**3. Results**

The rise and fall of the exceptionally hot and dry summer are well captured by the monthly time series of *wdi* maps shown in Figure 6. Of particular interest for us is the Apennine chain, which is covered by broad-leaved, deciduous forests. If we compare Figure 5 to the land cover map shown in Figure 1, we see that the *wdi* closely follows the forested area in the summer season. In July and August 2017, the index was above ~10 ◦C in the regions covered by forests, which shows that the vegetation ecosystem was suffering from a water deficit.

**Figure 6.** Level 3 map at a grid step of 0.05 degrees for the index *wdi* for 2017.

To understand the index's sensitivity to heat waves, we have compared the *wdi* parameter over three consecutive years, 2017, 2020, and 2021, for July. We know that July 2020 has been relatively wetter than 2017 and 2021 (e.g., see https://climate.copernicus. eu/esotc/2021 (accessed on 15 August 2022)). The comparison is shown in Figure 7, and we see that *wdi* is able to indicate that the year 2020 was less warm than the other two. This situation is reflected in the soil moisture maps shown for the same target area and year and month. When we focus on the forested area, especially in the southern part of the map, we see that the soil moisture follows the same spatial-time evolution as *wdi* and, in particular, the soil moisture is lower in 2017 and 2021 than in 2020. This is a significant result because it shows that the *wdi* is capable of capturing processes at the surface–atmosphere interface. A large *wdi* means a high rate of evapotranspiration; that is, trees lose water in the atmosphere. The fact that the soil moisture is getting lower means that the vegetation can catch less water from the surface.

**Figure 7.** Exemplifying the *wdi* evolution through the years. From left to right: July 2017, 2020, and 2021.

The anti-correlation between *wdi* and soil moisture proves that *wdi* is a good metric for monitoring water deficit during intense heatwaves. The more significant values we saw in summer are not merely a consequence of the hotter weather, but also reflects the decrease in water vapour exchange between the surface and the atmosphere. We stress that, unlike other indices, *wdi* considers the surface-air temperature and humidity fields simultaneously.

A further comparison with other parameters sensitive to vegetation stress is shown in Figures 8 and 9. Concerning the 2017 heatwave, Figure 8 compares the surface soil moisture (*ssm*) against *wdi* for the period June to August. It is seen that while *wdi* tends to increase with time, *ssm* does the opposite. The leaf area index (LAI) is another crucial parameter to be monitored for investigating vegetation stress. Indeed, under the action of an intense heat wave, trees tend to lose leaves to protect from the fierce evapotranspiration. Trees use this mechanism, e.g., in winter, when the light is not enough to sustain the photosynthesis activity. The comparison with LAI is shown in Figure 9, and we see that consistently with the increasing *wdi* behaviour, LAI is decreasing from June to July. In normal situations, the LAI. decrease is not expected in the summer when there is a more significant availability of light to sustain photosynthesis.

**Figure 8.** Comparison of *ssm* vs. *wdi* for the period of June to August in 2017. Top to bottom, June to August.

**Figure 9.** Comparison of LAI (m2/m2) vs. *wdi* for the period of June to August in 2017. Top to bottom, June to August.

We have checked that the good consistency among *ssm*, LAI, and *wdi* also persists at the local scale. In fact, for the two stations of S. Paolo Albanese and Gorgoglione, shown in Figure 1, we have computed the monthly time series of *ssm* and *wdi* for 2017. The time series are shown in Figure 10, and we see that starting from May until September, *wdi* goes up, whereas *ssm* has the opposite behaviour. Again, this is an important result because it shows that the *wdi* is capturing a water deficit condition for the vegetation, especially in the area where we know there are declining trees [6,24].

The most striking agreemen<sup>t</sup> is seen when comparing in situ observations for the flux exchange of CO2 and H2O from trees to the *wdi* parameter. In the summers of 2020 and 2021, CO2 exchange measurements were performed at the leaf scale on declining and non-declining *Q. frainetto* trees growing at the S. Paolo Albanese study site. In each tree, net photosynthesis rate (An, μmolCO2 m<sup>−</sup><sup>2</sup> s<sup>−</sup>1), stomatal conductance (gsw, mmolH2O m<sup>−</sup><sup>2</sup> s<sup>−</sup>1), and intrinsic water use efficiency (WUEi, μmolCO2 mmol−<sup>1</sup> H2O) were measured by using a portable Photosynthesis System LiCOR 6400xt equipped with a 6400-40 Leaf Chamber Fluorometer.

**Figure 10.** Monthly time series of *ssm* and *wdi* in 2017 for the two-tower stations of Gorgoglione (**left**) and S. Paolo Albanese (**right**). Data points are the mean values from a circle of diameter 0.1◦ around the stations. The error bars represent the variability (standard deviation) of the samples.

In the summers of 2020 and 2021, the ecophysiological response of *Q. frainetto* trees exhibiting decline and non-decline symptoms is shown in Figure 11. In 2020, when no heatwave occurred, *Q. frainetto* ecophysiological responses were similar for declining and non-declining trees, suggesting that there was no evident sign of water stress in the summer of 2020. From Figure 7, we see that *wdi* is in fact below 10 ◦C in July. In contrast, in 2021, not only is the water vapour exchange more than doubled, showing that the evapotranspiration has increased because of the larger difference *Ts* − *Td*, but also the declining trees behave differently with respect to the non-declining vegetation, showing that the non-declining trees are suffering from the water deficit much more than the healthy vegetation.

**Figure 11.** Ecophysiological responses of declining (D) and non-declining (ND) *Q. frainetto* trees of the San Paolo Albanese forest stand site. Panels (**<sup>a</sup>**–**d**) present the net photosynthesis curve (An, μmolCO2 m<sup>−</sup><sup>2</sup> s<sup>−</sup>1), while panels (**<sup>e</sup>**,**f**) show the average values of stomatal conductance (gsw, mmolH2O m<sup>−</sup><sup>2</sup> s<sup>−</sup>1) and intrinsic water use efficiency (WUEi, μmolCO2 mmol−<sup>1</sup> H2O) measured in the summers of 2020 and 2021. PPFD represents the photosynthetic photon flux density (μmol photons m<sup>−</sup><sup>2</sup> s<sup>−</sup>1). The black vertical bar represents the 1st deviation standard.

It is also interesting to note that CO2, flux exchange exhibited the opposite behaviour to H2O. In the summer of 2020, when there were good climatic conditions, we observed an exchange larger than in 2021. In 2021, the results showed that the vegetation had reduced photosynthesis activity because of stress conditions.
