The effect of terrain heterogeneities in one-point measurements is a continuous subject of discussion. Here we focus on the order of magnitude of the advection term in the equation of the evolution of temperature as generated by documented terrain heterogeneities and we estimate its importance as a term in the surface energy budget (SEB), for which the turbulent fluxes are computed using the eddy-correlation method. The heterogeneities are estimated from satellite and model fields for scales near 1 km or broader, while the smaller scales are estimated through direct measurements with remotely piloted aircraft and thermal cameras and also by high-resolution modelling. The variability of the surface temperature fields is not found to decrease clearly with increasing resolution, and consequently the advection term becomes more important as the scales become finer. The advection term provides non-significant values to the SEB at scales larger than a few kilometres. In contrast, surface heterogeneities at the metre scale yield large values of the advection, which are probably only significant in the first centimetres above the ground. The motions that seem to contribute significantly to the advection term in the SEB equation in our case are roughly those around the hectometre scales.

The surface energy budget (SEB) is the expression of the conservation of
energy for a volume across the atmosphere–surface interface, which should
take into account all the energy exchanges taking place in it. Traditionally
(see e.g. Oke, 1987, or Foken, 2008a, b) it is expressed as an equilibrium
equation between the net radiation (Rn) – usually the larger term – and the
three other principal terms, the turbulent sensible heat flux (

The second issue comes from the fact that the Earth's surface is not homogeneous. To check the validity of Eq. (1), one should look for flat homogeneous locations, distant from topographical features (even minor ones) or from changes in the soil uses (like different crops close to each other). These terrain heterogeneities may induce turbulent eddies and change the values of the turbulent heat flux compared to a completely homogeneous area.

The need of the scientific community to make experimental measurements, even in complex terrain, implies that these limitations should be progressively overcome. Another important factor to consider is that instrumental errors in the determination of the turbulent fluxes must be kept in mind, very often implying an underestimation of their value due to the non-capturing of certain scales by the measuring devices (Foken, 2008a). Taking this into account, Foken (2008b) acknowledged that, to progress in our understanding of the physics of the surface–atmosphere exchange, we must resign ourselves to work with imbalances of the order of 20 % in Eq. (1).

Cuxart et al. (2015) derive a complete SEB equation from the evolution
equation of the temperature of a volume. They take a conceptual box with the
top at the screen level and the bottom just under the surface. Simplifying
the equation accordingly, they produce a budget equation for the volume where
the turbulent fluxes are located at screen level and the conduction flux just
under the surface; the advection terms can be computed using the divergence
of temperature across the volume limits and the missing terms can be
accounted for explicitly when the information is available (see Fig. 1 in
that paper). The rationale in that paper leads to an extended SEB equation:

This approach is still insufficient because it implies several oversimplifications, such as not considering the internal variability of the volume, like the presence of objects over the ground or soil heterogeneity, or some inputs from outside the volume, like water pumped up from below the volume of interest by plant roots (Moene and Van Dam, 2014). All these effects are gathered into Ot, which is not estimated. Nevertheless, it accounts explicitly for some elements of the imbalance, trying to progress with some insight in the SEB approach used in many practical environmental applications.

The total imbalance is expressed by Cuxart et al. (2015, Eq. 7) as the sum of
the contributions of the tendency, the storage, the biological processes, the
advection effects and the other unaccounted factors
(Imb

In this work we concentrate on the importance of the advection term

The related timescale must be the one used for the computation of the other terms in the budget. If 30 min averages are used for the radiation or the turbulent heat fluxes, then the increments of temperature must be computed using 30 min averages of temperature. Coherent structures lasting longer than this averaging time are most likely contributing significantly to this term, as would be the case for circulations between adjacent parcels of terrain at different temperatures, of a spatial scale still to be determined.

The term has some arbitrariness, especially in the value that must be taken
for the dimensions of the box

The BLLAST experiment (Lothon et al., 2014) provided the opportunity to
gather several teams with different experimental and modelling expertise
at the Lannemezan Plateau (Gascony, France) in summer 2011. In this work, we
analyse data from different sources operating during BLLAST with the aim of
estimating the order of magnitude of

As mentioned above, a number of simplifications are made to collectively
treat a large amount of heterogeneous information. We will confine our
estimations of

The concept of a “footprint” is not used in this work because the area is composed of patches of different land use with a characteristic size of 100 m in all directions and this approach would be difficult to implement considering 30 min averages (for a discussion see Foken and Leclerc (2004) or, more recently, Hartogensis, 2015). The average vertical wind speed is taken as 0, acknowledging that this implies neglecting vertical advection, therefore implicitly included in the Ot term. Finally, the concept of a “blending height” is only used sporadically since, as Foken (2008a) indicates, it may be not very appropriate when analysing the effects of heterogeneity at relatively small scales.

In Sect. 2 the different sources of information are described, highlighting
their potentialities and limitations. This is followed in Sect. 3 by a
description of the SEB for the period 30 June to 3 July and an analysis of
the method. Section 4 provides a short description of the estimates of

During BLLAST a large number of teams contributed instrumentation. While the main purpose of the experiment was to study the late afternoon and evening transition regimes of the atmospheric boundary layer (Lothon et al., 2014), a second objective was to understand the effect of small-scale terrain heterogeneities in the boundary layer. This paper focusses on the latter goal. Ideally one should compare a perfectly homogeneous location with an inhomogeneous one, the former being actually very difficult to find over land, at least in midlatitudes. The approach taken here, as described in the Introduction, is to use the available data to estimate the value of the advection term corresponding to the existing heterogeneities as detected by various observations.

BLLAST had two supersites. At site 1 there were vertical profiling devices, including radiosondes, and a number of surface-layer measurements, some intended to assess the effect of the surface heterogeneities. Site 2 was intended to study well-defined heterogeneities measuring over corn, moor and forest sites, each of an approximate scale of 1 km, larger than the average heterogeneities on the Lannemezan Plateau (van de Boer et al., 2014). The small-scale experiment under analysis here took place in site 1.

A complete SEB station was installed by the universities of Bergen and the Balearic Islands over a square of 160 m side over which there was previously a radar, currently installed at a nearby location. This “small square” is at a first look approximately flat and homogeneous, but a closer inspection shows that there is a very smooth slope towards the southwest (SW) and that the vegetation cover is irregular, some small areas being covered by grass and dead grass, while others are bare and most of them are a mixture of short grass and bare soil.

The small square was surrounded by areas of grass for cattle, some wooden spots and fields of different crops – essentially the same landscape surrounding the area for several kilometres, with the exception of the city area of Lannemezan. The average scale of each of these landscape units was a few hundreds of metres at most, and most typically they had 100 m of characteristic size.

The BLLAST campaign was characterized by the passage of weather fronts approximately each third or fourth day, with clear skies and weak pressure gradients in between, when the wind dynamics over the Lannemezan Plateau were dominated by the up-valley and down-valley circulations from the nearby Vallée d'Aure (Jiménez and Cuxart, 2014). Therefore, the moisture availability at the surface was high, resulting in large daytime evapotranspiration fluxes (Bowen ratios below 1). We will focus in this work on the anticyclonic period between the rainy events of 29 June and 3 July, which includes three BLLAST intensive observational periods.

Left: topography of southwestern France which corresponds to the larger domain of the model simulation (D1). The inner area inside the purple square corresponds to domain D2. Right: domains D2 and D3. The cross indicates the location of Lannemezan. Surface temperatures for areas with heights above sea level between 50 and 700 m (in green in left panel) are used to compute the average LST and its standard deviation.

The model uses a standard one-dimensional turbulence 1.5 order scheme in the three domains (Cuxart et al., 2000), the ISBA soil scheme (Noilhan and Planton, 1989) and the radiation scheme of Morcrette (1990) as the more relevant parameterisations. It is initialised with the analysis of the ECMWF for 29 June at 00:00 UTC and is run until 00:00 UTC of 3 July, with lateral boundary conditions provided as well by the ECMWF. A sponge layer is activated at its top. The numerical estimations of the surface temperature field and of the air temperature at different heights are used.

As a first guess, it will be assumed that the depth of the volume for which the SEB will be computed is 2 m, since this is the typical distance between measurements at the surface layer and at the ground, which allows computation of vertical divergences. The horizontal dimension of the box will be the subject of this work, since we will explore what would be the contribution of the advection term to the budget depending on the horizontal scale of the thermal heterogeneity. It is clear that these computations will be rough estimates of the effect of the advection in the SEB, but it provides a reasonable starting point.

For simplification purposes, we will

neglect the vertical advection (taking

take 1 m s

approximate the average horizontal surface temperature gradient in
an area by the standard deviation of the surface temperature, supported by
SUMO measurements, keeping in mind that we are concerned solely with orders
of magnitude of

consider the LST variability as a good estimation of the variability of the air temperature at the surface layer, as supported by the measurements of the multicopter;

take the factor

Surface energy budget in the small square for the period 30 June to 3 July, between two rainy events (left), and zoom for the nighttime periods (right).

It is clear, from the large number of hypotheses made and its significance,
that the results presented below will be broader estimations of the value of

The SEB is computed for the station in the small square for the period 30 June at 12:00 UTC to 3 July at 12:00 UTC, between two rainy events. It shows a progressive drying of the upper soil as it will be shown in the next section. The evolution of the different terms of the budget for the whole period is shown in Fig. 2.

The turbulent fluxes are computed every 30 min using the eddy-correlation method with the standard corrections, the same used for all equipments in BLLAST (De Coster and Pietersen, 2011), using the EC-pack (van Dijk et al., 2004) that includes the computation of the planar fit angles to virtually rotate the sonic into the mean flow (Wilczak et al., 2001) and the Webb correction for the fluctuations of density (Webb et al., 1980). Errors in the values of the turbulent fluxes are estimated to be approximately 10 %. Furthermore, the ensemble of the BLLAST data set was quality controlled. This includes verifying record timing and de-spiking.

The net radiation term in Eq. (1) is the result of the budget of the four terms measured by the CNR1 (long-wave and short-wave upward and downward fluxes). While the ground flux is measured at 5 cm below the surface, corrections are required due to unrealistic measured values of the upper soil temperature. Specifically, corrections are made to surface temperature values using harmonic analysis (Heusinkveld et al., 2004) and simplifying the heat flux to a single sinusoidal function (Hillel, 1998). This correction results in an average increase in the ground heat flux of 40 % and a delay of 90 min.

Similar to what is done in Cuxart et al. (2015), we consider positive terms
those giving energy to the volume and negative those extracting energy from
it. In this 72 h series, shown in Fig. 2, we see that in the daytime, Rn is
the only input of energy and this energy is transported vertically away from
the surface by turbulent latent and sensible fluxes and downward through the
ground flux. However, there is an excess of incoming energy that is not
accounted for by these processes. This daytime imbalance is similar in
magnitude to the latent heat flux and larger than the sensible and the
ground heat fluxes. In the small-scale square, the amount of vegetation is
small, so the

Top left: evolution of the average air temperature for some levels of the model and LST, the available MODIS images and Meteosat Second Generation for model domain D1 for a period of 4 days; top right: standard deviation of the same variables in D1; bottom left and right: as above for domain D2, which was run only for the night 2 to 3 July. Values for the temperature at 1.5 m average and standard deviation at D1 are given for comparison in the bottom figures.

Figure 2 also displays a zoomed-in view of the budget for the three nights.
Taking the second night for discussion, which is the one showing the most
smooth time evolution, Rn is the largest term, now a loss, and the
compensating heat fluxes are

In the following sections, we will explore, using the available modelling and observational information, the order of magnitude of the values of the advection term in the SEB, making use of the observed horizontal temperature gradients in Eq. (4).

The order of magnitude of the advection term at scales close to 1 km or larger can be estimated using model outputs and satellite data. The green colour in Fig. 1 shows the areas in domains D1 and D2 where the terrain has a height above sea level between 50 and 700 m. This selection avoids coastal areas and mountainous terrain, so that the terrain complexity is comparable to that around Lannemezan. The average values of LST and air temperature at some levels and the standard deviations are computed for these areas in green. The same statistics are computed from the available LSTs provided by MODIS (about 4 per day) and MSG (every 15 min).

Figure 3 shows the evolution of LST as seen by the model, MODIS on Aqua and Terra satellites, and SEVIRI on MSG for domains D1 and D2. Also, the average values of the air temperature at 1.5, 10, 50 and 100 m above the surface are shown. It is noteworthy to point out that the model and satellite LST values are comparable, allowing us to use the model statistics with some confidence.

In Fig. 3, we see that at a resolution of 2 km (D1) the standard deviation
value of the air temperature does not change with height, varying between 1
and 2 K with maximal values in the afternoon and minimal at the end of the
night. The LST standard deviation is higher, with values around 3 K in the
day and 2 K in the night. These values are from the three different
available sources (D1, MODIS and MSG). Note that large sporadic values of
standard deviation for MSG on 29 June are due to cloud passages. Taking the
1.5 m values of the standard deviation as an approximation to the typical
changes of temperature over 2 km, the advection term according to
Eq. (

For the higher resolution run D2, we see that the standard deviation
decreases with height, indicating that at this resolution the model is able
to react significantly to the prescribed surface variability. The model has
the largest values of the standard deviation at the 1.5 m level, varying
between 0.7 and 1.8 K for the series shown. The corresponding rough order of
magnitude according to Eq. (

Therefore, for scales larger than 1 km the expected contribution of the
advection term to the SEB would be of the order of 10 W m

Surface temperature on 30 June 2011 at 14:32 UTC (left) and on 1 July at 20:24 UTC (right) as measured by SUMO from an approximate height of 65 m a.g.l. The red rectangle indicates the position of the small square of 160 m of side, where many surface-layer measurements were made. The units in the colour bar are degrees centigrade.

Small-scale thermal heterogeneities may generate corresponding small-scale
circulations. If these patterns are short lived (few minutes), the
corresponding circulations can be considered turbulence, but if they are
relatively persistent (longer than the averaging time for the computation of
the turbulent fluxes) then these circulations should contribute to the
advective term in the equation of

As mentioned previously, SUMO flew at approximately 65 m a.g.l. over a square of 1.6 km of side (the “SUMO square”), from sunrise to shortly after sunset. It provided, among other data, values of air temperature at that height and of LST sampled at 1 Hz, respectively at resolutions of 10 and 100 m, the latter with overlapping areas, always including the small-scale square at site 1, with a flight duration typically of 10 min. Figure 4 shows two typical examples of the LST, one in the afternoon, when the small square is warmer than its surroundings, and one for the evening, when the small square does not show a significant departure from the average value of the area. With the horizontal resolution of the IR sensor being close to the size of the small-scale heterogeneities site, the related thermal contrasts are probably underestimated.

If we split the measured LST by SUMO in two categories, one from inside the
small square and one from outside, we can compute thermal differences, as
shown in Fig. 5 (left panel); the site warms during the first 5 h of the day
(up to 5 K), and the difference slowly decreases afterwards from 10:00 UTC
until sunset, when it becomes negative and has values of about

If we estimate the order of magnitude of the advective term in the SEB
(Eq.

A very important result is that the standard deviation of LST
(

Mean air temperature difference between the SUMO square measurements taken inside and outside the small square for all flights during the whole BLLAST campaign, displayed by hour of the day for the LST (left) and the air temperature at approximately 65 m a.g.l. (right). Vertical lines indicate approximate sunrise (04:20 UTC) and sunset (19:40 UTC).

Standard deviation for the SUMO square for all flights during the whole BLLAST campaign, displayed by hour of the day for the LST (left) and the air temperature at approximately 65 m a.g.l. (right). Vertical lines indicate sunrise (04:20 UTC) and sunset (19:40 UTC).

The Meso-NH model with domain D1, covering the Garonne basin and surroundings, was run for 4 days of the BLLAST campaign, whereas D2 and D3, covering respectively the Lannemezan Plateau and surroundings and the SUMO square and surroundings, were only run for the night 1 to 2 July due to the limitations of computational resources (D2 from 18:00 to 10:00 UTC and D3 from 00:00 to 10:00 UTC). Using a model at high resolution has the advantage of having all the model information for the relevant variables, whereas the main disadvantage is the unavoidable departure from observations; in our case, the variability of prescribed surface characteristics may be distant from reality.

The SUMO square is described by 25 model columns in D2 and by 441 model
columns in D3 (D1 has insufficient resolution to provide variability for the
area). During the available hours for D2,

The variability for air temperature is explored taking four levels (1.5, 10, 50 and 100 m a.g.l.) for every column of the SUMO square in both domains (Fig. 7). The standard deviation diminishes with height to values around 0.2 K at 50 m independently of the hour, allowing us to consider that the effect of the surface heterogeneities is mixed by convection in the daytime or does not reach these heights in the nighttime.

In the surface layer, represented here by the 1.5 and 10 m model levels, we
see that the standard deviations are similar to the ones for the surface
temperature in the nighttime (about 0.6 K) but significantly smaller in the
daytime (0.4 K compared to about 1 K for the LST), when turbulence manages
to reduce the differences effectively. This indicates that it is a fair
approximation to take

Therefore, estimating the advection terms with these standard deviations
(taking 0.5 K for the whole day in both domains) we get values of the order
of 2 W m

Evolution of the standard deviation of temperature over the SUMO square computed from D2 (left; run only between 1 July at 18:00 UTC and 2 July at 10:00 UTC) and from D3 (right; run only between 00:00 and 10:00 UTC of 2 July).

For several days during BLLAST, instantaneous point measurements of
superficial SM (defined as the percent of water in the soil
volume) were made inside the small square using manual Delta-T devices, which
provided an integrated value for the layer between the surface and

Maps of the soil moisture (first 5 cm, in percent of volume) in the small square derived from point measurements from 30 June to 2 July. Measurement on 23 June is included for reference, since that day the terrain was at field capacity. Units of the colour bar are percent of volume.

Figure 8 shows the progressive and inhomogeneous drying over the square for 3 days after the rainy event of 29 June. The day after the rain (30 June) most of the square has values of SM above 30 % increasing westwards to more than 40 % and with water over the ground in the SW corner, with SM close to 60 %. During the second day (1 July), there is a progressive drying and the bare soil areas on the eastern side have reduced values of the SM of less than 20 %, whereas the western part has values between 25 and 60 %. These heterogeneities imply very different values locally of the Bowen ratio and of the surface temperature. On the third day (2 July) drying continues, but the surface variability is similar along the square.

This information is not transported into any quantitative estimation – this will be done in the next subsections using IR sensors. However, it may be deduced from these observations that heterogeneities at the decametre scale are large and of longer timescale than the turbulent motions. They may force a relatively steady distribution of eddies inside the square, diminishing the representativity of any point measurement within it.

The OWL multicopter flew over the small square in the period 1 to 5 July at
different times of the day. Flights were of short duration (several minutes)
and consisted of horizontal transects at an approximate height of 5 m. In
addition, some vertical profiles were made up to about 30 m a.g.l. over
some selected points. The spatial resolution of the LST measurements from
this height, with a cone of view of the IR sensor of 40

Multicopter: LST and air temperature standard deviation for the
small square for the ensemble of flights during 5 days, blue and purple lines
indicating respectively sunrise and sunset times (top left); vertical
profiles, in a different colour for each nearby position, inside the small
square in the afternoon, made within 5 min in a sunny afternoon (top right).
Nocturnal flight pattern and air temperature at 5 m a.g.l. (bottom left)
and LST values from that height (bottom right) for the flight at 03:25 UTC
of 5 July 2011. Units in the colour bar are

Figure 9 displays the standard deviations of the air temperature and of the
LST as a function of the hour of the day, each point corresponding to a
flight made during the 5 days. The values for LST are between 0.5 and 1 K
late at night and during the morning transition. They increase to 3.5 K
during the morning decreasing to values essentially between 1 and 2 K in the
evening transition. The pattern is very similar to what has been found from
the model and the SUMO data, but the values are larger except for the late
night and morning transition. Some large values of

Here

If we translate these estimations of

Variability inside a WUR IR image for a grass area at 18:20 UTC on
21 June (left); standard deviation of LST for 10 similar measurements in the
small square from a height of 1.5 m a.g.l. during the evening of the same
day, the numbers in white are minutes from the start of measurements, those
made after minute 33 were after sunset (right). Units in the colour bar are

NW corner of the small square as seen from the UCSD IR camera mounted at 50 m at 03:00 UTC on 5 July (left) and 12:00 UTC (right) on 3 July 2011. The picture is oriented in a way that the top part looks to SE and the axes are different from those of Fig. 10. Units in the colour bar are Celsius.

To help making a compact discussion, a summary of the previous results is
given in Table 1. Let us recall that the main aim of this work, provided the
available methods and data, is to provide comprehensive qualitative results
for

Secondly, as seen in Fig. 3 (bottom right) for the 400 m resolution run of
Meso-NH and, more clearly, in Fig. 9 (top left), when comparing the standard
deviations of the air temperature in the surface layer and of LST obtained by
the multicopter on the small square, it is reasonable to assume that the
standard deviation of these quantities (temperature of air in the surface
layer and LST) have values of the same order of magnitude. These
approximations exclude us providing meaningful values for the
advection term

An important issue to mention is that the uncertainties inherent to each method should be considered in Table 1, even if they are already conceptually taken into account in the term Ot of Eq. (2). The model, as seen in Fig. 3, has an error for our case not larger than 1 K, as it is also the case for most remote sensing determinations of the surface temperature (see e.g. Coll et al., 2005, for MODIS). Thermal cameras report uncertainties of the order of 0.1 K.

Estimation of the order of magnitude of the advection term

One obvious result is that the order of magnitude of the advection term increases as the scale becomes finer. Therefore the usual assumption that this term is very small compared to the main ones of the SEB equation stands for scales as fine as 1 km or broader. This is in agreement with the previous argumentations of Foken (2008a, b) and Leuning et al. (2012), which indicated that the advection term was not large enough to explain a substantial part of the imbalance in the measured SEB using only the four main terms (Eq. 1).

When the attention is turned to the smallest scales as the ones provided by the multicopter and the thermal cameras, of the order of 1 to 10 m, we see that the standard deviation of the surface temperature is of the same order as at larger scales, providing very high estimations of the advection term. In fact, Mahrt (2000) indicates that these heterogeneities may be restricted to the roughness sublayer (“the layer below the surface layer”) that extends to the blending height, above which the effect of these small-scale heterogeneities is perceived as integrated by the surface layer. In the roughness layer, typically of the order of magnitude of the roughness elements of the surface, Monin–Obukhov similarity is not applicable because the turbulence is not in equilibrium with the local gradient. These roughness elements are of the order of a few centimetres in most of the small square.

This allows us to exclude the heterogeneity of very small scales from our analysis as detected by the multicopter and the thermal cameras that, in fact, overpass by far the values of the imbalances at day and at night. In practical terms, it also means that these thermal differences in the roughness layer do not manage to organize persistent circulations at the level of the measuring screen. Instead, the persistence of such heterogeneities may indicate that circulations between the centimetre and the metre scales very close to the ground may establish, which could contribute to the fact that the surface does not experience nocturnal runaway cooling, contrarily to what models generate in flat areas that they treat as homogeneous. This subject should be explored further in an independent research action.

Therefore, the most relevant range of scales is that comprising the
hectometre and the decametre scales. The former ones correspond to the actual
scales of landscape heterogeneities in the area, such as crop fields and
wooden areas in between, or farms and small villages. Even the town of
Lannemezan is structured in areas of characteristic sizes smaller than 1 km. These patterns are either permanent (wooden areas, farms and
villages) or slowly varying with the seasons (crops and grass lands). That
is, these heterogeneities are fixed at the daily scale and generate
circulations that may persist for several hours and cannot be treated as
turbulence. The estimations provided by the model and the SUMO indicate that
these circulations may easily account for advections of the order of
10 W m

The scales of the order of a decametre, illustrated here with the multicopter
data, indicate that the heterogeneities are large in the daytime, very much
in accordance with the picture provided by LES and DNS of the convective
boundary layer (Van Heerwaarden et al., 2014), where small plumes exist
everywhere in the first 10 m above the ground and only a few plumes (at a
scale close to 100 m) manage to grow and make part of the mixed layer. It is
difficult then to consider conceptually this variability as a contribution to
the advection term, although there is no reason not to be able to compute the
advection term, and in fact it may be behind some of the imbalance,
explaining some tens of W m

The heterogeneities in the surface temperature at the decametre scale in the nighttime as seen by the multicopter are weak, of the order of 0.2 K, a value that we considered not relevant when found for the air temperature at 65 m as sampled by the SUMO. Therefore, even if the estimated advection term could explain largely the imbalance, we prefer to refrain from making any strong statement about this issue due to the few data available at night and conclude that more measurements are needed, also indicating that these scales may generate motions that could be included in the turbulence fluxes.

As the main point, it seems relevant to state that for scales of the order of
hectometres, the circulations generated by surface heterogeneities may be
relatively persistent and explain a substantial part of the imbalance in the
SEB, especially at night. For larger scales the contributions are small,
whereas for finer scales the subject is still open to discussion, but
probably these motions are small and restricted to very close to the surface
or taken into account in the turbulence. Since the surface temperature field
seems to have a variability close to that of air temperature at the screen
level, a possible estimation of the contribution of the subgrid or subpixel
variability to the SEB might be provided using

This work has explored the order of magnitude of the advection term in the
SEB using broad estimations of the surface-layer thermal variability provided
by a number of sources, including model outputs at different resolutions,
satellite images, remotely controlled measuring devices (SUMO and
multicopter) and thermal cameras. The SEB is computed using the measurements
on a small squared area in BLLAST that provides an estimation of the
imbalances, which is of the order of 200 W m

The variability of the surface temperature fields as provided by the different sources has been explored and it has been compared with the variability of the air temperatures in the surface when possible. It is seen that this variability has similar values for all the scales inspected, implying that the advection term is increasingly larger as the scale becomes finer. The variability of the air temperature close to the surface is similar to that at the surface, using the information that we have, essentially from the model outputs and the multicopter transects.

The advection term corresponding to scales greater than a kilometre are much smaller than the other terms and cannot explain any significant part of the imbalance, either because there are no real circulations performing the transport or because the steady state regime makes the net advection very small. On the other extreme of the spectrum of scales, those of the order of a metre still show very significant temperature variability, but the associated values of advection are too high to be meaningful and are probably related to redistribution of heat in the first centimetres above the surface within the conceptual box of computation of the SEB and therefore not relevant for the SEB.

The current analysis points to the hypothesis that long-lasting terrain heterogeneities at the hectometre scale, like cultivated fields or small woods typical for the area, may generate motions that last longer than the averaging time of the turbulent fluxes and explain a significant part of the imbalance. Instead, the contribution of motions generated at the decametre or the metre scale, usually within the surface layer, provide unrealistically high values of the imbalance, indicating that most likely they are already taken into account in the turbulent fluxes. To proceed towards more conclusive evidence of these qualitative results, specifically designed experiments should be conducted, providing better quantitative estimations and informing about the sign of the advection term.

Metadata and data from the BLLAST campaign are available after registration at

The BLLAST field experiment was made possible thanks to the contribution of several institutions and supporters: INSU-CNRS (Institut National des Sciences de l'Univers, Centre National de la Recherche Scientifique, LEFE-IDAO program), Météo-France, Observatoire Midi-Pyrénées (University de Toulouse), EUFAR (EUropean Facility for Airborne Research) and COST ES0802 (European Cooperation in the field of Scientific and Technical). The field experiment would not have occurred without the contribution of all participating European and American research groups, which have all contributed a significant amount (see supporters). BLLAST field experiment was hosted by the instrumented site of Centre de Recherches Atmosphériques, Lannemezan, France (Observatoire Midi-Pyrénées, Laboratoire d'Aérologie). BLLAST data are managed by SEDOO, from Observatoire Midi-Pyrénées. We wish to particularly acknowledge Felipe Molinos, who assisted the University of the Balearic Islands team in the field, and the students of the Wageningen University that took the pictures with the thermal camera, especially Linda Kooijmans and Daniel Kunne. ECMWF and AEMET have provided computing time through the research project “Effect of the surface heterogeneities in the atmospheric boundary layer”. The Spanish Ministry of Research has partially funded this action through grants of the Spanish Government, CGL2009-12797-C03-01 and CGL2012-37416-C04-01, supplemented with FEDER funds, CGL2015-65627-C3-1-R and PCIN-2014-016-C07-01, the latter part being of the NEWA ERA-Net+ project of the European Union. Edited by: E. Pardyjak Reviewed by: V. Caselles and one anonymous referee