# Multivariate Relationship in Big Data Collection of Ocean Observing System
## 3 Results
Firstly, histograms of \(\text{NO}_{3}^{-}\), \(\text{PO}_{4}^{3-}\), Si(OH)\({}_{4}\), and chlorophyll-a show good and fairly homogeneous coverage in terms of latitude, while the latitude distribution is biased by the presence of the three major basins in the Mediterranean Sea (western, Adriatic and L'ervative basins). Alkalinity shows a biased distribution, with the largest number of observations being gathered in the Northern Adriatic Sea. \(\text{NH}_{4}^{+}\) shows a biased coverage with observations mainly sampled in the Adriatic Sea. The distribution of 10%HE in the predictions is uniform along the horizontal dimension (both latitude and longitude) for all the variables, except for \(\text{PO}_{4}^{3-}\) and Si(OH)\({}_{4}\). These two variables present a higher frequency of 10%HE for latitudes ranging between 41-42 N. In particular, the percentage of 10%HE prediction in this area are 30% and 20% for \(\text{PO}_{4}^{3-}\) and Si(OH)\({}_{4}\), respectively. On the other hand, the distribution of 10%HE on the depths dimension (third column of the plots) shows that the predictions are more accurate on the surface for all variables and that the percentage of samples characterized by 10%HE increases along the depth. Specifically, the ratio between 10%HE samples and total samples available is about (always above)20% for depths over 100 m.  
These plots can be exploited as further indicators for the reliability of a prediction, e.g., if our model is applied to samples that belong to a geographical area that the model has proven to predict with higher precision, the corresponding result can be labeled as reliable with higher confidence. Conversely, geographical areas showing the presence of 25%HE or 10%HE cases higher than usual should be more carefully investigated given the presence of peculiarities diverging from the mean model. The diagnostic metrics of Figures 2-4 provide an overall picture to assess the level of goodness of the reconstruction for each of the six variables. Figure 3: Comparison between the prediction’s error and the corresponding interquartile range (i.e., the difference between the third and the first quartile) for all the considered variables: (**a**) nitrate (\(\text{NO}_{3}^{-}\)), (**b**) phosphate (\(\text{PO}_{4}^{3-}\)), (**c**) silicate (Si(OH)\({}_{4}\)), (**d**) alkalinity (\(\text{A}_{T}\)), (**e**) chlorophyll-a, and (**f**) ammonium (\(\text{NH}_{4}^{+}\)). The color denotes the depth of the samples, from green (shallow) to blue (deep). Regarding the nitrate, Figure 2a shows that the prediction satisfactorily approximates the observations. For the phosphate variable (Figure 2b), a similar behavior with respect to the nitrate emerges: the model skillfully predicts both the lower and higher ranges of values. The prediction of silicate is the one that leads to more satisfactory results, as shown in Figure 2c. Figure 4: Histograms displaying the testing distribution for all the considered variables: NO\({}_{3}^{-}\), PO\({}_{4}^{-}\), Si(OH)\({}_{4}\), A\({}_{T}\), chlorophyll-a, and NH\({}_{4}^{+}\). Histograms in the first, second, and third columns represent the distribution of the results according to, respectively, their latitude, their longitude, and their depth. Both 25% (25% HE) and 10% (10% HE) of the predictions leading to a higher error are highlighted in different colors. The lighter color represent the total number of samples. Positive results are also obtained for alkalinity (Figure 2d), even if the bias distribution of the observations (Figure 4) may prevent us from drawing adequate conclusions on error distribution in these zones. As regards chlorophyll-a (Figure 2e), a clear difference emerges in the quality of prediction for different ranges of values: lower values are predicted more accurately than higher ones. The underlying reason is the gap between the quantity of high- and low-value samples available in the training set. Finally, taking into account ammonium, Figure 2f shows that this marine variable is the one predicted less accurately.