Conformal Prediction for River Total Dissolved Solids (TDS) Prediction and Risk Quantification

Probabilistic machine learning models estimate total dissolved solids (TDS) levels and exceedance probabilities, enabling risk-based regulation and safeguarding public health. This study develops a probabilistic machine learning framework to forecast monthly TDS in the Lam Tsuen River in Hong Kong using long‑term monitoring data from 2000 to 2023, split into 80% for training and 20% for testing. Four routinely measured variables, pH, salinity, turbidity, and water temperature, were used as predictors of TDS. Five gradient boosting‑based algorithms (Gradient boosting, LightGB, XGBoost, CatBoost, and GPBoost) were calibrated, and predictive uncertainty was quantified using three conformal prediction schemes: Split Conformal Prediction (SplitCP), Cross Validation Plus (CV+), and Conformal Quantile Regression (CQR). Probabilistic prediction was implemented via the Treeffuser framework, enabling consistent construction of prediction intervals and exceedance probabilities. Among the tested models, GPBoost delivered the best deterministic performance, with Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and correlation coefficient (CC) of 85.968 mg/l, 59.943, and 0.902 on the test set, respectively, outperforming gradient boosting (RMSE 88.855 mg/l, MAE 61.067, CC 0.906), LightGB (RMSE 89.837, MAE 62.054, CC 0.905), XGBoost (RMSE 97.723, MAE 68.792, CC 0.885), and CatBoost (RMSE 108.758 mg/l, MAE 66.886, CC 0.840). The conformal prediction methods produced well‑calibrated prediction intervals, with the narrowest and most stable bands obtained for GPBoost. SHAP analysis further showed that salinity and turbidity were the dominant predictors, followed by pH and water temperature, providing hydrochemically consistent insight into the drivers of TDS variability. These methods can be extended to river quality/quantity for probabilistic forecasting and adaptive planning.