## 2 Materials and Methods
### Model Selection and Hyperparameter Tuning  
The algorithms evaluated in this study are random forest regressor (RF) [37], support vector machine regressor (SVR) [38] and multi-layer perceptron regressor neutral network (MLP) [39; 40]. These were chosen to be widely used and to present available information that allows the easy application in any level of knowledge concerning ML. Compared with deep learning approaches, traditional machine learning does not need large amounts of data to train and the computer processing can be performed in low-end machines without a GPU (Graphics Processing Unit) [41]. SVR is a kernel-based nonlinear regression method. It transforms the original input data space into a high-dimensional input space (hyperplanes) and performs linear regression in the high-dimensional space by defining a maximum margin separator, which minimizes expected generalization error instead of the prediction error in the training dataset. The kernel functions, which take as input the dot products of pairs of input points, allows the SVR to map the inputs efficiently compared to calculating the corresponding points of each input in the high-dimensional space. Basically, SVR finds hyperplanes that minimize the errors and maximize the margins of continuous data [6]. RF is a machine learning technique that utilizes an ensemble of decision trees for regression tasks. It randomly takes subsets of the data and input variables, and the results of all trees are averaged to achieve a better result than individual trees. The use of random samples of the training data for multiple decision trees reduces overfitting compared to using the entire training set with a single decision tree [42]. MLP is an artificial neural network and it consists of connected nodes, resembling the neurons in a biological brain. It consists of at least three layers of nodes: the input layer, hidden layer and output layer. Excluding the input layer nodes, each node receives inputs from the other nodes, and the outputs are calculated using a nonlinear activation function. The learning process for MLP involves continually adjusting weights in the network to minimize the error rate using backpropagation. Backpropagation computes the gradient of the loss function with respect to the weights and updates the weights in the network using methods such as stochastic gradient descent [42]. Depending upon the study cases, different ML algorithms usually require some adjustments. These are often crucial for the development of a successful application. Each ML algorithm has parameters, so-called hyperparameters, which define the setup of the machine to modelling the target function. For each model, a search range of hyperparameters was tested. In cases where a value was selected at the edge of the search range, a new cross-validation was conducted including more values. All hyperparameter tuning of the models (Table 4) is based on GridSearchCV in the Scikit-Learn package, which can evaluate all possible given combinations of hyperparameter values using 10-fold cross-validation. This procedure determines the best combination of hyperparameters of the model that gives the best accuracy, in terms of coefficient of determination (R\({}^{2}\)). Cross-validation is a model validation technique for obtaining reliable and stable models. The use of multiple models in the evaluation removes possible biases of some models with some data sets. We used the training dataset to search for the best parameters, and \begin{table}
\begin{tabular}{c c} \hline \hline  & **Features** \\ \hline  & SST\({}_{-}\)15 \\  & Salinity\({}_{-}\)1 \\  & Chl\({}_{-}\)1 \\  & Chl\({}_{-}\)4 \\  & Chl\({}_{-}\)5 \\  & Chl\({}_{-}\)7 \\  & Chl\({}_{-}\)8 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._reported the prediction performances on the test dataset using these parameters [43]. The mentioned grid search was performed independently for each model on the training subset.