# Combining Landsat optical/thermal and LiDAR High Definition data to estimate turbulent fluxes over Mediterranean forests

Victor Penot, Olivier Merlin

► To cite this version:

Victor Penot, Olivier Merlin. Combining Landsat optical/thermal and LiDAR High Definition data to estimate turbulent fluxes over Mediterranean forests. Science of Remote Sensing, 2025, 12, pp.100323. 10.1016/j.srs.2025.100323. hal-05385233

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Full length article

# Combining Landsat optical/thermal and LiDAR High Definition data to estimate turbulent fluxes over Mediterranean forests

Victor Penot ID *, Olivier Merlin ID

Université de Toulouse, CNES/CNRS/IRD/INRAe, CESBio, 18 avenue Edouard Belin, Toulouse, 31401, France

## ARTICLE INFO

**Keywords:**

Turbulent fluxes

Thermal remote sensing

Mediterranean forest

LiDAR

Contextual methods

## ABSTRACT

The performance of thermal-based models for estimating sensible (H) and latent (LE) heat fluxes over semi-arid forests is still not well documented, largely due to the difficulty of accounting for canopy height (hc) effects on satellite land surface temperature (LST). This study addresses this limitation by integrating LiDAR-derived hc into the classical contextual method, which combines Landsat-derived LST and green vegetation fraction. Landsat LST is first normalized to remove the influence of hc, and the resulting normalized LST is then used to estimate H and LE using the classical contextual approach. The method is applied over a nine-year period in two Mediterranean forest sites with eddy covariance stations - Puechabon and Fontblanche. The threshold canopy height (hcmax), above which LST becomes insensitive to turbulent fluxes, is estimated as hcmax = 42 +/- 4 m for Puechabon and hcmax = 35 +/- 3 m for Fontblanche. For both sites, the normalization of LST for hc effect significantly improves the correlation between remotely sensed and in situ H (LE) measurements from 0.40 (0.06) to 0.72 (0.43), respectively. Moreover, by setting the dry edge by a simple soil energy balance model, the bias between remotely sensed and in situ H (LE) measurements is much reduced from -163 (+132) W.m⁻² to -56 (+25) W.m⁻², and the slope of the linear regression much closer to 1 from 0.28 (0.07) to 0.84 (0.60), respectively. This is the first study to incorporate LiDAR-derived hc into contextual methods, significantly improving thermal-based estimates of turbulent fluxes in forested semi-arid environments.

## 1. Introduction

Around the world, forests are threatened by climate change, which is imposing rapid changes and more intense meteorological forcing (Dyderski et al., 2018; Hartmann et al., 2022). Forests in the Mediterranean region suffer from increasing drought and prolonged heat waves, although they are accustomed to long periods of high temperature and low rainfall (Ameztegui et al., 2024; Peñuelas et al., 2017; Alderotti et al., 2024). Therefore, monitoring the health of these forests over large areas is of paramount importance to forest managers and public policy-makers.

Among the key results of forest health assessment, those related to water fluxes are highly relevant, as they can be used as an early warning of possible dieback (Castellaneta et al., 2022; Colangelo et al., 2017). Plants can dissipate the received solar energy by transpiration, quantified by the latent heat flux (LE [W m⁻²]), or by heat convection through their canopies, quantified by the sensible heat flux (H [W m⁻²]) (Jones and Rotenberg, 2011). LE and H are related to each other by the surface energy balance, since their sum approximately equals the net available energy on forests (Jones and Rotenberg, 2011). Satellite remote sensing offers a good trade-off between large spatial

coverage, high spatial resolution and high revisit frequency, and therefore appears suitable for monitoring forest health. In particular, the optical/thermal spectrum provides complementary information on land use/land cover and can be used to estimate turbulent fluxes, namely LE and H (Moran et al., 1994; Boulet et al., 2015; Trebs et al., 2021).

Two distinct approaches have been used to estimate turbulent heat fluxes from land surface temperature (LST) data, namely the energy balance (EB) models and the semi-empirical contextual methods. For three decades, these two approaches have been applied intensively and extensively to relatively low (height of 1–2 m max.) vegetation cover (Chirouze et al., 2014; Delogu et al., 2018; Hu et al., 2023), but much more rarely to forest cover (Trebs et al., 2021; Vidal and Devaux-Ros, 1995).

EB models derive H as the solution of a system of physical equations whose inputs are meteorological and LST data (Boulet et al., 2015; Su, 2002) and estimate LE as the residual term of the EB. The vast majority of EB models operate at the pixel level and use the Monin–Obukhov similarity theory to express key parameters describing the influence of surface geometry on turbulent fluxes (via aerodynamic resistance), namely zero-plane displacement height and roughness heights for heat

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: victor.penot@laposte.net (V. Penot).</footnote>
and momentum (Boulet et al., 2015; Su, 2002; Trebs et al., 2021). In this physical approach, zero-plane displacement and roughness heights particularly influence aerodynamic resistance through their interaction with wind speed and are explicitly expressed as functions of several canopy parameters including canopy height (*hc*), leaf area index (LAI) and frontal area index (Trebs et al., 2021; Tian et al., 2011; Shaw and Pereira, 1982; Maurer et al., 2015; González-Dugo et al., 2021). Thus, EB modeling requires intensive parameterization at the pixel level (Delogu et al., 2018; Chirouze et al., 2014) to account for forest structure and then to retrieve turbulent fluxes from LST. This calibration problem is all the more pronounced in the case of Mediterranean forests within dry ecosystems, comprising sparse and dense tree cover of varying heights as well as shrubs, which present a high degree of structural heterogeneity (Bottalico et al., 2017).

Regardless of the ecosystem (crop, forest, etc.), EB models tend to overestimate *LE* and underestimate *H* in arid and semi-arid regions (Gokool et al., 2020; Gokmen et al., 2012; Morillas et al., 2013; van der Kwast et al., 2009; Hu et al., 2023; Burchard-Levine et al., 2022). van der Kwast et al. (2009) conducted a sensitivity analysis to identify which variables most influence the *H* derived from the Surface Energy Balance System (SEBS) model. Their results showed that roughness parameters (specifically, zero displacement height and roughness height for momentum, both dependent on *hc*) can cause significant deviations in the modeling of *H*. To address this, Gokmen et al. (2012), Pardo et al. (2014) and Chen et al. (2013) modified the expressions of roughness parameters, incorporating variables such as soil moisture and optical vegetation index, to improve SEBS estimates of *H* and *LE*. More recently, Hu et al. (2023) compared three EB models: Surface Temperature Initiated Closure (STIC), SEBS, and Two-Source Surface Energy Balance (TSEB). They found that the STIC model, which does not rely on a priori expressions of roughness parameters, demonstrated relatively robust performance. They emphasized that no universal methodology currently exists for estimating roughness parameter expressions that can adequately represent water-limited conditions.

More specifically, under water-limited and forested conditions, Trebs et al. (2021) evaluated *H* and *LE* using three different EB models: Soil Plant Atmosphere and Remote Sensing Evapotranspiration (SPARSE), SEBS, and STIC. All models were driven by LST data from the Moderate-Resolution Imaging Spectroradiometer (MODIS) satellites, combined with in situ meteorological and radiation measurements. Their study encompassed nine Australian forest and shrubland sites, spanning a gradient of *hc* (ranging from 3.0 m to 40.0 m) and diverse ecoregions, including Mediterranean (semi-arid) woodlands. Similarly, Bartkowiak et al. (2024) and Njuki et al. (2023) applied the TSEB model with Sentinel-3 LST data and the SEBS model using in situ data only, respectively, across multiple sites (forested and non-forested, water-limited and non-water-limited, Mediterranean and non-Mediterranean). Across these studies, different mathematical formulations of the roughness parameters were employed.

Across these three studies (Trebs et al., 2021; Bartkowiak et al., 2024; Njuki et al., 2023), a consistent pattern has emerged: *H* tends to be underestimated, while *LE* is correspondingly overestimated at forested sites under water-limited conditions. Trebs et al. (2021) showed that arid and semi-arid environments exhibit a pronounced underestimation of *H*, resulting in an average overestimation of *LE* by up to 50%. These biases were not observed at wetter, energy-limited (mesic) sites. Similarly, Bartkowiak et al. (2024) reported a negative correlation (*R* = -0.18) and a positive bias between satellite-derived and in situ *LE* measurements at the French Mediterranean site of Puechabon. In parallel, Njuki et al. (2023) documented an underestimation of *H* at forested sites (including Puechabon) reaching up to 50% at midday during the April–October period.

One suggested explanation for these apparently systematic errors is that, under high hydric stress, forests exhibit high efficiency in transferring heat fluxes from the surface to the atmosphere (Njuki et al.,

2023; Banerjee et al., 2017), while current aerodynamic resistance and surface roughness parameterizations fail to adequately capture this behavior. As a result, the applicability of existing EB models for retrieving turbulent heat fluxes is limited in forested areas experiencing water-limited conditions.

Contextual methods use the semi-empirical spatial relationship between LST and a satellite-derived vegetation index to derive the evaporative fraction (EF) (Moran et al., 1994; Jiang and Islam, 1999; Wang et al., 2006). The fractional green vegetation cover ($f_{gv}$) is often used as a vegetation index (Merlin, 2013; Chirouze et al., 2014) in the so-called LST-$f_{gv}$ feature space to weight the EF (LST) relationship from bare soil to full-cover conditions (Chirouze et al., 2014).

This approach requires the estimation of boundary i.e. dry (LE ≈ 0) and wet (H ≈ 0) conditions from bare soil ($f_{gv}$ = 0) to full vegetation cover ($f_{gv}$ = 1). In practice, assuming that the wet and dry boundary conditions evolve almost linearly between $f_{gv}$ = 0 and $f_{gv}$ = 1 (Moran et al., 1994), this problem is reduced to find four temperature endmembers that define the dry and wet edges of the LST-$f_{gv}$ space. These dry and wet temperature endmembers are either estimated statistically from the observed surface conditions within a sufficiently wide study area (Merlin, 2013; Tang et al., 2010) or simulated by an EB model (Moran et al., 1994; Sun et al., 2017; Long et al., 2012; Long and Singh, 2012; Stefan et al., 2015). In both cases, meteorological data are assumed to be uniform within the study area. In addition, the statistical approach for estimating temperature endmembers assumes that dry and wet extreme conditions are present and observed at the sensor resolution (Stisen et al., 2008; Merlin, 2013).

Contextual methods have been shown to be effective on crops (Tang et al., 2010; Merlin, 2013; Chirouze et al., 2014) and their simplicity makes them promising for operational use over extended areas (Gallego-Elvira et al., 2013). However, classical contextual methods do not consider the impact of surface roughness on LST. Especially, the variability of *hc* within the study area is neglected, or it is assumed to be strongly correlated with the vegetation index used to form the feature space with LST observations. The point is that, over natural landscapes such as Mediterranean forests, it is very likely that the same $f_{gv}$ values correspond to very different canopy structures (different roughness and *hc* values). Current contextual methods should therefore fail in landscapes with heterogeneous canopy structure and *hc* (Penot and Merlin, 2023; Adeline et al., 2024).

At the same time, the increasing availability and spatial coverage of high-resolution (HD) Light Detection And Ranging (LiDAR) data allows the determination of canopy structure metrics, especially the simplest one, *hc*, at common satellite spatial resolution (IGN, 2024; Potapov et al., 2021; Schwartz et al., 2024). LiDAR data are not suitable to monitor the *hc* of crops because they are not updated frequently enough, but they are deemed suitable to estimate the *hc* of forests on relatively short time scales (<10 years). New high-resolution LiDAR monitoring capabilities pave the way for integrating these data into evapotranspiration and EB models.

Currently, few studies have utilized LiDAR-derived canopy metrics for estimating turbulent fluxes from EB models. Khan et al. (2021) incorporated *hc* data from the Ice, Cloud, and land Elevation Satellite/Geoscience Laser Altimeter System (GLAS) into the SEBS model to estimate *LE* using LST data from the Landsat missions. They focused on three wet forest sites in East and Southeast Asia, with in situ *hc* values of 8, 13, and 15 m, and the GLAS-derived *hc* values of 10, 16, and 18 m. The findings highlighted that *hc* is a crucial parameter that can introduce uncertainties in SEBS model estimations. Additionally, using LiDAR-derived *hc* data improved the estimation of *H*, reducing the root mean square error (RMSE) by up to 46% (though with a mean bias of -69 W m⁻²), and enhanced the correlation coefficient for *LE* by up to 9%. Ma et al. (2022) used the GLAS LiDAR-derived *hc* as an input parameter to the SEBS model in southwest China, but they did not compare their results with SEBS estimates without LiDAR-derived *hc* information. Aboutalebi et al. (2020) utilized drone-derived metrics
at very high spatial resolution to evaluate the sensitivity of the TSEB model. They compared the use of mean/nominal values in footprints against the spatial distribution of fractional canopy cover, *hc* ranging from 0 to 1.5 m, and canopy width information within a 3.6-m grid. Their study was conducted over two vineyards (two flux towers) and involved four flights in California. The results demonstrated that incorporating spatially-distributed canopy structure parameters significantly improved the agreement between TSEB model outputs for *H* and *LE* with tower measurements, reducing the *RMSE* by 58% for *H* and 46% for *LE*. Similarly, Neale et al. (2011) used very high (1-m) resolution LiDAR-derived *hc* data as input in two EB models (TSEB and Surface Energy Balance Algorithm for Land (SEBAL)) to study water use among riparian species.

The preceding literature review reveals a critical gap in current research: while existing studies using LiDAR data have largely focused on the accuracy of *hc* as a model input (Khan et al., 2021; Ma et al., 2022; Neale et al., 2011; Aboutalebi et al., 2020), they have not adequately addressed the persistent challenge of parameterizing surface roughness, specifically zero displacement height and roughness length for momentum in EB models. This issue is compounded by the complexity and non-uniqueness of these parameter expressions (Hu et al., 2023; Gokmen et al., 2012; Pardo et al., 2014; Chen et al., 2013), particularly in dry or semi-arid environments such as Mediterranean forests, where EB models currently fail (Trebs et al., 2021; Bartkowiak et al., 2024). Our study seeks to answer two key scientific questions:

1. How can LiDAR-derived *hc* be leveraged to represent the effect of forest roughness without relying on non-unique roughness parameter expressions in EB models?

2. How can contextual methods be effectively applied to forested landscapes?

To address these questions, we propose a novel approach that utilizes *hc* as a proxy for surface roughness effect on *LST*, thereby circumventing the need for a priori surface roughness parameterization for forest. Specifically, we normalize Landsat-derived *LST* using *hc*, isolating its influence prior to integrating *LST* into the classical feature space of a contextual method.

Specifically, this paper aims to (i) quantitatively assess the effect of *hc* on *LST* over extended areas, (ii) develop a normalization method of Landsat *LST* for *hc* effect, and (iii) evaluate the Landsat-derived *H* and *LE* estimates obtained from the new (*LST*<sub>norm</sub>-*f*<sub>gv</sub>) and the classical (*LST*-*f*<sub>gv</sub>) contextual method. To achieve these objectives, the study focuses on two Mediterranean sites, differing in their vegetation structure, in southern France, where in situ flux measurements are available for a nine-year period. Section 2 describes the study areas, the in situ and remote sensing data used and presents the methodology to normalize *LST* for *hc* effect. Section 3 presents and discusses the results obtained by the normalization of *LST* and by the different methods in terms of *H* and *LE* estimates. Finally, Section 4 summarizes the main findings and paves the way for future research.

## 2. Materials and methods

In this Section, the study area and the eddy-covariance (EC) sites (Section 2.1) and the remotely sensed and meteorological data used (Section 2.2) are first presented. Then, the principle and basic assumptions of the classical contextual method to estimate *EF* are briefly reminded (Section 2.3). Next, the new contextual method is described (Section 2.4), by relying on the normalization of *LST* for *hc* effect. Section 2.5 presents the estimation of turbulent fluxes from *EF* estimates of both (classical and new) approaches. Finally, a method for analyzing the sensitivity of the new approach to its input data is proposed (Section 2.5).

### 2.1. Study areas

#### 2.1.1. Eddy covariance sites

The Puechabon site (43°44′29″N; 3°35′46″E, 270 m above sea level (a.s.l.), see Fig. 1) is an evergreen broadleaf forest characterized by dense coppice. The dominant tree species is the holm oak (*Quercus ilex*), with an average height of 5.5 m, while the understory consists of sparse shrubs about 2 m high (Ollivier et al., 2021). The site experiences a mean annual temperature of 14.7 °C and an average annual precipitation of 895 mm, with significant intra-annual variations. Summers are typically dry and hot, whereas heavy rainfall occurs mainly in the fall and spring. For illustration, Fig. 2(a) shows the monthly cumulative rainfall and the monthly mean air temperature from 2013 to 2022. The soil at Puechabon is silty clay loam, with a rock and stone volumetric content of 75% in the top 50 cm and 90% throughout the entire profile (Rambal et al., 2003). Despite the soil's poor water retention (Ollivier et al., 2021), it has been demonstrated that *Quercus ilex* can extract water from depths greater than 4 m during drought conditions (Allard et al., 2008; Rambal et al., 2003).

The Fontblanche site is located in a mixed Mediterranean forest in south-eastern France (43°14′27″N, 5°40′45″E; 425 m a.s.l.). The two dominant tree species are Aleppo pine (*Pinus halepensis*) in the upper tree stratum, 13-m high, and holm oak (*Quercus ilex*) in the intermediate stratum, 5-m high (Ollivier et al., 2021). Both species show different functional strategies to cope with drought (Moreno et al., 2024; Vicente et al., 2018) that can be related to *LST*. On the one hand, Aleppo pine is said to be drought avoidant as it closes its stomata at a relatively high water potential, corresponding to the water potential inducing full stomatal closure. On the other hand, holm oak is said drought tolerant as it delays stomatal regulation. The mean annual temperature is 14.3 °C and the mean annual precipitation is 676 mm with strong intra annual variations (see 2 (b)). The soil, a silty claim loam, has a maximum depth of around 50 cm, and a volumetric rock fraction of about 50% at the top, and up to 90% at the bottom (Ollivier et al., 2021) while the bedrock is karstified limestone.

Both sites have been active in monitoring Mediterranean forests in the context of climate change. The Puechabon site has gained a lot of scientific interest during the previous years, regarding the monitoring and modeling of turbulent fluxes. An increasing number of studies have been undertaken at the Puechabon EC site using 1 km resolution MODIS/Sentinel-3 thermal data (Jiang and Ryu, 2016; Hu et al., 2015; Ryu et al., 2012; Bartkowiak et al., 2024), using 100 m resolution Landsat thermal data (Penot and Merlin, 2023), or to evaluate different models of turbulent fluxes (STIC, Community Land Model (CLM) 5.0, SEBS) (Mallick et al., 2024; Njuki et al., 2023). The Fontblanche site has been more confidential in terms of modeling and monitoring turbulent fluxes, since there is no published study on the use of remotely sensed thermal data. It is however a dynamic site in terms of water balance/flux modeling (Ollivier et al., 2021; Simioni et al., 2016) and studies of mixed canopy in the context of climate change (Simioni et al., 2013, 2016, 2020).

#### 2.1.2. In situ measurements

Both sites are equipped with an EC flux measurement system that continuously monitors meteorological data (relative humidity (*RH* [–]), air temperature (*Tair* [K]), wind speed (*WS* [m s⁻¹]), solar radiation (*Rg* [W m⁻²])) and surface energy fluxes (*LE*, *H* and net radiation (*Rn* [W m⁻²])) at height 12 m and 17 m (for Puechabon and Fontblanche respectively) every 30 min. Flux and meteorological data from 2014 to August 2022 (Puechabon) and from 2013 to 2021 (Fontblanche) were downloaded from the European Fluxes Database Cluster and Integrated Carbon Observation System database.

The instantaneous Bowen ratio (*β*<sub>insitu</sub>) [–] is defined as the ratio between *H* and *LE* instantaneous in situ measurements, at the satellite
<figure><img src="image_3.png" /><figcaption>Fig. 1. Map of the location of the two EC sites.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Fig. 2. Monthly cumulative rain, monthly mean temperature and Landsat satellite mission (7/8/9) overpass dates during the study periods at Puechabon (a) and Fontblanche (b) site.</figcaption></figure>

overpass time (Crago and Brutsaert, 1996). The instantaneous in situ EF [−] is expressed from the βᵢₘₐₜ as (Crago and Brutsaert, 1996):

$$EF_{insitu} = \frac{1}{1 + \beta_{insitu}} \qquad (1)$$

To check the quality of EFᵢₘₐₜ, we calculate the daily Bowen ratio βdᵢₘₐₜ, a value that is assumed constant during daytime. βdᵢₘₐₜ is the ratio of the sum of in situ H from 8 a.m. to 3 p.m. by the sum of in situ LE from 8 a.m. to 3 p.m. Jiang et al. (2009). The daytime in situ EF (EFdᵢₘₐₜ) is estimated by means of βdᵢₘₐₜ (1). EFᵢₘₐₜ evaluated against EFdᵢₘₐₜ shows a good quality: the correlation is 0.97/0.93 and the slope is 0.99/1 for the Puechabon/Fontblanche EC site, respectively. Hence the instantaneous EFᵢₘₐₜ is kept as a reference value. In situ flux observations are corrected using the Bowen ratio method for closing the EB as in Trebs et al. (2021):

$$H_{insitu} = \frac{\beta_{insitu} Rn_{insitu}}{1 + \beta_{insitu}} \qquad (2)$$

$$LE_{insitu} = \frac{Rn_{insitu}}{1 + \beta_{insitu}} \qquad (3)$$

With Rnᵢₘₐₜ [W m⁻²] the net radiation measured at the flux tower.

### 2.1.3. Study areas

For both sites, a study area is selected so that meteorological conditions around the EC tower can be considered to be relatively homogeneous, including topographical conditions that are unlikely to affect Tair (adiabatic gradient) significantly. It must also offer the widest possible range of land cover characteristics, from bare soil to a fully vegetated surface.

Fig. 3 presents the two selected study areas surrounding the Puechabon ((a) and (b)) and Fontblanche ((c) and (d)) EC sites. Background images in Fig. 3 correspond to Spot 6–7 visible images acquired in 2023 and the natural land cover map provided by the French National Geographic Institute (IGN) (BD Topo - 2016). The Puechabon and Fontblanche areas are 6400 ha and 5164 ha, respectively. The Puechabon study area is covered with closed broad leaf forest (Holm oak), as next to the EC site. The remaining of the area is covered with open forest and vineyard. The great majority of the surface of the Fontblanche
<figure><img src="image_5.png" /><figcaption>Fig. 3. Extent of the study areas with background 2023 Spot images (left) and 2016 IGN land cover map (right) for Puechabon (top) and Fontblanche (bottom).</figcaption></figure>

study area is covered with closed coniferous forest (Aleppo pines), as encountered next to the EC site, which generally has a greater average height than closed Mediterranean broadleaf forest and shrublands. For both sites, the white area (in the land cover map) is covered with roads, urban areas, or quarries. The mean elevation (and its standard deviation) within the selected area is 192 m (87 m), and 322 m (99 m) for Puechabon and Fontblanche respectively.

### 2.1.4. Spatialized meteorological data

Two meteorological datasets are used in this study. The meteorological measurements at the EC station are interpolated at the satellite overpass hour. As a first approximation, they are assumed to be representative of the meteorological conditions within the whole study area. As an alternative to station-based measurements, the SAFRAN reanalysis dataset is also used for RH, Tair, and WS. The SAFRAN reanalysis dataset (Vidal et al., 2010) provides hourly meteorological data on an 8-km grid. Tair, WS (at 10 m height) and RH are linearly interpolated and averaged over the whole study area at the satellite overpass hour. The Rg is provided by EC-site measurements only. The two (in situ and SAFRAN) meteorological data sets for Tair, WS and RH are used to assess the impact of the uncertainty in the reanalysis data on the estimates of turbulent fluxes in the two study areas.

## 2.2. Satellite and airborne data set

### 2.2.1. Optical/thermal data

Landsat-7 Enhanced Thematic Mapper and Landsat-8/9 Operational Land Imager and Thermal Infrared Sensor provide reflectance and LST data with a 16-day revisit period, with an 8-day shift between Landsat-7/9 and Landsat-8. Landsat data for Path/Row 197/030 (Puechabon), 196/030 and 195/030 (Fontblanche) were downloaded from USGS Earth Explorer platform/Landsat Collection 2 Level-2 Science Products from 2014 to 2022 (Puechabon) and from 2013 to 2021 (Fontblanche).

Shortwave optical data are provided as bottom of atmosphere reflectances at their native resolution of 30 m. Landsat-7 data were processed with the Landsat Ecosystem Disturbance Adaptive Processing System (LEDAPS) algorithm (Version 3.4.0) (Schmidt et al., 2013) and Landsat-8/9 data with the Land Surface Reflectance Code (LaSRC) algorithm (Version 1.5.0) (Vermote et al., 2016).

$f_{gv}$ is estimated using the expression of Carlson and Ripley (1997):

$$f_{gv} = \left( \frac{NDVI - NDVI_{min}}{NDVI_{max} - NDVI_{min}} \right)^2 \qquad (4)$$

with NDVI being the Normalized Difference Vegetation Index defined as the difference of near-infrared (NIR) and red (Red) reflectances divided by their sum. $NDVI_{min}$ (bare soil) and $NDVI_{max}$ (full green cover) are set to 0.19 (0.24) and 0.86 (0.83) for Puechabon (Fontblanche), respectively. Endmembers correspond to the quantile 0.01 and 0.97 of NDVI values within the study area and during the study period, as in Penot and Merlin (2023).

Landsat-7 and Landsat-8/9 LST data sets are processed with the Landsat surface temperature algorithm to produce LST maps from raw thermal radiances (Cook, 2014; Cook et al., 2014). They are provided over the same 30-m resolution grid of Landsat reflectances. Since the actual spatial resolution of Landsat LST is close to 100 m, all Landsat-derived variables (LST, NIR and Red before $f_{gv}$ calculation) are aggregated to 90 m resolution using a 3 × 3 pixel moving window (90 × 90 m).

### 2.2.2. Airborne LiDAR data

A high-resolution airborne laser scanning (ALS) campaign led by the IGN started in 2021 and will end in 2025. Data acquisition flights over the two study areas took place in June 2021. LiDAR point clouds, which are publicly available, were downloaded from the IGN platform (IGN, 2024). The point clouds are provided already classified by IGN, and classes corresponding to ground and vegetation are used. For pre-processing LiDAR data, we followed the steps provided by Martin-Ducup et al. (2025) who used the same data set to derive $hc$: (1) point clouds filtering to keep ground and vegetation points and a statistical outlier removal filter (filter parameters were k = 5 and m = 10) and (2) height normalization using a spatial interpolation algorithm (with k and m parameters of 5 and 10 respectively) based on Delaunay triangulation over points classified as ground category. Finally, we rasterized the quantile 0.90 of the normalized $hc$ to remove outliers at the Landsat spatial resolution of 90 m. All the above steps were computed with the R package lidr (Roussel et al., 2020).

Fig. 4 shows the ALS-derived $hc$ maps over the study areas including the EC sites. In addition, the density plot for $hc$ is also provided for both
<figure><img src="image_6.png" /><figcaption>Fig. 4. *hc* maps (left) and *hc* density histogram (right) over Puechabon (top, a–b) and Fontblanche (bottom, c–d) study area.</figcaption></figure>

sites. The LIDAR-derived *hc* at the EC-site-centered pixel (90 m resolution) is 5.0 m and 12 m for Puechabon and Fontblanche, respectively. These values are near the dominant tree values of the EC sites (5.5 m and 13 m for Puechabon and Fontblanche respectively (Ollivier et al., 2021)). The slight underestimation could be due to the fact that we use the 0.90 quantile of the normalized *hc* in the point clouds, but also to the subpixel variability of *hc* at the 90-m scale.

Both study areas show very different spatial patterns of *hc*. The great majority of *hc* values is near 5.0 m in the Puechabon study area and very few pixels have *hc* values larger than 10 m (see Fig. 4(b)). This is consistent with a land cover of olm oaks that commonly reach a height of 5 m. The highest *hc* values are encountered along the Herault river where riparian trees are present (see Fig. 4(a)). On the contrary, the *hc* values in the Fontblanche study area are more heterogeneous, with the vast majority of *hc* values ranging from 2 to 15 m (see Fig. 4(d)). This is also consistent with the different tree species that grow in this area (Olm oaks and Alepo pines), which may be mixed.

### 2.2.3. Date selection

The methodology used in Penot and Merlin (2023) to select the Landsat overpass dates is followed. First, we select the hottest period of the year, that is from April to October from 2014 to August 2022 (Puechabon) and from 2013 to 2021 (Fontblanche) so that LST is in moisture-driven conditions at the surface rather than in energy-driven conditions (Karnieli et al., 2010; Chirouze et al., 2014). Next, a threshold of 75% of clear pixels (according to the quality assessment flag of Landsat-7/8/9) within the study area is chosen to filter out cloudy conditions and get representative conditions within the study area. Finally, for each date when the minimum value of LST (within the study area for the pixels qualified as clear by the Landsat-7/8/9 quality flag) is significantly lower than air temperature (a threshold is set to the measured air temperature minus 5 K), the image is considered as contaminated by clouds and is hence removed from the dataset (Zhang et al., 2014).

In addition, after 2017 Landsat-7 has an earlier overpass time than before 2017. Although, changes in reflectance and thermal data had been limited until 2020 (Qiu et al., 2021), we chose to keep only Landsat-7 acquisitions after 10:00 a.m. and before 2020 (2020 included) in the data set, for consistency between Landsat-7 and Landsat-8/9 data.

## 2.3. LST-f<sub>gv</sub> contextual method to estimate EF

### 2.3.1. Estimating EF

The classical contextual method based on the LST-f<sub>gv</sub> feature space is used (Moran et al., 1994; Jiang and Islam, 1999; Venturini et al., 2004; Carlson, 2020; Tang et al., 2010). Fig. 5(a) plots the LST-f<sub>gv</sub> feature space on the 25th, October 2018 over the Fontblanche study area. The LST-f<sub>gv</sub> space is bounded by a linear upper edge, called "dry edge", and a linear lower edge, called "wet edge". These linear boundaries define the extreme moisture values, from EF = 0 for a point on the dry edge, to EF = 1 for a point on the wet edge. Particularly, the endmembers of the dry edge are called Tsd (f<sub>gv</sub> = 0) and Tvd (f<sub>gv</sub> = 1) for dry soil and dry vegetation temperature, respectively.

For an observed point C in the LST-f<sub>gv</sub> space, EF is estimated as the ratio of the distance between the point C and the point A of same f<sub>gv</sub> on the dry edge, and the distance between the point A and the point B of same f<sub>gv</sub> on the wet edge (Moran et al., 1994; Merlin, 2013; Penot and Merlin, 2023). Thus, this method allows to take into account the impact of vegetation cover on LST-derived EF. This value of EF, derived from the classical method ("LST - f<sub>gv</sub>(context)" ) is used as a benchmark in this study.

One of the challenges using this method, is to estimate the dry and wet edges (Sun et al., 2017; Tang et al., 2010; Stisen et al., 2008; Long et al., 2012; Long and Singh, 2012) over areas and on dates when such extreme conditions are not met at the spatial resolution of the satellite sensor.

### 2.3.2. Estimating the wet edge in the Mediterranean context

As wet conditions are rare in the Mediterranean context between April and October, low LST values are generally misleading if interpreted as representative of wet conditions. Therefore, in this study the wet edge is set to the *Tair* (see Fig. 5(a)) at the Landsat overpass time (around 10:30 am), by assuming that LST in wet conditions is close to *Tair*. Such an assumption has been made by many other studies conducted in (semi-arid) environments (Merlin, 2013; Zhang et al., 2014; Amazirh et al., 2018; Long and Singh, 2012; Long et al., 2012; Sun et al., 2017), including the Puechabon area (Penot and Merlin, 2023).
<figure><img src="image_7.png" /><figcaption>Fig. 5. Feature spaces for data collected over the Fontblanche study area on the 25th, October 2018: (a) classical LST-f<sub>gv</sub> space, (b) new LST<sub>norm</sub>-f<sub>gv</sub> space. For each space the contextual dry edge is plotted in red and the wet edge in blue.</figcaption></figure>

### 2.3.3. Estimating the dry edge

Since the Mediterranean region has generally dry conditions during late spring, summer and early autumn, we assume, as a first guess, that dry conditions are present at Landsat resolution within the study areas. Therefore, the same statistical technique is used to estimate the dry edge for each study area independently, and for each satellite acquisition date separately. The dry edge is defined as the linear regression of the 99% quantiles of LST, computed within equal-sized bins of f<sub>gv</sub>, plotted against f<sub>gv</sub> as in Virlet et al. (2014) and Penot and Merlin (2023) (see Fig. 5(a)).

## 2.4. New contextual method by integrating hc

In this Section the interpretation of the new LST-hc feature space is first presented (Section 2.4.1), then the estimation of the decreasing rate of LST with hc is described (Section 2.4.2) and LST is normalized for hc effects (Section 2.4.3). Finally, EF is estimated from the new LST<sub>norm</sub>-f<sub>gv</sub> space (Section 2.4.4).

### 2.4.1. Interpreting the new LST-hc feature space

Fig. 6 shows LST plotted against hc- referred to as the LST-hc space – for the Fontblanche site on 26th April 2019. In this space, the point cloud is bounded at the top by a clearly visible, linearly decreasing upper edge (in red). This edge illustrates the decrease of LST with increasing hc, known as the “hc effect”. The slope of this edge quantifies the rate at which LST decreases with hc. Along this upper boundary, the evaporative fraction (EF) is close to 0, meaning H dominates the turbulent energy dissipation. This pattern aligns with physical principles used in many EB models (Choudhury et al., 1986; Boulet et al., 2015; Trebs et al., 2021; Sun et al., 2017), where roughness parameters derived from hc explain the observed LST decrease under given meteorological conditions.

<figure><img src="image_8.png" /><figcaption>Fig. 6. LST-hc feature space for data collected over the Fontblanche study area on the 25th, October 2018. The contextual upper edge is plotted in red and the lower edge in blue.</figcaption></figure>

The intersection of the upper edge and the lower edge (set to Tair, in blue) defines the canopy height hc at which LST = Tair. This value is referred to as hc<sub>max</sub>. Physically, LST = Tair at hc = hc<sub>max</sub> implies no convection (H = 0) on both edges. However, on the upper edge, all available energy is dissipated through H. Thus, hc<sub>max</sub> represents the threshold above which LST becomes decoupled from turbulent fluxes.

We assume that the decreasing rate of LST with hc is spatially uniform across the study area. Therefore, it can be estimated from the slope of the dry edge. This assumption is supported by the use of hc as a proxy for aerodynamic roughness in many models. Especially, the roughness parameters derived from hc are generally independent of EF or hydric stress (Banerjee et al., 2017; Trebs et al., 2021).

### 2.4.2. Estimating the decreasing rate of LST with hc

The slope and intercept (LST<sub>max,hc</sub>) of the upper edge are derived from a linear regression of the 97% quantiles of LST, calculated within equal-length hc bins, plotted against hc. This approach is done for each study area and for each satellite acquisition date independently. The slope represents the rate at which LST decreases with increasing hc. The intercept (LST<sub>max,hc</sub>) serves as a proxy for the maximum LST in the study area under hc = 0 conditions.

By extrapolating this upper edge, the canopy height at which LST equals Tair is defined as hc<sub>max</sub> (see Fig. 6). This LST-hc feature space is interpreted similarly for all Landsat overpass dates and for each study site.

We define $Hc_{max}$ as the median of daily $hc_{max}$ values. When calculated across both sites, referred to as the All-Site dataset, $Hc_{max}$ is the median of all $hc_{max}$ values combined. When calculated separately for each site, referred to as the Per-Site dataset, $Hc_{max}$ is the median of the site-specific $hc_{max}$ values.

### 2.4.3. Normalizing LST for hc effect

$Hc_{max}$ is used to normalize LST for hc effect: If LST > Tair

$$LST_{norm} = LST + \frac{hc}{Hc_{max}} (LST_{max|hc} - Tair) \quad (5)$$

else:

$$LST_{norm} = Tair$$

LST<sub>norm</sub> is a conceptual LST, representing the value that LST would reach as hc approaches zero. As an initial approximation, Eq. (5) assumes a linear decrease in LST with hc, independent of hydric stress. The linear upper boundary thus represents the maximum LST achievable regardless of hc. Assuming hydric stress is consistently represented across all hc values, the slope of this linear upper edge – i.e., the rate of decrease – is considered independent of variations in hydric stress. Consequently, this rate of decrease remains valid for any LST. This
decreasing rate is explicitly defined as a function of $hc_{max}$ for each date, which is statistically derived and therefore subject to uncertainty. Normalizing LST using $Hc_{max}$ implies the existence of a temporally constant $hc_{max}$ value in the study area, while also helping to reduce uncertainties associated with its estimation.

### 2.4.4. Estimating EF from the new LST<sub>norm</sub>-f<sub>gv</sub> space

Two approaches are considered to estimate EF in the new LST<sub>norm</sub>-f<sub>gv</sub> space. In both cases, the wet edge is set to Tair. In LST<sub>norm</sub>-f<sub>gv</sub>(context), the dry edge is estimated using the same statistical method as the LST-f<sub>gv</sub>(context) approach (see Fig. 5(b)). In LST<sub>norm</sub>-f<sub>gv</sub>(EB), the dry edge is simulated using a simple soil energy balance (EB) model (see Appendix A), driven by meteorological inputs.

LST<sub>norm</sub> - f<sub>gv</sub>(EB) is proposed to address limitations of LST<sub>norm</sub>-f<sub>gv</sub>(context), especially on Landsat overpass dates following rainfall events. On such dates, the statistically derived dry edge may be underestimated due to the lack of dry conditions across the study area (Stisen et al., 2008). This issue has been previously highlighted as a challenge for dry edge estimation (Long et al., 2012). See Appendix A for more details on the estimation of the dry edge from EB modeling. The two approaches are carried out for each study area independently, and for each satellite acquisition date separately.

### 2.5. Estimating H and LE turbulent fluxes

For both classical and new contextual approaches, the satellite-derived turbulent fluxes are estimated as:

$$H = (1 - EF) Rn_{mod} \qquad (6)$$

$$LE = EF \times Rn_{mod} \qquad (7)$$

with the EF derived from the LST - f<sub>gv</sub>(context)/LST<sub>norm</sub> - f<sub>gv</sub>(context)/LST<sub>norm</sub> - f<sub>gv</sub>(EB) approach and Rn<sub>mod</sub> as:

$$Rn_{mod} = (1 - \alpha) R_g + \epsilon R_a - \epsilon \sigma LST^4 \qquad (8)$$

where $\alpha$ is the satellite-derived albedo [-], $\epsilon$ = 0.97, the surface emissivity [-], $R_a$ the downward atmospheric longwave radiation [W m<sup>-2</sup>] and $\sigma$, the Stefan-Boltzmann constant [W m<sup>-2</sup> K<sup>-4</sup>]. For details on the evaluation of $R_a$, see Appendix A. $\alpha$ is estimated with the expression of Courault et al. (2008) and used in Chirouze et al. (2014), Merlin (2013):

$$\alpha = 0.645 Red + 0.382 NIR \qquad (9)$$

### 2.6. Sensitivity analysis to input data

Both the normalization of LST for $hc$ effects and the use of an EB model to estimate the dry edge (Tsd and Tvd) rely on uncertain input parameters or data. To address this, a sensitivity analysis is proposed to evaluate how variations in these factors affect the satellite-derived H and LE.

#### 2.6.1. Sensitivity analysis to $Hc_{max}$

To evaluate the sensitivity of turbulent flux estimates to uncertainties in $Hc_{max}$, we apply both the All-Site and Per-Site values of $Hc_{max}$ for LST normalization. We then compare the resulting performance metrics to assess the impact of each choice on H and LE estimates.

#### 2.6.2. Sensitivity analysis to meteorological data

Tair, Rg, and RH are required in all methods (LST - f<sub>gv</sub>(context), LST<sub>norm</sub>-f<sub>gv</sub>(context), and LST<sub>norm</sub>-f<sub>gv</sub>(EB)). Tair is used to define the wet edge, while Rg and RH are needed to compute $Rn_{mod}$. In addition, WS is required in LST<sub>norm</sub>-f<sub>gv</sub>(EB) to estimate the dry edge.

Meteorological data are initially sourced from in situ measurements (see Section 2.1.4). To evaluate the impact of uncertainties in these inputs on H and LE estimates – particularly for LST<sub>norm</sub>-f<sub>gv</sub>(EB), which is assumed to be the most sensitive to meteorological variability – we also use SAFRAN reanalysis data (see Section 2.1.4) as an alternative input. We then compare the performance metrics of turbulent heat flux and EF estimates obtained using the two meteorological datasets.

## 3. Results and discussion

First, the rate at which LST decreases with $hc$ is quantified, and LST is normalized to account for the $hc$ effect (Section 3.1). Next, the results of the LST - f<sub>gv</sub>(context), LST<sub>norm</sub>-f<sub>gv</sub>(context), and LST<sub>norm</sub>-f<sub>gv</sub>(EB) approaches are presented and discussed in terms of H, LE, and EF estimates (Section 3.2). Finally, Section 3.3 provides the results of the sensitivity analysis, evaluating the impact of input data uncertainties on the different methods.

### 3.1. Decreasing rate of LST with $hc$

Figs. 7 and 8 present the LST-$hc$ spaces for nine randomly selected dates (one per year) in the Puechabon and Fontblanche study areas, respectively. Across all dates and both sites, the linear upper edge of the LST-$hc$ space is consistently well defined and shows a clear decreasing trend. Despite variations in the difference between LST<sub>max, hc</sub> and Tair, the intersection of the upper and lower edges (LST = Tair) occurs at a relatively stable $hc_{max}$ value.

Fig. 9 presents boxplots of $hc_{max}$ based on 96 and 110 dates for the Puechabon and Fontblanche sites, respectively. At both sites, $hc_{max}$ values are consistently positive and bounded between 28 m and 62 m, confirming the systematic decrease of LST with increasing $hc$. While this LST-$hc$ relationship can be represented by an EB model, few studies have directly quantified it across a wide range of $hc$ values. On a continental scale, (Zhang et al., 2022) showed that, across the contiguous United States, LST decreases with $hc$ regardless of forest type (evergreen, deciduous, or mixed). Similarly, (Shaik et al., 2023) found that in Sardinia, MODIS LST also decreases with $hc$ on a monthly scale (e.g., October 2021). In that study, the slope of the linear regression of LST versus $hc$ was estimated per land cover type as a mean of -0.47 ± 0.13 K m<sup>-1</sup>. These values are consistent with our findings, where the slope of the linear upper edge is -0.53 ± 0.14 K m<sup>-1</sup>.

The Per-Site $Hc_{max}$ values differ slightly between the two study areas: $Hc_{max}$ = 42 m for Puechabon and $Hc_{max}$ = 35 m for Fontblanche. The All-Site $Hc_{max}$ is 39 m. The daily variability in $hc_{max}$ is similar, with 6 m for Puechabon and 5 m for Fontblanche. The difference in centrality may result from variations in $hc$ distributions between the sites. Fontblanche shows a wider range of $hc$ values and a more even distribution between its minimum and maximum than Puechabon (see Fig. 4). As a result, the estimation of the upper edge of the LST-$hc$ relationship is likely to be more robust for Fontblanche than for Puechabon.

To explore the relationship between $hc_{max}$ and the Monin-Obukhov similarity theory, we conducted a simulation of Tvd as a function of $hc$ at the Puechabon site. For consistency with the Monin-Obukhov similarity theory, the analysis was restricted to canopy heights below the flux tower height (12 m). All available meteorological conditions from our dataset were used. The methodology is detailed in Appendix A of the revised manuscript. We computed the mean Tvd and mean air temperature (Tair) for all Landsat dates, and examined their relationship in Fig. 10. A linear trend was added to project the point at which
<figure><img src="image_9.png" /><figcaption>Fig. 7. LST-hc spaces for the Puechabon study area for data during the study period.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 8. LST-hc spaces for the Fontblanche study area for during the study period.</figcaption></figure>

Tvd equals *Tair*. Except for the flux tower height, the model used is identical to that applied at Fontblanche. In this context, Tvd is assumed to represent dry conditions across varying *hc* values, particularly those observed along the linear upper edge of the LST-hc space.

The simulation shows that *Tvd* decreases as *hc* increases (see Fig. 10). For *hc* below 1 m, the relationship is strongly nonlinear, while for *hc* greater than 1 m, it can be reasonably approximated by a linear expression. This matches the empirical observations in the LST-hc feature space. The linear projection indicates that *Tvd* equals *Tair* at an estimated *hc*max of approximately 16 m. This suggests that *hc*max, as a theoretical canopy height, can be modeled in accordance with Monin-Obukhov theory. For LST values corresponding to *hc*max, both wet and dry conditions correspond to the same LST value (close to *Tair*) and consequently, LST becomes decoupled from surface fluxes. We assume that the discrepancy between this theoretical *hc*max and the observed values in our study (approximately 40 m) is primarily due to the

limitations of Monin–Obukhov similarity over complex environments
theory and the simplified expressions of roughness parameters when
applied to forested environments.

3.2. Estimating turbulent heat fluxes

In Section 3.2.1, we first present a qualitative analysis of the LST, LST<sub>norm</sub>, hc, and EF maps derived for a specific Landsat overpass date over the Fontblanche study area. This is then followed by a quantitative evaluation of the Per-Site datasets. Results for turbulent heat flux and EF estimates are next discussed for the LST − f<sub>gv</sub>(context) and LST<sub>norm</sub> − f<sub>gv</sub>(context) methods in Section 3.2.2, and for the LST<sub>norm</sub> − f<sub>gv</sub>(EB) method in Section 3.2.3.

3.2.1. Qualitative analysis on a particular date

Fig. 11 displays maps of LST (a) and LST<sub>norm</sub> (b) over the Font-
blanche study area, based on Landsat data for 25th October 2018. As
<figure><img src="image_11.png" /><figcaption>**Fig. 9.** Boxplot of $hc_{max}$ for Puechabon (96 dates) and Fontblanche (110 dates) study areas.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Fig. 10.** EB-modeled Tvd vs. hc with the Puechabon meteorological data.</figcaption></figure>

expected, $LST_{norm}$ values are larger than $LST$ values across the entire area, particularly in forested zones (see Fig. 3(c) and (d)), where hc values are relatively large (see Fig. 4(c)).

The figure also includes maps of EF estimated using the $LST - f_{gv(context)}$ (c), $LST_{norm} - f_{gv(context)}$ (d), and $LST_{norm} - f_{gv(EB)}$ (e) methods. Compared to the $LST - f_{gv(context)}$, the $LST_{norm} - f_{gv(context)}$ approach results in a general decrease in EF across the area. Differences between the two methods are minimal in areas with low hc and low $LST - f_{gv(context)}$ EF. However, notable differences appear in regions where $LST_{norm}$ significantly exceeds $LST$, especially in the southwest. The $LST_{norm} - f_{gv(EB)}$ method produces higher EF values than $LST_{norm} - f_{gv(context)}$ across most of the study area, highlighting the influence of the physically based dry edge simulation.

### 3.2.2. $LST - f_{gv(context)}$ and $LST_{norm} - f_{gv(context)}$ results and discussion

Fig. 12 presents scatter plots of satellite-based H, LE, and EF for $LST - f_{gv(context)}$ (a) and $LST_{norm} - f_{gv(context)}$ (b) against in situ measurements (Per-Site dataset, $Hc_{max}$ set to 42 m for Puechabon and 35 m for Fontblanche). Overall, satellite-derived H, LE, and EF show poor visual agreement with in situ data. $LST - f_{gv(context)}$ underestimates H, leading to an overestimation of LE and EF. No clear linear relationship is observed. Regardless of the flux, scatter point clusters remain distinct for each EC site. The estimates of turbulent

fluxes and EF, using an EB-derived dry edge are similar to those found with the $LST - f_{gv}$ approach. They are available in Appendix B.

In contrast, $LST_{norm} - f_{gv(context)}$ estimates align better with in situ measurements than $LST - f_{gv(context)}$ estimates. Although high H values are still underestimated and low LE/EF values overestimated, a linear trend is visually evident. Moreover, LE estimates for both EC sites exhibit almost similar bias and slope, as indicated by overlapping point clouds.

From a quantitative perspective, the modeled net radiation ($Rn_{mod}$) aligns well with in situ data, showing $R = 0.98$ and a regression slope of 0.90. Table 1 summarizes performance metrics (R, RMSE, slope, and bias) for satellite-derived H, LE, and EF against in situ values. The $LST - f_{gv(context)}$ approach underestimates high H and overestimates low LE, with low correlations ($R = 0.40$ and 0.06) and strong biases (–163 and 132 W m⁻²). It also overestimates EF (bias = 0.24) with no correlation ($R = 0.02$). In contrast, $LST_{norm} - f_{gv(context)}$ accounting for hc normalization – significantly improves estimates. Correlations increase for H ($R = 0.72$), LE ($R = 0.43$), and EF ($R = 0.40$). However, H remains underestimated (bias = –93 W m⁻², slope = 0.61), and LE is still overestimated (bias = 162 W m⁻², slope = 0.32). Consequently, EF remains significantly biased (bias = 0.13).

The same analysis was conducted separately for each site, using site-specific $Hc_{max}$ values (Per-Site dataset). Figs. 13 and 14 compare satellite-derived and in situ H, LE, and EF for $LST - f_{gv(context)}$ (a) and $LST_{norm} - f_{gv(context)}$ (b), at the Puechabon and Fontblanche EC sites.

$LST - f_{gv(context)}$ results vary between sites. At Puechabon, H, LE, and EF estimates show less underestimation or overestimation than at Fontblanche. While no clear relationship is observed between satellite and in situ LE/EF at either site, a linear trend is visible for H.

$LST_{norm} - f_{gv(context)}$ reduces absolute bias by nearly one-third at Fontblanche for all variables, while maintaining the H correlation. However, it does not improve estimates at Puechabon. In fact, underestimation of H and overestimation of LE and EF increase, and regression slopes remain far from 1.

Table 2 reports the performance metrics of the $LST - f_{gv(context)}$ and $LST_{norm} - f_{gv(context)}$ approaches for H, LE, and EF at each site individually. Under the $LST - f_{gv(context)}$ approach, H and LE are reasonably well estimated at the Puechabon site, with biases of –82 and 47 W m⁻² and correlations of $R = 0.50$ and 0.35, respectively. In contrast, at Fontblanche, H is strongly underestimated (bias = –233 W m⁻²) and LE is overestimated (bias = 206 W m⁻²), though correlations remain acceptable ($R = 0.70$ and 0.33).

These trends are consistent with EF performance. The $LST - f_{gv(context)}$ approach yields a substantial overestimation of EF at Fontblanche (bias = 0.36), while the bias is notably lower at Puechabon (bias = 0.11). Correlation is slightly higher at Fontblanche ($R = 0.36$) than at Puechabon ($R = 0.22$).

The $LST_{norm} - f_{gv(context)}$ approach does not provide clear quantitative improvements at the site level. At Puechabon, the bias increases for both H (–113 W m⁻²) and LE (78 W m⁻²). At Fontblanche, the bias is reduced for both fluxes (–75 and 47 W m⁻²), but remains significant.

The $LST - f_{gv(context)}$ approach yields strongly biased estimates of H, LE, and EF at the Fontblanche EC site, whereas biases are less pronounced at the Puechabon site. Given the similar climatic conditions at both sites (Fig. 2), these discrepancies likely stem from differences in land cover structure (Fig. 4), which influence LST. One key structural factor is hc, a proxy for surface roughness, which affects surface thermal behavior.

Normalization of LST for hc ($LST_{norm} - f_{gv(context)}$) has a dual effect. It improves estimates of H, LE, and EF at Fontblanche but degrades them at Puechabon. Despite this, $LST_{norm} - f_{gv(context)}$ reduces inter-site discrepancies in error metrics (slope, and RMSE), leading to more consistent satellite-derived estimates across both sites. This suggests that removing the hc effect from LST helps harmonize flux estimates, enabling the treatment of both sites as a unified dataset. This
<figure><img src="image_13.png" /><figcaption>Fig. 11. Maps over the Fontblanche study area on the 25th, October 2018 of: (a) LST, (b) LST<sub>norm</sub>, (c) LST − f<sub>gv</sub>(context) EF, (d) LST<sub>norm</sub> − f<sub>gv</sub>(context) EF, (e) LST<sub>norm</sub> − f<sub>gv</sub>(EB) EF.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Fig. 12. Scatter plots of satellite vs. in situ H, LE, and EF for the Per-Site dataset ($H_{cmax}$ set to 42 m for Puechabon and 35 m for Fontblanche), using: (a) LST - f<sub>gv</sub>(context) method with in situ meteorological data, (b) LST<sub>norm</sub> - f<sub>gv</sub>(context) method with in situ meteorological data, (c) LST<sub>norm</sub> - f<sub>gv</sub>(EB) method with in situ meteorological data, and (d) LST<sub>norm</sub> - f<sub>gv</sub>(EB) method with SAFRAN meteorological data.</figcaption></figure>

is notable given the large difference in $hc$ ($hc_{insitu}$ = 5.5 m at Puechabon vs. 13 m at Fontblanche).

Thus, the $hc$ normalization represents a meaningful advancement. Unlike traditional EB modeling, which requires site-specific parameterization, using $LST_{norm}$ – the hypothetical LST that would be observed for the same vegetated pixel but for $hc$ ≈ 0 – offers a practical and scalable method for improving contextual approaches across varying $hc$ conditions. However, $LST_{norm} - f_{gv}(context)$ does not fully correct persistent biases in the mean and variance of satellite-derived H, LE, and EF. In particular, the dynamics are absent from the estimates derived using the statistically defined dry edge in $LST_{norm} - f_{gv}(context)$.

### 3.2.3. $LST_{norm} - f_{gv}(EB)$ results and discussion

The EB model is integrated into the $LST_{norm} - f_{gv}(EB)$ approach to constrain the dry edge of the contextual method, and the resulting estimates of H, LE, and EF are evaluated. As shown in Fig. 12(c) and Table 1, $LST_{norm} - f_{gv}(EB)$ significantly improves performance compared to both $LST - f_{gv}(context)$ and $LST_{norm} - f_{gv}(context)$. It notably reduces the underestimation of H and the overestimation of LE and EF, while maintaining the improved correlations observed with $LST_{norm} - f_{gv}(context)$. Specifically, biases in H and LE decrease to –56 and 25 W m<sup>-2</sup>, respectively, with slopes increasing to 0.84 and 0.60, and correlations reaching R = 0.72 and 0.46. The correlation for
<caption>**Table 1**</caption>

Root mean square error (RMSE), bias, correlation (R) and slope of the linear regression between satellite-derived and in situ H, LE and EF. For each site $Hc_{max}$ is set to its Per-Site value.

<table><thead><tr><th rowspan="2">Variables</th><th rowspan="2">Performance metrics</th><th>LST - f<sub>gv</sub>(context)</th><th>LST<sub>norm</sub> - f<sub>gv</sub>(context)</th><th>LST<sub>norm</sub> - f<sub>gv</sub>(EB)</th><th>LST<sub>norm</sub> - f<sub>gv</sub>(EB)</th></tr><tr><th>In situ meteo</th><th>In situ meteo</th><th>In situ meteo</th><th>SAFRAN meteo</th></tr></thead><tbody><tr><td rowspan="4">H</td><td>RMSE [W m<sup>-2</sup>]</td><td>197</td><td>123 [7]<sup>a</sup></td><td>111 [3]<sup>a</sup></td><td>142 [14]<sup>a</sup></td></tr><tr><td>Bias [W m<sup>-2</sup>]</td><td>-163</td><td>-93 [-11]<sup>a</sup></td><td>-56 [-10]<sup>a</sup></td><td>-111 [-19]<sup>a</sup></td></tr><tr><td>R</td><td>0.40</td><td>0.72 [0.01]<sup>a</sup></td><td>0.72 [0.00]<sup>a</sup></td><td>0.71 [0.00]<sup>a</sup></td></tr><tr><td>Slope</td><td>0.28</td><td>0.61 [-0.07]<sup>a</sup></td><td>0.84 [-0.07]<sup>a</sup></td><td>0.72 [-0.11]<sup>a</sup></td></tr><tr><td rowspan="4">LE</td><td>RMSE [W m<sup>-2</sup>]</td><td>176</td><td>101 [6]<sup>a</sup></td><td>105 [1]<sup>a</sup></td><td>129 [13]<sup>a</sup></td></tr><tr><td>Bias [W m<sup>-2</sup>]</td><td>132</td><td>62 [11]<sup>a</sup></td><td>25 [10]<sup>a</sup></td><td>86 [19]<sup>a</sup></td></tr><tr><td>R</td><td>0.06</td><td>0.43 [-0.02]<sup>a</sup></td><td>0.46 [-0.02]<sup>a</sup></td><td>0.47 [-0.05]<sup>a</sup></td></tr><tr><td>Slope</td><td>0.07</td><td>0.32 [-0.06]<sup>a</sup></td><td>0.60 [-0.05]<sup>a</sup></td><td>0.59 [-0.09]<sup>a</sup></td></tr><tr><td rowspan="4">EF</td><td>RMSE</td><td>0.31</td><td>0.19 [0.01]<sup>a</sup></td><td>0.19 [0.00]<sup>a</sup></td><td>0.23 [0.02]<sup>a</sup></td></tr><tr><td>Bias</td><td>0.24</td><td>0.13 [0.02]<sup>a</sup></td><td>0.06 [0.02]<sup>a</sup></td><td>0.16 [0.03]<sup>a</sup></td></tr><tr><td>R</td><td>0.02</td><td>0.40 [-0.02]<sup>a</sup></td><td>0.48 [-0.02]<sup>a</sup></td><td>0.47 [-0.04]<sup>a</sup></td></tr><tr><td>Slope</td><td>0.02</td><td>0.31 [-0.07]<sup>a</sup></td><td>0.67 [-0.06]<sup>a</sup></td><td>0.60 [-0.11]<sup>a</sup></td></tr></tbody></table>

<figure><img src="image_15.png" /><figcaption>**Fig. 13.** Same as Fig. 12 but for Per-Site data set of Puechabon ($Hc_{max}$ set to 42 m).</figcaption></figure>

EF also improves ($R = 0.48$), and the bias is substantially reduced to 0.06.

Similar improvements are observed at the site level (Figs. 13 and 14, Table 2). At the Puechabon site, $LST_{norm} - f_{gv}(EB)$ reduces the bias in $H$ to -81 W m$^{-2}$ and in $LE$ to 46 W m$^{-2}$. At the Fontblanche site, the bias in $H$ is reduced to -35 W m$^{-2}$ and in $LE$ to 8 W m$^{-2}$. For EF, the bias decreases to 0.11 at Puechabon and 0.02 at Fontblanche. Additionally, the slopes of the linear regressions for $H$ (0.58/0.76, Puechabon/Fontblanche), $LE$ (0.47/0.49), and $EF$ (0.41/0.58) are closer to unity, and RMSE values are generally lower.

The results of $LST_{norm} - f_{gv}(EB)$ are placed in the context of previous studies at the Puechabon site, since to the authors' knowledge, there was no prior evaluation of LST-derived fluxes for the Fontblanche site. Bartkowiak et al. (2024) assessed the TSEB model using Sentinel-3 LST data downscaled to 100 m over various sites (2017–2021). While TSEB performed well over vineyards ($R = 0.93$) and grasslands ($R = 0.55$), it was less effective over forests ($R = 0.22$), with a negative correlation for $LE$ at Puechabon ($R = -0.18$). Njuki et al. (2023) evaluated the SEBS model at Puechabon using in situ LST and meteorological

data at a half-hourly scale (2010–2011), reporting $R = 0.78/0.86$, RMSE = 133/108 W m$^{-2}$, and bias = -44.76/-35 W m$^{-2}$ for H/LE. Despite overall good performance, midday $H$ was underestimated by up to 50% between April and October. Penot and Merlin (2023) applied the LST-$f_{gv}$ contextual method using Landsat data (2015–2021, May–September), reporting EF metrics of $R = 0.57$, slope = 0.50, RMSE = 0.12, and bias = -0.02. In comparison, $LST_{norm} - f_{gv}(EB)$ clearly improves the estimation of all turbulent fluxes and EF at the time of satellite overpass (late morning) at the Puechabon site, outperforming previous approaches in both accuracy and consistency.

More broadly, our results are consistent with those obtained using EB models under similar environmental conditions in Australia. Trebs et al. (2021) applied three EB models (STICS, SEBS, SPARSE), fed with in situ $hc$ measurements and MODIS data across nine sites. Notably, the Gingin site presents environmental conditions comparable to those of Puechabon and Fontblanche ($hc_{insitu} = 6.8$ m; annual cumulative precipitation = 560 mm). Their study reported similar performance across the three EB models when compared with in situ measurements of $H$ and $LE$, with average $R$ of 0.85 and 0.33, biases of -54 W m$^{-2}$

<footnote><sup>a</sup> The brackets show the difference between the performance metrics per site of the All-Site estimates and the performance metrics of the Per-Site estimates of H, LE, and EF.</footnote>
<figure><img src="image_16.png" /><figcaption>Fig. 14. Same as Fig. 12 but for Per-Site data set of Fontblanche ($H_{cmax}$ set to 35 m).</figcaption></figure>

<caption>Table 2</caption>

RMSE, bias, *R* and slope of the linear regression between satellite-derived and in situ *H*, *LE* and *EF* for the Per-Site dataset and $H_{cmax}$ set to 42 m and 35 m for the Puechabon and Fontblanche EC sites respectively.

<table><thead><tr><th>EC site</th><th>Variables</th><th>Performance metrics</th><th>LST - f<sub>gv</sub> (context)</th><th>LST<sub>norm</sub> - f<sub>gv</sub> (context)</th><th>LST<sub>norm</sub> - f<sub>gv</sub> (EB)</th><th>LST<sub>norm</sub> - f<sub>gv</sub> (EB)</th></tr><tr><td></td><td></td><td></td><td>In situ meteo</td><td>In situ meteo</td><td>In situ meteo</td><td>SAFRAN meteo</td></tr></thead><tbody><tr><td rowspan="10">Puechabon</td><td rowspan="4">H</td><td>RMSE [W m<sup>-2</sup>]</td><td>118</td><td>139 [-5]<sup>a</sup></td><td>116 [-4]<sup>a</sup></td><td>143 [-4]<sup>a</sup></td></tr><tr><td>Bias [W m<sup>-2</sup>]</td><td>-82</td><td>-113 [6]<sup>a</sup></td><td>-81 [7]<sup>a</sup></td><td>-122 [4]<sup>a</sup></td></tr><tr><td>R</td><td>0.50</td><td>0.50 [0.00]<sup>a</sup></td><td>0.59 [0.00]<sup>a</sup></td><td>0.64 [0.00]<sup>a</sup></td></tr><tr><td>Slope</td><td>0.40</td><td>0.27 [0.00]<sup>a</sup></td><td>0.58 [0.01]<sup>a</sup></td><td>0.56 [0.01]<sup>a</sup></td></tr><tr><td rowspan="4">LE</td><td>RMSE [W m<sup>-2</sup>]</td><td>99</td><td>110 [-4]<sup>a</sup></td><td>103 [-2]<sup>a</sup></td><td>124 [-3]<sup>a</sup></td></tr><tr><td>Bias [W m<sup>-2</sup>]</td><td>47</td><td>78 [-6]<sup>a</sup></td><td>46 [-7]<sup>a</sup></td><td>93 [-4]<sup>a</sup></td></tr><tr><td>R</td><td>0.35</td><td>0.41 [0.00]<sup>a</sup></td><td>0.43 [0.00]<sup>a</sup></td><td>0.48 [0.00]<sup>a</sup></td></tr><tr><td>Slope</td><td>0.30</td><td>0.28 [0.00]<sup>a</sup></td><td>0.47 [0.00]<sup>a</sup></td><td>0.47 [0.00]<sup>a</sup></td></tr><tr><td rowspan="4">EF</td><td>RMSE</td><td>0.19</td><td>0.22 [-0.01]<sup>a</sup></td><td>0.20 [-0.01]<sup>a</sup></td><td>0.25 [-0.01]<sup>a</sup></td></tr><tr><td>Bias</td><td>0.11</td><td>0.16 [-0.01]<sup>a</sup></td><td>0.11 [-0.01]<sup>a</sup></td><td>0.19 [-0.01]<sup>a</sup></td></tr><tr><td>R</td><td>0.22</td><td>0.16 [0.00]<sup>a</sup></td><td>0.36 [0.00]<sup>a</sup></td><td>0.40 [0.00]<sup>a</sup></td></tr><tr><td>Slope</td><td>0.18</td><td>0.08 [0.00]<sup>a</sup></td><td>0.41 [0.01]<sup>a</sup></td><td>0.42 [0.00]<sup>a</sup></td></tr><tr><td rowspan="10">Fontblanche</td><td rowspan="4">H</td><td>RMSE [W m<sup>-2</sup>]</td><td>247</td><td>108 [19]<sup>a</sup></td><td>106 [10]<sup>a</sup></td><td>140 [29]<sup>a</sup></td></tr><tr><td>Bias [W m<sup>-2</sup>]</td><td>-233</td><td>-75 [-26]<sup>a</sup></td><td>-35 [-24]<sup>a</sup></td><td>-101 [-39]<sup>a</sup></td></tr><tr><td>R</td><td>0.70</td><td>0.72 [0.00]<sup>a</sup></td><td>0.66 [0.00]<sup>a</sup></td><td>0.62 [0.00]<sup>a</sup></td></tr><tr><td>Slope</td><td>0.50</td><td>0.52 [-0.03]<sup>a</sup></td><td>0.76 [-0.02]<sup>a</sup></td><td>0.63 [-0.06]<sup>a</sup></td></tr><tr><td rowspan="4">LE</td><td>RMSE [W m<sup>-2</sup>]</td><td>222</td><td>92 [16]<sup>a</sup></td><td>108 [4]<sup>a</sup></td><td>133 [25]<sup>a</sup></td></tr><tr><td>Bias [W m<sup>-2</sup>]</td><td>206</td><td>47 [26]<sup>a</sup></td><td>8 [24]<sup>a</sup></td><td>80 [39]<sup>a</sup></td></tr><tr><td>R</td><td>0.33</td><td>0.19 [0.01]<sup>a</sup></td><td>0.35 [0.02]<sup>a</sup></td><td>0.39 [0.00]<sup>a</sup></td></tr><tr><td>Slope</td><td>0.29</td><td>0.09 [0.01]<sup>a</sup></td><td>0.49 [0.03]<sup>a</sup></td><td>0.56 [-0.02]<sup>a</sup></td></tr><tr><td rowspan="4">EF</td><td>RMSE</td><td>0.39</td><td>0.16 [0.03]<sup>a</sup></td><td>0.18 [0.01]<sup>a</sup></td><td>0.22 [0.04]<sup>a</sup></td></tr><tr><td>Bias</td><td>0.36</td><td>0.09 [0.04]<sup>a</sup></td><td>0.02 [0.04]<sup>a</sup></td><td>0.14 [0.06]<sup>a</sup></td></tr><tr><td>R</td><td>0.36</td><td>0.19 [0.01]<sup>a</sup></td><td>0.40 [0.01]<sup>a</sup></td><td>0.35 [-0.01]<sup>a</sup></td></tr><tr><td>Slope</td><td>0.32</td><td>0.09 [0.00]<sup>a</sup></td><td>0.58 [0.01]<sup>a</sup></td><td>0.49 [-0.04]<sup>a</sup></td></tr></tbody></table>

and 20 W m⁻², and RMSE values of 105 W m⁻² and 88 W m⁻² for *H* and *LE*, respectively. Unfortunately, slope values were not provided. These results are of the same order of magnitude as ours (noting that their larger number of study dates, 1707, may contribute to higher *R* values), despite their reliance on in situ *hc* measurements. Complementarily, Khan et al. (2021) integrated LiDAR-derived *hc* data into the SEBS model, achieving RMSE values of 108 W m⁻² and

73 W m⁻², biases of -69 W m⁻² and 6.8 W m⁻², and *R* values of 0.76 and 0.84 for *H* and *LE*, respectively, averaged across three study sites. These sites are considered wet environments (mean annual precipitation >1300 mm). Their findings align with ours, despite being conducted under wetter conditions, and underscore the importance of roughness parameters (particularly the momentum roughness length) in determining model performance. In contrast, our empirical

<footnote><sup>a</sup> The brackets show the difference between the performance metrics per site of the All-Site estimates ($H_{cmax}$ = 39 m) and the performance metrics of the Per-Site estimates of *H*, *LE*, and *EF*.</footnote>
yet physically consistent approach does not require explicit roughness parameterization, offering a robust alternative for flux estimation in heterogeneous and dry environments.

The $LST_{norm} - f_{gv}(EB)$ approach represents a significant breakthrough in the estimation of EF and turbulent fluxes. First, it demonstrates that a contextual approach can yield accurate estimates in areas with substantial variation in *hc*. While contextual methods are well established in areas with low *hc* (Moran et al., 1994; Sun et al., 2017; Long et al., 2012; Long and Singh, 2012), the normalization of LST to account for *hc* effects enables their application in landscapes with greater heterogeneity in canopy height. This marks a notable advancement, as previous efforts to incorporate *hc* into EB models could only imperfectly address the influence of surface roughness in forested environments. Consequently, this simple and low-parameter contextual approach can now be effectively applied in complex forest ecosystems.

Additionally, the integration of an EB model to constrain the dry edge in the $LST_{norm} - f_{gv}$ feature space ($LST_{norm} - f_{gv}(EB)$) significantly reduces bias and enhances sensitivity (i.e., slope closer to 1) in flux estimates across sites with contrasting *hc* values ($hc_{insitu} = 5.5/13$ m for Puechabon/Fontblanche). The novelty of our approach lies in the use of a simple EB model, applied solely to estimate two extreme conditions (dry soil and dry vegetation), with identical parameterization across both sites. Unlike conventional EB models, the $LST_{norm} - f_{gv}(EB)$ approach does not require complex spatial calibration or aerodynamic resistance parameterization, making it both robust and operationally efficient.

The strong performance of $LST_{norm} - f_{gv}(EB)$ suggests that the simulated dry edge effectively reintroduces meteorological dynamics influencing *H*, *LE*, and *EF* – dynamics that are absent in the statistically derived dry edge used in $LST_{norm} - f_{gv}(context)$. The marked increase in regression slopes for all fluxes indicates a more realistic temporal evolution of the dry edge, as captured by the EB model rather than by purely contextual methods. On the ground, this highlights that extreme conditions are not necessarily present at satellite resolution across the full gradient of vegetation cover. However, these conditions can be reintroduced through an EB-derived dry edge. This reinforces the complementarity between using a simple EB model to represent extreme conditions and applying a low-parametrized contextual approach when LST reflects low canopy height environments.

Despite these good results, residual biases persist in the flux/EF estimates. Two hypotheses may explain this. First, directional effects are not accounted for in the EB-derived dry edge. These effects arise from interactions between sub-pixel canopy structure, satellite viewing geometry, and solar angles, which can reduce LST (Michel et al., 2023). In Mediterranean forests, shadowing from sub-pixel tree structures has been shown to contribute to EF overestimation (Penot and Merlin, 2023). This study does not consider intra-pixel variability in *hc*, and thus omits potential directional impacts on LST and $LST_{norm}$. Second, both Puechabon and Fontblanche forests exhibit relatively high *H* and low *LE* compared to other biomes. In arid ecosystems where *H* >> *LE*, forests may maintain lower-than-expected LST due to enhanced turbulent exchange – known as the “canopy convective effect” – driven by greater surface roughness (Banerjee et al., 2017, 2018; Rotenberg and Yakir, 2010, 2011). This effect may contribute to the remaining bias in flux estimates, even after *hc* normalization and EB-based dry edge simulation.

In this study, both sites were selected based on their Mediterranean ecosystems, which are prone to dry conditions, and the availability of high-resolution, consistent LiDAR data acquired within a time frame close to the study period. While the sites differ markedly in vegetation structure, they are relatively similar in terms of geology, pedology, and climate. The Puechabon site features a dense, homogeneous coppice, whereas the Fontblanche site exhibits a taller and more structurally diverse canopy. Both sites are dominated by common Mediterranean species – namely Holm Oak and Aleppo Pine – which are widely

distributed from southern France to North Africa (Suicmez and Avci, 2023; Barbero et al., 1992; Vennetier et al., 2018; Schiller et al., 1986; Mauri et al., 2016). This species distribution supports the generalizability of the findings across similar ecosystems. Despite these considerations, our findings need to be evaluated across additional sites to assess their applicability at a global scale. Our study focuses on French Mediterranean ecosystems due to the availability of high-quality LiDAR data, which is essential for accurate *hc* estimation. One of the main challenges for broader implementation is obtaining reliable *hc* data, which is critical for determining both *hc* and $hc_{max}$, two key parameters in the normalization of LST for canopy height effects.

### 3.3. Sensitivity analysis

#### 3.3.1. Sensitivity to $H_{cmax}$

The sensitivity analysis to $H_{cmax}$ evaluates how variations in the $hc_{max}$ used for LST normalization affect the estimation of *H*, *LE*, and *EF*. Specifically, performance metrics (*R*, *RMSE*, slope, bias) are compared between fluxes derived using the All-Site $H_{cmax}$ (39 m) and the Per-Site $H_{cmax}$ values (42 m for Puechabon, 35 m for Fontblanche), as shown in Tables 1 and 2.

Overall, the results indicate that flux estimates, including *EF*, are weakly sensitive to these variations. Differences in *R* are often negligible or zero, suggesting that a common $H_{cmax}$ value of 39 m can be used across both sites without significantly affecting accuracy.

#### 3.3.2. Sensitivity to meteorological data

The sensitivity analysis to meteorological data assesses how uncertainties in input data propagate through the estimated *H*, *LE*, and *EF*. The SAFRAN reanalysis dataset is assumed to be less accurate than localized in situ measurements at the site level. Figs. 12 (d), 13 (d), and 14 (d) show flux and *EF* estimates from the $LST_{norm} - f_{gv}(EB)$ approach when the EB model is forced with SAFRAN data (except for *Rg*). Corresponding performance metrics are reported in Tables 1 and 2.

Compared to $LST - f_{gv(context)}$ and $LST_{norm} - f_{gv(context)}$, the use of SAFRAN data in $LST_{norm} - f_{gv}(EB)$ still yields improved results, particularly in terms of regression slopes. These findings are promising, as they suggest that the method can be extended to larger areas without relying on in situ meteorological data. However, biases persist: *H* is underestimated, while *LE* and *EF* are overestimated relative to $LST_{norm} - f_{gv}(EB)$ using in situ data. This is partly due to SAFRAN overestimating *Tair* (bias = +0.87 K) on both study areas, which shifts the wet edge position.

## 4. Conclusion

To extend the applicability of thermal-based turbulent flux estimation to forested ecosystems, this study integrates LiDAR-derived canopy height (*hc*) into a contextual modeling framework. Specifically, Landsat LST is normalized for the *hc* effect, and the resulting $LST_{norm}$ is used in the $LST_{norm} - f_{gv}$ feature space to estimate *H*, *LE*, and *EF*. The method is evaluated using Landsat-7/8/9 optical and thermal data, along with in situ flux measurements from two French Mediterranean forest sites – Puechabon and Fontblanche – covering 110 and 96 overpass dates between 2013 and 2022, respectively.

The approach consists of four main steps. First, LST is plotted against *hc* to derive the upper-edge slope, interpreted as the decreasing rate of LST with *hc*. The extrapolated *hc* value at which LST equals air temperature defines $hc_{max}$, the threshold beyond which LST is no longer sensitive to turbulent fluxes. Second, LST is normalized using the median $hc_{max}$ (either per site or across all sites), and $LST_{norm}$ is plotted against $f_{gv}$. Third, the wet edge is fixed at air temperature, while two strategies are tested for the dry edge: a contextual approach ($LST_{norm} - f_{gv(context)}$) and an energy balance model-based approach ($LST_{norm} - f_{gv}(EB)$). Fourth, the performance of $LST - f_{gv(context)}$
(no normalization), LST<sub>norm</sub> − f<sub>gv</sub>(context), and LST<sub>norm</sub> − f<sub>gv</sub>(EB) is compared over a 9-year period at both sites.

Based on this study, the following conclusions can be drawn:

* The median *hc<sub>max</sub>* values differ slightly between sites: 42 m for Puechabon and 35 m for Fontblanche, with a combined value of 39 m. Physically, *hc<sub>max</sub>* represents the *hc* at which LST approximates *Tair*, regardless of *EF*. For *hc* greater than *hc<sub>max</sub>* , LST becomes decoupled from turbulent fluxes.

* The LST − f<sub>gv</sub>(context) approach yields highly biased estimates of H and LE (−163/132 W m<sup>−2</sup>) and low sensitivity (slopes of 0.28/0.07) when both sites are considered together. These results align with previous studies. Site-specific analysis reveals that Fontblanche exhibits biases nearly three times greater than Puechabon, reflecting differences in canopy structure (*hc<sub>insitu</sub>* = 5.5 m vs. 13 m). Normalizing for *hc* and applying a contextually derived dry edge (LST<sub>norm</sub> − f<sub>gv</sub>(context)) improves correlations (*R* = 0.72/0.43 for H/LE), but biases remain substantial (−93/+62 W m<sup>−2</sup>). Notably, normalization harmonizes error trends across sites (slopes), enabling consistent inter-site analysis.

* Incorporating the EB-modeled dry edge (LST<sub>norm</sub> − f<sub>gv</sub>(EB)) further reduces bias (−56/+25 W m<sup>−2</sup>) and increases sensitivity (slopes of 0.84/0.60 for H/LE). The improved regression slopes suggest that the EB model effectively reintroduces meteorological variability into the dry edge definition of the LST<sub>norm</sub> − f<sub>gv</sub> space.

* Sensitivity analyses confirm the robustness of LST<sub>norm</sub> − f<sub>gv</sub>(EB) to variations in *Hc<sub>max</sub>* and meteorological inputs. The main conclusions remain valid despite uncertainties in input data.

Despite the promising results, the methodology presented in this study warrants further investigation. First, the analysis was limited to two forest sites only. To evaluate the stability of *Hc<sub>max</sub>* (approximately 40 m in this study), the approach should be extended to additional water-limited forest ecosystems. This would help determine whether *Hc<sub>max</sub>* is a site-specific or site-independent parameter. The determination of *hc<sub>max</sub>* currently depends on high-precision estimates of *hc*, which are not yet available at a global scale. However, promising developments are emerging from approaches that combine remotely sensed data with machine learning techniques (Potapov et al., 2021; Schwartz et al., 2024).

Moreover, the performance of the EB model used to simulate the dry edge should be tested under a broader range of meteorological and land cover conditions. It is important to note that factors other than surface roughness can influence LST in forested environments and may not be adequately captured by *hc* normalization alone. For instance, directional effects (Michel et al., 2023) and canopy convective effects (Banerjee et al., 2017; Rotenberg and Yakir, 2010, 2011) are not represented in classical EB models and require further exploration.

In this context, conducting multiple EC measurements within the same study area but under varying land use and canopy structure (eg different *hc* values) could provide valuable insights into the actual positioning of the dry edge in contextual feature spaces.

### CRediT authorship contribution statement

**Victor Penot:** Writing – review & editing, Writing – original draft, Methodology, Investigation, Conceptualization. **Olivier Merlin:** Writing – review & editing, Writing – original draft, Methodology, Investigation, Conceptualization.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Appendix A. EB model

Dry bare soil temperature and dry vegetation temperature are the solution of the surface energy balance (EB) equation for dry conditions (*LE* = 0) (Malbéteau et al., 2017; Stefan et al., 2015):

$$Rn(1 - C_g) = H \qquad (A.1)$$

where C<sub>g</sub> [–] is the ground heat flux (G [W m<sup>−2</sup>]) to net radiation (R<sub>n</sub> [W m<sup>−2</sup>]) ratio, equal to 0.32 for bare soil and 0 for vegetation (Kustas and Daughtry, 1990). R<sub>n</sub>, the net radiation, is expressed using the general equation:

$$R_n = (1 - \alpha) R_g + \epsilon (R_a - \sigma LST^4) \qquad (A.2)$$

with α [–] being the bare soil/vegetation albedo set equal to 0.20/0.19 (Puechabon) and 0.15/0.14 (Fontblanche) (Napoly, 2016; Napoli et al., 2017), and ε [–] the emissivity of bare soil/vegetation set equal to 0.97 (Liu et al., 2007) for both sites, σ = 5.670374.10<sup>−8</sup> W m<sup>−2</sup> K<sup>−4</sup> the Stefan–Boltzmann constant, and R<sub>g</sub> [W m<sup>−2</sup>] the incoming short-wave radiation. R<sub>a</sub> [W m<sup>−2</sup>] is the downward atmospheric radiation expressed as:

$$R_a = \epsilon_{air} \sigma Tair^4 \qquad (A.3)$$

with ε<sub>air</sub> [–] being the effective atmospheric emissivity:

$$\epsilon_{air} = 0.553 \left( \frac{e_{air}}{100} \right)^{\frac{1}{7}} \qquad (A.4)$$

where ε<sub>air</sub> [Pa] is the air vapor pressure linked to the saturated vapor pressure ε<sub>sat</sub> [Pa] at air temperature *Tair* [K] using 0≤ *RH* ≤ 1 [–] the relative humidity:

$$e_{air} = e_{sat} (Tair) RH \qquad (A.5)$$

With:

$$e_{sat}(T) = 611\exp\left(\frac{17.27T - 273.15}{T - 35.9}\right) \qquad (A.6)$$

The sensible heat flux *H* [W m<sup>−2</sup>] is expressed as :

$$H = \rho C_p \frac{LST - Tair}{Rah} \qquad (A.7)$$

With ρ [kg m<sup>−3</sup>] being the air density and C<sub>p</sub> [J kg<sup>−1</sup> K<sup>−1</sup>] the air specific heat. We use the “semi-empirical” formulation of Rah presented in Choudhury et al. (1986) and based on the Richardson number *Ri* [–] to represent the importance of natural relative to forced convection:

$$Rah = \frac{Rah_0}{(1 + 5Ri)^\eta} \qquad (A.8)$$

With η [–] being a coefficient set to 0.75 in unstable conditions (LST ≥ *Tair*) and 2 in stable conditions (LST < *Tair*), and *Rah*<sub>0</sub> is the neutral aerodynamic resistance expressed as in Choudhury et al. (1986):

$$Rah_0 = \frac{1}{k^2 W S} \ln \left( \frac{z - d}{z_{0m}} \right) \ln \left( \frac{z - d}{z_{0h}} \right) \qquad (A.9)$$

With *k* [–] being the Von Karman constant and *d* = 0 [m] the zero displacement height over bare soil (Nishida et al., 2003). Over vegetation, the zero displacement height is *d* = 0.67hc (Verhoef et al., 1997; Brutsaert, 1982; Allen et al., 1998). Herein, the dry vegetation temperature is simulated by setting *hc* to 0.10 m (equal to the RMSE of the LiDAR measurements (IGN, 2024)). *z* [m] is the reference height of measurements, W S [m s<sup>−1</sup>] the wind speed measured at *z*, and *z*<sub>0 m</sub> = 0.001 m, the roughness length for momentum transfer for soil (classical values for bare soil *z*<sub>0 m</sub> span the 0.001–0.009 m interval (Nishida et al., 2003; Yang et al., 2008; Allen et al., 2007; Liu et al., 2007)). For vegetation *z*<sub>0 m</sub> = 0.13hc (Brutsaert, 1982; Allen et al., 1998). For both soil and vegetation, the roughness length for heat is *z*<sub>0h</sub> = 0.10*z*<sub>0 m</sub> (Allen et al., 1998).
<figure><img src="image_17.png" /><figcaption>Fig. B.15. Scatter plots of satellite vs. in situ H, LE, and EF, using the same methods as the LST - f<sub>gv</sub> (context) approach, except the dry edge is simulated following the LST<sub>norm</sub> - f<sub>gv</sub> (EB) approach.</figcaption></figure>

The Richardson number is expressed as in Malbéteau et al. (2017), Stefan et al. (2015):

$$Ri = \frac{g(z - d)(LST - Tair)}{WS^2Tair} \qquad (A.10)$$

With g [m s<sup>-2</sup>] being the gravitational constant.

## Appendix B. Flux and EF estimates in the LST-f<sub>gv</sub> feature space with an EB-derived dry edge

See Fig. B.15.

## Data availability

Data will be made available on request.

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