## 2 Materials and Methods
### Modeling of Grid-Level Siltration Using a Random Forest  
This study proposes a structured, data-driven framework for grid-level siltration prediction by integrating temporal hydro-environmental dynamics with riverbed topography, utilizing a robust ensemble learning approach. The objective is to estimate sediment accumulation over two distinct periods in 2024. The target variable--siltation volume for each interval--was calculated as the difference in riverbed elevation between the start and end of each period. The predictive features include riverbed topography at the beginning of each time window and the corresponding hydrological and meteorological conditions. For the first period (from 1 April to 17 May 2024), the model used bathymetric data from 1 April, along with environmental observations from that period. Similarly, the second period (from 17 May to 3 July 2024) incorporates bathymetry from 17 May and its corresponding hydro-meteorological data.  
To account for the differing lengths of the two periods, the total siltation volumes were normalized by the number of days in each interval, resulting in average daily siltation as the modeling target. This normalization is defined as follows:  
\[\overline{S_{l}}=\frac{S_{i}}{T_{i}} \tag{1}\]  
where \(\overline{S_{l}}\) denotes the average daily siltation during the \(i\)-th time period, \(S_{i}\) is the total observed siltation volume, and \(T_{i}\) is the number of days in the respective period.  
A total of 746 valid grid cells was obtained as model samples, including 185 from the 1 April-17 May period and 561 from 17 May-3 July. These samples represent spatially heterogeneous sedimentation responses, each associated with its initial riverbed elevation and environmental features. The full dataset was randomly split into training (80%) and testing (20%) subsets for model development and evaluation. The selected algorithm is the RF Regressor, an ensemble learning method that constructs multiple decision trees using bootstrap samples and random feature selection at each node. RF was chosen for its well-established effectiveness in handling structured tabular data, its robustness to overfitting, and its capacity to model nonlinear relationships without extensive parameter tuning, making it particularly suitable for environmental prediction tasks with mixed resolution and limited datasets. The final prediction is the average output from all the individual trees:  
\[\hat{y}=\frac{1}{N}\sum_{j=1}^{N}T_{j}(x) \tag{2}\]  
where \(\hat{y}\) is predicted daily silitation, \(T_{j}(x)\) is the output of the \(j\)-th decision tree, and \(N\) is the total number of trees.  
To enhance model robustness and predictive accuracy, hyperparameter optimization was conducted using Bayesian Optimization with 5-fold cross-validation. This probabilistic optimization framework efficiently explores the hyperparameter space by modeling the objective function and iteratively selecting promising configurations. The tuned parameters include the number of estimators (n_estimators), maximum tree depth (max_depth), minimum samples per leaf (min_samples_leaf), and the number of features considered when splitting (max_features). Model performance was evaluated using three regression metrics: Mean Absolute Error (MAE), Mean Squared Error (MSE), and the coefficient of determination (R\({}^{2}\)). These are defined as follows:  
\[MAE=\frac{1}{n}\sum_{j=1}^{N}|y_{i}-\hat{y}_{l}| \tag{3}\]  
\[MSE=\frac{1}{n}\sum_{j=1}^{N}(y_{i}-\hat{y}_{l})^{2} \tag{4}\]  
\[R^{2}=1-\frac{\sum_{i=1}^{n}(y_{i}-\hat{y}_{l})^{2}}{\sum_{i=1}^{n}(y_{i}- \overline{y})^{2}} \tag{5}\]  
where \(y_{i}\) is observed silitation, \(\hat{y}_{l}\) is the predicted value, \(\overline{y}\) is the mean of observed values, and \(n\) is the number of test samples. These metrics collectively evaluate the prediction accuracy, sensitivity to large errors, and the model's explanatory power, respectively.