## 3 Results and Discussion
Figure 6: Residuals for different time periods (upper left: spatial distribution of residuals grouped into four magnitude intervals, upper right: residuals according to latitude, lower left: residuals according to longitude, lower right: histogram of residuals). (**a**) period 1; (**b**) period 2; (**c**) period 3; (**d**) period 4; and (**e**) Period 5. Figure 7: (**a**) average estimated noise level; and (**b**) average prediction error. correlated in both coordinates. This spatial correlation observed in Figure 6 is probably related to the orientation of most of the streets in the town. If the orientation of the streets is considered in the plan of the town, they are mostly oriented in the predominant direction North-South. The adjustment of exponential isotropic variograms for the five data sets is done by using the Restricted Maximum Likelihood method (REML), which allows combining recursively the coefficients of the tendency \(\beta_{i}\), \(i=0,1\), and the components of the variogram. These values are shown in Table 4.  
The goodness of the fitted model to each time period has been evaluated from the predictions of the noise level in the 10 locations of the validation set. The mean squared error (MSE) of these predictions has been obtained. Table 4 shows two values of the MSE. The first, MSE.lm, is calculated with the predictions obtained using the model fitted to the trend without making use of the residuals spatial modeling. The second, MSE.glm, is obtained from the predictions provided by the OK method. An alternative way to measure the goodness of the fitting is based on cross-validation (CRV) over the modeling set itself, as suggested in [36]. The authors introduce three quantities to measure the goodness of model fitting: CRV1 contrasts with the unbiasedness of the prediction and its value must be equal to 0; CRV2 measures the accuracy of the standard deviation of the prediction error and its value is around 1; and finally CRV3 which measures the prediction error. The last row of Table 4 shows the values of these three parameters. From the observation of Table 4, it appears that, from the point of view of the spatial prediction, modeling does not seem to have any advantage over the simple use of the trend. However, the goodness of fit is enhanced by spatial techniques, the values of the CRV.glm clearly improve the CRV.glm (these values are not shown in the table for this reason). In order to cross-check the validity of the number of selected points, a Leave-One-Out-Cross-Validation algorithm in R (with the \"Regularized Random Forest\" method) has been used for the whole set of time averaged measurements. Table 5 shows the results of this test to select the nodes and generates a model to predict the % established in the first column (%test/%training). In this table, mtry stands for the number of randomly selected predictors, coefReg is the regularization value and coeffmp is the importance coefficient. The RMSE is the minimum of the list of results obtained with this algorithm. According to this table, the selection of the validation set is enough for our network of measuring nodes. The test set has been checked against the model and the difference is in the range of the recommendation of the ISO 1996-2. Figure 8 shows a representation of the time evolution of the noise levels in Algemesi. This representation shows that the entrance to the city and its main roads (corresponding to Generalitat Av. and Ronda del Calvari in the left and upper part of the Figure) are the most noise polluted. This is due to the amount of vehicles passing through these main streets. In addition, in this area, the mean speed was reported to be higher than in other locations. From the models obtained by using this analysis, we have been able to make predictions and their variances with OK. Using geoR library [37], Figure 9 shows a representation of the average noise levels in Algemesi on a 50 by 50 grid for the average value of the \(L_{eq}\) taking into account all the time periods.