**1. Introduction**

Evapotranspiration (ET) is an important component of the forest hydrological budget, and influences the flow of water to downstream users, including aquatic habitats and human populations. Furthermore, it represents a considerable water loss in the landscape [1,2]. As an example, ET has been reported to inject into the atmosphere approximately 70% of annual precipitation in a loblolly pine (*Pinus taeda*) plantation in south-eastern USA [3], more than 85% in a Canadian black spruce (*Picea mariana*) forest [4] and more than 85% in a ponderosa pine (*Pinus ponderosa*) forest in Arizona [5]. Consequently, the magnitude and

**Citation:** Torresani, M.; Masiello, G.; Vendrame, N.; Gerosa, G.; Falocchi, M.; Tomelleri, E.; Serio, C.; Rocchini, D.; Zardi, D. Correlation Analysis of Evapotranspiration, Emissivity Contrast, and Water Deficit Indices: A Case Study in Four Eddy Covariance Sites in Italy with Different Environmental Habitats. *Land* **2022**, *11*, 1903. https://doi.org/ 10.3390/land11111903

Academic Editor: Jin Wu

Received: 5 September 2022 Accepted: 23 October 2022 Published: 26 October 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

seasonality of forest ET are important regulators of water resources available to humans and ecosystems. ET represents a crucial process within a broad range of systems, including ecology, hydrology and meteorology. For this reason, different methodologies have been developed in order to measure it at different spatial scales, ranging from individual plants to entire watersheds [6]. Various techniques have been developed to measure ET [6], including sap flow analysis [7], by weighing lysimeters [8], plant chambers, stable isotope [7,9], soil water budgets [10], land surface models [10] and eddy covariance (EC) [7,11]. More recently, remote sensing data, offering large area coverage, frequent updates and consistent quality, have been used in different studies to collect a quantitative information of ET over different ecosystems world-wide [12,13].

ET cannot be measured directly from remote sensing data. Indirect approaches [14], such as the energy balance approach [15], the Priestley–Talor approach [16,17] and through the use of spectral indices [18], are commonly applied. In general, process-based models that couple remote sensing information and ET have been widely used in science in the last several years, at both local and global scale. The models reproduce physical and plant physiological mechanisms that regulate ET, such as stomata processes, radiation absorption and water interception [14]. Different remote sensing approaches use land surface characteristics such as the leaf area index (LAI) and the albedo to estimate ET via surface energy balance or within-scene scaling [19,20]. Remote sensing thermal infrared measurements have also been largely used for the retrieval of ET information [21,22]. As an example, Hamberg et al.[23] illustrated the potential of thermal information derived from the ECOSTRESS satellite sensor for inferring land surface temperature and ET in different forest sites in Southern Ontario, Canada. Carlson et al. [24], again using the HCMM satellite, introduced a method for inferring different variables, including the distribution of evaporative fluxes and surface heat, in the cities of Los Angeles and St. Louis (USA). We refer to the following articles for an exhaustive overview of the use of infrared thermal radiation for ET retrievals [25–28]. For more general information about ET estimation techniques based on remote sensing data, Zhang et al. [12] provided an exhaustive review.

The thermal infrared (TIR) spectral region is also susceptible to soil moisture, allowing for the retrieval of the atmosphere's thermodynamic state along with the hydrometeorological conditions near the surface. The thermodynamic state close to the surface and the surface itself can be related straightforwardly to surface ET. A recent study by Masiello et al. [29] made use of the remote-sensed emissivity contrast index (ECI) based on TIR emissivity data derived from infrared atmospheric sounding interferometer (IASI) measurements [30,31] and demonstrated that it correlates with the water deficit index, or WDI, defined as the difference between the surface and dew point temperature close to it [32]. In [29], both the ECI and WDI have been obtained with a technique that enables the simultaneous retrieval of spectral emissivity and the vertical distribution of temperature (T), water vapor (Q) and other trace gases [33]. The WDI can be computed using in situ measurements or using modeled information, such as that of the European Centre for Medium Range Weather Forecasts (ECMWF) .

The ECI, firstly introduced by French et al. [34], in Masiello et al. [35] has been computed as the difference between the CAMEL emissivity channels (derived from the CAMEL database CAM5K30EM v002 [36–39]) at 8.6, 10.8 and 12.1 μm. The index was developed with an NDVI synergy to better classify vegetation cover and to overcome the limitations of the vegetation index, particularly in the discrimination of bare soil and senescent vegetation. It showed promising results in the classification of changes in land use when, for example, a vegetation regeneration follows the deforestation or forest degradation events [35]. The CAMEL dataset, where the emissivity information is stored, is produced by the combination of two distinct databases to take advantage of each product's characteristics. The first is the ASTER Global Emissivity (ASTER GEDv4), developed at the Jet Propulsion Laboratory (JPL): it has a temporal resolution of 1 month, a spatial resolution of 5 km and a spectral range from 8 to 12.0 μm. The MODIS baseline-t emissivity (MODBF) represents the second database: it is provided by the University of Wisconsin-Madison

and it has a spectral emissivity range from 3.6–12.0 μm. The resulting dataset is available globally in mean monthly time-steps with a spatial resolution of 5 km, with several layers providing information of emissivity (13 bands ranging from 3.6–14.3 μm), NDVI, snow fraction and related quality flags. The CAMEL dataset has been produced to design a uniform, long-term and calibrated emissivity database in order to advance the analysis of different applications, such as atmospheric retrievals and radiative transfer simulations. Within such a coarse spatial resolution, the environmental heterogeneity could be very high. For this reason, there is need for a sub-pixel heterogeneity assessment. The concept behind the spectral variation hypothesis (SVH) [40] could be used to assess the environmental heterogeneity within each pixel. This concept hypothesizes that the spectral response of a remotely sensed image could be used as a proxy to assess habitat heterogeneity and species diversity. Areas with a high spectral heterogeneity (SH) in a remotely sensed image have a high environmental heterogeneity with a higher number of available ecological niches. This concept was established firstly by Palmer et al. [40] and later developed by other authors [41]. The SVH has been tested in different ecosystems using various remote sensing data through the use of different SH indices. In the last few years, Rao's Q index (developed by Rao [42] for ecological purposes) has been proposed as an original SH measure [43] and has gained popularity due to the positive results obtained in various studies [44,45]. As stated by Rocchini et al. [43], "*given an image of N pixels, the Rao's Q is related to the sum of all the pixel values pairwise distances, each of which is multiplied by the relative abundance of each pair of pixels in the analyzed image".* Hence, Rao's Q index, in comparison to other heterogeneity indices, has the advantages of considering both the values (through the distance/difference between the pixel) and the abundance of the pixels in a considered image [46].

The main aim of this paper is to analyze the relationship between ET, derived from ground-based eddy-covariance (EC) surface measurements at four different sites in Italy, and both the ECI (based on emissivity data from the CAMEL database) and the WDI (based on the difference in the surface and dew-point temperature modeled by ECMWF data). In the first relationship, the effects of the snow cover, the different vegetations and the environmental heterogeneity (calculated through the concept of the SVH using Rao's Q index) were analyzed. The paper is organized as follows. Section 2 deals with data and methods. Results are shown in Section 3 and discussed in Section 4. Conclusions are drawn in Section 5.
