*3.3. Break Point*

As already highlighted in the analysis of trends in the time series, not all of the terms analyzed for the assessment of the hydrological balance of Lake Candia revealed trends. The additional tests to identify break points verified that there were no significant changes in the volume variation of the lake (ΔV) and no turning points in the rainfall (PL) and in the overall lake water inflow (E) (Table 1 and Figure 4). Groundwater (GS), lake level (H), and surface discharge at the outlet (Q) revealed significant breaks (Table 1 and Figure 4); two of the timing of changes for GS and H overlap in 2003 and 2013. Only H seems to be affected by the change in different cultivation of rice, with a break point in 2008.

#### *3.4. Drivers of Water Balance*

The first estimate on the correlation among different predictors is reported in Figure 5; QS (underground component of the groundwater term) has a high correlation value (0.88) with only GS (groundwater source) retained in the regression model.

**Figure 5.** Correlogram of multicollinearity between the main water balance components adjusted for seasonality. Graphs in the diagonal, plots below the diagonal, and numerical values above the diagonal.

No multicollinearity was found by using the performance model, and non-normality of residual and homoscedasticity was not a problem (Figure 6).

The robust linear regression model comparing lqs (method = "lqs" and "lts"), and rlm (method = psi.huber, psi.bisquare) suggested that the most appropriate model was rlm with Huber psi. Model check supported the reliability of model fit.

**Figure 6.** Verification of model assumptions (multicollinearity, non-normality of residuals, and homoscedasticity).

The selected model of robust regression (Table 3) provides the formula:

$$
\Delta \mathbf{V} = 0.77 \mathbf{P}\_{\mathrm{L}} - 0.37 \mathbf{Q} + 0.30 \mathbf{G}\_{\mathrm{S}} + 0.52 \mathbf{E} - 103820.06 \mathbf{Q}
$$

**Table 3.** Coefficient and standard error of robust regression model, where ΔV is the dependent variable explained by PL, Q, GS, and E, and relative importance metrics of regressors PL, Q, GS, and E with response variable ΔV.


The analyses of the relative importance of the four regressors indicates that direct rainfall on lake (PL) has more importance than the other regressors with R<sup>2</sup> equal to 0.58 and the groundwater sources (GS) has the lowest R2 value, equal to 0.05.

#### **4. Discussion**

The analyses conducted on the complex hydrogeological system that characterizes Lake Candia show that the direct rainfall on lake (PL) and the entrances (E) to lake as, for example, runoff, have an importance greater than the groundwater resource (GS), even if a reliable inference was not possible without further validation and in situ measurements [6]. Groundwater seems to have less importance than surface water entrance on lake level variation, probably because the exchange between groundwater and lake water is slow, even when prolonged in time. Direct rainfall and runoff have more impact on lake level because they carry more water in a short time. With direct measurement of groundwater, it would be possible to define which inflow determines the permanence of a certain level in the lake rather than that its high variation, thus defining the actual importance of groundwater. The response of groundwater source to rainfall was highly variable in our system and it is known that it depends on physical characteristics of soil and aquifer, size of lakes, and their catchments [58,59]. The analyses of the main water balance components during the period 1993–2019 revealed that only the outflow, the groundwater source, and the lake level had a significance and positive trend. The variability in rainfall, water inflow, and the consequent variability in lake volume were likely too high, masking potential temporal trends.

The analyses on break points, to verify if water balance components could change their behavior in particular circumstance or for particular events, revealed that no changes could be detected for water inflow and for volume variation, probably due to the high variability of their behavior and to the variables that affect them. Rainfall varies greatly through time and no trend or changing points were identified. Entrance has a behavior depending on rainfall and on agricultural need, which depend, in turn, on temperature and cultivation. Lake volume is more stable and for this reason its behavior is not subject to particular trend or change points. Break points in the outflow were found in 1997 and 2010; in the groundwater source in 2003 and 2013 but not in 2008; and in the lake level in 2003, 2008, and 2013. Regarding the outflow, the two years detected as changing points are linked with an unexpected decrease (in 1997) in comparison to previous years, and with an increase (in 2010) after a series of years with low values.

Between 2003 and 2008, lake levels were characterized by low values whereas since 2008 and even more since 2013, an increase of their values occurred. Probably the flooding of the marsh (located in the northeastern part of the lake) during 2008–2009 by a LIFE project (http://www.life.trelaghi.it/eng/tasks5.htm, accessed date 2 November 2021) increased minimum lake level, in addition to allowing more water quantity into the lake catchment. This greater water quantity since 2013 was also pointed out by a groundwater source break point, which showed an increase of groundwater. This increase is in contrast with [49], who considered a reduction in groundwater source because of changes in water use owing to increasing cultivation, but it is in line with unpublished results of a study on Lake Viverone, from the same morainic amphitheater, showing an increase of groundwater level since 2008 measured from a well into the catchment of the lake. An explanation for the increase could be related to a greater contribution by the alpine glaciers from which it is fed, due to warmer and longer summers melting more glacial mass [60,61].

The evaluation of temporal variability of different climatic variables related to climate change is surely relevant for water resource management, to allow knowledge-based planning uses and to understand the effect of human disturbance, and the application of break point detection can be a key tool to achieve the goal [43]. Yet, the problem of break point is not often included in climate change studies, which are more interested on the magnitude of changes in temperature, rainfall, or solar radiation, instead of detecting when such changes occurred. The field of analysis of sudden changes and tipping points in the behavior of environmental variables represents a rising scenario in ecological studies [62,63] and will surely provide new insights in the understanding of the effects of climate change.

To better understand relationships among the different components of water balance, the regression analysis provides a model that can be used to improve water management.

The groundwater resource can be followed by monitoring water table levels, and management policies implemented to respond in advance to changes in water table considering that it is the most important reservoir of the Piedmont Region [64]. Furthermore, the preservation groundwater quantity and quality are extremely important topics to protect groundwater from pollution and exploitation [65]. Such an approach, combining management of outfall and water table monitoring, can be adopted for the protection of the water resource together with the sustainable uses and protection of the ecosystem of Lake Candia. Rainfall is a meteorological parameter, which has direct influence on agricultural production and on water resources and water availability; a decrease in rainfall will prompt greater extraction of groundwater for irrigation and will result in a decline of groundwater level, with consequences on water balance. The scenario of changing water availability in the future needs to be properly taken into account for long-term water management at the catchment scale [41], as needed for Lake Candia.
