Study of a prototypical convective boundary layer observed during BLLAST : contributions by large-scale forcings

We study the influence of the large-scale atmospheric contribution to the dynamics of the convective boundary layer (CBL) in a situation observed during the Boundary Layer Late Afternoon and Sunset Turbulence (BLLAST) field campaign. We employ two modeling approaches, the mixed-layer theory and large-eddy simulation (LES), with a complete data set of surface and upper-air atmospheric observations, to quantify the contributions of the advection of heat and moisture, and subsidence. We find that by only taking surface and entrainment fluxes into account, the boundary-layer height is overestimated by 70 %. Constrained by surface and upper-air observations, we infer the large-scale vertical motions and horizontal advection of heat and moisture. Our findings show that subsidence has a clear diurnal pattern. Supported by the presence of a nearby mountain range, this pattern suggests that not only synoptic scales exert their influence on the boundary layer, but also mesoscale circulations. LES results show a satisfactory correspondence of the vertical structure of turbulent variables with observations. We also find that when large-scale advection and subsidence are included in the simulation, the values for turbulent kinetic energy are lower than without these large-scale forcings. We conclude that the prototypical CBL is a valid representation of the boundary-layer dynamics near regions characterized by complex topography and small-scale surface heterogeneity, provided that surfaceand large-scale forcings are representative for the local boundary layer.


Introduction
The daytime convective boundary layer is essentially governed by heating at the surface and the conditions of the free troposphere. The surface heating causes warm air to rise to the top of the boundary layer in the form of coherent turbulent structures and entrain air from aloft. As a consequence the convective boundary layer (CBL) Introduction proximately 40 km north of the central range of the Pyrenees mountains. This site was located on a plateau at a height of 600 m a.s.l. at the foot of the Pyrenees mountain range with heights of approximately 2000-2500 m. The BLLAST campaign provides us with a continuous and comprehensive observational data set of surface and boundarylayer observations, in particular extended by conducting 11 intensive observations pe-5 riods (IOPs) that took place during June and July 2011. The main goal of our research is to identify the relevant processes that drive the formation, evolution and decay of the atmospheric boundary layer during BLLAST. Due to the proximity of the mountain range and the characteristic synoptic situation, we place special emphasis on how the boundary-layer dynamics interact with large scale atmospheric phenomena. In this re- 10 search, both synoptic and meso-scale influences are considered as large-scale from the local boundary layer perspective. This leads us to the following questions: -What is the magnitude of the contributions of the large-scale forcing, in particular subsidence motions and horizontal advection of heat and moisture, compared to the surface and entrainment processes?

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-Do these large-scale forcings influence the turbulent characteristics before and during the afternoon transition?
To place these questions in the context of the BLLAST experiment, Fig. 1 sketches the main processes and contributions influencing the boundary-layer dynamics above the main location of the field experiment. In short, the local surface forcing represented 20 by sensible and latent heat flux and the entrainment at the top of the CBL is strongly influenced by large scale advection and subsidence.
Our methodology employs two numerical models to reproduce the observed boundary layer, using both the upper air-and boundary-layer observations as modeling constrains and to evaluate the model performance. This combination of models and obser- 25 vations enables us to quantify the processes that govern the boundary-layer structure. Previously, numerical simulations of the boundary layer including subsidence have been performed mainly in marine stratocumulus studies (e.g. de , 1997;Stevens et al., 1999), using a constant surface heat flux and a constant subsidence rate. Within BLLAST and in this special issue, Blay-Carreras et al. (2013) have reproduced another IOP influenced by subsidence but also with a constant subsidence rate. Instead, their study focused mainly on the importance of the residual layer. Studies of convective cloud-free cases like the one presented here, character-5 ized by diurnal variations of the surface and large scale forcings, based on an intensive comparison of models and observations do not exist to our knowledge. This paper will first introduce the BLLAST experiment, its goals, set-up and location and give a brief overview of the dataset in Sect. 2, including a detailed analysis of the study case, from synoptic to local spatial scales. Special attention is given to the 10 selection criteria for the case and the large scale conditions during this day. Section 3 describes the set-up of the numerical experiment and introduces the models that are used. In Sects. 4 and 5 the results of the numerical experiment are compared to the observations with special attention on the evolution in time and the vertical structure of the boundary layer. Finally, conclusions are drawn, followed by recommendations for 15 future research.

Observational description of the representative boundary layer
First we set up criteria to select which IOP of BLLAST to study. After that we treat in detail the large scale situation and the evolution of the energy exchange at the surface during this day. 20

Case selection
The main aim of the BLLAST campaign is to study the transitional period between the fully developed convective daytime boundary layer and the nighttime stable surface layer with an overlying residual layer . To this end, a very comprehensive set of instrumentation was deployed from 14 June to 8 July 2011 in Introduction Campistrous, France to monitor the boundary layer in detail. Whilst the main focus was on measuring the boundary-layer properties, attention was also paid to surface measurements, especially because the campaign took place in an area characterized by large surface heterogeneity. To characterize the synoptic conditions, the entire troposphere was monitored extensively. Together, all these observations create a high qual- 5 ity dataset, combining up to 8 methods to estimate the boundary-layer height. Using all surface data and boundary-layer observations, this dataset gives a unique opportunity to carry out a detailed study of the local atmospheric boundary layer influenced by heterogeneous surface conditions and the proximity of complex topography. Most of the instruments were operating continuously, but there were several platforms that 10 operated intermittently. Among these were: tethered balloons, manned and unmanned aircraft and radiosoundings. The operation of these platforms was limited to favorable weather conditions due to constraints in financial and human resources. These periods of intensive observation (IOP) included the the clearest and least disturbed days of the campaign. However, due to logistics and instrumental performance, not all platforms 15 operated simultaneously all the time. Therefore, there may be differences in instrumental availability between different IOPs. Our aim is to investigate whether the prototype CBL (Stull, 2000) is a useful concept to be applied in regions characterized by large surface heterogeneity and mesoscale phenomena driven by topography. The analysis of the data is supported by the use of 20 a conceptual model that enables us to quantify the individual contributions to the heat and moisture budget. More detailed numerical experiments are made with a large-eddy simulation that allow us to study the turbulent structure and its evolution.
From the 11 IOPs, we therefore define a set of criteria to select the most representative IOP period to study the deviations from the CBL prototype due to the large-scale Introduction and 16:44 UTC, confirm the two regimes with winds sharply turning with height (Fig. 3). In general, the winds during this day are weak in the lower troposphere, not exceeding 6 m s −1 . Close to the surface, the wind the wind is easterly, but at approximately 1500 m, there is a sharp turning of the wind to WNW. This zone of directional shear remains present during the day, but remains at a height of approximately 1500 m. This 5 is distinctly higher than the boundary layer reaches during this day, and therefore it can be expected to exert no influence on the boundary-layer dynamics.
On the meso-scale, the proximity of the Pyrenees to the south of the site often leads to a mountain-plain circulation . The behavior of the boundary layer during the day and the general conditions leads us to postulate that large scale 10 forcings such as subsidence and advection should be taken into account to understand the behavior of the boundary layer during the day (see Fig. 1).
25 June 2011 was the second of three consecutive IOPs with fair weather and increasingly high temperatures. On this day the 2 m-temperature rose as high as 28 • C in the afternoon at the BLLAST site. In the plains to the north of the BLLAST site, 15 temperatures exceeded 30 • C.

Case description: surface conditions
In addition to the nearby complex topography, the BLLAST experiment took place in an area with large scale surface heterogeneity. Figure 4 shows the land-use and the location of the surface flux stations in the vicinity of the main sites. The heterogeneity 20 is characterized by different length scales ranging from 100 m to 1-2 km. In Fig. 4 the categories represent aggregate land-use types. Especially within the cropland category there is still a large variety. In the BLLAST campaign, turbulent measurements were made above a number of different land-uses, including wheat, grass, maize and natural moor-like vegetation. From this, fluxes are calculated with a uniform processing method 25 (De Coster and Pietersen, 2011). In Fig. 5a and b the radiation budget and surface energy balance of a grass covered site during BLLAST IOP5 is shown (site 2 in Fig. 4) ation show a smooth diurnal cycle with absence of clouds. The averaged Bowen ratio during the day is around 0.3. In conjunction with the initial profiles (not shown), these surface forcings should lead to boundary-layer heights of 1100 m during the afternoon. However, the boundary layer only reached a height of 600 m during this day. This behavior suggests that the development of the boundary layer was influenced by 5 processes besides surface heating and entrainment. To be able to investigate the transition period where weak forcings interact, the development of the daytime boundary layer should be understood first.
The BLLAST campaign took place in a topographically diverse landscape. Although the main site is on a plateau, the height differences in the area are large. Several valleys 10 with a depth of 100-200 m radiate outward to the north of the site. To the south, the foothills of the Pyrenees start and height differences increase. The highest peaks of the Pyrenees, at a distance of 45 km, reach heights of more than 3000 m a.s.l. Figure 5c and d shows the latent and sensible heat flux for the seven stations and the average value for all these stations. All fluxes were computed using the eddy covari- 15 ance technique, with a sampling rate of at least 10 Hz. These eddy-covariance stations were installed at heights lower than 2.5 m above the surface. This means that not all BLLAST-eddy-covariance stations were used. Most of the land-uses are represented, although the forest site is excluded due to the station height. The data from the flux stations were all processed following the same procedure (De Coster and Pietersen, 20 2011). The 5 min fluxes of each station are shown in blue, the average of these fluxes is indicated with the red pluses in Fig. 5c and d. The fluxes above the different surfaces show a variability of more than 100 % for the sensible heat flux and approximately 50 % for the latent heat fluxes. To represent gradually evolving fluxes and to eliminate effects due to fast changing surface conditions, a sinusoidal function is matched with 25 the average values (dashed black lines). This function is used as the surface boundary condition in the numerical experiments (see Table 1

Numerical experiments
We design a series of numerical experiments to reproduce IOP5 by means of largeeddy simulation and mixed-layer theory. Our strategy is use the models to support the data interpretation in order to identify and quantify the main contributors in the development of the boundary layer. In the numerical experiment, the observations of 5 the boundary layer both guide and constrain the models.

Experimental strategy
The design of the numerical experiment is set-up to reproduce the boundary layer of IOP5 as well as possible within the conceptual framework. This means that special attention is paid to the inclusion of all important large scale processes, their magni-10 tude and evolution. The horizontal variation of these large scale contributions are not treated.
First, a conceptual model is used to determine the evolution of the bulk properties of the CBL (van Heerwaarden et al., 2009). Secondly, the Dutch Atmospheric Large-Eddy Simulation (DALES, Heus et al., 2010) is employed to study the case where turbulence 15 is explicitly simulated. The initial vertical model profiles of potential temperature (θ) and specific moisture content (q) are derived from the early morning soundings. The observations during the day will be used to evaluate the models. The starting point is a simple case, using the initial profiles and surface fluxes from the observations as input (Sect. 4). Subsequently, we will use the observations as a guide to obtain the 20 correct values for subsidence and advection of heat and moisture (Sect. 5).

Model description
In this section, both models are introduced: a mixed-layer model and a large-eddy simulation. The first model is a highly conceptualized model of the boundary layer. The second is a model that explicitly calculates most of the turbulence and gives a detailed 25 ACPD 14,2014 CBL prototype and large-scale forcing H. Pietersen et al. picture of the structure of the boundary layer. Combining these two models, we can unravel and quantify the various contributions to the heat and moisture budgets. Furthermore, we can obtain a detailed insight in the structure of temperature and humidity inside the boundary layer and we are able to see how the turbulent structures evolve during the day.

Mixed-layer model
The mixed-layer model is a bulk model that allows a conceptual representation of the boundary layer. We have included this mixed-layer model to reproduce the essential processes of the CBL prototype. This model uses the boundary-layer thermodynamic equations proposed by Tennekes and Driedonks (1981). The implementation of these 10 equations into the model is similar to van Heerwaarden et al. (2009). The boundary layer is represented as a single model layer and at the entrainment region (top of the CBL), the exchange of heat and specific moisture is parameterized by a jump of the potential temperature and specific moisture over an infinitesimally small height (a 0-order model). The potential temperature and specific humidity in the overlying free tropo- 15 sphere are initialized with a constant lapse rate with height. The use of the mixed-layer equations implies that the turbulence inside the boundary layer is not explicitly calculated, and assumes that the potential temperature and the specific humidity are well mixed and constant in height. This assumption is supported by the efficient turbulent mixing under convective conditions. The entrainment flux at the top of the boundary 20 layer (β θ v ) is calculated as a fixed fraction of the surface heat flux (in our numerical experiments equal to 0.2), which means that the entrainment flux is subjected to the same diurnal evolution as the prescribed surface heat flux. An important feature of the model is the possibility to represent subsidence. The subsidence velocity is a function of the divergence of the mean horizontal wind and the evolving boundary-layer height.

Large-eddy simulation
The large eddy-simulation (LES) model that is used is the latest implementation of DALES (Heus et al., 2010). DALES solves the filtered three-dimensional thermodynamic equations, and as result produces three-dimensional time-evolving fields. In convective boundary layers like the one observed on IOP5, DALES explicitly reproduces 5 approximately 80-90 % of the energy contained by the eddies in the boundary layer. The smaller turbulent scales are parameterized using a sub-grid scale model that depends on the sub-grid turbulent kinetic energy and is formulated according to Deardorff (1974). DALES gives us a detailed insight in the vertical structure of the boundary layer and enables us to compare measured fluxes inside the boundary layer with simula-10 tions, thus giving a detailed quantification of the structure of the boundary layer. In the numerical experiments, we have used a grid of 128 3 with a horizontal resolution of 25 m and a vertical resolution of 10 m, leading to a domain of 3200 m×3200 m×1280 m. The simulation time is 14 h. The subsidence velocity is imposed by a function that is zero at the ground and increases linearly to the CBL top. Above the CBL, the subsidence 15 velocity is constant in height. Similar to the mixed-layer model, the subsidence strength can change over time.

Boundary-and initial conditions
Both models, DALES and mixed-layer, use identical initial conditions and surface forcings. The models are initialized with profiles that were derived from the morning sound-20 ings of IOP5. The representative surface fluxes from the observations (see Sect. 2.3) are used to provide the lower boundary conditions. To make sure that the boundary layer is well mixed and that all surface stability has disappeared, the models are not started at sunrise, but at 10:00 UTC. In this way we ensure that the mixed-layer equations of the mixed-layer model hold. The soundings 25 that were taken during the early morning and at 10:34 UTC were used to construct the initial profiles for both the mixed-layer model and the large-eddy simulation. The ACPD 14,2014 CBL prototype and large-scale forcing H. Pietersen et al. boundary-layer height at this time was matched to the estimate made with the UHF radar and the LIDAR (Fig. 6a). In Table 1 the initial conditions for both the mixed-layer model and DALES are listed. As winds were light during IOP5 (see Fig. 3) and we seek to perform a numerical experiment that resembles the prototypical boundary layer, no wind was prescribed in the models. 5 Two different numerical experiments (Cases 1 and 2) are set up to determine the influence of the large scale forcings on the boundary layer during IOP5. In short, these cases are: -Case 1: a boundary layer governed by surface forcings, i.e. a locally driven prototypical boundary layer.

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-Case 2: same initial and boundary settings as Case 1, except that now we add the contributions of subsidence and advection of heat and moisture, i.e. including contributions of the larger scales.

Case 1: prototypical boundary layer
The prototype CBL is driven by the surface and entrainment processes. In order to 15 study whether IOP5 follows this classical prototype, we reproduce a situation that is only forced by the surface fluxes, without any other external forcings. This enables us to determine the influence of the surface forcing and it provides us a first indication which large scale influences are of importance. The results are evaluated with surface and upper air observations. 20

Boundary-layer height
We show the boundary-layer height during IOP5 estimated by 10 different methods (8 observational and 2 based on modeled results) in Fig. 6a. Two of the observational methods are based on remote sensing instruments: a vertical UHF radar and an ACPD 14,2014 CBL prototype and large-scale forcing H. Pietersen et al. aerosol LIDAR. Other methods to determine the boundary-layer height are based on the profile of virtual potential temperature inside the boundary layer. The maximum gradient of the virtual potential temperature is manually selected as the top of the boundary layer. Three methods rely on profiles made with soundings: two classical radiosondes (manufactured by MODEM and GRAW) and a new method of making frequent ra-5 diosoundings developed by Meteo-France (Legain et al., 2013) where the sondes can be retrieved and re-used. Three additional methods are based on profiling by aircraft, one remotely piloted aircraft system (the SUMO platform, Reuder et al., 2009) and two manned aircraft (the Sky Arrow operated by IBIMET/CNR and the Piper Aztec operated by SAFIRE). The last two methods to determine the boundary-layer height are 10 based on the interpretation of model results from the mixed-layer model and DALES.
The mixed-layer model explicitly calculates the boundary-layer height. In DALES, the boundary-layer height is diagnosed by assuming that the top of the boundary layer is at the height where the buoyancy flux has its largest negative value. As shown in Fig. 6a, there is a large amount of scatter between different estimates. 15 In analyzing the observations in more detail, we find that, even if we do not take outliers into account, the differences in boundary-layer height can be in the order of 100 m. This number (≈ 100-200 m) is similar to the depth of the entrainment zone measured by the Lidar. From the observations, we notice that the soundings generally report lower boundary-layer heights than the remote sensing methods, which is to be expected as 20 different physical parameters are used to deduce the boundary-layer height. Not all observation profiles were taken at the same location. A site near stations 4 and 5 ( Fig. 4) was used for UHF, LIDAR and soundings, the remotely piloted aircraft soundings were taken near stations 6 and 7. The manned aircraft, the Piper Aztec and Sky Arrow, were even further away from the site (up to 20 km) because of airspace regulations. 25 Due to the mentioned surface heterogeneity, differences can occur between observations. Most of the soundings are point measurements, whereas the aircraft makes a helical profile, sampling a greater volume of the boundary layer. In Fig. 6a there is a discrepancy of roughly 400-500 m between the observations and the results from the numerical experiments. This is a clear indication that other processes than surface heating and entrainment play a role. The observations of specific humidity show a lot of scatter between the different instrumental platforms. Especially within the mixed-layer moisture observations from the 20 soundings (the triangles in Fig. 6b) the differences are large and can amount up to 1.5 g kg −1 . Overall, we first observe a slight increase, followed by a gradual decline, probably controlled by the entrainment of dry air. After 15:00 UTC, the specific moisture content starts to rise again. This pattern is the strongest in the tall tower of station 5 (the crosses in Fig. 6b), although on average the soundings also show a slight moist-25 ening trend. This could be related to moisture advection in the late afternoon. Although both models show a small drying around noon, it is much less than observed near the surface at the 60 m-tower. duced by the models. Note that there is a discrepancy between the specific moisture content of the model and the observations of the 60 m-tower at the start of the model run. This is because the initial profiles are based upon soundings of the entire boundary layer. These can differ significantly from the observations at 60 m height as can be seen in the observations later during the day. 5 It is relevant to point out that here one would expect lower values of the model results compared to the observations of the specific humidity because of enhanced entrainment. Since the model overestimates the specific humidity as shown by Fig. 6b, we receive further evidence on the importance of other processes in the budget of heat and moisture during IOP5 besides the surface forcing.  Table 1. Note that the advection is applied only inside the boundary layer. From Fig. 7, we observe that subsidence velocity has a dependence 20 on time that follows a diurnal evolution with maximum values of −0.028 m s −1 between 13:30 and 14:00 UTC. The values from the ECMWF model are lower and have far less temporal detail than the ones estimated iteratively. Figure 7 indicates that in regions with nearby complex topography it might be required to have estimations of subsidence with higher temporal frequency to properly reproduce the boundary-layer dynamics. 25 This variation on time of the subsidence can be a relevant process in modelling this situation with more complex numerical weather prediction models (Couvreaux et al., 2014). Together with the subsidence, Fig. 7 shows the resulting values of entrainment velocity for both the mixed-layer model and DALES. The entrainment rate of both models is calculated following Lilly (1968):

Mixed-layer potential temperature and specific humidity
In the mixed-layer model, the two right hand terms of Eq. (1) are known. The buoyancy flux at the entrainment zone (−w θ v e ) is a fixed fraction (0.2) of the prescribed surface flux. The potential virtual temperature jump at the boundary layer top (∆θ v zi ) is calculated explicitly. In DALES, both right hand terms in Eq. (1) have to be approximated 10 using the vertical profiles of the buoyancy flux and the potential temperature using a zero-order approach, similar to Angevine (1999). The differences of the entrainment velocities between DALES and the mixed-layer model results are due to the slightly different methods used. Notwithstanding, the diurnal evolution of the entrainment is very similar in both models. 15 By analyzing the magnitude of subsidence and entrainment velocities, both are comparable and nearly cancel each other after 12:00 UTC. This is in agreement with the evolution of the observed boundary-layer height that remains almost constant during the afternoon. Note that the entrainment is mainly driven by the heat flux at the surface and has a clear diurnal evolution. The subsidence shows a very similar evolution, thus 20 suggesting the influence of non-local processes that are forced by the diurnal cycle. An induced circulation such as a mountain circulation could lead to such an evolution of subsidence (see Fig. 1).
In Fig. 8, we show the temporal evolution of the boundary-layer height, the mixedlayer potential temperature and mixed-layer specific humidity. For Case 2, the obser- 25 vations and the models show a satisfactory agreement for boundary-layer height and ACPD 14,2014 CBL prototype and large-scale forcing H. Pietersen et al. bulk potential temperature (Fig. 8a). The observations of bulk specific moisture content are more scattered, thus making a comparison between model and observations more difficult. In general, the models calculate a boundary layer that is slightly overestimated. However, as we will show in Sect. 4.2, the models reproduce the vertical structure of the boundary layer satisfactorily.

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The evolution of the mixed-layer potential temperature agrees well with the measurements (Fig. 8b). The moisture content shows a decline in the early afternoon, somewhat later than the observations from the 60 m tower. The moistening at the end of the afternoon is not represented in the models. This moistening signal comes mainly from the stations near the surface and could be related to moist advection in the late 10 afternoon. However, as the observations show a lot of scatter, this change of moisture advection in time is not included in the simulations. A meso-scale modeling study could give more insight in the evolution of the advection of heat and moisture.

Vertical profiles of potential temperature and specific moisture content
In Fig. 9a we show the vertical potential temperature profiles calculated by the two 15 models and by observations taken at 12:57 UTC. The potential temperature profiles of both models are comparable to the observations. Just above the boundary layer, the observed free troposphere is more stable than higher up. The models however are initialized with a single lapse rate for the entire free troposphere. Comparing the potential temperature jump at the top of the boundary layer, both the sounding and 20 DALES show an entrainment zone with an inversion depth of approximately 100 m. It is also interesting to stress that the observed profile shows a weak stable stratification above 300 m. Two reasons can create this stratification within the well-mixed boundary layer: (a) land-surface heterogeneity (Ouwersloot et al., 2011) and (b) the presence of absorbing aerosols (Barbaro et al., 2013). Our tentative explanation is the following. 25 Aerosol optical depth measurements range between 0.08 and 0.11 which can lead to a reduction of the incoming shortwave radiation (≈ 10-20 W m −2 ) ( Barbaro et al., 2013) and depending on the aerosol absorbing and scattering characteristics a stabilization 19264 Introduction of the upper region in the boundary layer. Additionally, the patchy surface around the BLLAST experimental site induces secondary circulations that are superimposed to the boundary-layer structures. These induced circulations enhance the entrainment of warmer and drier air originating from the free troposphere, stabilizing the upper region of the CBL. 5 In Fig. 9b the calculated and observed vertical profile of specific moisture at 12:57 UTC are presented. The specific moisture profile is less well mixed with height than the potential temperature profile. Both models compare well with the sounding inside the boundary layer. DALES reproduces the values of specific moisture at the top of the boundary layer and the transition to the free troposphere better than the 10 mixed-layer model. However, both models are approximately 1 g kg −1 too dry in the free troposphere. The initial values of specific moisture were matched to the soundings, but there could be moistening of the free troposphere during the day that is not taken into account in the numerical experiments. Similar to the 12:57 UTC potential temperature profile, the specific humidity profile shows microstructures, suggesting a signature 15 of the land surface heterogeneity with drier air in the upper region of the convective boundary layer (between 300 and 600 m). Figure 10 shows the profiles of potential temperature and specific moisture at 16:50 UTC, taken by the Sky Arrow aircraft. These soundings were taken in a helical profile with a sampling frequency of 50 Hz. This profile was made approximately 7 km 20 southwest of the main site, relatively close to the mountains. The advantage of a helical sounding is that more of the boundary layer is sampled at each level. In this way, the measurements have a larger footprint and in consequence are representative for a larger area. If we compare Fig. 9a and Fig. 10a, the profile taken at 16:50 UTC shows more small scale fluctuations. This is partly due to the higher sampling frequency and 25 partly due to the helical profile. Moreover, the profile is characterized by an almost constant value, indicating well mixed conditions. By comparing models and observations at 16:50 UTC, the mixed-layer potential temperature compares well to the observations. For this specific profile, the boundary-layer height is slightly overestimated by the mod-ACPD 14,2014 CBL prototype and large-scale forcing H. Pietersen et al.  Fig. 8a). This sounding was taken in close proximity to the Pyrenees (7 km southwest to main site), which means that although the soundings are described in height a.g.l., this column of air was higher in an absolute sense. With the specific moisture content taken at 16:50 UTC (Fig. 10b), the signal is even more turbulent than the signal of potential temperature. The mixed-layer averaged specific moisture con-5 tent is underestimated by 1 g kg −1 , but the magnitude of the jump of specific moisture at the top of the boundary layer is similar between observations and models. The specific humidity of the free troposphere is underestimated by both models, which could be explained by the moistening trend described for the sounding at 12:57 UTC. 10 Our second aim was to determine whether large-scale forcings exert an influence on the turbulent structure of IOP5 and if this structure is consistent with the prototypical CBL. Therefore, we calculate the higher-order moments of the thermodynamic fluxes and variances from the high frequency aircraft observations and compare them to the DALES calculations. To this end, we employ two observational data sets: 15 1. Turbulent data collected by two aircraft at various heights within the boundary layer.

Turbulent structure
2. Time series of turbulent kinetic energy (TKE) taken at surface flux stations. Here, similarly to the sensible and latent heat fluxes, we calculate an average TKE from all the stations shown in Fig. 4. 20 Note that the calculated flux along a flight leg represents an integrated value over a large horizontal distance, thus providing a larger footprint, as opposed to the smaller footprints of the local point measurements of the eddy covariance stations. This enables us to do a more adequate comparison with DALES results that are forced by a horizontally homogeneous surface flux, derived from the average of the flux obser- the temporal evolution of the turbulence in the surface layer. We compare this with the vertically integrated TKE using the DALES results. This dataset has a high temporal resolution which consequently enables us to describe and explain the decay of turbulence during the late afternoon transition. 5 In order to obtain a more detailed understanding of the boundary-layer dynamics, we study the variation with height of the potential temperature and specific humidity fluxes. The profile of the sensible heat flux is shown in Fig. 11. Observations and model are in good agreement. The entrainment zone, where the heat flux is negative, is clearly de-20 fined in both observations and the model and shows a good match. The linear decrease from the surface flux to the negative heat flux in the entrainment zone corresponds well between model and observations. It is in this region that there is a countergradient sensible heat flux with positive values for the flux and the potential temperature gradient. The variation of the modeled heat flux at the surface indicates that this period is already 25 in a phase of the day where the heat fluxes decline (Fig. 5c). Figure 12 shows the observed and modeled latent heat flux vertical profiles.  (2002) and Górska et al. (2008) have discussed underestimations of the flux measurements taken by aircraft compared to surface point measurements. At the three highest observations, close to the entrainment zone, model and observations compare well, indicating that here the turbulent exchange is modeled correctly. However, inside the boundary layer, the modeled fluxes 5 are roughly twice as high as the observed fluxes. Both model and observations do show latent heat flux profiles that are almost constant with height indicating that the evaporation at the surface is compensated by the drying at the entrainment zone. Consequently, the moisture content inside the boundary layer is in a near steady-state during this period. This is further corroborated by the observations of the specific moisture 10 content near the surface (see the 60 m observations in Fig. 8b). In Fig. 13, the non-dimensional buoyancy flux for the same period as Figs. 11 and 12 is shown against the dimensionless height. The buoyancy flux is scaled with the surface buoyancy flux, the height is scaled with the boundary-layer height from the mixedlayer model. Modeled buoyancy fluxes from DALES are shown together with aircraft 15 observations. Because the fluxes are scaled with the surface flux, the spread due to the difference in timing disappears. Overall, the model results match closely with the observations and confirm the notion that the boundary layer for IOP5 behaves similarly as the prototypical boundary layer. Model and observations show a clear linear decrease with height in the lower 75 % of the boundary layer. In the top 20-25 % 20 of the boundary layer, the entrainment zone is well defined. The buoyancy flux ratio (β θ v = −w θ e /w θ o ) is very similar to values found by Davis et al. (1997) and Górska et al. (2008) 15-0.20). The model results are horizontally averaged and the aircraft measurements integrate over a distance of roughly 40 km. All values presented in Fig. 13

Decay of turbulent kinetic energy
We complete the study by analyzing a relevant aspect of the afternoon transition extensively studied in more academic LES studies (Nieuwstadt and Brost, 1986;Sorbjan, 1997;Pino et al., 2006;Beare et al., 2006;van Driel and Jonker, 2011): the decay of TKE. This decay plays a key role in the transition from CBL to SBL. We employ the 5 same strategy as before: combining Cases 1 and 2 from DALES with surface observations. We show in Fig. 14 how TKE evolves in time from 12:00 UTC to 20:00 UTC.
It is important to note that the surface observations are an average of the 7 surface stations and that these measurements have been taken 2 or 3 m above the surface. In contrast, the LES includes bulk averaged TKE for the entire boundary layer, where 10 for these purposes the top of the boundary layer is defined as 30 m below the level where the buoyancy flux reaches its minimum value. In doing so, we exclude the local processes generating or destroying TKE at the entrainment zone. Note that both LES cases are forced without any wind. Observations indicate that the wind was very weak during the day (< 6 m s −1 , see Fig. 3). Still, the exclusion of wind reduces the amount 15 of TKE that is produced due to the conversion from mean kinetic energy. In Fig. 14, the surface observations show the highest values of TKE whereas Case 2 shows the least. The turbulent fields generated by both DALES simulations show an earlier decay of TKE than the observations, even when we take the lower amount of TKE during the early afternoon into account. Case 2 starts decaying earlier than 20 Case 1. The TKE decay rate of the surface observations is slower than the models in the late afternoon. After 18:00 UTC the sensible heat flux (see Fig. 5b) becomes zero, and the observations show a sharp decline in TKE. To complete this discussion, we refer to the research of the TKE evalution during the by Darbieu et al. (2014)  The difference between Cases 1 and 2 is explained by the fact Case 1 is characterized by much more vigorous growth during the afternoon, with the boundary layer becoming much deeper, enabling the formation of larger length scales. Case 2, which includes subsidence and advection, has a much more suppressed growth, limiting the growth and size of the largest eddies. Therefore, the turbulent motions also become 5 more suppressed. That means that if we take large scale forcings into account, the levels of TKE become lower and the decay of TKE starts slightly earlier.
By scaling the TKE evolution using the convective velocity (w * ) and the moment of maximum sensible heat flux, and the time with the eddy turnover time (t * = z i /w * ) similarly to Nieuwstadt and Brost (1986), we made Fig. 14b. Employed scales are: t 0 = 10 11:55 UTC, t * = 0.1172 h (approximately 7 min) and w * = 1.457 m s −1 . Here, we observe the earlier decay of Case 2 more clearly, although the difference remains fairly small. Both model runs show lower levels of TKE than the surface observations. Other factors that might lead to lower levels of TKE are: the exclusion of wind in the models (absence of the contribution of shear to maintain TKE) and local secondary circulations due to 15 surface heterogeneity, as suggested in Sect. 5.1. Our final explanation in analyzing the modeled TKE evolution is that the largest turbulent scales in Case 1 maintain larger levels of turbulence, slightly delaying the decay process.

Conclusions
We find quantitative evidence that subsidence motions and the large-scale advection 20 of heat and moisture are key components of the atmospheric boundary layer observed during the BLLAST experiment. Focusing on IOP5, we quantify these two components in a numerical experiment forced by surface observations and resulting entrainment to describe the diurnal evolution of the budget of heat and moisture. We intensively employ vertical radiosoundings and remote sensing observations combined with large- The systematic numerical experiments enable us to break down the various components of the heat and moisture budget that determine the boundary-layer height evolution. As a result, we find that by only taking surface and entrainment fluxes into account, we overestimate the boundary-layer depth by 70 %. With an iterative method, constraining our numerical experiments with the observations of the boundary-layer 5 depth and bulk quantities, we are able to quantify the magnitude and temporal evolution of subsidence and advection. The subsidence velocity shows a diurnal evolution and is slightly larger in magnitude than the values found with the ECMWF model. This diurnal evolution of subsidence suggests the influence of processes that are governed by the diurnal heating cycle, such as a mountain circulation. When these large-scale forcings 10 are included, LES and mixed-layer model represent satisfactorily the boundary-layer dynamics.
In analyzing the sensible heat flux, we find a satisfactory agreement between the measurements and large-eddy simulations. The observations show a close match with existing theory and the CBL prototype. For the latent heat flux, the discrepancy be-15 tween models and observations is larger, but both yield similar values of the ratio between entrainment-(drying) and surface flux (evaporation). Especially at the end of the afternoon, when observations show a rise in specific moisture content, models and observations diverge. For TKE, we do find a fast decay rate around the time the sensible heat flux becomes zero. The large-eddy simulations show a more gradual de-20 cline. Even though the large-scale forcings do not directly disturb the turbulent vertical structure, we find that the numerical simulation including subsidence and advection is characterized by smaller turbulent kinetic energy and starts to decay earlier than the simulation only driven by surface and entrainment processes. This is mainly due to the shallower and weaker large turbulent eddies. Therefore, we recommend to adequately 25 identify the large-scale forcings in studying the afternoon decay.
Finally, we advocate that the applied estimation of subsidence and large-scale advection by combining observations and mixed-layer theory can be very useful in the interpretation of the observed heat and moisture budget, yielding complementary data to the estimations given by numerical weather forecast models. The approach proposed here can be applied to other cases with sufficient observational density and can be of particular use for the other IOPs of the BLLAST campaign. A major advantage of our proposed method is that the higher temporal resolution enables in-depth studies of the diurnal evolution, as opposed to ECMWF model output that provides values every 5 6 h. The quantification of subsidence and advection can further support a reliable representation of the most important processes during the transitional period. However, attention should be paid to the role played by heterogeneity of the surface. As such, representative surface fluxes for the region under study should be employed. In relation to the validity of the prototypical CBL, the results obtained here with the mixed-layer 10 model ensure us that the canonical CBL is still a valid representation of the diurnal atmospheric boundary layer and afternoon transition, provided that the large-scale influences are properly quantified, considering their large influence on the budget of heat and moisture.

Case description: Surface conditions
In addition to the nearby complex topography, the experiment took place in an area with large scale su erogeneity. Figure 4 shows the land-use and th of the surface flux stations in the vicinity of the m 255 The heterogeneity is characterized by different len ranging from 100 m to 1-2 km. In Fig. 4 the catego sent aggregate land-use types. Especially within the category there is still a large variety. In the BLLA paign, turbulent measurements were made above ACPD 14,2014 CBL prototype and large-scale forcing H. Pietersen et al.    ACPD 14,2014 CBL prototype and large-scale forcing H. Pietersen et al.  tures. These induced circulations enhance the entrainment of warmer and drier air originating from the free troposphere, stabilizing the upper region of the CBL. In Fig. 9b the calculated and observed vertical profile of specific moisture at 12:57 are presented. The specific mois-645 ture profile is less well mixed with height than the potential temperature profile. Both models compare well with the sounding inside the boundary layer. DALES reproduces the values of specific moisture at the top of the boundary layer and the transition to the free troposphere better than 650 the mixed-layer model. However, both models are approxi-−1 Figure 6. Temporal evolution of (a) boundary-layer height and (b) mixed-layer potential temperature and specific humidity at 25 June 2011. 14,2014 CBL prototype and large-scale forcing H. Pietersen et al.  layer potential temperature compares well to the observations. For this specific profile, the boundary-layer height is slightly overestimated by the models (see also Fig. 8a). This sounding was taken in close proximity to the Pyrenees (7 km southwest to main site), which means that although the 680 soundings are described in height above ground level, this column of air was higher in an absolute sense. With the specific moisture content taken at 16:50 UTC (Fig. 10b), the signal is even more turbulent than the signal of potential temperature. The mixed-layer averaged specific moisture content is 685 latent heat fluxes, we calculate an average TKE from all the stations shown in Fig. 4.

705
Note that the calculated flux along a flight leg represents an integrated value over a large horizontal distance, thus providing a larger footprint, as opposed to the smaller footprints of the local point measurements of the eddy covariance stations. This enables us to do a more adequate comparison 710 with DALES results that are forced by a horizontally homogeneous surface flux, derived from the average of the flux observations (see section 2.3). The data from the eddy co- . Vertical profile of (a) potential temperature (θ) and (b) specific humidity (q) at 12:57 UTC: frequent radiosounding, DALES and mixed-layer model. 14,2014 CBL prototype and large-scale forcing H. Pietersen et al. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Fig. 9. Vertical profile of a) potential temperature (θ) and b) specific humidity (q) at 12:57 UTC: frequent radiosounding, DALES and mixed-layer model a) b) Fig. 10. Vertical profile of a) potential temperature (θ) and b) specific humidity (q) at 16:50 UTC: aircraft profiling, DALES and mixed-layer model Figure 10. Vertical profile of (a) potential temperature (θ) and (b) specific humidity (q) at 16:50 UTC: aircraft profiling, DALES and mixed-layer model. 14,2014 CBL prototype and large-scale forcing H. Pietersen et al.   ACPD 14,2014 CBL prototype and large-scale forcing H. Pietersen et al.  The difference between cases 1 and case 1 is characterized by much m ing the afternoon, with the bound deeper. Case 2, which includes s has a much more suppressed grow 835 size of the largest eddies. Theref also become more suppressed. T large scale forcings into account, lower and the decay of TKE starts By scaling the TKE evolution u 840 ity (w * ) and the moment of maxim with the eddy turnover time (t * =z stadt and Brost (1986), we obtain F are: t 0 = 11:55 UTC, t * = 0.1172 h and w * = 1.457 m s −1 . Here, we 845 of case 2 more clearly, although th small. Both model runs show low surface observations. Other factor levels of TKE are: the exclusion o local secondary circulations due to 850 suggested in section 5.1. Our fin ing the modeled TKE evolution is Figure 13. Same as Fig. 11, but now for the non-dimensional buoyancy flux and height.

ACPD
ACPD 14,2014 CBL prototype and large-scale forcing H. Pietersen et al. and mixed-layer model represent satisfactorily the boundarylayer dynamics.
In analyzing the sensible heat flux, we find a satisfactory agreement between the measurements and large-eddy simu-885 lations. The observations show a close match with existing theory and the CBL prototype. For the latent heat flux, the discrepancy between models and observations is larger, but both yield similar values of the ratio between entrainment-(drying) and surface flux (evaporation). Especially at the 890 ables in-depth studies of the diurnal evolution, as opposed to ECMWF model output that provides values every 6 hours.

915
The quantification of subsidence and advection can further support a reliable representation of the most important processes during the transitional period. However, attention should be paid to the role played by heterogeneity of the surface. As such, representative surface fluxes for the region 920 under study should be employed. In relation to the validity of the prototypical CBL, the results obtained here with the mixed-layer model ensure us that the canonical CBL is still