*2.2. Eddy Covariance Data*

Renon, Lavarone and Monte Bondone eddy covariance sites are part of the FLUXNET Network, where CO2 fluxes, water vapour and other ancillary meteorological variables are measured at half-hourly intervals. Data are processed and quality controlled following the Fluxnet methodology [53]. Within the Fluxnet network, the data availability for the Renon site ranges from 1998 to 2013, for Lavarone, from 2003 to 2014 and, for Monte Bondone, from 2003 to 2013.

Bosco della Fontana is part of the ICOS Ecosystem Network. The eddy covariance tower measures half-hourly turbulent fluxes of CO2, water vapor and different meteorological data following the ICOS protocols [54].

Despite the corrections applied in the calculation of EC fluxes, sensible and latent heat fluxes are usually underestimated at most EC sites with respect to the available energy at the surface [55], resulting in some uncertainty in the quantification of water lost by ecosystems through ET. For this reason, in our analysis, we used the latent heat flux adjusted by a correction factor based on the ratio between available energy and the sum of turbulent energy fluxes for each half hour [53]. The half-hourly latent heat flux data from the eddy

covariance sites obtained from the FLUXNET and ICOS datasets were converted to ET using "LE.to.ET" function of the "bigleaf" R package, applying the correlation parameter between depth units and energy of ET [56] (Formula (1)). The conversion was corrected using the half-hourly air temperature.

$$\text{ET} = \text{LE}/\lambda \tag{1}$$

where:


Successively, daily ET values were then accumulated and converted into monthly ET in order to be correlated to the ECI and WDI that were assessed on a monthly basis.

### *2.3. Emissivity Data and ECI Estimation*

The ECI (that ranges in the interval [0, 1]) has been developed to discriminate between bare soil and vegetation [34] and to better classify vegetation cover [35]. For this present study, the methods introduced by Masiello et al. [35] were used to calculate the ECI from the CAMEL dataset. We used only the CAMEL pixels that had a "good" emissivity quality flag (value 1) in order to have an adequate overall accuracy.

The ECI is based on the channels at 8.6, 10.8 and 12.1 μm for the CAMEL dataset. According to different studies [34,35], these channels are indeed the most sensitive to bare, green and senescent vegetation. As a consequence, ECI is calculated as:

$$\text{ECl} = 1 - \delta \epsilon \tag{2}$$

where *δ* represents the difference between the maximum and the minimum value of emissivity () among the three CAMEL spectral channels.

For each study area, monthly ECI was successively correlated to the monthly ET by a time series analysis and, successively, by linear regression. *R*<sup>2</sup> and p values were used to assess the strength and significance of the correlations. Due to the different temporal range data availability of ET and ECI, the correlations were tested differently for each study area. For the Renon study area, the time-series range from 2008 to 2013, for Lavarone, from 2008 to 2014, for Monte Bondone, from 2010 to 2013 and, for Bosco della Fontana, only the data from 2013 were available.

Furthermore, snow cover information, derived from the "snow fraction" layer of the CAMEL dataset, was included in the time-series correlation ET–ECI data. This layer provides information of snow cover on the basis of the normalized difference snow index (NDSI) [57], which ranges from 0 (no snow cover) to 100 (full snow cover). It is used to identify possible anomalies in the ET-ECI index correlation, particularly in the mountain sites (Renon, Lavarone and Monte Bondone), where snow remains on the ground for several winter months.

### *2.4. Meteorological Data and WDI Calculation*

Monthly modeled data of surface temperature (Ts*ECMWF*) and dew point temperature (Td*ECMWF*) derived from the ECMWF [58] were used to compute the water deficit index, or WDI. ECMWF data were from the "Operational Analysis", and were released over a regular grid of 0.125◦ × 0.125◦. For each EC site, the closest point of the ECMWF grid was chosen. Surface temperature (Ts*ECMWF*) and dew point temperature (Td*ECMWF*) were, respectively, the skin temperature and the 2 m dew point temperature from surface analyses.

WDI was then computed according to [32]:

$$\text{WDI} = \text{Ts}\_{ECMWF} - \text{Td}\_{ECMWF} \tag{3}$$

For this reason, WDI values depend on surface and dew point temperatures. High WDI values are expected in summer, especially in dry conditions, when the surface temperature becomes significantly higher than the dew temperature near it, whereas lower values are expected in winter.

Because of its definition and calculation, the WDI has a coarser spatial resolution than the ECI. However, the temperature and humidity fields are expected to be more homogeneous than the surface emissivity, which can have space scales of variability of a few meters or less.

As for the correlation ECI-ET, for each study area, the monthly WDI was successively correlated to the monthly ET by a time series analysis and, successively, by linear regression. *R*<sup>2</sup> and p values were used to assess the strength and significance of the correlations. Due to the different temporal range data availability of WDI and ET, the correlations were tested differently for each study area. In the Renon study area ,the correlation range was from 2010 to 2013, for Lavarone, from 2010 to 2014, for Monte Bondone, from 2010 to 2013 and, for Bosco della Fontana, only for 2013.

### *2.5. Assessment of the Environmental Heterogeneity*

In order to assess the effect of the environmental heterogeneity within the ECI pixel (Figure 2), the SVH was assessed through Rao's Q index (Formula (4)) using an NDVI MODIS image (resolution of 500 m) captured on 8 June 2014. The choice of this date is related to the work of Torresani et al. [59], where they stated that the NDVI at this time of the year (summer), when it reaches the highest seasonal values, is more able to capture small variations in reflectance of different vegetation and, thus, of different ecosystems. For this purpose, the R-package function "Rao" of the R package *rasterdiv* [60] was implemented to retrieve a Rao's Q value for the single ECI pixel.

$$Q\_{rs} = \sum\_{i=1}^{F-1} \sum\_{j=i+1}^{F} d\_{ij} \* p\_i \* p\_{j\prime} \tag{4}$$

where:


The relative abundance *p* was calculated as the ratio between the considered pixel (*pi* and *pj*) and the total number of pixels in *F*. The distance matrix *dij* can be built in different dimensions, allowing for the consideration of more than one band or raster at a time. In our case, the *dij* was calculated as a simple Euclidean distance based on the NDVI image.

**Figure 2.** Google earth image with the location of the four eddy covariance towers (yellow points) for each site. In red, the CAMEL pixel used to derive the ECI. Date picture: Lavarone and Monte Bondone 6 December 2017; Renon 19 October 2017; Bosco delle Fontana 18 June 2013.
