*2.1. Material and Data*

The retrieval from space observations of *T*s and *T*d have been performed using the Infrared Atmospheric Sounder Interferometer (or IASI) [21]. IASI has been developed in France by CNES and is flying on board the Metop platforms, which are satellites of the EUMETSAT European Polar System (EPS). IASI has been primarily designed as a meteorological mission; hence, its main objective is to provide relevant information on temperature and water vapour profiles. The spectral coverage of the instrument extends from 645 to 2760 cm<sup>−</sup>1, and its sampling interval is Δσ = 0.25 cm<sup>−</sup>1; therefore, the instrument provides 8461 channels, i.e., spectral observations for every spectrum.

IASI is a cross-track scanner with 30 adjacent fields of regard (FOR) per scan, spanning an angular range of ±48.33◦ on either side of the nadir. The FOR viewing geometry consists of a 2 × 2 matrix of instantaneous fields of views (IFOVs). In turn, the single IFOV has a diameter of 0.8394◦, corresponding to a ground resolution of 12 km per nadir for a satellite altitude of 819 km. The 2 × 2 IFOV matrix is centered on the viewing direction. At nadir, a FOR of 4 IASI IFOVs (or pixels) covers the ground a square area of ≈50 × 50 km2. The corresponding FORs (among the 30 views) are ±1.67◦ on each side from the nadir direction. Further details about IASI and its mission objectives are referred to in [21].

Figure 1 shows the target area we have focused on in the paper. The site corresponds to southern Italy, with the Apennine chains covered by forest, as exemplified by the 2018 CORINE land cover (https://land.copernicus.eu/pan-european/corine-land-cover (accessed on 15 August 2022)). The black dots identify two dieback forest areas, where forest monitoring, by ecophysiological and dendrochronological approaches, has been running since 2013 [24].

The two locations circled in the maps of Figure 1 correspond to the forest stands of San Paolo Albanese (40.02◦ N, 16.34◦ E, 950–1050 m.a.s.l.) and Gorgoglione (40.40◦ N, 16.14◦ E, 800–850 m.a.s.l.), which are suffering from long-lasting drought-induced tree mortality (e.g., [4]). In the San Paolo Albanese site, the vegetation is formed by a pure high forest of *Quercus frainetto Ten.* for a stand density of 348 trees ha−1. As far as the most affected stands are concerned, recent studies observed that more than 50% of the mature specimens showed symptoms of death, while about 15% died recently [25]. On the other hand, the Gorgoglione woodland is a highly mixed forest, with an average density of about 600 stems ha−1. The vegetation is dominated by *Quercus cerris* L. (71%), followed by *Quercus pubescens* L. (25%) and, at a lower density (4%), other species of deciduous trees [25].

The two main studied tree species (i.e., *Quercus cerris* L. and *Quercus pubescens* L.) have shown recent drought-induced decline symptoms since the early 2000s (shoot dieback, summer leaf loss, withering, growth decline, and high mortality). According to local reports about the study area, the yearly oak mortality affected ca. 450 ha. The incidence of the decline syndrome raised mortality from 5 to 10%, from 2002 to 2004 [24].

IASI soundings have been acquired for the whole year of 2017 when an intense heat wave hit Europe and the Mediterranean area in summer (e.g., see [5]). For comparison, we have also acquired IASI data for 2020 and 2021.

For a proper comparison with our IASI *T*s − *T*d index, for the same target area and the year 2017, the Copernicus Global Land Service (https://land.copernicus.eu/global/ products (accessed on 15 August 2022)) was used to obtain data about the surface soil moisture (*ssm*) and the leaf area index (*LAI*).

**Figure 1.** Target region for which IASI data have been selected for the present analysis. The figure also shows the CORINE land cover for 2018 to help identify forest regions, which are primarily of interest for this study. The two upper panels help to determine the target area (magenta square) on the globe and Italy.

The surface soil moisture was derived by observing the band C SAR onboard the satellite Sentinel-1. Data were provided with a timeliness of one day at a spatial resolution of ~1 km. For details about the *ssm* product, we refer the interested reader to [26].

The leaf area index was globally estimated at a spatial resolution of about 300 m through a neural net approach. The input to the net was obtained from instantaneous top-of-canopy reflectances from the OLCI (Ocean and Land Colour Imager) instrument onboard the Sentinel-3 satellite, or daily top-of-aerosol reflectances from the PROBA-V satellite. We refer the interested reader to [27] for further details about the LAI data.

Finally, data about the ecophysiological responses of trees for the forest stands of San Paolo Albanese and Gorgoglione were measured and used in the present analysis during two field campaigns performed from July–September in 2020 and 2021.
