# Machine Learning Reconstruction of Wyrtki Jet Seasonal Variability in the Equatorial Indian Ocean
## 2 Data and Methods
### Methods  
XGBoost is an advanced machine learning algorithm based on the Gradient Boosting Decision Tree (GBDT) framework proposed by [PERSON] et al. [62]. GBDT is an additive model rooted in the Boosting ensemble learning paradigm. During model training, it employs a forward stagewise algorithm to achieve greedy optimization. In each iteration, the model learns a new Classification and Regression Tree, which fits the residuals between the predictions of the previous t-1 trees and the true values of the training samples. XGBoost retains the core principles of GBDT but introduces significant enhancements, particularly in its node-splitting criterion. For both regression and classification tasks, XGBoost requires the definition of a differentiable loss function. It then evaluates all possible tree structures by computing the first-order and second-order derivatives of the loss function for each sample. By comparing the losses across all candidate tree structures, the algorithm selects the structure with the minimum loss as the new learner for the current iteration. XGBoost is an advanced distributed gradient boosting based decision tree algorithm capable of high precision predictions. By using the second order Taylor expansion of the loss function, it speeds up model convergence, offering faster training than traditional Gradient Boosting Machines (GBM). XGBoost is widely used in remote sensing research [63; 64; 65]. In WJ zonal speed reconstruction using XGBoost, the core idea is to reduce the discrepancy between model outputs and OSCAR reanalysis data through multiple base learners. Specifically, each new base learner focuses on correcting the residuals from the previous one's predictions, effectively cutting down model deviation. Starting from \(U_{i}^{0}=0\), the final velocity reconstruction \(U\) is the sum of all base learners' contributions, as shown in \(U_{i}^{t}=\sum_{k=1}^{t}f_{k}(S_{i})\), where \(S_{i}\) represents sea surface related features and \(U_{i}^{t}\) denotes the \(t\)-th base learner's contribution to the velocity reconstruction. \[ \begin{split} U_{i}^{0}=0\\ U_{i}^{1}=f_{1}(S_{i})=U_{i}^{0}+f_{1}(S_{i})\\ U_{i}^{2}=f_{1}(S_{i})+f_{2}(S_{i})=U_{i}^{1}+f_{2}(S_{i})\\ U_{i}^{t}=\sum\limits_{k=1}^{t}f_{k}(S_{i})=U_{i}^{t-1}+f_{t}(S_{i}) \end{split}  \tag{1}\]  
The XGBoost algorithm has several advantages that make it suitable for reconstructing ocean currents from large-scale marine remote sensing data. Not only can it process vast datasets efficiently, but it also delivers fast and accurate results. Additionally, its regularized model formulation helps prevent overfitting. These features give XGBoost a significant edge in handling large-scale marine remote sensing data for ocean current reconstruction. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Index** & **Input Variable** & **Data Source** & **Output Variable** & **Data Source** & **Time Range** & **Time/Spatial Resolution** \\ \hline \multirow{6}{*}{Data} & Tx & & & & \\  & Ty & ERA5 & & & \\  & Curlz & & & & \\  & D20 & & U & OSCAR & 1993–2022 & Monthly \\  & SSS & & & & \(1^{\circ}\times 1^{\circ}\) \\  & SST & & & & \\  & MLD & & & & \\  & SLA & AVISO & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of data used in this study. The mean absolute error (\(MAE\)) is a useful metric for quantifying model reconstruction errors. It reflects the model's accuracy by averaging the absolute differences between reconstructed and observed current speeds. As shown in Equation (2). \[MAE=\frac{1}{n}{\sum\limits_{i=1}^{n}}{|{{\hat{y}}_{i}}-{{y}_{i}}|} \tag{2}\]  
Here, \(n\) is the sample size, \(y_{i}\) represents the OSCAR-observed current speed and \({\hat{y}}_{i}\) is the model-reconstructed speed. \(MAE\) offers a clear measure of the average absolute deviation between model predictions and observations, with lower \(MAE\) values indicating better model performance. Its simplicity and clarity make it widely used in model evaluation.