In order to monitor the evolution of the mean structure of the PBL during the AT (and initialize the simulation), we used standard radiosoundings launched every 6 h, from 06:00 to 18:00 UTC, and hourly radiosoundings of the lower troposphere (up to 3 to 4 km), from 13:00 to 18:00 UTC. The launching sites of the two types of radiosoundings were 4 km apart. The radiosondes measured temperature, water vapour content and the sonde location from which the horizontal wind components were deduced.

Surface energy balance and turbulence structure in the surface layer were provided by several ground stations over different vegetation coverages (wheat, corn, grass, pine forest and moor (composed of heather and gorse)). A permanent 60 m tower provided integrated turbulence measurements in the surface layer above the heterogeneous surface. The statistical moments were estimated over detrended 30 min periods from 10 Hz raw measurements. The surface heat fluxes are used as surface forcing in the simulation.

Two aircraft, the French Piper Aztec (PA) from SAFIRE (Service des Avions Français Instruments pour la Recherche en Environnement) and the Italian Sky Arrow (SA) from Ibimet (Istituto di Biometeorologia del CNR) and Isafom (Istituto per i Sistemi Agricoli e Forestali del Mediterraneo) , carried out flights throughout a wide area during the afternoon, at 65 and 40 m s-1, respectively. They measured temperature, moisture, pressure, CO2 mixing ratio and 3-D wind at 50 Hz (SA) and 25 Hz (PA) on 25 to 40 km legs stabilized in attitude and altitude. The detailed instrumentation of both aircraft is given in .

On the basis of meteorological criteria and data coverage, 20 June 2011 was selected as our case study. The synoptic situation was a high-pressure system over the southwest of France, with a light westerly wind leading to fair and cloud-free weather.

Figure  shows the normalized altitude z/zi of the stacked legs flown by the aircraft as well as the different launching times of the radiosoundings (the method used for the PBL height (zi) estimation is discussed later). The two aircraft flew simultaneously, the PA flying above the SA. They flew along west–east parallel legs, at three latitudes and, as shown in Fig. , at six heights within the PBL and at two different time periods: the first one from 14:30 to 15:30 UTC, the second one later, from 17:45 to 19:00 UTC. This flight strategy provides access to six heights to study the vertical structure of the turbulence within the PBL.

Figure  presents the evolution of the potential temperature (θ) and the wind direction in the PBL at several hours from 05:00 to 18:00 UTC on 20 June 2011. During the day, the PBL warms by about 7 K and the PBL depth zi grows up to about 1100 m above ground level. Figure a also shows evidence of a warm advection above the PBL between 05:15 and 11:00 UTC that must be taken into account in the simulation. After 11:00 UTC, the θ profile hardly changes in the free atmosphere, meaning that the temperature advection is very weak.

Figure b shows an easterly wind within the PBL, veering to westerly above. The wind intensity remains constant all throughout the day (not shown): it is weak within the PBL (less than 4 m s-1) and increases with height, up to 10 m s-1 at 1500 m.

The water vapour mixing ratio (r) increases from 8 to 10 g kg-1 in the PBL until 13:00 UTC and decreases afterward. The temporal evolution of the PBL mean vertical structure is further analysed in Sect. .

The surface sensible and latent heat fluxes (H and LE, respectively) measured above various vegetation coverages are presented in Fig. . The maximum value of H varies from 100 to 130 W m-2 over grass and moor to 450 W m-2 over pine forest. LE shows much less variability between vegetation coverage, maximum values varying from 250 to 350 W m-2. The measurements at 60 m height integrate a large footprint and should give flux estimates of the heterogeneous landscape. As such, H measured at 60 m height is encompassed in all the other measurements and is close to the moor and grass, the dominant vegetation , which represents about 40 % of the vegetation cover on the plateau.

In this study, the AT is defined as the period from the time when the surface buoyancy flux is maximum, to the time where it goes to 0 (the surface buoyancy flux is defined as the turbulent vertical transport of virtual potential temperature and is approximated as a linear combination of observed surface sensible and latent heat flux). This period varies according to the surface . For the moor coverage, whose surface fluxes will be used to drive the simulation of 20 June 2011, this period starts at 12:00 UTC and ends at 1750 UTC, while it ends 20 min earlier when considering H instead of the buoyancy flux. This delay is observed for all the intense observation period (IOP) days of the BLLAST campaign implying that the latent heat flux reaches its minimum value systematically later than the sensible heat flux. Thus, the forcing timescale of the surface flux decay τf is around 5.8 h over the moor surface.

Our LES is initialized with early morning radiosoundings and forced with homogeneous surface fluxes, based on those measured over the moor surface. Temperature and humidity advection are prescribed. The lateral boundary conditions are periodic.

The LES code from the National Center for Atmospheric Research () is based on the Boussinesq equations, including conservation laws for momentum and mass and the first law of thermodynamics. The subgrid-scale model includes a turbulent-kinetic-energy–eddy-viscosity model suggested by , used by and improved by .

The simulation resolves a domain of 10.24 km × 10.24 km horizontally and 3.072 km vertically, with Δx=Δy=40 m and Δz=12 m of horizontal and vertical resolution, respectively. This results from a compromise between the computation time and three constraints: (1) the domain size and resolution were chosen after a sensitivity study (not shown) so that the LES spectra were able to represent the main characteristics of the observed spectra, (2) the resolution was chosen so that the ratio of zi to (Δx×Δy×Δz)1/3 was large enough to ensure that the results were independent of the resolution , and (3) the ratio of Δx to Δz was kept rather small but with a high enough vertical resolution to correctly represent the entrainment zone . The time step evolves during the simulation and is about 1.4 s for fully convective conditions.

The simulation was initialized early in the morning, in order to ensure a fully turbulent convective PBL by the afternoon. The wind, potential-temperature and specific-humidity initial profiles for the LES were deduced from the 05:15 UTC radiosounding (see dashed lines in Fig.  for temperature and wind speed). No geostrophic wind is prescribed. This simple representation of the wind leads to a simulation with very low wind speed, as is the case in the observations, but does not allow us to simulate the shear in wind direction. A homogeneous and flat surface is considered in the LES, with imposed surface fluxes which are those measured at the moor site (Fig. ).

Vertical profiles of large-scale total advection (horizontal plus vertical advection) of heat and moisture were hourly prescribed in the simulation and linearly interpolated in between. They were derived from the AROME (Application of Research to Operations at Mesoscale) forecast model (horizontal resolution of 2.5 km), using the 16 grid points in a box surrounding the experimental site. This model confirms predominant zonal advection, especially during the morning.

From 05:15 to 10:00 UTC, temperature advection is important and about 10 K day-1 from 500 m up to 1500 m (not shown). After 11:00 UTC, it decreases and is negligible in the afternoon. This is consistent with what is observed regarding the evolution of the potential temperature (Fig. a). From sunrise to 14:00 UTC, the moisture advection is about -10 g kg-1 day-1 from the surface up to 500 m, and about 10 g kg-1 day-1 above. After 14:00 UTC, the moisture advection weakens (not shown).

The data files used to run this case (initial profiles, surface flux and advection profiles) are available on the website of the BLLAST database (http://bllast.sedoo.fr/database).

The bracket notation 〈ψ〉 for any simulated variable ψ is used to represent the 2-D horizontal average over the LES domain. The same notation is used for the 1-D horizontal average of the airborne measurements along the legs. For the surface data set, ψ¯ represents the time average notation. For these three types of data sets, the turbulent fluctuations ψ′ are defined as deviations from the corresponding mean. For a fairer comparison with the simulated variances, the observed variances are estimated by integration of the spectra over the wave number range resolved in the simulation. Finally, all the simulated mean vertical profiles are averaged over 30 min and depicted, for simplicity, with the bracket notation 〈ψ〉, which then indicates both horizontal and temporal average.

The evolution of the simulated θ vertical profiles is compared with observations in Fig. a from 05:30 to 17:50 UTC. The simulated θ is close to the observations in the mixed layer (differences lower than 0.1 K) and in the free atmosphere, simulating the change in θ profile between 05:15 and 11:15 UTC due to the prescribed advection.

In the first 100 m, the differences in stability profile at 11:30 UTC might be due to the different locations of the soundings and the moor site where the surface flux is observed. The 17:30 UTC LES profile is already neutral, whereas the observation at 17:50 UTC still has a superadiabatic region. The differences are due to the fact that as soon as the surface buoyancy fluxes turn negative, the LES potential temperature profile becomes stable in the lower layers of the PBL. This delay between the time when the buoyancy flux goes to 0 and the time when the local gradient of virtual potential temperature changes sign has been observed and analysed in . It can be of the order of 30 min to 1 h.

Figure b presents the evolution of the water vapour mixing ratio. The temporal evolution of r profiles shows a well-simulated daily humidification. A departure of 1 g kg-1 from the value actually observed can be seen at 13:05 and 17:50 UTC.

The horizontal mean wind speed is well reproduced in the simulation during the day: the wind remains weak and about 2 m s-1 in the PBL. u∗ evolves from 0.2 to 0.1 during the afternoon for both observed and simulated data. The wind increases with altitude above the PBL and reaches 10 m s-1 at 2000 m. No wind forcing is prescribed in the simulation; therefore, the observed wind direction change from west to east within the mixed layer between 05:30 and 11:30 UTC is not simulated (Fig. d). Whilst the wind speed shear is well simulated, the wind direction shear is evidently underestimated. Consequently, shear-driven processes might not be as important in the simulation as in the observations.

The simulated vertical profiles of the buoyancy flux normalized by the surface buoyancy flux at the start of the AT (Fig. ) have quite a classical shape until 13:30 UTC, with a linear decrease with height and negative flux above 0.8 zi. In the simulation, zi is estimated as the height of the mixed layer, determined with a threshold on the θ vertical gradient (0.01 K m-1). This method was preferred to the one used for radiosoundings (see below) because of the complex humidity profiles which lead to more fluctuating zi estimates. However, the difference between these two estimates is less than 50 m. After 13:30 UTC, the upper layer, characterized by negative entrainment flux, deepens and goes down to 0.6 zi at 18:00 UTC. During the AT the entrainment rate (ratio of the buoyancy flux at the top of the PBL to the buoyancy flux at surface) remains constant and about -0.13 (not shown). Unfortunately, this value cannot be compared to observations since the fluxes deduced from airborne measurements in the PBL vary substantially at that time and because of the lack of statistics on the large scales in a less and less stationary PBL. Flight legs long enough to obtain accurate statistical moment estimates in convective PBL are even more relevant during the AT.

The temporal evolution of zi has been estimated from ultra high-frequency radar wind profiler (hereafter UHF) and radiosounding measurements and has been compared to the simulation (Fig. ). zi is estimated from UHF as the maximum of the refractive index structure coefficient . From radiosoundings, zi is estimated as the altitude of the maximum relative humidity below 2500 m (this criterion has been shown to be consistent in time and height during the BLLAST experiment; ).

Until 09:00 UTC, the UHF detects the residual layer of the previous day. After 10:00 UTC, the zi increase is similarly depicted by the UHF and radiosoundings, with a maximum value of 1100 m. The simulated PBL grows slower than the observed PBL and reaches 850 m. This discrepancy between observed and simulated zi (which is larger than the uncertainty of the zi estimate) might be partly explained by a weaker entrainment effect in the simulation due to a lack of wind shear.

The temporal evolution of the simulated and observed TKE at several heights is presented in Fig. . TKE(z,t)=12(σu2(z,t)+σv2(z,t)+σw2(z,t)), where σu2, σv2 and σw2 are the variances in the horizontal u, v and vertical w wind components. For a better comparison, simulated and observed TKE are estimated using the wind component variance deduced from the integration of the spectra over the wave number range of the simulation. By doing this, the TKE associated with large and small eddies observed, but not simulated or resolved in the LES, is removed from the observed TKE. Even with this method, LES underestimates the observed TKE by a factor which is sometimes as high as 1.5.

In summary, the simulated boundary layer is comparable to the observed one in terms of boundary layer height, wind speed, and dynamical and thermal stability (not shown) near the surface. The lower development of the PBL height of about 200 m and the TKE underestimated by a factor of 1.5 can be partly explained by the directional wind shear which is not simulated. The latter might increase the entrainment and the turbulence dynamical production at the top of the boundary layer. Despite these differences regarding the main PBL structure, the simulation is realistic enough to evaluate how the turbulence evolves in a convective boundary layer during the AT and the comparison of the simulated and observed boundary layer will be analysed accordingly.

Most previous studies investigated either vertically integrated simulated TKE over PBL depth or measured TKE in the surface layer. The TKE decay according to height remains sparsely documented .

Figure a shows the evolution of half-hour averaged hourly vertical profiles of simulated TKE from 11:30 to 18:30 UTC. The profiles show that TKE decreases within the whole depth of the PBL but that there is a 1-hour delay between the start of the decay at the top and the start at the bottom: at 12:30 UTC, the TKE continues to increase in the lower PBL, while it has started to decrease in the upper part. After 15:30 UTC, the decay is homogeneous over the vertical. This differential TKE decay will be named TKE top–down decay hereafter. This result is consistent with the and studies which revealed, with remote-sensing observations, a decay of TKE dissipation rates from top to bottom. also studied the decay with direct numerical simulation (DNS), based on a realistic surface flux decay. They found that the turbulence is maintained at the surface relative to upper layers, which they explain with shear at the surface.

In this study, the simulation likely shows this top–down evolution because the shear in wind direction at the top of the boundary layer is weak and does not maintain the dynamical turbulence production. We can expect a reduced top–down effect in reality since there is shear in direction which is not simulated.

Turbulence anisotropy (see Fig. b), considered here as the ratio of the horizontal to the vertical wind variances, highlights the turbulence structure evolution during the TKE decay. Before 16:30 UTC, turbulence anisotropy remains smaller than unity in the mid-PBL, which is in agreement with the dominant vertical motion of the convective eddies. In the upper and lower parts of the PBL, turbulence anisotropy is larger than unity, due to small vertical velocity variance close to the surface and the entrainment zone (so-called “squashed” turbulence; ).

The anisotropy ratio becomes larger than 1 only after 17:30 UTC in the middle of the PBL but increases close to the top as early as 12:30 UTC. The change in anisotropy, like the TKE, starts early in the upper PBL, with an increasing momentum transfer from vertical to horizontal components during the decay process.

The previous results illustrate the changes in turbulence characteristics throughout the afternoon according to height. The times when these characteristics start to change are now quantified using the simulation data above 0.15zi, the tower measurements at 60 m, and the near surface moor and corn data. The time of change for a parameter x is denoted by tx (Fig. ). For μ, lw and the slope, it is the time when the decay rates of these spectra parameters depart from their mean value by more than 3 times their standard deviation (the decay rates are estimated over 1.5 h and their means and standard deviations are calculated between noon and 14:00 UTC). Because of the diurnal cycle of the TKE and the horizontal and vertical velocity variances, this method could not be applied to determine the time change in these parameters. tTKE, t<w′2> and t<u′2>+<v′2> were thus the times when the decaying rate of the parameter (estimated by linear regression over 1.5 h) becomes larger than for an arbitrary threshold of -1.11 ×10-5 m2 s-3 (meaning a TKE decrease of -0.02 m2 s-2 for a time interval of 30 min).

As already noticed in Sect. , the TKE first decreases at the top of the boundary layer half an hour after the start of the AT (Fig. ). That is, once the surface flux starts to decrease, the surface-driven turbulence does not rise up to the top of the boundary layer anymore. This indicates that turbulence decreases first at the top of the PBL, whereas it is maintained longer under 0.15 zi. The TKE decrease is exclusively driven by the vertical velocity variance, which decreases at the top of the PBL 1.5 h before the maximum of the surface buoyancy flux. The early decrease in the vertical velocity variance is counterbalanced in TKE by the delayed change in the horizontal wind variance. This implies an increase in the anisotropy of the velocity variances in the early stage of surface flux decrease.

The change in other spectral parameters (length scale, sharpness and slope) is observed much later, during the last 2 h before the zero surface buoyancy flux. The vertical profiles of tlw, tslope and tμ indicate an increase in integral scales, a flattening of the inertial subrange slope and a flattening of the spectra, appearing first at the top of the boundary layer and rapidly reaching the lower layers.

Near the surface and at 60 m, a very weak evolution of the spectra is observed. The spectra keep the same sharpness, similar to Kaimal spectra, with a constant slope of -2/3 in the inertial subrange, and a very slightly decreasing lw. These results are consistent with the spectral behaviour above 0.15 zi. Indeed, μ decreases from around 2 in convective conditions to 0.5 at the end of the AT in the whole upper layer, and the lw increase in the upper layers is less and less pronounced with decreasing height.

The above analysis of the evolution of the turbulence structure during the AT suggests that we should separate this period into two stages: early and late afternoon.

In the early afternoon, from the occurrence of the buoyancy maximum until about 2 h before sunset, (1) the TKE decreases within the whole PBL, with a 1-hour delay between the upper part (earlier decay) and the lower part of the PBL (postponed decay), (2) the vertical profile of anisotropy does not change much within the PBL, except close to the top, and (3) the spectra maintain the characteristics of the fully developed convective boundary layer, with similar integral scales and sharpness parameters.

In the late afternoon, from 2 h before sunset until when the surface buoyancy flux reduces to 0, (1) the TKE decreases more rapidly than during the early AT within the whole PBL, (2) turbulence anisotropy increases abruptly within the PBL, starting initially near the PBL top, and (3) the shape of the spectra evolves, with a decrease in the sharpness parameter, a flattening of the inertial subrange slope, and an increase in the integral length scales in the mid and upper PBL. The higher in the PBL the integral scales are, the stronger their increase, with very slight changes in the spectra shape observed close to the surface.

The two stages of the TKE decay found in this study remain consistent with previous results found by and . Both authors showed a decrease in the TKE following a t-n power law with a continuous increase in n. defined two main stages characterized by n around 2 and 6. added a preliminary stage with n equal to 1. Our first stage includes t-1 and t-2 power laws, and the second one includes t-6. However, it seems somehow arbitrary to characterize our two stages by a specific value of n since it evolves continuously. This study focuses on the link between the structure of the turbulence and the TKE evolution. Also, the TKE budget evolution in time was not of any help to explain the two stages of the TKE decrease. Whilst the different terms do decrease with time, their respective contribution to the TKE tendency hardly changes from the first to the second stages (not shown).

Our understanding of the two different stages of the AT is that during the early afternoon, the buoyancy flux remains large and its decay is slow enough to give the PBL time to adjust to the change and to remain in quasi-steady balance. In other words, the convective timescale t* is small enough (∼ 9 min) relative to τf (∼ 5.8 h) to allow this quasi-steady state. The spectral characteristics remain similar to what they are at maximum surface buoyancy flux. Buoyancy remains a dominant influence during this stage, leading to the vertical velocity variance and convective structures being predominant. The latter, with a characteristic horizontal length typically linked to the PBL depth, could maintain a sharp spectral peak. The predominance of convective structures might also be the cause of the steep inertial subrange slope. Close to the surface, where these convective structures are not yet well shaped, the inertial subrange slope is -2/3.

On the contrary, during the late afternoon, t* increases (about 20 min at 17:00 UTC) and the buoyancy flux gets too small for the PBL to maintain the vertical consistency of the turbulence structure from the surface up to the top of the PBL. The impact of surface buoyancy decreases faster than that of entrainment during this period: although the entrainment flux magnitude diminishes, entrainment occurs over a broader vertical depth extending down to 0.6zi (Fig. ).

An increase in the entrainment role could explain the increase in the vertical velocity integral scales (), which is observed in the upper PBL during the late afternoon during our BLLAST case. The increase in vertical velocity integral scales is consistent with the results of but disagrees with those of . This could be due to the progressive cessation of the surface flux in and versus the sudden shut-off in . In the surface layer, the decrease in the integral scales is consistent with the observations made by and with the results of .

The flattening observed in the inertial subrange during the late afternoon is difficult to explain because one might expect a steeper slope in inertial subrange when the flow becomes less turbulent, assuming that the smaller scales will dissipate faster than the larger scales. However, hypotheses could be made to explain the observed flattening of the spectra in the inertial subrange: (1) the increase in anisotropy might be associated with such a change in the cascade; (2) if the turbulence is now freely decaying, without influence of coherent structures and vertical velocity dominance, the cascade could become more efficient, resulting in a flattening slope according to . In any case, it seems that with the turbulence being no longer fully forced, the criteria for locally isotropic turbulence are no longer met. The theoretical model of the TKE spectrum proposed by could be an interesting tool to further understand this slope change since it considers anisotropy of turbulence through the KL89 analytical spectrum and also considers the terms of the TKE budget which might impact on the inertial subrange slope.

The progressive shut-off of the surface heat fluxes is shown to be an important aspect of the AT. and , who analysed simulations with a sudden shut-off of the buoyancy flux, pointed out what they called a demixing process, which implies a negative buoyancy flux within the whole PBL. The impact of entrainment in this case might be overestimated. Similar to , when progressively transitioning through the afternoon from a surface-buoyancy-dominated to an entrainment-dominated regime, the demixing process is strongly reduced and limited to the upper half of the PBL.

One might wonder whether these results could be impacted by the initial conditions. The use of all the airborne measurements acquired during the BLLAST experiment shows the general trend of an increasing integral scale during the late afternoon (not shown). However, it would be useful to complete this study with some additional simulations either targeting other BLLAST IOPs or performing some sensitivity analyses. Wind shear could be an important focus as , and found that strong wind shear at the top and bottom of the PBL delays the decay.