# Multivariate Relationship in Big Data Collection of Ocean Observing System
## 3 Results  
Individual training and testing fitness (both MAE and RMSE) are computed for each of the six variables. Only testing fitness is reported in Table 3, together with a comparison with \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\mathbf{NO_{3}^{-}}\) & \(\mathbf{PO_{4}^{3-}}\) & \(\mathbf{Si(OH)_{4}}\) & \(\mathbf{A_{T}}\) & \(\mathbf{Chl-a}\) & \(\mathbf{NH_{4}}^{+}\) \\ \hline
20.686 & 25.335 & 16.187 & 1.292 & 6.040 & 9.900 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Dimension of the training set for each variable, after the removal of noisy and unreliable data. Figure 1: Flow chart illustrating the two-step quality check routine. results achieved by [15], which represents the current state of the art for the Mediterranean Sea application. The results show a general decrease in both fitness metrics. The largest decreases in the skill metrics (30-45%) are in NO\({}_{3}^{-}\), PO\({}_{4}^{3-}\) and Si(OH)\({}_{4}\), while alkalinity showed the lowest improvements (15%). Figure 2 compares, via scatter-plot, the real value of the in situ measurements (on the \(x\)-axis) with the corresponding prediction of the model (on the \(y\)-axis). The nearer a point is to the diagonal, the more the prediction has been performed correctly. The plots confirm that, among the variables, the NO\({}_{3}^{-}\), PO\({}_{4}^{3-}\) and Si(OH)\({}_{4}\) points are fairly well distributed along the diagonal. Chlorophyll-a and NH\({}_{4}^{+}\) points are more scattered. The number of data of A\({}_{T}\) are lower than the other variables, and this might represent a limit in the robustness of the results. Figure 3 shows, via scatter-plots, the relation between the error obtained by our model (on the \(x\)-axis) and the range between the third quantile and first quantile (on the \(y\)-axis), which represents the confidence interval. These scatter plots show that a small quantile difference corresponds to small errors in the prediction, confirming the reliability of this metric for computing the confidence interval. The fact that the dispersion of the ensemble predictions is generally low when the errors are low also highlights that predictions are less sensitive to the topology of the network. A few points lie on the bottom-right of the plot, showing low dispersion for poor predictions, which may indicate the presence of outliers  
Figure 2: Scatter-plot comparing the in situ measurements and the model’s output for all the considered variables: (**a**) nitrate (NO\({}_{3}^{-}\)), (**b**) phosphate (PO\({}_{4}^{3-}\)), (**c**) silicate (Si(OH)\({}_{4}\)), (**d**) alkalinity (A\({}_{T}\)), (**e**) chlorophyll-a, and (**f**) ammonium (NH\({}_{4}^{+}\)). The color denotes the depth of the samples, from green (shallow) to blue (deep). \begin{table}
\begin{tabular}{c c c c c c c} \hline  & & **NO\({}_{3}^{-}\)** & **PO\({}_{4}^{3-}\)** & **Si(OH)\({}_{4}\)** & **A\({}_{T}\)** & **Chl-a** & **NH\({}_{4}^{+}\)** \\ \hline MAE & Canyon-Med & 0.47 & 0.026 & 0.40 & 6.5 & & \\ \hline MAE & Our method & 0.26 & 0.019 & 0.31 & 5.6 & 0.09 & 0.13 \\ \hline RMSE & Canyon-Med & 0.73 & 0.045 & 0.70 & 11.1 & & \\ \hline RMSE & Our method & 0.50 & 0.031 & 0.58 & 8.2 & 0.017 & 0.21 \\ \hline \end{tabular}
\end{table} 
Table 3: Comparison of the fitness values (MAE and RMSE) between the current state of the art, _Canyon-Med_[15], and our method. not identified by our two-step analysis. Among the variables, \(\text{NO}_{3}^{-}\), \(\text{PO}_{4}^{3-}\), and Si(OH)\({}_{4}\) are those with a larger number of poor predictions with low dispersion. Figure 4 displays a series of histograms collecting the distribution of the test data as a function of their latitude, longitude, and depth. For each distribution bin, the number of predictions with the 25% (25%HE) and 10% (25%HE) highest errors is reported in the darker colors. The figure allows investigation of the presence of inhomogeneity between data distribution and error distribution.