## 4 Discussion  
Machine learning analysis was conducted on the Helgoland Roads time series to develop the best fit of chlorophyll-a concentrations over time using different parameters and their lagged correlates. For the three algorithms implemented, the model results were virtually equal in the evaluation metrics, presenting similar results in prediction, with slightly better values for the model SVR. For the time predictions, each of the three models' performances are acceptable with high R\({}^{2}\) values greater than 0.70 and RMSE lower than 1.5 \(\upmu\)g L\({}^{-1}\), -40% smaller than the chlorophyll-a concentration standard deviation of 2.9 \(\upmu\)g L\({}^{-1}\). However, all of the algorithms were unable to predict extreme values (Figure 8). It was expected that a certain degree of decrease in accuracy would be incurred because of the difficulty in capturing and reproducing these extreme peaks [45]. One hypothesis that would explain the underestimation of extreme values is the absence of predictive features, e.g., hydrodynamics can result in the transport of chlorophyll from other areas as an input event, even though salinity and wind parameters are reliable indicates for current and wave dynamics in the German Bight [46]. As these events do not present as a temporal pattern, the ML models do not recognize the influence on the target. Figure 8: Cross-plots of the modeled and observed chlorophyll values in (**a**) SVR, (**b**) MLP and (**c**) RF. It is possible to notice the deviation in extreme values, showing the limitation of the ML models in deal with these data values. Figure 7: Result of SARIMA fit (black dashed) in the test dataset (gray solid). The better fit in extreme values is counter-balanced by the estimation of negative values, decreasing/increasing R\({}^{2}\)/RMSE compared to the ML models results. Because each algorithm is based on different algebraic assumptions and procedures, they can result in different predictions. Between SVR and MLP, [14] points to differences in the nonlinear equalization performance and the structural risk minimization principle of SVR being more effective than the empirical risk minimization principle of neural networks in terms of minimizing error. According to [47], in MLP the method for determining global solutions is difficult to converge because of its inherent algorithm design and model parameters are more complex than SVR, whereas the SVR has ready access to global optimal solutions, obtained by solving a linearly constrained quadratic programming problem [14]. Between SVR and RF, as we saw, the linear base model gave good results. There is the possibility of a linear dependency that is better captured by SVR, probably a result from the linear interpolation in the preprocessing step of this study. The feature selection and tuning of hyperparameters was extremely important and improved the results substantially. This was noticeable in the adj R\({}^{2}\) results for default and optimized models. Analyzing the 17 features used in SVR and described in the results section, the algorithm considered SST, lagged SST, lagged chlorophyll, salinity and Secchi depth to reach the best results presented in this work. It is important to point that ML is a data-driven approach, but it is possible to make inferences about the selected features. The number of selected features was a response of balancing bias and variance in the learning algorithms [48]. For this study, we noticed the choice of SST as an important feature, probably representing the seasonal patterns in the chlorophyll target. Better R\({}^{2}\), adj R\({}^{2}\) and RMSE results in the independent validation dataset are possibly due to less variability and absence of extreme values, and shows the good generalization that the ML models are capable of. All of the good results, for both the test and independent validation data, show the better prediction power of the three ML algorithms evaluated in this study.