Submitted:
02 August 2025
Posted:
04 August 2025
Read the latest preprint version here
Abstract
Keywords:
1. Introduction
1.1. Remote Sensing Approaches for PCC Retrieval
1.2. Study Contribution and Approach
2. Methods
2.1. Data Preparation and Feature Selection
2.2. Model Choice
2.3. Hyperparameter Optimization and Model Training
2.4. Sensitiviy Analysis to Spectral Resolution through Band Downsampling
2.5. Model Evaluation and eXplainable AI (XAI)
2.5.1. Prediction Explainability
2.5.1.1. Code Availability
3. Results
3.1. Hyperparameter Optimization (HPO)
- Learning Rate (learning_rate): - This moderate learning rate suggests the model takes reasonably sized steps when updating that are neither too aggressive (which might lead to overshooting the optimum) nor too conservative (which could slow down convergence).
- Max Depth (max_depth): 10 - A depth of 10 allows the trees to capture complex interactions. This may indicate that the data has non-linear relationships that benefit from deeper trees. Such a depth can be associated with overfitting. The cross-validation process during HPO should minimize this however.
- Number of Estimators (n_estimators): 466 -Building around 466 trees indicates the ensemble haa to tackle inherent complexity in the data that was not apparetn during the Exploratory Data Analysis phase. A larger number of trees generally improves performance—up to a point before overfitting becomse a risk. This number in conjunction with the cross validation process suggest this number strikes a balance between performance and overfitting.
- Subsampling (subsample): - This indicates each of the 466 trees is using roughly 66% of the data. This introduces randomness that helps prevent overfitting as not all samples in any cross-validation fold are used to build every tree.
- Features used per tree (colsample_bytree): - Using about 89% of the features per tree indicates that most features are informative, and the model is allowed to consider almost the full feature set at each split. - See features used in the Methods section.
- Gamma (gamma): - An extremely low gamma value means that almost no minimum loss reduction is required to make a split. This implies that the algorithm will split more readily, potentially capturing fine details. Awareness of this hyperparameter values is important as low gamma can risk overfitting.
3.2. Optimized Model Validation

3.2.1. Explanation of metrics
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Mean Squared Error (MSE):MSE is the average of the squared differences between the predicted and true values. Squaring the errors emphasizes larger deviations, making MSE sensitive to outliers. In our context, MSE is expressed in units of (mg L−1 Chla)2. Lower MSE values indicate better model performance.
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Root Mean Squared Error (RMSE):RMSE is the square root of the MSE, bringing the error metric back to the original units (mg L−1 Chla). It provides a direct measure of the average prediction error magnitude. Lower RMSE values suggest that the model’s predictions are closer to the true values.
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Mean Absolute Error (MAE):MAE calculates the average absolute difference between predicted and true values. Unlike MSE, it does not square the errors, so it is less sensitive to large outliers. MAE is also expressed in the same units as the target variable (mg L−1 Chla). A lower MAE indicates better predictive accuracy.
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Coefficient of Determination (R-squared):R-squared measures the proportion of the variance in the dependent variable that is predictable from the independent variables. It ranges from 0 to 1, where a value closer to 1 indicates that the model explains a high proportion of the variance in the data. In our results, high R-squared values generally indicate strong model performance, although lower values (e.g., for dinoflagellates) suggest room for improvement.
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MAE/StDevtrue:This ratio compares the mean absolute error to the standard deviation of the true values. It provides a relative measure of error by indicating how the average error compares to the inherent variability in the data. A lower ratio implies that the model’s prediction error is small relative to the natural variability of the observations.
3.3. XAI with Shapley Values

3.4. Spectral Resolution Sensitivity Analysis
4. Discussion
5. Conclusions
References
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| Hyperparameter | Low bound | High bound | Sampling Distribution |
|---|---|---|---|
| Learning rate | Log Uniform | ||
| Max. tree depth | 3 | 10 | Uniform Integer |
| Estimator number | 50 | 500 | Uniform Integer |
| Row sample fraction | Uniform Float | ||
| Column sample frac. | Uniform Float | ||
| Gamma | Log Uniform |
| Metric | Diatom | Chloroph. | Cyanoac | Coccolith. | Dinoflag. | Phaeo | Tot. Chl_a |
| MSE | 0.00034 | 0.00010 | 2.89e-06 | 8.59e-05 | 1.96e-05 | 0.00011 | 0.000193 |
| RMSE | 0.0184 | 0.0100 | 0.0017 | 0.00927 | 0.00443 | 0.0105 | 0.0139 |
| MAE | 0.00878 | 0.0042 | 0.00078 | 0.0042 | 0.000637 | 0.00313 | 0.00728 |
| R-squared | 0.979 | 0.958 | 0.996 | 0.985 | 0.530 | 0.999 | 0.999 |
| MAE/StDev | 0.0691 | 0.0858 | 0.0302 | 0.0563 | 0.0986 | 0.00754 | 0.0182 |
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