Evapotranspiration (ET) is the main link between the natural water cycle and
the land surface energy budget. Therefore water-balance and energy-balance
approaches are two of the main methodologies for modelling this process. The
water-balance approach is usually implemented as a complex, distributed
hydrological model, while the energy-balance approach is often used with
remotely sensed observations of, for example, the land surface temperature
(LST) and the state of the vegetation. In this study we compare the
catchment-scale output of two remote sensing models based on the two-source
energy-balance (TSEB) scheme, against a hydrological model, MIKE SHE,
calibrated over the Skjern river catchment in western Denmark. The three
models utilize different primary inputs to estimate ET (LST from different
satellites in the case of remote sensing models and modelled soil moisture
and heat flux in the case of the MIKE SHE ET module). However, all three of
them use the same ancillary data (meteorological measurements, land cover
type and leaf area index, etc.) and produce output at similar spatial
resolution (1

Evapotranspiration (ET) acts as a coupling between two of the
most important natural processes affecting the land surface: the water (mass)
exchange and the energy exchange

The two types of modelling approaches have been compared previously, for
example recently by

The remote sensing models of evapotranspiration

There are a number of remote sensing modelling methodologies being actively
used by the research community ranging from simpler, empirical ones to more
complex, physically based ones. One of the simpler approaches consist of the
so-called “triangle” models, named after the shape resulting from plotting
the pixel values of an LST map against pixel values of a vegetation index
map. The evaporation fraction can then be derived by interpolating between
the edges of the triangle

The distributed physically based hydrological models, in contrast to the
remote sensing models, are heavily parametrized and calibrated for each
individual catchment or study area

Since the hydrological models are calibrated using detailed hydrological
observations, it is our hypothesis that the catchment-wide evapotranspiration
estimated by those models is more accurate than the one derived with remote
sensing models. On the other hand, we expect the energy-balance models driven
by remote sensing observations to better represent the spatial patterns of
the fluxes present within the catchment. We evaluate this hypothesis by
running a hydrological model, MIKE SHE, described in
Sect.

The output land surface fluxes, and in particular the latent heat flux, from
the three models are then inter-compared. The comparison is performed on a
pixel-by-pixel basis as well as on catchment scale, and both systematic and
unsystematic differences are analysed

The study area covers the Skjern River catchment (Fig.

Land use map of the study area: the Skjern river catchment in the west of Denmark's Jutland peninsula. Model input meteorological data were interpolated from the measurements taken by the stations shown on the map.

In order to compare the performance of the three models and not the accuracy
of their inputs, the models used the same auxiliary input data whenever
possible. Those common inputs consisted of maps with meteorological forcings,
LAI, albedo and land cover types. For the meteorological forcing data, kriged
fields of wind and temperature corrected precipitation from 43 rain gauges
were used

Land cover dependent parameters for the three models. The equations
referred to in the table are (Eq. a)

All common input data maps were delivered in UTM32-WGS84 projection. The LST observations used by the different models, as well as data used only by a single model, are described in the sections below.

The implementation details of the hydrological model used in this study,
MIKE SHE SW-ET, are presented in

As input the model requires gridded meteorological forcing data, soil
hydraulic parameters and a number of parameters related to vegetation. The
meteorological forcing data, LAI, albedo and land use maps are described in
Sect.

The TSEB approach

In the single-angle TSEB models, the latent heat flux of the canopy,
LE

In the dual-angle TSEB models,

The two TSEB based models used in this study follow the principles described above but differ in other implementation details as described in the subsections below.

The DTD model minimizes the influence of systematic error in the retrievals
of LST and air temperature by replacing absolute temperature measurements
with temperature change between two observations

The

The model uses MODIS LST estimates from the MYD11A1 product, together with
land cover, LAI and albedo values derived as described in
Sect.

When TSEB is applied with single-angle LST, some assumptions are needed based
on the expectation that plants transpire at their potential rate. This
assumption may lead to significant errors in cases when plants are stressed,
or when the potential canopy transpiration is not well defined. For that
reason, the green fraction of vegetation (

The TSEB-2ART model

TSEB-2ART has been evaluated over three flux tower sites within the HOBE
area, obtaining more accurate flux retrievals than both the original
dual-angle

The spatial comparison was performed by selecting all the pixels in the
Skjern catchment on all the days between 2003 and 2010 when at least 10 %
of the catchment was cloud free during the night and day Aqua overpasses and
which met the following conditions:

the pixel is not classified as water or urban area (met by 96 % of the catchment area);

all three models produce valid results, meaning LE

The comparison was performed using the instantaneous modelled sensible heat flux, latent heat flux and available energy (AE) defined as the net radiation minus the ground heat flux. The magnitude of those fluxes is strongly influenced by the incoming solar radiation and so it has a cyclic annual component with generally larger fluxes during the summer months and lower during the winter months. This could potentially influence the correlation between the fluxes modelled with different models. To remove this time dependent component and instead to evaluate the influence of water availability on the partitioning of the available energy into latent and sensible heat fluxes by the different models, the evaporative fraction (EF), defined as the ratio of energy used for evapotranspiration to the total available energy, was also used during the comparison.

When comparing the fluxes estimated by the three different models the time at
which the fluxes are estimated must be taken into account. The TSEB-2ART
fluxes are estimated at the time of the Envisat overpass, which is around
11:30 local time (LT), while the DTD fluxes are estimated at the time of
Aqua overpass, around 12:00–13:00 LT. The MIKE SHE fluxes are estimated at
hourly intervals throughout the day. Therefore, when comparing the fluxes
between MIKE SHE and one of the satellite based models a linear interpolation
was performed between the two MIKE SHE estimates bracketing the satellite
based estimate (e.g. if satellite overpass was at 11:48, MIKE SHE estimates
from 11:00 and 12:00 would be used). When comparing the fluxes from two
satellite based models there is an offset present due to this time
difference, although it should be reduced when comparing EF

A number of statistical measures are used to explore the relation between the
fluxes, and temperatures, estimated by the three models. The first one is the
Pearson correlation coefficient,

The temporal patterns of evapotranspiration were evaluated at catchment
scale, meaning that all the valid non-urban and non-water pixels within the
catchment were averaged to determine the catchment-scale fluxes. It should be
noted that since MIKE SHE also simulates the fluxes over water and urban
pixels, this average is not the whole catchment evapotranspiration as
modelled by MIKE SHE. However, since the number of water and urban pixels is
quite small (Fig.

Density scatter plot of over 95 000 points comparing the sensible heat flux (top left), latent heat flux (top right), available energy (bottom left) and evaporative fraction (bottom right) modelled by MIKE SHE and DTD. Red colour indicates higher density of points, blue colour lower density.

Density scatter plot of over 95 000 points comparing the sensible heat flux (top left), latent heat flux (top right), available energy (bottom left) and evaporative fraction (bottom right) modelled by MIKE SHE and TSEB-2ART. Red colour indicates higher density of points, blue colour lower density.

The results of pixel-to-pixel comparisons of fluxes between the three model
pairs are presented in Figs.

Density scatter plot of over 95 000 points comparing the sensible heat flux (top left), latent heat flux (top right), available energy (bottom left) and evaporative fraction (bottom right) modelled by TSEB-2ART and DTD. Red colour indicates higher density of points, blue colour lower density.

The bias between the turbulent fluxes modelled with MIKE SHE and DTD is
significant with a value of 19

The comparison of fluxes produced with MIKE SHE and TSEB-2ART follows
a similar pattern as in the previous section, with relatively low correlation
and significant RMSD but with much lower bias (maximum magnitude of
8

Statistical comparison between MIKE SHE, DTD and TSEB-2ART models
for sensible and latent heat fluxes (

The correlation between the turbulent fluxes modelled with TSEB-2ART and DTD
is the highest of any model pairs, with correlation coefficient of 0.42 for

Average catchment-wide latent heat fluxes on the days when at least 70 % of non-water and non-urban pixels were modelled by either DTD (left) or TSEB-2ART (right). In the main graph the blue circles represent catchment fluxes modelled by MIKE SHE and the red crosses represent the catchment fluxes modelled by the remote sensing models on the same year and day of year (DOY) and at the same time of day. The figure contains dates from the 8 years under investigation and the blue solid line shows an 8-year averaged whole catchment ET for a particular DOY as modelled by MIKE SHE around the time of Aqua (left) or Envisat (right) overpass. The blue broken line shows potential ET for the same data set estimated using the Priestley–Taylor approach and MIKE SHE AE. The inset image contains a scatterplot of the MIKE SHE and remote sensing fluxes with black indicating fluxes from January to April, green from May to August and brown from September to December.

Statistical comparison of catchment-wide latent heat fluxes
estimated by the model pairs (MIKE SHE–DTD and MIKE SHE–TSEB-2ART) for
predominantly cloud-free days over the period of 8 years. Statistics used:
correlation coefficient (

Histogram of the pixel-wise differences between evaporative fraction
(EF) estimated by MIKE SHE at the time of Aqua overpass and Envisat overpass.
The differences between the two sets were evaluated using the two-sample

The results of comparing DTD and TSEB-2ART catchment-wide evapotranspiration
estimates against MIKE SHE are presented in Fig.

Even though DTD and TSEB-2ART estimate fluxes at different times during the
day, the correlation between

Density scatter plot comparing the vegetation latent heat flux modelled by MIKE SHE and DTD (left), MIKE SHE and TSEB-2ART (centre) and TSEB-2ART and DTD (right). Red colour indicates higher density of points, blue colour lower density.

Statistical comparison between MIKE SHE, DTD and TSEB-2ART models
for latent heat flux of the canopy (LE

When the seasonal signal of the available energy is removed by replacing the
turbulent fluxes by EF, the spatial patterns produced by the remote sensing
models are still more strongly correlated than when either of them is
compared to the hydrological model. The correlation coefficient of TSEB-2ART
and DTD EF is 0.33 compared to the second highest value of 0.25 between
MIKE SHE and TSEB-2ART EF. However, it should once again be kept in mind that
the remote sensing models estimate the fluxes at different times of the day.
Usually it is assumed that during clear sky days the EF remains constant
throughout the daytime and especially around noon

Figure

When considering the causes of the remaining differences in the modelled fluxes, some factors can be directly removed. The three models used many of the same spatial data sets as input: LAI maps, land cover map and meteorological forcing data (air temperature, incoming solar radiation, humidity and wind speed). In addition, DTD and MIKE SHE used the same albedo maps and MIKE SHE was calibrated using the same Aqua MODIS LST observations as used by DTD. The mismatch caused by image misregistration was reduced by applying the median filter over the output maps, although on cloudy days there are many isolated pixels, making the filtering less efficient. The available energy is very highly correlated in all three comparisons, with small RMSD and bias in the case of the two comparisons for which fluxes are estimated at the same hour, so this is also not a major contributor to the differences between the turbulent fluxes.

The remaining major causes of the observed differences in the model outputs could be (1) parametrization used in different land cover classes; (2) the LST input maps estimated by different sensors, in the case of DTD (MODIS) and TSEB-2ART (AATSR), or modelled, in the case of MIKE SHE; and (3) the differences in the modelling approach between the three models even though all of them apply the two-source modelling scheme.

Figures

Box plots of sensible heat flux (top left), latent heat flux (top right), net radiation (bottom left) and evaporative fraction (bottom right) modelled by MIKE SHE (leftward box in each category) and DTD (rightward box in each category) and split by land cover class. The red horizontal line indicates the median value with the upper and lower box edges indicating the 75th and 25th percentiles respectively. The whiskers extend to the furthest point within 1.5 times the inter-box range above or bellow the box edges with points beyond that categorized as outliers and marked individually as a red crosses.

Box plots of sensible heat flux (top left), latent heat flux (top right), net radiation (bottom left) and evaporative fraction (bottom right) modelled by MIKE SHE (leftward box in each category) and TSEB-2ART (rightward box in each category) and split by land cover class. The red horizontal line indicates the median value with the upper and lower box edges indicating the 75th and 25th percentiles respectively. The whiskers extend to the furthest point within 1.5 times the inter-box range above or bellow the box edges with points beyond that categorized as outliers and marked individually as a red crosses.

Box plots of sensible heat flux (top left), latent heat flux (top right), net radiation (bottom left) and evaporative fraction (bottom right) modelled by TSEB-2ART (leftward box in each category) and DTD (rightward box in each category) and split by land cover class. The red horizontal line indicates the median value with the upper and lower box edges indicating the 75th and 25th percentiles respectively. The whiskers extend to the furthest point within 1.5 times the inter-box range above or bellow the box edges with points beyond that categorized as outliers and marked individually as a red crosses.

When looking at the median and 25th and 75th percentile values of
evapotranspiration, the differences do not appear as significant as could be
expected from the results shown in Table

In the case of TSEB-2ART, the range between the 25th and 75th percentile
values of ET is smaller in croplands and grasslands when compared to MIKE SHE
ET, while the median value of conifer forest ET is a bit larger. The range of
values between the 25th and 75th percentiles of

Finally, the time difference between Envisat and Aqua overpasses is clearly
visible when comparing TSEB-2ART and DTD LE and AE, but it is not reflected
in the values of

The large number of outliers present in the
modelled

Maps of correlation, RMSD and bias between LE modelled with different model
pairs (Fig.

Table

Although the high spatial correlation of LST would indicate that the
different sources of LST are not a major component in the discrepancies
between the modelled fluxes it must be noted that the fluxes are strongly
dependent on the LST–

Statistical comparison between MIKE SHE, DTD and TSEB-2ART models
for sensible and latent heat fluxes (

Maps of spatial patterns of correlation (

Statistical comparison between MIKE SHE, DTD and TSEB-2ART models
for the land surface temperatures (LST), canopy temperatures
(

Density scatter plot of over 95 000 points comparing land surface
temperature (top left), canopy temperature (top right), soil temperature
(bottom left) and in-canopy air temperature (bottom right). Land surface
temperature on the

Density scatter plot of over 95 000 points comparing land surface
temperature (top left), canopy temperature (top right), soil temperature
(bottom left) and in-canopy air temperature (bottom right). Land surface
temperature on the

In addition, the canopy, soil and in-canopy air temperatures (

Density scatter plot of over 95 000 points comparing land surface
temperature (top left), canopy temperature (top right), soil temperature
(bottom left) and in-canopy air temperature (bottom right). Land surface
temperature on the

Despite those three different methods the correlation between the
temperatures is quite high (Table

Furthermore, since the TSEB-2ART model relies on the differences observed
between the nadir and forward LST of AATSR in order to derive

Although there are differences in the estimated temperatures that could lead
to larger unsystematic differences in the fluxes estimates, it is likely that
there are also other factors contributing to the inconsistencies between
fluxes. One of the factors could be the methodology employed by the different
models for splitting of the available energy into the sensible and latent
heat fluxes and in particular the way they estimate the resistances to heat
and moisture transport. The two remote sensing models ensure the land surface
energy balance by calculating latent heat flux as the residual of the other
fluxes, i.e. LE

Statistical comparison between MIKE SHE, DTD and TSEB-2ART models
for sensible and latent heat fluxes (

Another possible factor for the observed differences between the estimated
fluxes could be the actual formulations used for resistances of heat transfer
between the soil, vegetation, in-canopy air and above-canopy air. While the
two remote sensing models use equations based on

The results are presented in Table

Finally, Fig.

Density scatter plot of over 95 000 points comparing resistance of
heat transfer from the soil surface (

Both remote sensing models are reasonably accurate in matching MIKE SHE
catchment-wide estimates of evapotranspiration, with the seasonal curve
clearly visible for both models (Fig.

Figure 5 also highlights another weakness of the remote sensing models, namely that they only produce results on clear sky days. The great majority of latent heat fluxes estimated by the remote sensing models, and by the hydrological model on the same dates as the remote sensing models, lie above the line representing an average, all-weather ET for a particular DOY for all the years under study. This is also true when considering an 8-year averaged potential ET. The reason is because in the Skjern River environment the evapotranspiration is mainly driven by availability of energy (and not of water), and therefore on clear sky days the evapotranspiration will be higher than average. This has to be taken into account when extrapolating temporal patterns of evapotranspiration derived purely by the remote sensing input based models.

There are a couple of cases where the clear sky evapotranspiration modelled by MIKE SHE is much below the average line, even though the remote sensing models estimate much higher latent heat fluxes on those days. This most probably corresponds to days with soil drier than normal and could indicate: (1) a problem of the hydrological model in estimating the moisture of the upper layer of the soil or of the root zone during dry conditions, or (2) be related to uncertainties in the interpolated rainfall data due to omission by the rain gauges of local convective rainfall during the summer period.

Two remote sensing models and one hydrological model were run over an area covering a river catchment in western Denmark and the spatial and temporal patterns of the modelled evapotranspiration were compared. The spatial patterns of latent and sensible heat fluxes as well as EF produced by the remote sensing models were more strongly correlated with each other than the patterns produced by either of the remote sensing models compared to the hydrological model. This was the case even though the two remote sensing models use both different data (MODIS and AATSR LST) and different approaches to estimating the fluxes and, additionally, those estimates were produced at different time of the day, due to different overpass times of satellites. This indicates that the remote sensing models might contain some additional information that is not currently present in the hydrological model. At the same time, the temporal patterns of evapotranspiration produced by both of the remote sensing models and the hydrological model were strongly correlated, with relatively small RMSD and small bias. Those observations would appear to support the hypothesis that the remote sensing models would better represent the spatial patterns of evapotranspiration present throughout the catchment, while the hydrological model would better represent the catchment-wide evapotranspiration.

This points towards a possibility of using the remotely sensed
evapotranspiration to improve the spatial accuracy of distributed, physically
based hydrological models. This could be achieved either through using the
estimated latent heat flux as one of the calibrating parameters or through
data assimilation during the model run. Certain attempts at incorporating
spatial distributed data derived through remote sensing into hydrological
models, either through data assimilation or calibration, have already been
made but they were mostly focused on soil moisture

The work has been carried out under the HOBE project funded by the VILLUM FOUNDATION. Edited by: H. Cloke