2.4.2. Spatial Analyses

To estimate the error in the sampling e ffort reduction, spatial interpolations of the two (original and reduced) monitoring networks of the whole Venice Lagoon were performed by Kernel interpolation with barrier available in the ArcMap toolbox of ArcGIS Desktop 10.1 (http://esri.com). Barriers were represented by islands and salt-marshes (Figure 1). Exponential equations were used during the regression analysis as Kernel function, while the other parameters were optimized by default in ArcMap. Mean prediction errors and root-mean-square errors (cross-validation) were calculated to test the interpolation maps obtained. The relative error (RE) reduction was computed by the modified formula reported by [19]:

$$RE(\%) = \frac{KBSE\_{original} - KBSE\_{reduced}}{KBSE\_{original}} \times 100\tag{3}$$

where *KBSEoriginal* and *KBSEreduced* are the Kernel standard error of the MaQI network of 2011 (original) and the new one (reduced), respectively.

Finally, for each WB, the ecological classes resulted by the original network and the reduced one were also calculated by averaging the interpolated EQR values of all Kernel interpolation grid cells. The significance of the di fferences between the two networks were tested using Student's *t*-test.
