Machine learning-based quantitative analysis of internal phosphorus release flux in coastal lakes

Purpose  As the issue of water eutrophication intensifies, the impact of internal phosphorus release becomes increasingly prominent. However, studies on the internal phosphorus release flux in coastal lakes remain limited. This study aims to identify and quantify the key factors, providing scientific references for coastal lake water quality management.

Methods  In this study, 45 surface sediment samples were collected from a coastal lake in Fujian, China. Factors were identified using the Variance Inflation Factor and Boruta models. These factors served as inputs, with internal phosphorus release flux as the output. Six models including Linear Regression, K-Nearest Neighbor, Support Vector Regression, Random Forest, Bayesian Ridge Regression, and Artificial Neural Network were evaluated. They were compared based on six performance metrics: mean absolute error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE), median absolute logarithmic error (MALE), root mean squared logarithmic error (RMSLE), and Coefficient of Determination (R²), to identify the best predictive model. The optimal model was further analyzed using a one-dimensional partial dependence plot to interpret the results and predict the threshold effects of factors on internal phosphorus release.

Results  The study area was characterized by a weakly alkaline (pH = 7.34) and reducing (redox potential = -51.25 mV) environment. Internal phosphorus release flux ranged from -0.020 mg g⁻¹ to 0.291 mg g⁻¹. Total phosphorus had the highest feature importance (0.020), followed by salinity (0.010), copper (0.009), potassium (0.007) and calcium (0.006). Negative factors included phosphorus in surface water (-0.010), total organic carbon (-0.007) and chloride (-0.007). The Random Forest model showed the best predictive performance (Train: R² = 0.768, Test: R² = 0.663), high accuracy (MAE = 0.022, RMSE = 0.030, MAPE = 60.949, MALE = 0.021, RMSLE = 0.027). One-dimensional partial dependence plot analysis revealed that total phosphorus, total organic carbon, chloride, potassium, copper, and calcium displayed concentration-dependent response patterns, with distinct regulatory mechanisms at 624 mg kg⁻¹, 2075 mg g⁻¹, 8291 mg kg⁻¹, 18,000 mg kg⁻¹, 35 mg kg⁻¹ and 13217 mg kg⁻¹.

Conclusion  Internal phosphorus release is mainly driven by the dynamic concentration gradient at the sediment–water interface, with ion exchange acting as a secondary regulatory factor. The Random Forest model demonstrates strong predictive capability for internal phosphorus release flux. Each element exhibits a concentration-dependent dual regulation of phosphorus release, with distinct effects observed at specific concentration thresholds. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.