The Two-Source Energy Balance (TSEB) modelling scheme was proposed by and afterwards refined and applied in a multitude of applications and studies including the Sen-ET framework and implemented as open source in pyTSEB Python package . In this modelling scheme the directional radiometric LST (TR(θ)) is split into the temperatures of vegetation (TC) and soil (TS) based on Leaf Area Index (LAI) and LST observation geometry. 1TR(θ)≈f(θ)TC4+[1−f(θ)]TS40.252f(θ)=1−exp⁡−0.5Ω(θ)LAIcos⁡θ where θ is the view zenith angle of the thermal observation and Ω(θ) is the clumping factor of the vegetation at view angle θ and has a value of less than 1 for clumped vegetation.

Based on this split, the energy fluxes of vegetation and soil (net radiation – Rn, sensible heat flux – H, latent heat flux – λE, soil heat flux – G) are estimated separately, before being combined to obtain the bulk surface fluxes. 3Rn,C=HC+λEC4Rn,S=HS+λES+G5Rn=(HC+HS)+(λEC+λES)+G=H+λE+G

The soil (canopy) sensible heat flux is computed from the gradient between the soil (canopy) temperature (TS and TC respectively) and the air temperature at the sink-source height. This transfer of heat between the two components and the atmosphere is modulated by resistances to heat exchange (ra,S and ra,C , respectively) organized in a series resistance network (in analogy to electrical systems) which depend on canopy structure (roughness) and weather (wind and atmospheric stability) conditions.

Since there are multiple solutions to TC and TS satisfying Eq. (), an iterative approach is employed. The initial assumption is that green canopy transpires at potential rate based on Priestley-Taylor formulation : 6λEC=αPTfgΔΔ+γRn,C where αPT is the Priestley-Taylor coefficient, fg is the fraction of vegetation that is green and thus transpiring, Δ is the slope of the vapour pressure to air temperature curve (hPa K⁻¹) and γ is the psychrometric constant (hPa K⁻¹). In all land-covers αPT has an initial value of 1.26, except for coniferous forests where it is lowered to account for reduction in stem conductivity (and therefore stomatal conductance) with height (αPT=max⁡(-0.269ln⁡(hc)+1.31,0.4)) and broadleaved and mixed forests where it is assigned a value of 0.82, both following . If unrealistic fluxes are obtained (λES<0 indicating condensation in the soil during daytime) during this first iteration, then the canopy transpiration (i.e., αPT) is sequentially reduced and soil and canopy temperatures and fluxes are recalculated until realistic values are obtained. This implementation of the TSEB scheme is called the TSEB-PT model.

TSEB-PT outputs instantaneous fluxes at the time of thermal image acquisition. The modelled instantaneous latent heat flux (λEinst), calculated during clear-sky conditions, can be extrapolated to daily ET values as λEdaily=λEinst×Sdaily↓Sinst↓ , where Sdaily↓ and Sinst↓ are the daily and instantaneous shortwave irradiances, respectively.

ETLook model is used in the WaPOR framework and is described in detail in the Methodology section of the WaPOR ETLook wiki (https://github.com/un-fao/wapor-et-look/wiki/Actual%20Evapotranspiration%20and%20Interception#methodology, last access: 22 January 2026) . Similarly to TSEB-PT, ETLook is a two-source model, meaning that it derives soil evaporation (E) and vegetation transpiration (T) as two separate fluxes, and it ensures conservation of energy at the land-surface. The model assumes potential rates of daily E and T based on the Penman–Monteith equation that are throttled down to actual E and T using stress factors: 7aE=Δ(Rn,S-G)+ρcpΔera,SΔ+γ1+rSra,S7bT=Δ(Rn,C)+ρcpΔera,CΔ+γ1+rCra,C where Δe (hPa) is vapor pressure deficit, ρ (kg m⁻³) is the air density, cp (J kg⁻¹ K⁻¹) is specific heat of dry air, ra,S and ra,C are aerodynamic resistances for heat turbulent transport for soil and canopy respectively calculated following and adjusted for buoyancy using Monin-Obukhov similarity theory in unstable conditions, and rS and rC are resistances of water transfer in respectively the soil and canopy. All resistances are in s m⁻¹.

The resistance of soil to water vapour transfer is calculated as 8rS=rs,minSetopc where rs,min is minimum soil resistance with constant value of 800 (s m⁻¹), c is a power factor with a constant value of -2.1 and Setop is relative top-soil soil moisture .

The canopy stomatal resistance is affected by air temperature stress (St), vapour pressure stress (Sv), radiation stress (Sr) and root-zone soil moisture stress (Sm) 9rC=rst,minLAIeff1StSvSrSm where rst,min (s m⁻¹) is the minimum stomatal resistance and LAIeff is effective leaf area index .

In addition, ETLook estimates evaporation from rainfall intercepted by the canopy (I in mm d⁻¹): 10I=0.2LAI1-11+FVC⋅P0.2LAI where P is precipitation, and FVC is fractional vegetation cover. The energy used in this process is subtracted from net radiation (Rn) before it is split into the soil and canopy components (Rn,S and Rn,C respectively) and used to estimate E and T in Eq. ().

The main difference between WaPOR implementation of ETLook and is the method of obtaining soil moisture required for E and T stress factors. In it is based on microwave observations while in WaPOR ETLook it is derived using a trapezoid constructed in the LST – vegetation fractional cover (fC) space . The trapezoid corner values are set based on theoretical calculations by inverting the Penman-Monteith equation for both dry and moist bare soil and vegetated conditions. Then the soil moisture of a pixel (representing both top-soil and root-zone) is estimated using the relative location of LST and fC of that pixel within that trapezoid. The CLMS implementation of ETLook adopts the WaPOR methodology. The one major difference between the WaPOR and CLMS ETLook-derived fluxes is that the former includes I as a separate sub-product while the latter does not. To ensure consistency of ETLook model formulations, we pass rainfall estimates to the ETLook and let it calculate I internally, before adding it to E calculated in Eq. (): 11EETLook,CLMS=E+I This aligns also with TSEB-PT model in which I is implicitly included in evaporation. EETLook,CLMS is referred to as evaporation from ETLook in the rest of this manuscript.

Apart from land-cover dependent parameters (see Sect. ), ETLook uses other spatially-distributed but temporally constant parameters (e.g. theoretical albedo of bare soil and full vegetation cover used during soil moisture estimation) which are provided as maps distributed by FAO.

Biophysical characterization of the land-surface is based on imagery obtained by two sensors on-board Sentinel-3 satellites: shortwave Ocean and Land Colour Intrument (OLCI); and combined shortwave and thermal infrared Sea and Land Surface Temperature Radiometer (SLSTR). Both sensors operate in the optical spectral domain, which is blocked by clouds and therefore cloud detection and masking needs to be performed before further analysis of these data.

Atmospherically corrected and geolocated Top-Of-Canopy (TOC) reflectances derived from shortwave optical detectors on OLCI and SLSTR sensors are generated and distributed by the CLMS . The cloud mask of this product is based on quality flags from Level 1 SLSTR and OLCI products and IDEPIX approach . No further cloud masking is performed during the ETa production and instead the recommendations on using the annotation flags from Sect. 5.1 of Product User Manual are followed.

Land Surface Temperature (LST) product (SL_2_LST___) is a Level 2 product based on thermal observations by the SLSTR sensor. It comes with quality layers indicating the presence of clouds. As recommended in the Copernicus Sentinel-3 SLSTR Land User Handbook (https://sentiwiki.copernicus.eu/__attachments/a_0b084365 0153c5e0933699cf9259d22d5995022524c99c86c744555f7 ebe3af4/OMPC.ACR.HBK.002%20-%20Sentinel%203%20 SLSTR%20Land%20Handbook%202024%20-%201.4.pdf? cb=e7c5d241da616f170b23f3a61f552a4e, last access: 27 August 2026), the probabilistic cloud mask is used during ETa production. This cloud mask uses a semi-Bayesian approach by estimating a probability of a clear-sky using radiative transfer modelling and meteorological conditions at the time of satellite overpass and observational climatology .

The TOC reflectance is used to derive land surface biophysical traits (Sect. ) and albedo (Sect. ) and to sharpen the LST (Sect. ). The reflectance values, as well as biophysical traits, usually show a clear seasonal cycle and spatial similarity, and have same or similar values in both cloudy and sunny conditions (e.g. leaf area index does not change day to day depending on cloudiness). Therefore, gaps in this data are highly suitable for filling using spatio-temporal gap-filling, e.g. StarFM , and smoothing methods, e.g. Whittaker-Eilers smoother used by WaPOR . On the other hand, LST is highly variable in both time (the temperature can change significantly at short time intervals even though it also has a strong seasonal cycle) and space. In addition, LST under clouds is different to LST in clear-sky conditions . This makes gap-filling of LST particularly difficult and using inaccurately gap-filled values can lead to energy imbalance at the land surface. Therefore, LST is usually not gap-filled, especially if it is to be used as input into ETa models.

In the case of the CLMS ETa product, we are using TOC reflectance and LST observations acquired by sensors onboard the same satellite platform and thus observing the land surface (and the clouds) at the same time. Therefore, since LST is not gap-filled, there is also no need to gap-fill TOC reflectance acquired at the same time and location. However, the Sentinel-3 OLCI sensor has a swath width of 1270 km, while the nadir pointing scan of SLSTR sensor has a swath width of 1400 km . Both sensors are tilted to reduce the sun glint effect and therefore larger part of the swath is located westwards of the satellite orbit path (Fig. , left).

The sensors are positioned such that their swaths align at the western edge, while on the eastern edge the coverage of OLCI ends at view zenith angle (VZA) of 24° while coverage of SLSTR ends at VZA of 35° (Fig. , right). When modelling ETa, LST observations acquired at high VZA (e.g. above 45° as in the Sen-ET approach; ) are usually omitted due to increased uncertainty caused by longer atmospheric path, LST anisotropy and larger pixel footprint. However, SLSTR observations from the eastern edge of the swath with VZA between 24 and 35° could still potentially be used if OLCI data for that part of the swath was gap-filled.

To assess whether it is worth to gap-fill the missing part of OLCI's eastern swath, and whether maximum VZA should be limited to 45° or 35° (threshold mission requirement value for planned Copernicus Land Surface Temperature Monitoring mission; ), we performed an analysis of number of monthly cloud-free Sentinel-3 LST acquisitions over Europe and Africa (Fig. ). This analysis was performed using 5 years of data (2020–2024) for months of March, June, September and December (apart from March 2020 and December 2024) and while limiting VZA of the western edge of swath to either 45° or 35° and eastern edge to either 35° or 24°.

Figure  shows a clear seasonal trend in the number of cloud-free SLSTR observations. In June and September, most of Europe has sufficient number of cloud-free observations for each dekad (at least 2 but often more than 4), while in March and, especially in December, there are areas where less than two or even less than one cloud free observations are available in each dekad. In the equatorial region of Africa, there are predominantly cloudy conditions throughout the year but they shift north in June and September and south in December and March. The difference between number of monthly cloud-free observations with eastern VZA limited to 35° or 24° is in large majority of cases less than 2, except in the Sahara region and southern Africa where there is sufficient number of observations in either case. The difference between limiting western swath to either 45° or 35° is more pronounced and can push some regions to having less than 1 observation per dekad.

Based on this analysis, it was decided to limit the western VZA to 45° and eastern VZA to 24°. This means that the extra processing that would be required to gap-fill the OLCI swath is avoided. Even though gap-filling of input imagery will not be performed, the filling of cloud gaps in the produced ETa maps is required to fulfill the requirements of the ETa product. Therefore gap-filling of outputs will be performed as described in Sect. .

A sound and generalizable approach to obtain the biophysical traits required by the ETa models is the inversion of canopy radiative transfer models (RTM), such as the combined PROSPECT and 4SAIL RTMs. Together those models can simulate the canopy spectra from 400 to 2500 nm at every nm based on the inputs listed in Table  . One computationally efficient inversion method consists of training a regression model based on large number of PROSPECT and 4SAIL simulations . Then this regression model is applied to the spectral imagery to obtain the biophysical traits maps.

In case of CLMS ETa, we are using a vectorized version of PROSPECT-D and 4SAIL models . This vectorized version allows us to run the RTMs very efficiently and thus enables us to generate specific regression models for each scene, given their actual observation and illumination conditions. This contrasts with other similar algorithms, such as the BiophysicalOp in the Sentinel-2 toolbox of Sentinel Application Platform , which applies the same generic hybrid inversion approach to all scenes. The biophysical processing framework is summarized as:

Estimating the proportion of spectral direct and diffuse irradiance using the 6S model and mean sun zenith and azimuth angles together with mean aerosol optical thickness and total column water vapor of Sentinel-3 TOC scene.

As outputs we obtain 8 products: leaf area index (LAI), mean leaf angle, leaf chlorophyll a+b concentration, leaf carotenoids concentration, leaf antocyanin concentration, brown pigments, leaf dry matter content, and leaf water content. The retrieved leaf pigments concentration gives us an idea about the canopy greenness, and we have observed an increase of Sentinel-3 estimated antocyanin concentration during vegetation curing in summer and the leaf senescence in fall. Indeed antocyanins are red pigments and thus may become dominant over other leaf pigments in those situations . For that reason, we can express the fraction of LAI that is green (fg) using an empirical piecewise linear relation to the antocyanins (Ant): 12fg=1,if Ant ≤5µg cm-21-0.8Ant-520,if Ant >5µg cm-2 and  Ant ≤25µg cm-20.2,if Ant >25µg cm-2

Net radiation (Rn) provides the energy that drives all other energy fluxes at the land-surface (including ET) and can be approximated as: 13Rn=Sn+Ln=S↓1-α+ϵL↓-σLST4 where Sn (S↓) and Ln (L↓) are the shortwave and longwave net radiation (incoming irradiances) respectively, α and ϵ are surface albedo and emissivity, respectively, LST is the Land Surface Temperature, and σ≈5.67×10-8 (W m⁻² K⁻⁴) is the Stefan-Boltzmann constant.

Considering the larger magnitude of shortwave irradiance (S↓) compared to the longwave irradiance (L↓), and the fact that Ln is usually computed internally by each ET model, we will focus on method for deriving Sn. In particular, this study concentrates on the canopy and leaf properties that influence albedo and radiation partitioning between soil and canopy. The albedo (α) is defined as the proportion of incident shortwave radiation that is reflected by the surface. The shortwave net radiation (Sn) is therefore the balance between the incident shortwave irradiance (S↓) and the reflected shortwave radiance (S↑=αS↓).

The spectral properties of the surface are key in determining the albedo. Leaves, due to their photosynthetic activity, absorb a large proportion of light due to the presence of chlorophylls, as well as other leaf pigments. On the other hand, soils can have a large range of albedo values, depending on their mineral composition, texture and topsoil moisture. Therefore, the albedo of a vegetated surface, and also radiation partitioning between soil and canopy, will depend not only on leaf chlorophyll concentration but also on canopy density and, in a lesser degree, on the soil albedo in situations of sparse vegetation or initial growth stages. Indeed, most of the Earth's surface show certain anisotropic behaviour when reflecting radiation i.e. it scatters different amounts of radiation depending on the scattering direction. Vegetation, as it is mainly composed by an array of leaves, is also affected by this anisotropic behaviour. Therefore, plants will reflect radiation differently depending on their structural characteristics as well as the illumination geometry (i.e. the solar position) and the scattering direction (i.e. the sensor position), changing their albedo with time.

To compute the net shortwave radiation and its partitioning between the canopy (SnC) and the soil (SnS) the model of is used. The key aspect of this model is the calculation of the transmitted shortwave radiation through the canopy (τC), which is wavelength dependent due to vegetation absorbing a greater portion of photosynthetically active radiation (PAR – 400–700 nm) than near infra-red (NIR – 700–2500 nm) wavelengths. τC is partitioned into two components (direct/diffuse) and in two spectral band (PAR/NIR).

14aSn,C=1-τC,DIR,PAR1-ρC,DIR,PARPARDIR+1-τC,DIR,NIR1-ρC,DIR,NIRNIRDIR+1-τC,DIF,PAR1-ρC,DIF,PARPARDIF+1-τC,DIF,NIR1-ρC,DIF,NIRNIRDIF14bSn,S=τC,DIR,PAR1-ρS,PARPARDIR+τC,DIR,NIR1-ρS,NIRNIRDIR+τC,DIF,PAR1-ρS,PARPARDIF+τC,DIF,NIR1-ρS,NIRNIRDIF where ρC,DIR is the canopy directional-hemispherical reflectance, ρC,DIF is the canopy bihemispherical reflectance, τC,DIR canopy directional-hemispherical transmittance, τC,DIF canopy bihemispherical transmittance, which depend on leaf spectral properties (absortance) and canopy structure (LAI and leaf inclination distribution parameter; ). On the other hand, ρS is the soil bihemispherical reflectance. In all cases τ and ρ are separated between the PAR and NIR regions of the solar spectrum. The calculation of canopy transmittances and reflectances is shown in Appendix .

Campbell RTM requires the leaf absorptance (ζ=1-ρ-τ) as input for calculating canopy transmittance and reflectance. To estimate this parameter, we are using the leaf traits retrievals from the biophysical processor described in Sect. . With the information of these traits, we can run the PROSPECT-D leaf RTM in forward mode to get a spectral reflectance (ρ) and transmittance (τ) that could then be integrated to the required broadband regions. However, running PROSPECT-D for a large array of pixels is too computationally expensive. For that reason, a PROSPECT-D emulator was developed : we generated broadband leaf reflectances and transmittances in the PAR and NIR from a large range of PROSPECT-D simulations, covering all plausible range of leaf traits from Table , which was then used to train a random forest model that relates the leaf traits to the broadband PAR and NIR leaf reflectance and transmittance. Figure  depicts the importance that each leaf trait has on the broadband reflectance emulator, showing that the most important pigment is the chlorophyll a+b concentration, due to its strong absorption of PAR radiation, followed by the leaf dry matter and water contents, which are the main absorbers of the NIR/SWIR radiation.

Soil reflectance has a smaller role in most situations, since the radiation reaching the ground is smaller due to the interception of light by the canopy. However, in sparse and semi-arid conditions, where vegetation is scarce or even not present, soil albedo plays a significant role. Furthermore, these semi-arid areas are usually characterized by brighter soils since they are composed by sands, salts and with a small fraction of organic matter. For that reason, developed a method to unmix the broadband soil reflectance (ρsoil,λ) from the TOC reflectance: 15ρsoil,λ=ρsurface,λ-1-P0θvρleaf,λP0θv where P0θv is the canopy gap fraction at the satellite observation angle θv computed by the Beer-Lambert law (e-κ(θv)LAI), ρsurface,λ is the broadband surface reflectance, and ρleaf,λ is the leaf broadband reflectance computed previously.

In order to convert the narrowband reflectances of the TOC product into broadband reflectances we have applied the approach proposed by , who derived a linear regression model between the satellite spectral bands and the broad bands corresponding to the PAR region (400–700 nm), NIR region (700–2500 nm) and the solar spectrum (SW – 400–2500 nm). Similarly to , to overcome the limited amount of in situ measurements of albedo, we again made use of the PROSPECT-D+4SAIL canopy RTM coupled with the 6S atmospheric RTM to run a large number of simulations covering all plausible illumination, atmospheric and canopy conditions. Once the RTM simulations are performed (at 1 nm step), we convolved the results to both Sentinel-3A and Sentinel-3B specific spectral response functions, and integrated these simulated spectra to the broadband regions defined above. Then, one multivariate linear regression model per broadband region and per platform is fitted with the broadband reflectances as dependent variables and the Sentinel-3 simulated TOC reflectances as explanatory variables. The resulting coefficients are shown in Table , showing the weight of each Sentinel-3 band has on the broadband reflectances. It is worth noting that the coefficients are consistent with the expected behaviour, since the spectral bands located in the PAR region have no influence on the NIR broadband reflectances, nor the spectral bands in the NIR/SWIR influence on the PAR broadband model.

The CLMS ETa product specification states a spatial resolution of 300 m. However, the spatial resolution of the SLSTR LST product is 1 km. Therefore, a method to perform thermal sharpening of the LST is required. Most such methods are based on machine learning approaches, of various complexities, which capture the relationships between shortwave spectral reflectance (and possibly other ancillary data) and the LST. The shortwave reflectance is of higher spatial resolution and is resampled to the resolution of LST to be used as explanatory variables for model training. Once trained, the model is applied to the reflectance at its original resolution to obtain a representation of LST at that resolution. In most approaches, this is followed by a bias correction step to ensure conservation of energy between the LST maps at both the original and sharpened spatial resolutions .

Both the Sen-ET and WaPOR (version 3) modelling frameworks use a Data Mining Sharpener (DMS) thermal sharpening approach as implemented in the pyDMS Python package (https://github.com/radosuav/pyDMS, last access: 30 July 2025). It is a quite complex method that however works well even for sharpening by a ratio of 50 i.e. sharpening Sentinel-3 LST from 1 km to 20 m using Sentinel-2 reflectance . Based on this work, we are applying it to sharpen Sentinel-3 LST using CLMS TOC product with 300 m spatial resolution. The DMS regression models are trained on the whole Sentinel-3 TOC tile (10° by 10°) as well as on subsets of 30 by 30 LST pixels in a moving window fashion.

In Sen-ET framework all relevant reflectance bands from Sentinel-2 or Sentinel-3 (depending on the target spatial resolution) covering visible, near-infrared and shortwave-infrared parts of the spectrum were used as explanatory variables. For Sentinel-3 this means the following 17 bands from CLMS TOC product: Oa02, Oa03, Oa04, Oa05, Oa06, Oa07, Oa08, Oa09, Oa10, Oa11, Oa12, Oa16, Oa17, Oa18, Oa21, S5N, S6N. This configuration of variables, in addition to DEM and cosine of solar inclination angle, is called “DMS – Reflectance” in Sect. . During the WaPOR project, feature engineering was performed and spectral bands were converted to indices before evaluating their usefulness in DMS . This resulted in following 11 spectral bands, reflectance indices and DEM-related products being used as explanatory variables: Oa04 (blue), Oa17 (NIR), Modified Normalized Difference Water Index (MNDWI), Plant Senescence Reflectance Index (PSRI), Normalized Difference Moisture Index (NMDI), Visible Atmospherically Resistant Index Red Edge (VARI_RED_EDGE), Bare Soil Index (BI), elevation, cosine solar inclination angle, aspect and slope. More details and the list of evaluated indices are available in the WaPOR wiki (https://github.com/un-fao/wapor-et-look/wiki/Land%20Surface%20Temperature#processing-approach, last access: 22 January 2026). This combination of explanatory variables is called “DMS – WaPOR” in Sect. . Finally, since the main influence of aspect and slope on LST is already captured in the solar inclination angle variable and their additional impact on sharpened LST accuracy is negligible (see Sect. ), those two variables were removed from the WaPOR list. The resulting combination of 9 variables (called “DMS – WaPOR selected” in Sect. ) is used in the ETa processing chain to sharpen the 1 km Sentinel-3 LST to the required 300 m spatial resolution.

Weather forcing is critical for accurate estimation of ET. Due to the 2 d timeliness requirements for the CLMS ETa product, the weather data source is Copernicus Atmosphere Monitoring Service (CAMS) forecasts , produced by the European Center for Medium Range Weather Forecasts and distributed freely and openly through the CAMS Data Store. CAMS data contain surface meteorological parameters with forecast runs every 12 h covering the whole Earth on a 0.4° grid and hourly temporal resolution. In this study we used CAMS forecasts with 12 h lead time also for the production of historical data to ensure fair comparison with the NRT dataset.

Instantaneous weather forcing at the satellite overpass are used to drive both ET models and include air temperature, vapor pressure, wind speed, surface pressure, and clear-sky solar irradiance (Table ). All instantaneous data were obtained by linear interpolation between two CAMS hourly forecasts to the time of Sentinel-3 SLSTR acquisition over the area of interest. Daily weather forcing is used to drive the ETLook ET model and to extrapolate and interpolate the instantaneous estimates of ET and include solar irradiance as well as air and dew temperatures, wind speed, and pressure, which are then used to calculate the FAO-56 reference ET required for the gap filling (see Sect. ). They are being integrated over a 24 h period starting at midnight local time.

The pre-processing of CAMS weather forcing, including topographic correction, was done using the open source Python software meteo_utils and as described in . The only differences from being the use of Copernicus DEM (COP-DEM_GLO-90-DTED – ) resampled to a resolution of 300 m for topographic correction and the use of REST2 model to estimate instantaneous clear sky solar irradiance and its PAR and NIR, beam and diffuse components. In addition daily total precipitation is calculated using 24 h integration of CAMS hourly total precipitation forecasts.

Resistance energy balance models need additional ancillary inputs, such as canopy height or roughness. The latter influences the efficiency of the turbulent transport of heat and water between the land surface and the overlying air . Vegetation structure and density are thus important for estimating turbulent transport of momentum, heat and water vapour in the canopy air space .

For that reason, the CLMS Global Dynamic Land Cover map is used to assign vegetation parameters, which are difficult to estimate directly from other Earth Observation data . Those parameters, and values assigned to different plant functional types, are listed in Table . The TSEB-PT model requires all of the parameters, apart from stomatal resistance, while ETLook requires only vegetation height and stomatal resistance. Values of all parameters, except for vegetation height of forested land covers, were adapted from .

Vegetation height is one of the most important of the ancillary parameters, especially for the TSEB model , as it influences the aerodynamic resistance to heat transport. In order to better estimate the obstacle (canopy) height in different land covers we use a framework that differs depending on predominant plant functional type of each land cover. For annual plant functional types, canopy height is dynamically computed considering its growth as: 16hc=hmin⁡+(hmax⁡-hmin⁡)×min⁡LAILAImax⁡, 1 where the symbols are described in Table .

For forest plant functional types we set a static canopy height based on a 10 m spatial resolution (averaged to 300 m resolution) global forest canopy height map developed by combining the Global Ecosystem Dynamics Investigation (GEDI) LiDAR and Sentinel-2 observations using a probabilistic deep learning model . Whenever the land cover map indicated a forest while the GEDI-based canopy height map was below the hmin⁡ parameter, the minimum value was enforced.

The biophysical traits were obtained by random-forest inversion of PROSPECT-D+4SAIL RTM (Sect. ). In order to test the sensitivity and robustness of such inversion method, we ran an independent set of PROSPECT-D+4SAIL simulations to compare how the regression model predicts the biophysical traits. Random white noise was added to this test dataset, considering that retrieved TOC have relative uncertainty of 10 % (ρtest=ρProSAIL[1+N(0,0.1)]). This is shown as an example in Table .

A more computationally efficient alternative for the retrieval of LAI and fg (but not pigments used for albedo estimation) would be to use the daily estimates of LAI and fraction of absorbed photosynthetically active radiation (fAPAR), which are internal CLMS datasets used to produce the 300 m dekadal biophysical CLMS product. In this case we could use a simple relationship between fg, LAI and fAPAR in order to derive the fraction of LAI that is green (fg). 19fg=fAPARfIPAR20fIPAR=1-eK(θs)LAI

where LAI is the total Leaf Area Index LAI=gLAIfg, fIPAR is fraction of intercepted photosynthetically active radiation and K(θs) is the shortwave beam coefficient of extinction at solar zenith angle θs.

Since CLMS LAI product actually represents the green LAI , and with fg and total LAI unknown, an iterative procedure proposed by is performed to find the optimal value of fg based on gLAI and fAPAR. An initial LAI is assumed equal to gLAI (i.e. fg=1), from which fIPAR is computed from Eq. () and then fg recalculated with Eq. (). This process is repeated until the fg value converges between iterations.

In order to evaluate whether both approaches provide consistent data, we ran the biophysical processor over sites included in the ICOS WarmWinter2020 database . These selected sites are listed in Table . We thus compared both LAI and fg retrieved between 2019 and 2021 using the method described in Sect.  against the and LAI/fAPAR approach using the CLMS FAPAR and LAI global products at 300 m, version 1. The density plots of Fig.  shows that overall the LAI products agree well, in particular at values lower than 2–3, with best agreement for green LAI (gLAI). Nonetheless, the larger scatter at higher LAI (i.e. denser vegetation) is not of great concern, as over these very dense canopies the interception (transmission) of radiation is already close to the maximum (minimum), i.e. near the light saturation, and thus these uncertainties have a minimal effect on ETa modelling. It is worth noting these results do not evaluate whether any of the two approaches is better than the other. Indeed, the CLMS gLAI has been intensively validated with a wide dataset of in situ LAI measurements and thus it can be trusted with great confidence.

However, the fraction of LAI that is green (fg) shows larger scatter and with the point cloud in Fig.  far from the 1 : 1 line. This deviation has indeed an effect on the comparison of total LAI with larger scatter and a slight positive bias towards the total LAI derived from the CLMS LAI/fAPAR. In order to better understand the different behavior of fg, Fig.  shows the timeseries for LAI, gLAI and fg over selected representative ICOS sites. These sites include both temperate and semi-arid conditions and a wide range of biomes: broadleaved and conifer forests, croplands, grasslands, savannas, and orchards/vineyards.

These timeseries confirm that LAI trends are mostly in agreement, with only some bias present in very dense vegetation: croplands during their peak development, broadleaved forests in summer and conifer forests. However, the behavior of fg shows discrepancies in certain cases. For instance, we would expect that herbaceous croplands (Fig. a) remain mostly green during the growing phase (spring) with fg values very close to 1 which then decrease during crop senescence in summer. However, thefg data derived from the CLMS LAI/fAPAR products shows values significantly lower than one during spring, and sometimes values close to 1 when LAI decreases during senescence. Another inconsistent behaviour was found in the savanna site (Fig. e), in which the CLMS LAI/fAPAR fg even shows an opposite trend as one would expect i.e. decrease of fg in late spring reaching a minimum in summer where most of the grass layer in this site is dead and only the evergreen oak canopy remains green and then a re-greening with the first rains of autumn. In addition, the fg derived with the CLMS LAI/fAPAR product seems to be also underestimated in the temperate grassland (Fig. b) and evergreen forest (Fig. d), as over these two temperate biomes the canopy should remain mostly green all year round.

PROSPECT-D model, through an emulator, was also used to derive leaf bihemispherical reflectances and transmittance (Sect. ). The evaluation of the performance of this emulator is shown in Fig. . There is a larger scatter for the NIR reflectances and transmittances, likely due to the fact that we are intentionally excluding the PROSPECT-D leaf structural parameter, that basically controls the multiple scattering within the leaf tissues, which is of a larger magnitude in the NIR region than in the PAR. However, the uncertainties when deriving the reflectances and transmittances seem to be cancelled out when computing the leaf absorptance and therefore the conversion from pigments to leaf spectra seems sufficiently robust.

To derive soil bihemispherical reflectance we converted narrowband reflectance values measured by Sentinel-3 satellites into broadband reflectance in PAR and NIR spectral regions using a linear regression approach (Sect. ). We evaluated the goodness of this approach by running an independent set of simulations and compared the retrieved broadbands using the coefficients of Table 5. For both platforms, the evaluation confirms the robustness of conversion from the Sentinel-3 TOC reflectances to the broadband PAR, NIR and SW spectral regions, with negligible mean bias (≈ 0), very low RMSE and very good correlation (≈ 1) (Fig. ).

In the case of CLMS ETa product, the LST sharpening needs to be performed by a ratio of around 3 (i.e. from 1 km to 300 m). Because of this relatively small ratio, the sharpening could potentially be achieved with methods which are more computationally efficient than DMS. Therefore, we also evaluated the performance of a classic and simple (and therefore faster) sharpening method called TsHARP . It relies on finding a linear regression between the Normalized Difference Vegetation Index (NDVI) and LST. The regression is derived on the whole LST scene to be sharpened with NDVI resampled to the LST spatial resolution. Afterwards, the linear regression is applied to NDVI at its native resolution to estimate the representation of LST at this resolution. Finally, a bias correction step is applied to ensure the consistency of LST between the original and sharpened maps.

The two LST sharpening methods were tested in a number of geographically distributed areas of interest (AOI) covering different climatic zones and PFTs (Fig.  left panel) and across different seasons (images from at least four dates were sharpened at each AOI) to ensure a robust comparison. SY_2_SYN___ (SYN) Sentinel-3 product was used as a proxy for CLMS TOC reflectance product since the latter was still in production at the time this analysis was performed. The two products share the same spectral bands and spatial resolutions. The DMS regression models are trained on the entire Sentinel-3 SYN 3 min product data unit (PDU) (around 1400 km by 1200 km) as well as on subsets of 30 by 30 LST pixels in a moving window fashion. The evaluation of the sharpening methods was performed using the Sentinel-3 LST (as shown in Fig.  right panel) due to the lack of in situ LST data which could be used to validate satellite LST with 300 m spatial resolution. The SLSTR LST product was first resampled from 1 to 3 km and the SYN reflectance product was resampled from 300 m to 1 km, as was the ancillary data. The two sharpening methods were then used to recreate the LST at 1 km resolution, and the resulting map was compared with the original LST product. This evaluation framework assumes that there are no significant differences in relations between the explanatory variables and the LST when sharpening from 3 to 1 km and when sharpening from 1 to 300 m.

The results of the comparison are summarized in Table . At all sites the DMS method produces more accurate sharpened LST compared to TsHARP (see supplementary Table ). The largest difference is at the Central Europe AOI where RMSE of DMS is up to 0.3 K lower than that of TsHARP and Mean Absolute Error (MAE) is up to 0.24 K lower. Looking at all sites, the RMSE of DMS is around 0.1 K lower compared to TsHARP (12 % difference) and MAE is around 0.06 K lower (10 % difference). Bias is minimal for both methods because bias correction is incorporated in both of them. Both methods also have similar and very high r2, with DMS being slightly better, and the slope of the linear regression between sharpened and original LST very close to 1.

Regarding the three sets of DMS explanatory variables (see Sect.  for details), the differences between them are negligible. Looking at the details, there is no site in which “DMS – WaPOR” performs better than the other two configurations, while “DMS – Reflectance” has slightly better performance at some sites and “DMS – WaPOR selected” at others. However, the reduction in explanatory variables from 19 (“DMS – Reflectance”) to 9 (“DMS – WaPOR selected”) results in speed-up of the execution by a factor of around 2.3.

Qualitative assessment of the sharpened LST maps reveals that, in some cases, when variability of NDVI is low, TsHARP fails to find a meaningful relation between NDVI and LST (i.e. the linear regression has a slope close to 0). In such cases, the resulting sharpened LST is mainly an output of the bias correction step and has a blurry appearance consistent with simple resampling of lower resolution LST to higher resolution (see Fig. ). In those cases, the quantitative analysis might still result in good accuracy statistics due to a small difference in spatial resolution between 3 and 1 km LST. DMS is less sensitive to, but not fully unaffected by, this issue because it relies on a range of spectral bands, indices, and DEM-based datasets. It is also noticeable that, in some cases, when there is insufficient information in the spectral data, DMS relies too heavily on DEM-based datasets, which can result in artifacts in the sharpened LST. One of the root causes of this issue could be the insufficient or incorrect atmospheric correction applied to SYN spectral bands. For operational production of CLMS ETa (and for production of data validated in Sect. ) the SYN product is replaced by CLMS TOC reflectance product. The latter has shown improved agreement with in-situ measurements and could therefore lead to an improvement in LST sharpening in such cases.

The suitability of the topographically corrected CAMS forecast data (Sect. ) for modelling of actual evapotranspiration was assessed by comparing modelled daily solar irradiance and reference ET against measurements from 43 EC flux towers located in western Europe (France, Belgium, western Germany, Switzerland Spain, and northern Italy), United States and Australia (Fig. ) for the year 2020. Those towers represent various topographical conditions from flat and low-lying to mountainous terrain as well as different climates, from arid to temperate. The statistical results of this comparison are shown in Fig.  and confirm the applicability of CAMS forecast for ETa modelling and suitability of the correction methods.

Apart from forcing the ET models, CAMS data was used for gap-filling of modelled ETa maps through the use of reference ET and precipitation (PR) (Sect. ). We evaluated three gap-filling approaches: ignoring rainfall (called GF_ETr – ); taking rainfall into account as described in (called GF_ETr+PR); conservative modification of GF_ETr+PR described in Sect.  (called GF_ETr+PR80). We also evaluated near real-time (NRT) gap-filling periods with different maximum durations: 15 d (as used by default in Sen-ET approach), 30 and 60 d (as used in WaPOR during reprocessing). Finally, a non-time-critical (NTC) gap-filling with a maximum duration of 60 d (i.e. up to 60 d before and after target date) was also evaluated.

To evaluate the behaviour of the methods in diverse climates, we performed an analysis using in-situ ET measured at geographically distributed ICOS stations (Table ). The daily ET at ICOS stations was calculated by summing up good quality instantaneous ET at hourly or half-hourly timesteps. Dates on which more than two measurements were of poor quality were ignored and no correction for lack of energy balance closure was performed. The determination of quality of ET data was based on ICOS quality flags associated with each measurement. Reference ET and rainfall sums were calculated from the stations' meteorological measurements. Cloudy days were identified as those for which measured solar irradiance was less than 80 % of theoretical surface solar irradiance in clear-sky conditions.

Table  presents the results on this evaluation. Statistics are calculated on daily basis and only for data points which were gap-filled and for which the rainfall adjustment is relevant. Neglecting rainfall can introduce an overall negative bias (underestimation) of up to -0.18 mm d⁻¹ on wet, gap-filled dates. When rainfall is taken into account the introduced bias can become negligible and this reduction in bias leads to a less significant reduction in introduced uncertainty. Method GF_ETr+PR performs well with shorter window size but performance degrades significantly as window size increases and for largest windows the uncertainty is higher than for method GF_ETr. Method GF_ETr+PR80 results in lowest introduced bias and uncertainty with 60 d window size, chosen for the CLMS ETa processing chain. Finally, the NTC gap-filling performs better than NRT gap-filling and with method GF_ETr+PR80 performing the best in this case. An example timeseries of ET gap-filled with methods GF_ETr and GF_ETr+PR80 is shown in Fig. .