest R² (0.834) and the smallest RMSE (0.267 μg/L). In particular, the uncertainty of a single machine learning model can be effectively reduced by the BMA method.