The decay of turbulence kinetic energy (TKE) and its budget in the
afternoon period from midday until zero-buoyancy flux at the
surface is studied in a two-part paper by means of measurements from
the Boundary Layer Late Afternoon and Sunset Turbulence (BLLAST)
field campaign for 10 intensive observation period days. Here, in
Part 1, near-surface measurements from a small tower are used to
estimate a TKE budget. The overall boundary layer characteristics
and mesoscale situation at the site are also described based upon
taller tower measurements, radiosoundings and remote sensing
instrumentation. Analysis of the TKE budget during the afternoon
transition reveals a variety of different surface layer dynamics in
terms of TKE and TKE decay. This is largely attributed to variations
in the 8
The atmospheric boundary layer (ABL) over land is inherently
marked by a diurnal cycle. The afternoon transition period can be defined as
the period from midday maximum heat flux until zero-buoyancy flux
Many studies, as discussed in
In general, it may be concluded from the extensive review of existing
literature provided in
Recent simulations
The figure is showing the two main measurement towers and the
Pyrenees mountain range in the background. The small divergence site
tower is marked with A and taller 60
In this study, we present a TKE budget from field observations and use it to
discuss the governing terms that influence TKE decay rate in the surface
layer over a grass surface during the afternoon transition. Our analysis is
based on 10 intensive observation period (IOP) days using measurements from
the small divergence site tower (see Fig.
The main data sets and methods used in this study are presented in Sect. 2.
For further information on the BLLAST data set, see also the overview paper
Here we describe the main data sets used in this study and provide details
about screening and treatment of the data. Turbulence data (20
The data set of UHF wind profiler data is available at an average
temporal resolution of 5 min and vertical spatial resolution of
75
We used software from
At times, it can be argued that the gap-filled wind direction fields miss too much
of the real variability that was indicated by the available non-gap-filled and
unsmoothed data (and sometimes at the 60
After manually checking time series of wind and temperature, the four upper
measurement levels at the small divergence site tower (2.23, 3.23, 5.27 and
8.22
Fluxes were calculated in a rotated coordinate system
The governing equation for TKE in a sheared convective boundary layer
under the assumption of horizontally homogeneous turbulence and no
advection is given by
Here TKE (
We have given the buoyancy term the subscript buoyancy production of
TKE since we limit our study to the afternoon period before stable
stratification starts. Hence, it is always a positive term in our
case. The physical interpretation of the six terms in Eq. (
Firstly, we determined TKE (
The variations in TKE on shorter timescales may potentially be related to
advection of TKE, temporary shading from clouds causing changes in the near-surface energy balance, fast variations in near-surface wind gradients and
fluxes, or other effects causing non-stationarity in TKE (and especially in
horizontal wind variances). Statistical sampling error is also a large
source of variability both for variances and turbulent fluxes
This term is evaluated from the shearing stress
This term requires only the measurement of the turbulent flux of
virtual temperature, which is nearly equal to the corresponding flux
of the directly measured “sonic” temperature at each turbulence
level, and measurements of the mean temperature. The 8.2
Dissipation (
Here
Boundary layer depth (
Time series of wind direction for each IOP day, color-coded according to
measurement height such that the small-tower measurements (2–8
Transport is given by two parts: pressure transport and turbulent
transport. Pressure transport,
The turbulent transport,
Therefore, we believe that a better estimate of the total transport
(being equal to the sum of turbulent and pressure transport) is
obtained from the residual of the TKE budget. Hence, we determine the
total hourly transport value
Here, we summarize some of the atmospheric conditions for 10 IOP days. The
description is based on boundary layer depths from radiosoundings (using
a maximum potential temperature gradient criteria), UHF wind profiler
(determined from reflectivity based on the refractive index of air, which is
related to pressure, temperature and specific humidity; see
Time series of wind speed with the same color-coding as used
in Fig.
For even further information about the synoptic situation and standard
radiosounding, we also refer the reader to the day-by-day description of IOP
days in
For these 10 IOP days many different conditions in terms of boundary layer
depth, wind speed and moisture conditions occurred. This was found even though there were mainly
fair-weather days with generally no, or a small amount of, cloud cover,
except on 24 and 30 June, which had more clouds
From the UHF wind profiler data provided in Appendix A it is clear that the
overall boundary layer flow situation involves an upper wind speed gradient
which is often present, for at least 6 out of 10 days, possibly excluding
25–30 June, when it was weaker and/or more diffuse. The height of the strong
wind speed gradient marks a dynamical separation of the boundary layer flow
with northerly or easterly wind (in daytime) from the dominant westerly flow
above. The northeasterly boundary layer wind is most of the time linked with
a mountain-breeze circulation on the site. The mainly westerly or weak flow
above the boundary is related to the synoptic weather situation on the
different days. When the boundary layer flow, related to the complex
mesoscale situation at the site, encounters and mixes with the flow above,
a layer of reduced wind speed in the upper parts of the boundary layer also
occurs, as can be observed for several days (see Fig.
On some of the warm days (25–27 June) the wind direction in the boundary
layer is more easterly in daytime. This is related to a low-pressure area in
the lower troposphere over the Gulf of Lion in the Mediterranean
Smaller differences in wind characteristics are generally observed on the
60
When the atmosphere is stably stratified, it is important to remember that
the surface TKE budget gives very limited information about upper layers. For
unstably stratified conditions there is, however, no reason to believe that
such decoupling issues exist, and as we shall see in Sect. 4.3, mixed-layer
dynamics (linked with boundary layer depth) have an influence on dissipation
rate even very near the surface. Surface layer wind is used in the TKE budget
analysis in the following sections. Many of the variations in observed
surface layer wind on the small tower are, however, clearly linked and caused
by variations in boundary layer wind observed on the 60
When comparing sensible heat fluxes shown in
Turbulence kinetic energy budget terms are shown on the
In Fig.
For buoyancy production (in blue), only very small height variations are observed near the surface and a general decrease with time during the afternoon is observed for all days. On 30 June, this general picture is partly interrupted by the presence of clouds changing the energy balance.
Also, the dissipation rate (in black) is observed to have a general decrease during the afternoon transition for 8 out of 10 IOP days. Most significant deviations are found on days with an increase in shear production during the afternoon, leading to a clear increase in dissipation. Hence, shear production plays an important role near the surface in the TKE budget for most of these 10 IOP days. It has the most pronounced height dependence out of all budget terms, with higher values near the surface. The strongest dissipation rate is also found closest to the surface, but the height variation in dissipation is smaller.
Given that the TKE tendency (in green) is much smaller (2 orders of
magnitude) than the other budget terms this implies that the sum of
turbulent and pressure transport (in magenta) compensates for remaining height
variation in the budget. Because the tendency term of TKE is much smaller
than the other budget terms, we will refer to the hourly TKE as evolving in
a quasi-stationary way. Here, we use the term quasi-stationarity to mean that the tendency
of TKE is small in comparison to the other budget terms. This result of quasi-stationarity is
consistent with the observed slowly evolving mean TKE levels in LES for
a large part of the afternoon of 20 June as described in
The height variation in transport is found to mainly be linked with local shear production. The transport term is consistently a negative term in the TKE budget. This implies transport of near-surface-produced turbulence to the surrounding environment and upper parts of the boundary layer. Only a few occasions with positive transport term were observed in connection to changing cloud cover and more variable dissipation estimates.
To investigate general differences between the different days, we calculated statistics for each budget term during the afternoon period. These statistics are provided in Appendix B and some of the most important findings are discussed in Appendix B and only briefly restated here.
Variations in shear production between afternoons in Tables
Vertical profile of mean near-surface wind speed for all 10 IOP afternoons with measurements at the small divergence site tower.
Average TKE tendency for each afternoon is shown as
a function of buoyancy production in panel
TKE budget classification of the 10 IOP afternoons. Here, wind speed, shear production, transport and dissipation have been classified into three categories (“h”: higher; “m”: moderate; “w”: weaker) and the buoyancy production into two categories (“h” and “m”) based on the mean values for the afternoon (see text for exact limits). Furthermore, in parentheses “p” denotes whether only part of the afternoon is considered to belong to the category. For the moderate category an extra “l” or “h” indicates whether the variable is mainly departing towards the lower or higher category. For dissipation, two days are denoted with “(inc)” to indicate that dissipation increased during the afternoon. To interpret some of the main effects of higher or weaker wind speed on the TKE budget, combinations of underlining, italics and bold font have been added to the table (see text for further explanation).
There are, of course, exceptions to the rule that a higher wind speed leads
to a higher TKE level; this topic needs to be further
discussed. In
Fig.
Nevertheless, it is interesting to note that a relatively high negative
correlation (
We do a broad summarizing classification of the 10 different afternoons in
Table
For this broad classification we take as a starting point the terms of
largest variation at the 2
If the mean value of shear production at the 2
For transport, a mean value below
For dissipation, a mean value equal to or lower than
Finally, for buoyancy production, we have classified higher buoyancy
production to imply a mean value for the afternoon of above
To compare these new measurements and estimated TKE budget terms in
the context of earlier studies, we first investigate the behavior of
each term in the budget after normalization by friction velocity
After normalization of Eq. (
Here, we have lumped together pressure and turbulent transport terms into one
total transport term
For buoyancy production, the expression by definition simply reads
Normalized hourly TKE budget terms for the 10 afternoons
shown as a function of the stability parameter
For shear production, we note that a commonly used form of
Normalized shear production was thus found to be low in the present data set in comparison to previously reported results. The scatter in our data was, however, found to be large enough that a von Kármán constant value of 0.4 was found to be within a 95 % confidence interval for neutral stratification. The reason for low normalized shear production is unclear, but it could be a reflection of measurement uncertainty, non-stationarity and heterogeneity.
In Fig.
Normalized production terms (buoyancy production
Dissipation is shown as a function of TKE and height near the
surface. In panel
For dissipation, we note a variety of different results in the literature
Both our shear production relationship and dissipation relationship was
determined by first producing least-squares fitted expressions, but these were slightly adjusted to
ensure that the transport data in the TKE budget could also still be reasonably well fitted by a residual
expression. For the sum of turbulent and pressure transport term (to be consistent
with observed small TKE tendency), our expressions in
Eqs. (
For
An alternative way to express dissipation in models is to relate it to the
TKE (
In Fig.
Dissipation coefficient
Comparison between observed and predicted dissipation is
shown for a model based on
In Fig.
Our final alternative form for expressing dissipation as a function of
TKE and a dissipation length scale then becomes
Figure
Both models behave relatively similar for cases with low observed dissipation
(
Using radiosoundings, UHF wind profilers and tower measurements, we
summarized an overall description of the prevailing boundary layer
situation for 10 intensive observation period (IOP) days. This
characterization showed that many different conditions in terms of
boundary layer depth, wind speed and moisture conditions occurred on
these days, despite being mainly high-pressure fair-weather
situations. Some common features are recognized, such as the following:
Mainly westerly flow above the boundary layer and an easterly or
northerly flow in the daytime boundary layer (linked with
mountain–plain circulation for most of the days), turning in the
evening and nighttime. As the boundary layer flow encounters and
mixes with the flow above, a layer of reduced wind speed is also
observed for several days. Wind direction at a small tower (2–8 In the evening, after the buoyancy flux switched sign and stable
stratification has begun, the wind direction at the small tower
turned rapidly towards south for several of the days related to
a shallow drainage flow. At the 60
These observations are important to emphasize for a couple of reasons:
In stable stratification, near-surface TKE budget analysis was
concluded to provide very little information about atmospheric
conditions above the very near-surface layers. This is because of
decoupling issues, and effects of shallow drainage flow, as well as
the mountain–plane circulation related to larger-scale topography
and some occasions of nocturnal low-level jets. During unstable stratification, in the afternoon transition our
surface layer analysis can, however, also be informative of what is
occurring above in the mixed layer since the two layers are more
closely coupled to each other. The height variation in TKE budget
terms could in these conditions be used to also interpret how the
mixed layer has an influence on surface layer dynamics.
The afternoon transition was studied using TKE budget analysis. Here,
we focused on the slow and persistent changes in TKE budget terms that
are well described by an hourly TKE budget analysis, leaving shorter
timescales and more temporary fluctuations of TKE for future
studies. Several important results were reached:
All terms of a TKE budget except those of
transport could be determined directly from field measurements near
the surface on an hourly basis for 10 fair-weather afternoons. This
allowed calculation of the total transport as a residual from the
other budget terms. The TKE tendency term was found to be much smaller than all the
other budget terms, suggesting that the surface layer turbulence
evolves in a quasi-stationary way during the afternoon
transition. Even though TKE tendency was small, we found
a relatively high correlation coefficient ( We found that several explanatory factors are needed to be able
to interpret the behavior of TKE and TKE tendency during the
afternoon transition. Both near-surface wind speed (causing shear
production) and buoyancy production of TKE were found to be
important production terms at 2–8 Larger variations between afternoons were observed in shear
production, transport and dissipation compared to buoyancy
production. This implies that all these terms are important to take
into account of in modeling of sheared convective surface layers. A summarizing classification of the 10 IOP afternoons showed
that, in general, windier days of the field campaign (20, 25, 26 and
27 June) had a higher transport of TKE out of the near-surface
layers as well as often a higher or moderate dissipation of
TKE. Afternoons with weaker wind (30 June and 2 July) instead had
less transport and weaker dissipation. But, for a more complete
picture, buoyancy production, as a key forcing, also needs to be
considered (e.g., 19 June), as do variations
within the afternoons. Normalization of TKE budget terms by friction velocity and
measurement height and fitting of empirical expressions
(Eqs. In general, it can be argued that our data suggest that about
50 % of the near-surface production of TKE is locally
dissipated, leaving about 50 % available for transport.
However, empirically fitted expressions (Eqs. For dissipation we also alternatively proposed a non-local
parametrization using a TKE–length scale model which takes into
account of boundary layer depth and distance above ground. The
non-local formulation was found to give a better description of
dissipation of TKE and is hence suggested to
provide an important component for simple modeling of surface layer
TKE, while still taking into account non-local influences. Such
modeling is attempted in our companion paper, Part 2.
The weather conditions were dominated by a cloud-free high-pressure situation
with very few disturbances in incoming shortwave radiation
The boundary layer depth from Fig.
Both days were characterized by moderate westerly winds (higher than about
8
Wind speed near the surface shows fewer differences between the
60
Wind speed from UHF profiler between 175 and
2500
Wind direction from UHF profiler data between 175 and
2500
June 24 may be considered the start of a general warming period which
lasted until the evening of 27 June. Temperatures increased from about
11
These days can also be characterized as high-pressure fair-weather situation
before the passage of an approaching frontal system reaching the site around
02:00 UTC on 28 June. The cloud cover varied among the days; 24 June had
some clouds (mostly cirrus) for most of the day but decreasing amounts in
the afternoon from 14:30 UTC. June 25 was completely cloud-free, whereas
clouds were observed on 26 June starting around 14:00 UTC. June 27 was
cloud-free until the late afternoon, around 16:30 UTC, when some pre-frontal
clouds (mainly cirrus) appeared. Relative humidity for the afternoon was
about 50–60 % on 24 June (hence comparable to 19 and 20 June) but less
for the warmer days: 30–40 % on 25 June, 25–35 % on 26 June and
30–50 % for 27 June. As noted in
The maximum boundary layer depth on 24 June was similar to 19 and 20 June
(1100
June 24 also experienced a strong westerly flow above the boundary layer, as
on 19 and 20 June, which, however, became weaker as time progressed, and in
the afternoon and evening mainly moderate upper wind gradients (between 0.5
and 1.0
For both 25 and 26 June, the boundary layer flow was stronger, with persistent
easterly winds turning southerly in nighttime. An average wind speed at
175
June 30 experienced the aftermath of a cold frontal passage that
occurred on the previous day and had some stratocumulus clouds in the morning
followed by cumulus for most of the day and clearing skies in the evening.
Pressure started to rise significantly at midday and during 1 July and also
remained relatively high on 2 July
On both 30 June and 1 July boundary layer depth was observed to be high,
reaching around 1500
June 30 had mainly weak winds in the boundary layer (below
4
July 1 and especially 2 July had higher wind speed (and still westerly flow)
above the boundary layer and mainly easterly (2 July) and northeasterly
(1 July) flow in the boundary layer. On both days a change towards south
took place in the evening after stable stratification started. This shift of
wind direction was slow and delayed and evolving to a full southerly flow at
175
Near-surface specific humidity from standard radiosoundings
[
Finally, the last IOP day studied was a completely cloud-free warm day
reaching up to 26
Boundary layer depth on 5 July was somewhat lower compared to 2 July
following a general decreasing trend from the high values observed on
30 June. Potential temperature gradients were often weak especially in the
afternoon, making boundary layer depth determination based on strongest
gradient below 2500
For 5 July the wind speed was again weak in the boundary layer but increased
during the late afternoon and evening, and at the same time winds were turning
counterclockwise from east or northeasterly flow towards mainly
west-northwesterly. At the same time, the flow just above the boundary layer
also turned counterclockwise from west or northwesterly towards southerly
flow. The upper winds were mainly weak to moderate (5–11
Afternoon statistics of wind speed, shear production, buoyancy
production, transport and dissipation for a measurement height of
2.23
In Tables
It is important to note from Tables
Afternoon statistics of wind speed, shear production, buoyancy
production, transport and dissipation for a measurement height of
8.22
Afternoon TKE statistics for the 10 IOP days for
measurement heights of 2.23 and 8.22
The first author thanks ANR for funding this postdoctoral work and
would also like to thank Jordi Vilà-Guerau de Arellano, Arnold
Moene and Oscar Hartogensis at Wageningen University for fruitful
discussions about this work during a research visit in
December 2014. The BLLAST field experiment was made possible thanks
to the contribution of several institutions and support: INSU-CNRS
(Institut National des Sciences de l'Univers, Centre national de la
Recherche Scientifique, LEFE-IMAGO program), Météo-France,
Observatoire Midi-Pyrénées (University of Toulouse), EUFAR
(EUropean Facility for Airborne Research) BLLATE-1 and 2, COST ES0802
(European Cooperation in the Field of Scientific and
Technical Research). This research was partially funded by the Office of
Naval Research Award #N00014-11-1-0709, Mountain Terrain
Atmospheric Modeling and Observations (MATERHORN) Program. The
authors thank Daniel Alexander for providing the technical support
for the divergence tower. The field experiment would not have
occurred without the contribution of all participating European and
American research groups, which all have contributed to
a significant extent. The BLLAST field experiment was hosted by the
instrumented site of Centre de Recherches Atmosphériques,
Lannemezan, France (Observatoire Midi-Pyrénées, Laboratoire
d'Aérologie). Its 60