2.3.1. Statistical Approach

The relationship between the sampling e ffort (N of stations) and the classification confidence (confidence interval "*L*" and level "α") was investigated by the following equation applied to each WB of the Venice Lagoon:

$$N = t\_{N\_j - 1, s/2} \, ^2 \frac{S\_j ^2}{L^2} . \tag{2}$$

Three scenarios with di fferent *L* values were investigated. The first two *L* values were selected considering the relationship between the width of the confidence interval, the distance between the class boundaries, and the maximum error of classification. Italian normative (Italian Ministry Decree 260/2010) provides equidistant boundaries for MaQI EQR (bad/poor = 0.2; poor/moderate = 0.4; moderate/good = 0.6; good/high = 0.8), therefore the width of the classes is 0.2. As a consequence, *L* = 0.1 (*L*0.1) entails a maximum error of one ecological class at only one direction (1st scenario), whilst *L* = 0.2 (*L*0.2) entails a maximum error of one ecological class at both directions (2nd scenario).

Finally, the mean confidence interval (*L*mean) was calculated as average *L* of all WBs and applied to each WB (3rd scenario), in order to obtain a more consistent (homogeneous) classification confidence between WBs within the Venice Lagoon.

### 2.3.2. Expert Judgment Criteria

Starting from the three above-mentioned statistical scenarios, a two-step expert judgment analysis was applied to define the final optimization of monitoring e ffort (number of stations), based on level of confidence and hydromorphological features.

First of all, a suitable *L* value (*L*opt) was defined in order to ensure higher homogeneity between WBs with an acceptable minimum level of reliability. Accordingly, to calculate *N* by Equation (2) for each WB, the following rules were adopted:


The risk of misclassification in relation to the critical boundary G/M was also considered.

Finally, the whole dimension and the hydrological and morphological heterogeneity within each WB were also taken into account, to avoid an oversized number of stations in small WBs or, vice versa, an excessive reduction in large WBs. Table 1 summarizes the elements considered for each WB of the Venice Lagoon.

**Table 1.** Dimension and hydrological and morphological characteristics considered for each water body (WB) during the optimization of the monitoring sampling e ffort of the Venice Lagoon.

