ArticlePDF Available
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Journal of Hydrology: Regional Studies
Volume 53, June 2024, 101785
Evaluation of the METRIC and TSEB remote sensing evapotranspiration
models in the floodplain area of the Thaya and Morava Rivers
Authors: T. Ghisi a, b, *, M. Fischer a, b, H. Nieto c, N. Kowalska b, G. Jocher b, L. Homolová b,
V. Burchard c, Z. Žalud a, b, M. Trnka a, b
a Global Change Research Institute of the Czech Academy of Sciences, Bělidla 986/4b, 603 00 Brno, Czech Republic
b Mendel University in Brno, Institute of Agrosystems and Bioclimatology, Zemědělská 1, 613 00 Brno, Czech Republic
c Institute of Agricultural Sciences-CSIC, Serrano 115 b, 28006 Madrid, Spain
*Corresponding author: E-mail address: ghisi.t@czechglobe.cz (T. Ghisi).
(This version of the paper was published in Journal of Hydrology: Regional studies)
As the funder requires the full Open Access to the research results of our team, we would like to
apply the CC-BY-SA licence and the full Open Access option.”
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Abstract
Study region: Floodplain ecosystem region at the confluence of the Morava and Thaya Rivers, the
Czech Republic.
Study focus: Accurate determination of actual evapotranspiration (ETa) is essential for understanding
surface hydrological conditions. The aim of this study was to evaluate two remote sensing models,
METRIC and TSEB, for estimating ETa and energy fluxes in two ecosystems using the eddy covariance
(EC) as a reference.
New hydrological insights for the region: Both models demonstrate the ability to quantify ETa
across the region. Compared with the METRIC, which had a mean bias error (MBE) = 0.12 mm/day,
the TSEB better detected ETa in the forest test site (MBETSEB = -0.03 mm/day). In contrast, the METRIC
improved detection of ETa (MBEMETRIC = -0.03 mm/day) in grassland test site, where the TSEB
overestimate daily ETa (MBETSEB = 0.52 mm/day). The models and EC indicate similar seasonal
dynamics of the evaporative fraction and Bowen ratio throughout the growing season. Despite the
overall agreement between the models and EC, the selected spatial outputs indicate some disagreement
among them in terms of the spatial patterns of ETa. This disagreement is related to the sensitivity of
TSEB to canopy height/roughness, as well as the a priori PriestleyTaylor coefficient in forests. Despite
these shortcomings, this study highlights the applicability of remote sensing energy balance-based
diagnostic models for studying hydrological processes in a spatially distributed manner.
Key words: Eddy covariance, Evapotranspiration, Floodplain ecosystem, Remote sensing models,
Water balance
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1 Introduction
Climate projections estimate an increasing probability of extreme meteorological and climatic event
occurrences, including droughts and floods, in Central Europe (Možný et al., 2020). In light of climate
change, water availability is critical for maintaining agronomic production in the lowlands of Central
Europe (Trnka et al., 2022a). Currently, a broad range of adaptations are being planned to mitigate the
negative impacts of climate change in the area (Hlásny et al., 2014; Komissarov and Klik, 2020).
Considering the negative climatic water balance in the lowlands and the vulnerability of these regions
to drought (Duethmann and Blöschl, 2018; Trnka et al., 2022b; Fischer et al., 2023), there is a need for
an appropriate tool to spatially detect ETa at the landscape level. This approach is vital for enhancing
the refinement of key strategic measures aimed at managing the water balance at different spatial scales.
Remote sensing appears to be a suitable tool for assessing landscape water balance because satellite
sensors can easily identify relevant land surface state variables and properties needed to model water
and energy fluxes (Anderson et al., 2012), and archives can be used to perform time series analyses.
While direct in situ evapotranspiration measurements of ETa, such as the EC method, are focused on the
individual ecosystem scale, remote sensing models allow mapping of ETa to the global scale as a whole
while maintaining the possibility of analyzing individual ecosystems and their role in catchment
hydrology (Allen et al., 2007a; Guzinski et al., 2020; Aboelsoud et al., 2023).
Physically based remote sensing models based on surface energy balance principle have been widely
used for the spatial estimation of ETa (Norman et al., 1995; Anderson et al., 1997; Bastiaanssen et al.,
1998; Allen et al., 2007a; Senay et al., 2007). Prominent energy balance models include one-source
energy balance models such as the SEBAL (surface energy balance algorithm for land) (Bastiaanssen et
al., 1998; Bastiaanssen et al., 2005) or METRIC (mapping evapotranspiration at high resolution with
internalized calibration) (Allen et al., 2007a); two-source energy balance (TSEB) models (Norman et
al., 1995); and three-source energy balance models (Burchard-Levine et al., 2022).
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The METRIC model (Allen et al., 2007a) is based on the pioneering foundation of the SEBAL model,
which uses two anchor pixels (“dry and wet pixels”) to determine the aerodynamic resistance and near-
surface vertical air temperature gradient of these two extreme endmembers. The main advantage of the
METRIC model is its self-calibration across the studied domain, which simplifies some physical
processes, prevents difficult-to-solve errors and is less sensitive to uncertainties in land surface
temperature retrievals (French, Hunsaker and Thorp, 2015). This approach makes it a suitable tool for
the robustness and estimation of ETa in areas with less known surface conditions (Chirouze et al., 2014).
Compared to the METRIC model, the TSEB model uses a more detailed parameterization of the energy
fluxes between the plant canopy and the soil surface. As such, the model is able to estimate transpiration
from vegetation cover and evaporation from the soil surface, which can be useful within an agronomic
sector where irrigation strategies strive to reduce water losses from evaporation rather than from
transpiration (Burchard-Levine et al., 2022). The TSEB requires a more detailed characterization of
surface biophysical conditions and is more sensitive to possible errors in land surface temperature
estimation (French, Hunsaker and Thorp, 2015).
Both models have demonstrated the ability to accurately detect ETa within various ecosystems and under
various environmental conditions (Allen et al., 2007b; Hankerson et al., 2012; Mkhwanazi and Chávez,
2012; Carrasco-Benavides et al., 2014; Zhang et al., 2015; Liebert et al., 2016; Nieto et al., 2019a, b;
Guzinski and Nieto, 2019; Guzinski et al., 2023). However, in Central Europe, the application of the
METRIC and TSEB models has been limited to only a handful of proof-of-concept studies (Fischer et
al., 2023; Ghisi et al., 2023). This study aimed to evaluate the METRIC and TSEB models in the
hydrologically and biologically unique area of the southern Moravia floodplain region in the Czech
Republic. Unlike the majority of studies evaluating remote sensing models within a specific vegetation
surface, the uniqueness of this study lies in the assessment of models at multiple sites representing
different ecosystems within the area of interest. The two selected test sites equipped with EC systems
represent structurally and aerodynamically contrasting land coversgrassland and forestensuring a
robust experimental design to evaluate remote sensing methods.
In this study, both of the selected models determine ETa through surface energy balance, yet by adopting
different sets of assumptions and different levels of complexity. The primary motivation for evaluating
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these models is their potential in addressing hypotheses associated with accurate detection of water
balance in the Central Europe regions where ETa represents the dominant loss component in the water
balance.
2 Methods
The workflow of this study was divided into three basic categories concerning 1. Processing of
available input data, 2. Evaluation of selected models, and 3. Testing and application of models. The
basic workflow of the study is depicted in the Work flowchart (Fig. 1).
Fig. 1 The work flowchart outlines the workflow applied in this study. Individual steps are described in
individual chapters.
2.1 Study area
The area of interest is located in the largest floodplain forest complex in the southernmost part of the
South Moravia region, in the Czech Republic, near the confluence of the Thaya and Morava Rivers (Fig.
2). The elevation of the area varies between 150 and 160 m. Fluvial soils are the dominant soil type in
the area. The 130-km2 region, nicknamed the “Moravian Amazon”, represents the wedge of floodplain
forest in the confluence area and is considered to become the 27th Protected Landscape Area in the Czech
Republic. The area includes two EC stations monitoring two structurally contrasting ecosystemsforest
and grassland. The forest test site (Forest) is located in a mature floodplain forest of English oak
(Quercus robur L.), European ash (Fraxinus angustifolia L.) and Common Hornbeam (Carpinus betulus
L.). The site is equipped with a flux tower with meteorological sensors at different heights (Kowalska
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et al., 2020), including an EC system (Tab 1). The Forest site contributes to the ICOS (Integrated Carbon
Observation System) network. The grassland test site (Grassland) is located in the floodplain meadow
approximately 850 m from the Thaya River and approximately 3 km northward from the Forest. A
similar EC system is installed at a height of 2 m above the ground (Tab. 1). Although a significant part
of the floodplain forest is inundated regularly during flood events or during the artificial release of flow
waves from the Nové Mlýny reservoir, both test sites typically remain a few meters above the flood line.
Fig. 2 Location of the floodplain area with Grassland and Forest test sites.
2.2 Meteorological data
The METRIC and TSEB models require instantaneous meteorological data at the satellite overpass time.
The meteorological station data from the Forest (36 m height) in the period 20152021 were used for
both models at half-hourly steps. While EC data were measured at a height of 44 m, meteorological data
of air temperature, wind speed and relative humidity from a height of 36 m were used as inputs to models
because these data provide a continuous time series of meteorological data compared to those measured
at 44 m, where meteorological data were missing during some parts of the monitored period. Both the
METRIC and TSEB models used the same meteorological data as the inputs except precipitation which
was required only by the METRIC model to simulate a soil moisture in the hot pixel where we assumed
non-zero values of ETa. (Tab. 1). While the data from the Forest site were available since 2015, the
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measurements from the Grassland began in June 2019; thus, the data were available since that period in
the Grassland.
2.3 Eddy covariance data
The two EC systems used in the study were equipped with various ancillary instruments (Tab. 1).
The instrumentation used in the study fulfilled the standards of the ICOS, which provides high-quality
long-term observations of greenhouse gases and greenhouse gas exchange (https://www.icos-cp.eu/).
Site
Measured parameter
Instrument
Height/Depth (m)
Monitored period
Meteorological
data (Forest)
Radiation balance (W/m2)
CNR4 Net Radiometer, Kipp&Zonen, NE
44
20152021
Air temperature (°C)
EMS33, CZ [1], HMP155, Vaisala, FI [2]
36
Wind speed (m/s)
Wind Sonic 2D, Gill Instruments, UK
36
20152021
Relative humidity (%)
EMS33, CZ [1], HMP155, Vaisala, FI [2]
36
Precipitation (mm)
Thies Laser Precipitation Monitor, DE [1]
44
July 20162021 [1]
Weighing Rain Gauge - OTT Pluvio², DE [2]
44
2015July 2016 [2]
Forest [1];
Grassland [2]
Soil heat flux (W/m2)
HFP01SC-05, Hukseflux, NE
0.05
20152021 [1]
June 20192021 [2]
Eddy covariance
Forest [1] [2];
Grassland [3]
Sensible heat flux (W/m2)
Latent heat flux (W/m2)
Gas analyzer Li-7200 (LI-COR
Environmental, Lincoln, NE); 3D sonic
anemometer Gill HS-50 (Gill Instruments,
Hampshire, UK)
44 [1]
48 [2]
2 [3]
2.3.1 Turbulent energy flux calculation and postprocessing
Turbulent energy fluxes determined by the EC method were calculated with the software EddyPro®
(version 6.2.0; LI-COR Biosciences, Lincoln, NE, USA). All required corrections of the calculated
covariances between the vertical wind component w and the quantity of interest, i.e., H2O concentrations
and sonic temperature, were applied to derive the final 30-minute averaged latent (LE) and sensible heat
(H) turbulent energy fluxes. The data were processed according to standard FLUXNET processing
methods (Pastorello et al., 2014). This includes, for example, filtering via a friction velocity threshold
(Papale et al., 2006) to ensure sufficient turbulent mixing and filtering via quality flags (Foken et al.,
2004) that test the data for stationarity and turbulence development, two of the main preconditions of
the EC method. This procedure ensures the highest possible quality of the used EC data. The uncertainty
Tab. 1 Instruments for measuring meteorological and EC parameters and their application during
the monitored period in the Forest and Grassland.
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range of EC data of highest quality is 1020% (Foken, 2008). Flux data gap filling was performed using
the R package REddyProc (Wutzler et al., 2018), applying marginal distribution sampling (Reichstein
et al., 2005. The method proposed by Kljun et al. (2015) for predicting flux footprint was employed to
estimate the daily average EC footprint for both stations. The daily average footprint was determined as
an average of footprints during the period representing 80% of the daily cumulative ETa. In this way,
the footprint was representing the part of day when ETa is high and e.g. the nighttime footprints with
potentially much larger extent were excluded. The footprint size for the Forest was 0.690 km2, and for
the Grassland, it was 0.020 km2 (Fig. 3).
Fig. 3 The average daily footprint of all available daily EC data of the Forest site (left) and Grassland
site (right). The black polygons represent cumulative contribution to measured ETa starting from 10%
around the tower (dark red color), through 30%, 50%, 70%, up to a 90% polygon (light blue color).
These EC data supplemented by soil heat flux (G) and net radiation (Rn) were used for the evaluation of
both the METRIC and TSEB models. At both test sites, G was measured at a depth of 0.05 m, and no
measurements of soil heat storage above the heat flux plate were conducted. The EC energy fluxes of
LE and H were not corrected for energy balance closure (EBC), and the residual energy was significant
in some cases. The average residual energy was 38% in the Forest and 30% in the Grassland during the
days from 2015 to 2021 with available satellite images. For this reason, the comparison of model-
projected fluxes with EC measurements was conducted both without EBC and with EBC adjustment.
The EBC adjustment was calculated according to the Bowen ratio adjustment (Twine et al., 2000; Foken
a
b
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2008; Fischer et al., 2018). This method fully closes the energy balance by distributing the residual
available energy to H and LE while preserving their ratio, i.e., the Bowen ratio H/LE.
2.4 Satellite data preprocessing
In this study, Landsat 8 data were used to estimate ETa and energy fluxes at a 30-m resolution during
the period between 20152021. Landsat imagery was downloaded from the United States Geological
Survey (USGS) Earth Explorer website (https://earthexplorer.usgs.gov/). The surface reflectance and
surface temperature datasets from OLI+ and TIRS retrieved from Landsat Collection 2 Level 2 Science
products were selected according to the occurrence of cloud cover over the area of interest. If clouds
were present only partly, the cloudy pixels were filtered, and only cloud-free pixels were subsequently
used. In total, 117 clear-sky images were available for the area of interest between 20152021.
2.5 Evapotranspiration models
The METRIC model (Allen et al., 2007a), available at https://github.com/midread/water, and TSEB
model (Norman et al., 1995), with code available at https://github.com/hectornieto/pyTSEB
(https://doi.org/10.5281/zenodo.594732), are diagnostic remote sensing models that estimate spatial ETa
based on surface energy balance calculations using satellite land surface temperature (LST) retrieval.
Although both models are based on the calculation of the surface energy balance, their approaches differ.
The METRIC model is a one-source model that utilizes so-called cold and hot pixels for internal
calibration to evaluate the surface temperature gradient between the land surface and air. The cold pixel
characterizes moister conditions, where the surface temperature is minimal and the LAI is maximal;
hence, the instantaneous LE should be the highest within the analyzed domain. Conversely, hot pixels
characterize dry conditions, where the surface temperature is maximal, the LAI is minimal, and the LE
should be the lowest (Allen et al., 2007a). In this study, automatic selection of hot and cold pixels
(Olmedo et al., 2016) was performed.
The TSEB model is a two-source model with an emphasis on partitioning fluxes into canopy and soil
categories; thus, more detailed characteristics of the canopy, such as green and total LAI, effective leaf
size, and soil and leaf spectra, are needed. The TSEB physically relates the radiometric temperature
acquired with thermal infrared satellite sensors to the aerodynamic temperature (defined as the
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extrapolation of air temperature profile down to an effective height within the canopy at which the
vegetation components of sensible and latent heat flux arise (Kalma and Jupp, 1990)) required to
accurately derive H without the need for using an excess resistance formulation typical for one-source
models (Kustas et al., 2016). The TSEB model uses an a priori guess of the PriestleyTaylor coefficient
(α), which is iteratively reduced within the model under stressed conditions until realistic canopy and
soil energy fluxes are achieved (i.e., fluxes >=0), yielding the determination of the energy flux
partitioning at the end of the iteration. The value of the α coefficient is set to 1.26 for lower vegetation
(grasslands, crops). In the forested areas, α coefficient is scaled according to the study of Guzinski et al.
(2013) after the work of Komatsu (2005), who focused on categorizing the α coefficient in forested areas
according to canopy height. The coefficient decreases with the increasing canopy height.
Both models calculate daily ETa values from instantaneous values at the time of satellite overpass, but
both utilize a different approach in this study. The concept behind the METRIC model assumes that the
ratio between the instantaneous ETa and the instantaneous reference evapotranspiration (ETo) remains
constant throughout the day. Therefore, the METRIC model calculates the daily ETa by using the
reference fraction (ETa /ETo) determined at the satellite overpass time. This fraction is then multiplied
by the daily ETo value (Allen et al., 2007a).
On the other hand, in the TSEB model, the total amount of latent energy (LE) is assumed to be directly
proportional to the amount of incoming solar radiation. Therefore, this scaling concept initially
calculates the daily LE value by computing the ratio between LE and shortwave solar incoming
radiation, which is subsequently multiplied by the daily incoming solar radiation. The daily LE,
expressed in energy units, is subsequently converted to ETa, expressed in terms of mm/day.
2.6 Determining the momentum roughness and canopy height in the models
Both models require the determination of a momentum roughness length (z0m) for accurate calculation
of H. A concept for determining the momentum roughness differs for forested (forests) and grassed
(grasslands, crops) areas. The Corine Land Cover 2018 (Cover, 2018) dataset was used to distinguish
different land cover types.
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The momentum roughness calculated in both the METRIC and TSEB models for forests, as described
by Raupach et al. (1994), is based on canopy height and LAI. In this study, canopy height was estimated
using the Global Forest Canopy Height data (Potapov et al., 2021), which was derived from Global
Ecosystem Dynamics Investigation Ecosystem (GEDI) Level 3 data (Dubayah et al., 2021) and has been
operational aboard the International Space Station.
In the case of herbaceous cover (grasslands, crops), z0m was scaled without determining canopy height
in either model. It was assumed that the crop height varies with the LAI and that z0m was directly defined
according to Tasumi (2003), where z0m was expressed as the LAI multiplied by 0.018.
2.7 Estimation of albedo, LAI and delta temperature
The albedo is quantified as the proportion of incident shortwave radiation reflected back into the
atmosphere, calculated as the ratio of reflected to incoming solar radiation. This albedo estimation was
conducted using satellite bands spanning from 2015 to 2021 at both sites. The LAI, as a critical
biophysical characteristic of the surface, was spatially determined utilizing data from the Landsat 8
satellite. The methodology for LAI derivation aligns with procedures established for Sentinel satellite
data, employing canopy radiative transfer models as outlined in Weiss et al. (2000). This LAI estimate
was further integrated into the METRIC and TSEB models, enhancing the detection and analysis of
vegetation parameters. Furthermore, the concept of the delta temperature (ΔT) was introduced,
representing the difference between the surface temperature and air temperature (recorded at 36 m above
ground) over the period from 2015 to 2021.
2.8 Gap-filling of daily ETa using clear-sky images
In this study, the daily ETa outputs of both model outputs were interpolated and approximated to annual
values. The available ETa data of models were interpolated using the ETa/ETo ratio. The calculated
ETa/ETo ratios were used for linear interpolation for dates between available model outputs. Then, the
interpolated daily ETa/ETo ratios were multiplied by daily ETo values to derive the daily gap-filled ETa.
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2.9 Data analysis
Data analyses of model outputs and surface conditions were performed using R statistical programming
language in RStudio (RStudio Team, 2020), version 1.4.7171 (R Core Team, 2020). The graphical
spatially oriented outputs (Fig. 14 and Fig. 15) were performed by software QGIS (QGIS Development
Team, 2024), version 3.18.3 (QGIS 3.18.3, 2024).
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3 Results
3.1 Surface conditions
The variation in albedo (Fig. 4 a) was related to seasonal variability during the year and corresponded
well to the variation in the LAI in the Forest (Fig. 4 b). A greater albedo was detected in the Grassland
with a maximum (0.19) in June 2017. The monthly LAI values ranged between 0.5 in the dormant season
and nearly 8 during the growing season in the Forest. Lower LAI values were detected at the Grassland
station, where average monthly values mostly range between 0.5 and 4. The lower LAI values were
influenced by regular site management in the Grassland, which involves a regular reduction in grass
cutting, consequently leading to a reduction in vegetation at the site during the year. ΔT (Fig. 4 c)
exhibited relatively low variation ranging between -5 and 5°C in the Forest; however, more pronounced
seasonal variability was observed in the Grassland, where ΔT ranged from -1 to 15°C. The higher values
of ΔT in the Grassland indicate a relatively high surface heating during summer periods. Also, the high
ΔT in the Grassland could be related to differences in microclimatic conditions between surfaces where
air temperature was measured above forest cover and surface temperature measured at grassland. These
variables represent a wide range of surface conditions at the two different EC sites, in which the
METRIC and TSEB models were evaluated during the period 20152021.
Fig. 4 Temporal variation of albedo (a), LAI (b) and ΔT (c) at the Forest (brown lines) and
Grassland (green lines) in 20152021. The points represent average monthly values for dates
where the clear sky satellite images were available. ΔT shown a difference between surface
temperature determined by satellite sensor and air temperature measured at ecosystem site.
b
c
a
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3.2 Evaluation of TSEB and METRIC to EC measurement
3.2.1 Comparison of energy fluxes without EBC of EC
These comparisons were made between the TSEB model and EC (Fig. 5 a, c) and between the METRIC
model and EC (Fig. 5 b, d) at satellite overpass times for the Forest and Grassland. Overall, good
agreement was observed between the TSEB model and EC method for H (MBETSEB = 26.77 W/m2,
R2TSEB = 0.37) and for LE (MBETSEB = 38.4 W/m2, R2TSEB = 0.60) in the Forest (Fig. 5 a). Similarly,
compared with the EC method, the METRIC model (Fig. 5 b) tended to overestimate H (MBEMETRIC =
64.2, W/m2, R2METRIC = 0.19), LE (MBEMETRIC = 76.04 W/m2, R2METRIC = 0.54), and Rn (MBEMETRIC =
77.62 W/m2, R2METRIC = 0.85). The METRIC model also estimated a few negative LE values, indicating
a condensation process on the surface. These values corresponded to the winter months.
a
c
d
b
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Fig. 5 Scatter plots of comparisons between the TSEB model and EC (a, c) and the METRIC model and
EC (b, d) for energy fluxes (Rn, LE, H, G) in the Forest (upper images) and Grassland (bottom images)
without the EBC adjustment of EC.
The comparison of these values for the Grassland (Fig. 5 c, d) revealed good correlations between the
models and the EC method. The TSEB well estimated H (MBETSEB = 1.78 W/m2, R2TSEB = 0.46 W/m2)
but overestimated LE (MBETSEB = 83.20 W/m2, R2 TSEB = 0.60 W/m2). The METRIC showed a
performance similar to that for the Forest and overestimated H (MBEMETRIC = 85.57 W/m2, R2METRIC =
0.29 W/m2) and LE (MBEMETRIC = 53.36 W/m2, R2METRIC = 0.48 W/m2). Compared to those from both
models, the measured G yields were lower at both test sites.
3.2.2 Comparison of energy fluxes with EBC of EC
For the purpose of evaluating the METRIC and TSEB models, the EBC of the EC method was enforced
in both comparisons using the Bowen ratio adjustment method. (Fig. 6). The results for the TSEB
indicate an underestimation in H (MBETSEB = -35.32 W/m2 and R2TSEB = 0.32) but good agreement in
LE (MBETSEB = -5.05 W/m2 and R2TSEB = 0.62) in the Forest (Fig. 6 a). Overall, the forced EBC showed
improved agreement between the METRIC model and the EC (Fig. 6 b) compared to that of the
comparison without forced EBC (Fig. 5 b). The METRIC model well estimated H, with MBEMETRIC =
3.43 W/m2 and R2METRIC = 0.23 (without forced EBC, MBEMETRIC = 64.20 W/m2, R2METRIC = 0.19) and
overestimated LE, with MBEMETRIC = 33.97 W/m2 with R2METRIC = 0.60 (without forced EBC,
MBEMETRIC = 76.07, W/m2, R2METRIC = 0.54). However, the METRIC model still exhibited few
significant differences in H, exceeding 200 W/m². In the Grassland, the TSEB model underestimated H,
with MBETSEB = -44.81 W/m2 and R2TSEB = 0.32, and slightly overestimated LE, with MBETSEB = 28.17
W/m2 and R2TSEB = 0.80 (Fig. 6 c). Similarly, as in the Forest, forcing EBC of the EC improved the
agreement with the METRIC model. However, the METRIC model still slightly overestimated H, with
a MBEMETRIC= 37.47 W/m2 and an R2METRIC = 0.29 but well estimated LE, with a MBEMETRIC = 0.41
W/m2 and an R2METRIC = 0.52 (Fig. 6 d).
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Fig. 6 Scatter plots of comparisons between the TSEB model and EC method (a, c) and the METRIC
model and EC method (b, d) for energy fluxes (Rn, LE, H, G) in the Forest (upper panel) and Grassland
(bottom panel) after the forced energy balance closure preserving the measured Bowen ratio (H/LE).
3.2.3 Comparison of ETa between models and EC
The instantaneous LE data from the METRIC and TSEB models were scaled to the daily ETa outputs
and compared to the EC measurements without and with the EBC adjustment in Forest and Grassland.
Overall, both models demonstrated satisfactory performance in estimating daily ETa values without EBC
adjustment at the Forest (Fig. 7 a, b), with both models indicating MBE values close to 0 (MBETSEB = -
0.03 mm/day, MBEMETRIC = 0.12 mm/day) and RMSE values lower than 1 mm (RMSETSEB = 0.70
mm/day, RMSEMETRIC = 0.86 mm/day). Although the models demonstrate good agreement with the EC
method without EBC adjustment, both indicate few values where the disagreement were greater than 2
mm at the Forest. A comparison of the models to the EC method with EBC adjustment showed worse
a
c
d
b
17
agreement when both models underestimated the daily ETa (MBETSEB = -0.5 mm/day, MBEMETRIC = -
0.39 mm/day).
In the Grassland (Fig. 7 c, d), a comparison of the models to the EC method without EBC adjustment
demonstrated slightly worse agreement for the TSEB model than for METRIC model (MBETSEB = 0.57
mm/day, MBEMETRIC = -0.03 mm/day). However, the TSEB model had improved R2 values (R2TSEB =
0.80, R2METRIC = 0.62) and lower RMSE values (RMSETSEB = 0.85 mm/day, RMSEMETRIC = 0.90
mm/day). The comparison of daily ETa between the TSEB model and the EC with EBC adjustment
showed improved agreement in the Grassland (MBETSEB = 0.1 mm/day) but worsened in the case of the
METRIC model (MBEMETRIC = -0.42 mm/day) in the Forest.
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Fig. 7 Comparisons of ETa daily values between the TSEB model and the EC method (a, c), the METRIC
model and the EC method (b, d) and average of the models’ ETa values and those of the EC method (e,
f) in the Forest (a, b, e) and Grassland (c, d, f). Red points depict model comparisons with the EC method
c
b
a
d
e
f
19
without EBC adjustment (EC_unclosed), while black points represent comparisons with EBC
adjustment (EC_forced).
Because both models often indicate opposite bias compared to EC, the daily ETa values of both models
were averaged and compared to those of the EC method with and without EBC adjustment in the Forest
(Fig. 7 e) and Grassland (Fig. 7 f). Compared to the agreement between the TSEB model and the EC
method (Fig. 7 a) and between the METRIC model and the EC method (Fig. 7 b) in the Forest, the
comparison of averages to EC method values without EBC adjustment (Fig. 7 e) demonstrated improved
agreement in all the metrics except for the MBE, where a similar value (0.04 mm/day) was detected as
in the case of the TSEB model and EC method (-0.03 mm/day). The same pattern was detected for the
comparison of the model averages to EC method values with EBC adjustment, where averages indicated
a worse MBE (-0.46 mm/day) than in the METRIC-EC comparison (MBEMETRIC = -0.39 mm/day).
In the case of Grassland (Fig. 7 f), the comparison of averaged model values showed improved
agreement with that of EC values without EBC adjustment, except for MBE, which was 0.22 for average
values and 0.03 for the METRIC model and EC method (Fig. 7 d). Comparison of averages to EC values
with EBC adjustment slightly worsened the agreement in error metrics compared to the TSEB EC
comparison (Fig. 7 c) in most metrics but improved agreement with the METRIC EC comparison (Fig.
7 d) in all metrics.
3.3 Intercomparison of the METRIC and TSEB models
3.3.1 Intercomparison of energy fluxes
Intercomparison between the METRIC and TSEB models was conducted within 99 common outputs.
In the Forest (Fig. 8 a), a comparison of H indicated generally lower H (y = 0.26x) and LE (y = 0.5x)
values in the TSEB model. Both models also demonstrated similar G values, where the TSEB model
yielded slightly lower outputs than did the METRIC model (y = 0.83x) and different estimates of Rn for
some outputs. In the Grassland (Fig. 8 b), the TSEB model showed lower Rn values and a significantly
lower H (y = 0.37x) than did the METRIC model. Nevertheless, there was slightly improved agreement
in the LE (R2 = 0.45, y = 0.73x).
20
Fig. 8 Scatter plots of comparisons of energy flux values (Rn, LE, H, G) between the TSEB and
METRIC models in the Forest (a) and Grassland (b) in the period 20152021.
3.2.2 Comparison of temporal variation of H
Both models and the EC method without EBC adjustment captured the seasonal variability in H
throughout the year (Fig. 9). The highest H values varied between years in the Forest (Fig. 9 a); however,
most H values occurred in the first half of the growing season (AprilMay) when the surface was not
fully covered by vegetation. The greatest average values at the time of satellite overpass were indicated
by the METRIC model (237.28 W/m²) compared to those from the TSEB model (194.70 W/m²) and EC
method (171.28 W/m²) in the Forest. The METRIC model also showed the highest instantaneous H
value on March 20, 2021 (479.16 W/m²), while the TSEB showed the maximal H value on July 10, 2021
(454.83 W/m²), and the EC method showed it on April 16, 2016 (411.21 W/m²). Both models and the
EC method also indicated similar standard deviation (σ) values TSEB = 104.34 W/m², σMETRIC = 110.80
W/m², σEC = 88.60 W/m²). A relatively high discrepancy between the models and the EC was shown in
the summer of 2019 and in the second part of 2021, where both models consistently overestimate H.
Compared with the TSEB model and the EC, the METRIC model also evidently indicated higher values
in the summer of 2015. A similar pattern was detected in the Grassland compared to the Forest (Fig. 9
b), where the METRIC consistently indicated greater H values than did the TSEB and EC. This was
confirmed by average instantaneous values at the satellite overpass, where good agreement was detected
between the TSEB model (100.14 W/m²) and the EC method (109.79 W/m²), while the METRIC model
a
b
21
indicated a higher H value (193.57 W/m²). The highest maximal H value was detected by the METRIC
model on March 20, 2015 (449.72 W/m²).
Fig. 9 Temporal variation of H data from the TSEB and METRIC models in the period 20152021 at
time of satellite overpass in Forest (a) and Grassland (b). The gray line depicts daily EC values while
the black crosses depict instantaneous EC data. The AVG show average daily values, max indicate
maximal daily measured values and σ mean standard deviation value.
b
a
22
3.3.3 Intercomparison of ETa
In the case of the ETa model intercomparison (Fig. 10), a relatively high disagreement was detected
between the TSEB and METRIC models in the Forest (R2 = 0.56, y = 0.68x). The results were more
consistent for Grassland (R2 = 0.61); however, it was also evident that the TSEB model shows higher
values than the METRIC model.
Fig. 10 Comparisons of ETa daily values between the TSEB and METRIC models in Forest (a) and
Grassland (b) in the period 20152021.
3.2.4 Comparison of temporal variation of ETa
Both models were able to capture seasonal variability during the years (Fig. 11). The average daily ETa
values between the models and the EC without EBC adjustment were similar (AVGTSEB = 2.1 mm/day,
AVGMETRIC = 2.3 mm/day, AVGEC = 2.2 mm/day) in the Forest (Fig. 11 b). The METRIC model outputs
revealed the greatest variability; however, the values of variability were almost identical between the
models and the EC method TSEB = 1.4 mm/day, σMETRIC = 1.6 mm/day, σEC = 1.7 mm/day). A maximum
daily value of 6.7 mm was recorded by the TSEB model on June 19, 2019, while in the METRIC model
this value reached 6.08 mm on July 26, 2021. These two values were approximately 2 mm greater than
the maximal value detected by the EC method (4.1 mm/day) among the available clear-sky satellite
images. The highest discrepancy between the two models was detected on June 19, 2019, when the
TSEB model exhibited a higher value of approximately 3.0 mm/day. In the Grassland (Fig. 11 b), the
b
a
23
TSEB model had the highest daily ETa average (2.8 mm/day) compared to those of the EC method (2.5
mm/day) and the METRIC models (2.1 mm/day). The TSEB model exhibited similar ETa variability to
that of the EC method TSEB = 1.3 mm/day, σEC = 1.5 mm/day) but greater than that of the METRIC
model METRIC = 1.1 mm/day). The maximal value for the TSEB model (5.9 mm/day) was observed on
June 12, whereas the METRIC model recorded the maximal ETa on July 26, 2021 (5.4 mm/day). Higher
values of ETa were detected in the last monitored year (2021). These higher values corresponded to the
detected H (Figure 9 b), which indicated lower H during that year in the Grassland.
Fig. 11 Temporal variation of ETa daily data of the TSEB and METRIC models during the period 2015
2021 in the Forest (a) and Grassland (b). The gray line represents all available EC daily ETa, while the
black crosses depict EC daily ETa data for the days of model outputs.
a
b
24
3.4 Instantaneous evaporative fraction and Bowen ratio
Both models and the EC method without EBC adjustment were utilized to calculate the evaporative
fraction and Bowen ratio. The evaporative fraction expresses how much available energy (Rn-G) is
partitioned into LE, i.e., LE/(Rn-G). In the Forest plots (Fig. 12 a), the median values ranged between
0.3 and 0.6 for both models during the growing season. The lowest median for both models and the EC
method was detected in April (medianMETRIC = 0.33, medianTSEB = 0.29, medianEC = 0.14). The highest
median was detected in August for both models (0.60 for METRIC and TSEB) and in July for the EC
method (0.49). Both models and the EC method also exhibited increasing tendencies during the spring
summer period and decreasing tendencies in August (July)September. These patterns can indicate
seasonal characteristics, where available energy was mostly partitioned into LE in summer and less
during the start and end of a growing period. The interquartile ranges detected by the models mostly
varied between 0.2 and 0.8 and exhibited a relatively large range during single months. The highest
interquartile range was detected in April for the METRIC model (0.31, between 0.23 and 0.54) and in
August for the TSEB model (0.23, between 0.50 and 0.73). The EC method indicates lower interquartile
ranges than the models with a maximum in August (0.18).
In the Grassland (Fig. 12 b), while the median range from the TSEB model was typically between 0.5
and 0.8, the median range from the METRIC model mostly falls between 0.4 and 0.7. The highest
median values were observed in September for the TSEB model (0.77) and in June for the METRIC
model (0.66) and EC method (0.56). The lowest medians were found in May for both models
(medianTSEB = 0.59, medianMETRIC = 0.43) and in April for EC (0.21). Moreover, the TSEB model
exhibited an increasing trajectory between May and September, and compared with the METRIC model
and EC method, the TSEB model exhibited lower differences between spring and summer period. The
TSEB model estimates that the available energy was more efficiently utilized for LE during the latter
part of the growing season. The interquartile range was widest in June for the TSEB model (0.19, ranging
from 0.58 to 0.77), in August for the METRIC model (0.24, ranging from 0.41 to 0.65) and in July for
the EC method (0.33 between 0.38 and 0.71).
25
Fig. 12 Boxplots show monthly evaporative fraction data of the TSEB (red) and METRIC (blue) models
supplemented by the EC method (gray) in the growing season in the Forest (a) and Grassland (b). The
range of the boxplots express daily values within months.
The Bowen ratio describes the ratio between H and LE, i.e., H/LE. The highest medians were detected
in April (2.03, 2.47 and 4.00 for the METRIC, TSEB and EC, respectively) in the Forest (Fig. 13 a).
The lowest median was detected in August for both models and for the EC method (0.65, 0.67 and 0.64
for the METRIC, TSEB and EC, respectively). The detected median values of the models and EC also
indicate a temporal variability during the growing season when the Bowen ratio decreases in spring,
with lower values occurring in summer and September. This trajectory indicates that the available
energy was more utilized for LE in the second part of the growing season, whereas H was predominant
in the first part of the season. This pattern corresponds to the temporal variation in H (Fig. 9 a). The
greatest interquartile range was displayed in April (for the METRIC model, 2.51; 0.85-3.36; for the
TSEB model, 1.34; 2.04-3.38; and for the EC method, 2.42; 5.48-3.05).
In the Grassland (Fig. 13 b), most of the median values detected by the models were less than 1 except
in May for the METRIC (1.32). A value less than 1 indicates that more available energy at the surface
was partitioned into LE in the Grassland. The median value from the EC was greater than 1 in April
(1.80) and May (2.00). The highest median for both models was detected in May (for TSEB, 0.70; for
the METRIC, 1.32). Both models indicate relatively well a decreasing pattern during the growing
season, when maximal medians were displayed during spring and minimal medians in summer (for the
TSEB, in September 0.31, for the METRIC, in June 0.69, and for EC in June 0.36). While the METRIC
model exhibited a greater interquartile range in most months than did the TSEB model during the
a
b
26
growing season, the highest interquartile range was observed for the EC in April (1.56). The TSEB
model exhibited the maximum interquartile range in June (0.42), while the METRIC had the highest
value in August (0.91).
Fig. 13 Boxplots show monthly Bowen ratio data of the TSEB (red) and METRIC (blue) models
supplemented by the EC (gray) in the growing season in the Forest (a) and Grassland (b). The range of
the boxplots express daily values within months.
3.5 Example of spatial outputs
While the footprints of the EC systems mostly capture a homogenous land surface, both stations are
surrounded by different ecosystems; therefore, there is an opportunity to identify spatial differences in
the distributions of model outputs (daily ETa, H, LE) and other variables (LST, LAI). The chosen image
series of two selected days (Figs. 14, 15) represents some of the disagreements between the models in
forested and grassed areas. In the first case (Fig. 14), the LST ranged between 22°C and 33°C, with high
LAI values of approximately 5 in the Forest. In these conditions, the TSEB model yielded higher H
values of approximately 110 W/m², lower LE values of approximately 130 W/m², and lower ETa values
of approximately 1 mm/day than the METRIC model at the Forest.
Differences between the models were shown for the Grassland. The LST was greater in the Grassland
(approximately 37°C) than in the surrounding forests, where the temperature varied approximately
around 27°C. Additionally, a significantly lower LAI of approximately 1 was detected in the Grassland
compared to the forest area around (LAI = 5).
a
b
27
The TSEB model indicated a similar ETa (4.0 mm/day) as the EC without EBC adjustment (3.9 mm/day)
in the Grassland, which was not included in the image series (Fig. 14). The METRIC model indicated
lower ETa (2.2 mm/day). The results demonstrated that the TSEB model estimated ETa relatively well
despite its low LAI (approximately 1). A significant disparity between the METRIC and TSEB models
became evident in the surrounding areas near the Grassland, where the forested area was mostly located,
and where both models indicated opposing patterns. In these areas, the TSEB model had significantly
greater H and markedly lower LE and ETa than the METRIC model. This disagreement between the
models could be caused by the reduction in the α coefficient in the TSEB model, which was significantly
greater in the grassed areas than in the forested areas, thus strongly reducing ETa in the forest in this
case. For this reason, the TSEB model results do not seem to correlate with high LSTs, which are greater
in grassed areas than in forests. The comparison of the models and the EC method without EBC
adjustment outputs also showed relatively unexpected results between the Forest and Grassland test
sites. Despite the greater difference in LAI among the Forest (approximately 5) and Grassland
(approximately 1), the difference was relatively low in ETa. The EC method indicated a lower ETa of
approximately 1.5 mm/day, and the TSEB model indicated a lower ETa of approximately 1 mm/day in
Grassland than in Forest stations.
28
Fig. 14 Map outputs illustrating the spatial distribution of selected variables (LST, LAI) and the outputs
(daily ETa, H, and LE) of the METRIC and TSEB models in Forest and Grassland for 20th August 2020.
The black polygons represent a daily footprint of EC measurement.
The second image series showed map outputs of instantaneous values and daily ETa values from
September 5th, 2021 (Fig. 15). The LST results indicated; an LST of approximately 22°C and a high
LAI of approximately 5 at the Forest. The results of the models indicated good agreement among
themselves at this site (the TSEB model estimated ETa = 2.27 mm/day, LE = 187 W/m2, H = 264 W/m2;
29
the METRIC model estimated ETa = 2.56 mm/day, H = 230 W/m2, LE = 245 W/m2). Compared to that
in the Forest site, the LST in the Grassland was greater (LST = 32°C) but was similar in the surrounding
forested areas around the Grassland station. The LAI was lower in the Grassland (LAI = 2.5 3) than
in forested areas (LAI5).
Fig. 15 Map outputs illustrating the spatial distribution of selected variables (LST, LAI) and the outputs
(daily ETa, H, and LE) of the METRIC and TSEB models in Forest and Grassland for 5th September
2021. The black polygons represent a daily footprint of EC measurement.
30
Both models indicated disagreement in terms of energy fluxes and daily ETa in the Grassland where the
TSEB model calculated a lower H of approximately 100 W/m2 than the METRIC model and therefore
calculated a higher LE of approximately 130 W/m2 and an ETa of approximately 2 mm/day. In contrast
to those of the METRIC model, the TSEB values also differed greatly between the Grassland and
surrounding forest area. The spatially oriented outputs of the TSEB model cannot fully correlate with
the LST, which was greater in the Grassland than in the surrounding forested area. Like in Fig. 14, this
disagreement could be caused by a decrease in the a priori α coefficient in the forested areas.
The results of the EC method without EBC adjustment yielded 3.1 mm/day for the Forest and 3.1
mm/day for the Grassland, demonstrating that METRIC (2.6 mm/day and 2.4 mm/day) more accurately
represented ETa than TSEB (2.3 mm/day and 4.4 mm/day) in the Forest and Grassland on this date. A
similar pattern between ETa and the LAI, as shown in Fig. 14, was detected between the Forest and
Grassland test sites. While the outputs of the LAI demonstrated a significant difference (Forest = 5,
Grassland = 2.5), the ETa values were similar in the Grassland and Forest as detected by the METRIC
and EC, and even greater in the Grassland as indicated by the TSEB.
3.6 Annual results of ETa
An interpolated ETa values from the METRIC and TSEB models supplemented by EC measurements
without and with EBC adjustment demonstrated annual values of ETa in the monitored years at both
sites for EC (Fig. 16). Annual values detected by models mostly vary between 400 and 600 mm/year in
the Forest. The highest annual ETa value detected by models (632 mm) was calculated in 2016 for the
METRIC outputs, while the TSEB and EC values were 504 mm and 556 mm, respectively, for the same
year. Greater agreement between models and EC daily measurements was observed for EC without EBC
compared to EC with EBC adjustment, where values were consistently greater in the Forest. At the
Grassland, the calculated values of the TSEB model were consistently greater than those of the METRIC
model and EC method. This pattern corresponds to other results (Figs. 10 b, 11 b) where TSEB mostly
overestimate daily ETa values compared to METRIC model. The highest annual ETa value detected by
models (722 mm) was calculated in 2019 for the TSEB, while the METRIC data had values of 527 mm
and 542 mm, respectively, for the same year. The greatest difference between TSEB and EC
31
values were detected in 2020, with a deviation of 200 mm, while the largest difference between the
METRIC and EC values was observed in 2021, when the METRIC model indicated lower values of
approximately 187 mm. The annual results from the EC method also showed larger differences in ETa
between 2020 and 2021. However, the EC value was only 427 mm in 2020 and 715 mm in 2021.
Fig. 16 Annually interpolated daily ETa values calculated from the TSEB (red columns) and METRIC
(blue columns) models and the EC method without EBC (black columns) and with EBC adjustment
(gray columns) in the Forest (a) and Grassland (b).
a
b
32
4 Discussion
4. 1 Assessing of ETa and energy fluxes
Both models demonstrated the ability to quantify ETa at both test sites, thereby illustrating the
considerable potential of remote sensing methods and models for the precise quantification of the
hydrological balance under conditions in Central Europe. An important aspect of the study involves the
comparison of daily ETa outputs between models and the EC. Both methods showed good agreement
with the EC without EBC adjustment in concordance with the findings of other studies, which generally
showed good agreement between the models (Choi et al., 2009; French, Hunsaker and Thorp, 2015;
Zhang et al., 2015; Peddinti and Kisekka, 2022). However, both methods presented opposite bias in the
Forest and Grassland. TSEB model demonstrated superior performance at the Forest, while the METRIC
model excelled at the Grassland. The opposite pattern in ETa was evident in the intercomparison, where
the TSEB model indicated lower values in the Forest and higher values in the Grassland. For this reason,
the daily ETa outputs from the METRIC and TSEB models were averaged, and the values were
compared to the EC measurements. The results demonstrated improved agreement with the EC method
compared to that of the individual models in the forested and grassland areas. Consequently, in focused
studies on hydrological balance, it is also possible to use the average ETa values from both evaluated
models instead of the outputs from individual models.
The challenge for accurate determination of ETa using the demonstrated method of estimating energy
fluxes (Rn, G, H, LE) on the surface lies in their proper quantification. Many of the studies evaluated
the METRIC or TSEB models over different land cover areas and indicated good agreement between in
situ measurements and models (Kustas et al., 2004; Allen et al., 2007b; Timmermans et al., 2007; Choi
et al., 2009), underestimation of H and overestimation of LE by models (Chirouze et al., 2014) or
overestimation of both H and LE by models (Carrasco-Benavides et al., 2014). Our study demonstrated
good agreement between both models and the EC method in terms of the energy fluxes even though the
TSEB model demonstrated slightly better agreement than the METRIC model, which mostly
overestimated the energy fluxes at both test sites. Both models also demonstrated higher values at both
sites than did the measured G. The lower G values were caused by the delayed response of the soil to
33
the increasing energy input during the morning hours at the time of satellite overpass. To avoid
disagreements between the models and measurements, the measured G values could be potentially
multiplied by the empirical coefficient 1.3 1.6 (Fischer et al., 2018; Pozníková et al., 2018). In this
work, the G values were not multiplied by any coefficient because the values of G constitute a negligible
part of the presented overall energy balance. Similarly, as in other studies (Twine et al., 2000; Choi et
al., 2009; Carrasco-Benavides et al., 2014; Foken et al., 2017; Fischer et al., 2018), we enforced the
EBC of EC energy flux values by applying the Bowen ratio adjustment, as a significant amount of
energy residue was detected at both EC sites (38% in the Forest and 30% in the Grassland). The outputs
of energy fluxes, whether within a closed or un-closed energy balance, likely include actual turbulent
fluxes from the tower footprint of the EC and serve as an indicator of observational uncertainty (Choi et
al., 2009). While adjustment of the EBC improved the agreement for instantaneous LE between the
METRIC and TSEB models and the EC method at both test sites, in the case of daily energy fluxes and
thus ETa, EBC adjustment improved agreement only for the TSEB model in the Grassland.
The estimation of daily values from instantaneous values measured at satellite overpasses is one of the
crucial parts of the precise calculation of ETa. A similar underestimation of approximately 5 10%
occurred in other studies that assessed daily ETa (Gurney and Hsu, 1990; Sugita and Brutsaert, 1991;
Brutsaert and Sugita, 1992). In this study, we use different scaling methods for both models. However,
overall, scaling of instantaneous values are still estimates of daily fluxes, and neither method fully
captures the true relationships between variables. For this reason, daily ETa values may be
underestimated even though instantaneous LE values were overestimated during satellite overpasses, as
shown in our results. Therefore, scaling values from instantaneous to daily values requires attention in
future studies.
3.2 The advantages and disadvantages of models
A primary limitation of the satellite based models in assessing annual trends lies in the availability of
clear-sky images. In this study, we presented one interpolation method for calculating missing daily ETa
values, which were then approximated to annual values; however, these results remain as estimates. The
34
issues regarding the availability of satellite images with clear skies in the presented spatial resolution
have been improved since 2022 with the launch of Landsat 9 into orbit.
The process of identifying cold and hot pixels is sensitive during the METRIC model implementation
(Choragudi 2011; Bhattarai et al., 2017). This requires precise detection and depends on the method
used for selecting anchor pixels or even searching for the most suitable hot and cold pixels in the area
of interest (Long and Singh 2013; Morton 2013). In this study, an automatic selection of the endpoints
described in Olmedo et al., (2016) was used. The selection of endpoints is identified as one of the
weaknesses of the METRIC model; however, model can be relatively tolerant when certain surface data,
such as biophysical parameters of vegetation, are lacking. The TSEB model is more sensitive to
uncertainties in LST and air temperature (Anderson et al., 1997) and requires more detailed biophysical
parameters to calculate the energy balance; however, such parameters cannot be easily determined, as
in the METRIC model (Chirouze et al., 2014; French, Hunsaker and Thorp, 2015; Peddinti and Kisekka,
2022). One advantage of the TSEB model is the partitioning of available energy into vegetation and soil,
which allows the separation of soil evaporation from canopy transpiration (Norman et al., 1995).
However, transpiration and evaporation partitioning in the TSEB model was beyond the scope of this
study.
In addition to direct evaluation via charts and scatter plots, spatially distributed LST and LAI data and
model outputs (H, LE, and ETa) were shown in this study. The series of spatial images from 2020 can
support a suggestion about the disagreement of models in sparse vegetation cover with low LAI (Choi
et al., 2009; French, Hunsaker and Thorp, 2015) because the TSEB model indicates strongly greater ETa
than the METRIC model on this day in the Grassland. However, despite the low LAI of approximately
1, EC without EBC adjustment indicates a slightly lower daily ETa than TSEB and demonstrates that
the TSEB model estimated ETa relatively well, while the METRIC model underestimated ETa. In
addition, the models and EC method effectively highlighted some inadequately confirmed hypotheses
captured in two selected series of images. For the first point, the outputs from the EC method and the
TSEB model suggest that vegetation, such as grassland, with a low LAI, still transpires (evaporate)
significantly. Second, the results indicate that ETa values may be comparable between grassed and
35
forested areas, despite the much lower LAI values detected in the grasslands. This assertion was
supported by both spatial images in which slightly different or similar values of ETa were detected
between forested and grassed areas despite the large difference in LAI. Despite the overall good
agreement between the TSEB model and the EC method, the application of the TSEB model requires
more attention given the reduction in the a priori estimate of the α PriestleyTaylor coefficient in
forested areas (Komatsu, 2015). It is essential to note that the ETa of the TSEB model is strongly
influenced by a reduction in the α coefficient in the forests; therefore, spatially distributed values of ETa
may not correlate with LST, as shown in Figs. 14 and 15, where LST was greater in grassed areas than
in surrounding forested areas. For this reason, we propose a more detailed study regarding the accurate
quantification of the α coefficient according to Komatsu (2005) in forested areas.
3.3 Assessing of evaporative fraction and Bowen ratio
The evaporative fraction and Bowen ratio are useful indicators because they can provide information
about the relationship between water stress and evaporation and can be used to monitor the water stress
of vegetation. For this reason, a section that evaluates the evaporative fraction is an important part of
this study, and it is also included in other studies that quantify water stress using remote sensing models
(Gentine et al., 2007; Anderson et al., 2011; French, Hunsaker and Thorp, 2015; Aboutalebi et al., 2019;
Kustas et al., 2019) or evaluate both models in the area of interest (Chirouze et al., 2014). The results
for the evaporative fraction, as detected by the models and the EC method, indicate that most of the solar
energy was converted into LE in the forest. This finding can correspond to the high level of vegetation
cover in the floodplain forest and suggest a relatively significant cooling effect.
The Bowen ratio results indicates that available energy was mostly utilized in H during spring and
mostly utilized in LE during the summer period. These seasonal temporal variabilities may correspond
to meteorological-surface conditions in summer, which necessitate greater transpiration from
vegetation. On the other hand, vegetation and meteorological conditions may not be as favorable for
latent heat flux in September or April, leading to lower evaporative fraction values than those during the
summer peak.
36
The results of the evaporative fraction and Bowen ratio detected by the models and EC could be affected
by seasonal variability due to grass cutting that takes place every growing season. The results from the
Grassland demonstrate the highest values of the evaporative fraction and lowest values of the Bowen
ratio during summer. This result should be related to the maximum vegetation cover and water
availability, which corresponds to our expectations during the occurrence of these conditions in the
summer periods when vegetation should be in full cover and have access to water, which is not present
in deep layers in floodplain-grassland ecosystems.
Significant disparities in both evaporative fraction and Bowen ratio were observed during the spring
period at Grassland test sites when comparing models to the EC measurements. The primary cause of
these disparities lies in the distinct calculation periods utilized by the models and EC. The monthly
averages of the models encompass the entire 20152021 period (7 growing seasons), in contrast to the
EC averages, which represent the period from June 2019 to 2021 (2-3 growing season). For example,
March, within the models, represents the monthly average for 7 Marchs (2015-2021), while for EC,
March is averaged only for 2 (2020, 2021). It is essential to note that the primary objective of these
analyses was not to directly compare the models with EC. Instead, the focus was on discerning temporal
variability throughout the growing season.
3.4 Potential research directions
Similarly, as in other studies (Allen et al., 2007b; Anderson et al., 2011; Zhang et al., 2015; Liebert et
al., 2016; Ghisi et al., 2023; Guzinski et al., 2020; Guzinski et al., 2023), this study demonstrated the
significant potential of both models for practical quantification of ETa and energy fluxes using satellite
sensors. For addressing scientific inquiries regarding the water balance in the landscape of Central
Europe, however, it may not be sufficient to evaluate models within floodplain ecosystem alone.
Therefore, it is necessary to evaluate models within typical landscape units using ground point ETa
measurement data. Additionally, there is the opportunity to evaluate these models using high-resolution
airborne sensors and drones. Subsequent studies have demonstrated promising results for both models
utilizing drones and aerial sensors, enabling precise water management with fine spatial resolution
37
within controlled ecosystems (Aboutalebi et al., 2019; Nieto et al., 2019a; Carrasco-Benavides et al.,
2020; Chandel et al., 2020; Peng et al., 2023).
5 Conclusion
This study focused on evaluating two satellite-oriented models for quantifying ETa and energy fluxes in
the hydrologically unique ecosystem of the floodplain area of Central Europe. The strong motivation
behind this study is the precise determination of the water balance under the conditions of Central
Europe in connection with adaptation and mitigation measures against the negative impacts of climate
change. The comparison demonstrated good agreement between the diagnostic models and the EC
method at both test sites, affirming the substantial potential of these methods for addressing various
practical hypotheses and challenges associated with water balance. However, accurate detection of
energy fluxes and ETa remains a challenge for further study in forested areas, where precise
quantification of physical parameters, such as the PriestleyTaylor coefficient, is crucial.
Acknowledgement
The authors acknowledge support from AdAgriF - Advanced methods of greenhouse gases emission
reduction and sequestration in agriculture and forest landscape for climate change mitigation
(CZ.02.01.01/00/22_008/0004635).
M. Fischer and G. Jocher were supported by Czech Science Foundation Grant No. 24-12935S.
L. Homolová was supported by grant TO01000345 from Norway and Technology Agency of the Czech
Republic within the KAPPA programme.
T. Ghisi was financially supported by the Internal Grant Agency of the Faculty of AgriSciences at
Mendel University in Brno as part of the research project no. AF-IGA2022-IP-033.
Z. Žalud contribution to the study was supported by the PERUN TAČR project no. SS02030040.
38
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