**4. Discussion**

In the summer of 2017, southern Europe and the Euro-Mediterranean were hit by an exceptional heat wave [6,42]. After an outstandingly warm June in western Europe, the heat returned to southern Italy in July. It contributed to more than 400 wildfires, which destroyed approximately 800 km<sup>2</sup> of forest and vegetated areas. The number of fires has been unprecedented in the last 20 years. Furthermore, early August saw a particularly intense heat wave described as the "worst heat wave since 2003", with the air temperature above 40 ◦C in many parts of Italy [42].

In the quest for possible satellite indices to assess and possibly mitigate the effect of long-lasting drought on vegetation, we have devised an index, *wdi*, which takes advantage of the IASI capability to retrieve surface data simultaneously with atmospheric parameters. Other methods that use satellite data exploit the visible region of the electromagnetic spectrum (e.g., NDVI, NDMI, and related indices) or the microwave band (e.g., *ssm* and LAI). The normalized difference moisture index (NDMI) (e.g., [43]) is mainly intended to detect humidity in vegetation using a combination of near-infrared (NIR) and shortwave infrared (SWIR) spectral bands. The index NDMI and the original greenness index, NDVI, with the same *ssm*, have also been used coupled to surface temperature and air temperature (e.g., see [8,11–14,18]). Other tools have tried to couple surface temperature and the humidity field, e.g., [6].

In contrast, our *wdi* exploits the thermal band of the Earth's emission spectrum and simultaneously uses the surface temperature, air temperature, and humidity. To our knowledge, this combination is unique. In effect, the water deficit index we have defined can monitor water deficit and assess vegetation stress, as the comparison with in situ measurements has demonstrated. It can be used complementary to *ssm*, LAI, and the set of NDVI-related indices to better understand the intensity and danger of heatwaves for the vegetation. Sequences of increasing *wdi* can help to identify the onset of water deficit for the vegetation, hence the increased risk of fire, especially in forests.

The *wdi* index is meant to identify regions where particular weather conditions can produce water deficits. The index is not intended as an estimate or an estimator of evapotranspiration. This process is also affected by vegetation/crop characteristics, environmental conditions, and cultivation types. Therefore, there is too much variability, which cannot be condensed into a single index. The *wdi* parameter is a bulk index, which can help to monitor forest and wood regions suffering from long-lasting droughts because of adverse weather conditions. It can be mapped on a regional and even global scale, allowing us to monitor drought processes at a glance. The *wdi* maps could be important to monitor and evaluate the risk of fires in the large forested area, which is otherwise inaccessible. In addition, we have shown that in regions where the vegetal ecosystem has a particular fragility to water deficit, the index can soon quantify the possible danger and require more accurate in situ observations.

In this respect, *wdi* is most effective in the case of a heatwave. In the wintertime, for example, large values of *wdi* could be linked to a dry atmosphere and low air temperature. In effect, this is the case in January 2017 for the more southern area on the map of Figure 5, which belongs to the high mountains of the Sila chain. Additionally, in summer, very humid and warm conditions could lead to *wdi* ∼ 0. For example, this is the case for the coastal regions in July–August 2017, as seen again in the map in Figure 5. For these cases, it is better to look separately at the maps of *Ts* and *Td*. In this respect, we observe that the dew point temperature has been individuated as a key parameter to compute sophisticated indicators of health stress for human beings during heatwaves [44].

Some words of caution should also be said about the temporal sampling of *wdi*. The occasional occurrence of a high *wdi* for one day should be of no concern. Drought is a process that takes several days or months. The severity of the process depends on its time continuity and persistence. Therefore, it is crucial to assess the persistence of the process, which can be done by looking at the time series. Averaging over several days can help to understand the persistence of the phenomenon. Another important point concerns the

capability of the retrieval system to solve the daily cycle, which cannot be done with the present polar satellite IASI instrument. During the night, the surface temperature could go below the dew point temperature and cause water vapour to condense at the surface. Therefore, it could be interesting to examine day and night separately. Hopefully, this could be the case when the MTG-IRS (https://www.eumetsat.int/mtg-infrared-sounder (accessed on 15 August 2022)) is put in orbit.
