Vertical mixing in the atmospheric boundary layer is mostly turbulent. The BLH is confined by a thin layer where steep vertical gradients of meteorological variables, trace gases, and aerosols occur. Consequently, all the observational devices built for the retrieval of BLH are based on the search of the height at which the strongest gradients occur. These gradients can be based either on the atmospheric potential temperature profile, the wind profile, or the aerosol backscatter profile. For meteorological data sets and atmospheric transport models, the bulk Richardson number (Rib), a dimensionless parameter defined as the ratio of turbulence due to buoyancy and the mechanic generation of turbulence by wind shear, has been widely used to determine BLHs (e.g. Vogelezang and Holtslag, 1996; Seibert et al., 2000; Seidel et al., 2012). Thus, the BLH is the vertical level at which the bulk Richardson number reaches a critical value (Ric) characterising the passage of turbulent flow to a laminar one. The general expression of Vogelezang and Holtslag (1996) used to compute Rib is given as follows: Rib=gθvsθvh-θvszh-zsuh-us2+vh-vs2+bu∗2, where g is the gravitational acceleration (9.81 m s-2), θv the virtual potential temperature, z the geopotential height, u the zonal wind speed, and v the meridional wind speed. The indices h and s denote the vertical layer, and the surface, respectively. bu∗2 depicts the turbulence production due to the surface friction, a term which also prevents an undetermined Rib in case of uniform high wind speeds relevant for neutral boundary layers. b is a coefficient estimated to be 100 (Vogelezang and Holtslag, 1996) and u∗ is the surface friction velocity. The geopotential height z is expressed in metres. The virtual potential temperature θv is in Kelvin, and the velocities are in m s-1.

The vertical profile of Rib is linearly interpolated between consecutive vertical layers. The BLH is defined as the height, where Rib reaches the Ric. Commonly, a Ric value of 0.25 has been used (e.g. Vogelezang and Holtslag, 1996; Seibert et al., 2000; Seidel et al., 2012). The boundary layer height is defined with reference to surface elevation, and not to sea level (Seidel et al., 2012).

The observed 222Rn activity concentrations are obtained from two different measurement methods:

The “two-filter” method developed by the Australian Nuclear Science and Technology Organisation (ANSTO) (Whittlestone and Zahorowski, 1998; Chambers et al., 2011). After drawing the sampled air continuously through a delay volume to let all short-lived 220Rn (thoron) gas in the sampled air decay, it passes through a first filter that removes all ambient 222Rn and 220Rn decay products. Filtered air then enters in a delay chamber in which new 222Rn progeny (218Po and 214Po) are produced. An internal flow loop within the delay chamber passes the air through a second filter, which collects the new 222Rn progeny formed under controlled conditions. Hence, in the ANSTO system 222Rn activity concentration in the sampled air is measured directly through its newly formed progeny within the controlled environment of the delay chamber (Whittlestone and Zahorowski, 1998; Zahorowski et al., 2004; Chambers et al., 2011). In routine operation, ANSTO monitors are calibrated monthly by injecting 222Rn from a well characterised (to about ±4 %) 226Radium source. For ambient air measurements at 1 Bq m-3 activity concentration, the total uncertainty of hourly measurements is of the order of 10 %, which includes uncertainty in flow rate as well as counting statistics. The ANSTO two-filter detectors have a response time of around 45 min, and are quite bulky (∼ 3 m2), which can hinder their deployment in constricted locations.

At the monitoring station Ispra, 222Rn activity concentration has been measured using an ANSTO instrument, sampling air at an inlet positioned at 3.5 m above the ground, close to the GHG-sampling mast with a height of 15 m. Recent additional 222Rn measurements using the 15 m inlet of the GHG mast (employing an Alphaguard PQ2000 (Genitron) instrument, calibrated against the ANSTO monitor) revealed significant differences of the 222Rn activity at the two sampling heights during periods with low wind speeds. These differences showed that there are significant vertical 222Rn gradients close to the ground. Based on the comparison of the two sampling heights during a 3-month period, we derive a wind-speed-dependent correction, in order to “normalise” the entire time series of the ANSTO measurements (at 3.5 m above ground) to the 15 m inlet, which is considered to be more representative. The uncertainty of this wind-speed-dependent correction (based on the 1 standard deviation during the 3-month comparison) is included in the time series shown in the Supplement (Fig. S24).

TM5 is a global chemistry transport model, which allows two-way nested zooming (Krol et al., 2005). In this study we apply the zooming with 1∘ × 1∘ resolution over Europe, while the global domain is simulated at a horizontal resolution of 6∘ (longitude) × 4∘ (latitude). TM5 is an offline transport model, driven by meteorological fields from the ECMWF Integrated Forecast System (IFS) ERA-Interim reanalysis (Dee et al., 2011). The spatial resolution of this data set is approximately 80 km (T255 spectral) on 60 vertical levels from the surface up to 0.1 hPa. We employ the standard TM5 version with 25 vertical levels, defined as a subset of the 60 layers of the ERA-Interim reanalysis. The extraction of the meteorological fields is performed through a pre-processing software, which supplies fully consistent meteorology data with those of ECMWF at the different spatial resolutions of TM5 (Krol et al., 2005). The boundary layer, the free troposphere, and the stratosphere are represented by 5 (up to 1 km), 10, and 10 layers, respectively. The temporal resolution of the data is 3 hourly for near-surface data (e.g. BLHs) and 6 hourly for three-dimensional (3-D) fields (e.g. temperature, wind, humidity, and convection).

Tracers in TM5 are transported by advection (in both horizontal and vertical directions), cumulus convection, and vertical diffusion. Tracer advection is based on the so-called “slopes scheme”, which considers a tracer mass within a grid cell as a mean concentration and the spatial gradient of the concentration within the grid box (Russel and Lerner, 1981), which is caused by the motion of the tracer into and out of the grid box. Non-resolved transport by shallow cumulus and deep convection in TM5 is parameterised by a bulk mass flux approach originally described in Tiedtke (1989). Such convective clouds are described by single pairs of entraining/detraining plumes representing the updraft/downdraft motion. The parameterisation of the vertical turbulent diffusion in the boundary layer is based on the scheme of Holtslag and Moeng (1991), while the formulation of Louis (1979) is considered in the free troposphere. The BLH is computed by using the expression of Vogelezang and Holtslag (1996), as described in Sect. 2.1. The exchange coefficients from the vertical diffusion are combined with the vertical convective mass fluxes to calculate the sub-grid scale vertical tracer transport. After redistributing the tracer mass by convection and diffusion, the slopes are updated.

Recently, van der Veen (2013) proposed a revised scheme to update the slopes. This “revised slopes scheme” results in enhanced horizontal transport in TM5 by increasing the horizontal diffusivity of the numerical scheme of the convection routine. Van der Veen (2013) found an improvement of the inter-hemispheric mixing gradient in TM5, which was initially underestimated as reported in, e.g., Patra et al. (2011). This “revised slopes scheme” has been used for the sensitivity tests described below. Furthermore, we performed sensitivity tests using directly the convection fields from the ECMWF IFS model, instead of the default convection scheme based on Tiedtke (1989). The ECMWF convection scheme includes several improvements of the parameterisations of deep convection, radiation, clouds, and orography, introduced operationally since the ECMWF ERA-15 analyses (e.g. Gregory et al., 2000; Jakob and Klein, 2000; Morcrette et al., 2001). Finally, we evaluate the combination of the “revised slopes scheme” and the use of ECMWF convection fields.

In the TM5 model, the full expression of Vogelezang and Holtslag (1996) is used to compute Rib, (Eq. 1). First, Rib is computed at each model level by using the Eq. (1). The vertical profile of Rib is then linearly interpolated between consecutive levels of the model. The BLH is defined as the height, where Rib reaches the Ric. In TM5, Ric is set to 0.3, and the minimum BLH is set to 100 m.

For consistent comparison with the IGRA data, we calculate the BLH in TM5 also based on the definition of Seidel et al. (2012) as used in the InGOS model validation exercise (i.e. Ric=0.25 and both surface wind and friction velocity are set to zero in Eq. 1; see Sect. 2.1). Furthermore, because InGOS and IGRA sites are not co-located, we extract the BLH in the model both at the location of the InGOS station and at the location of the nearest IGRA station, resulting in two sets of modelled BLHs labelled by the following acronyms:

“TM5_INGOS”: BLHs extracted at the InGOS station

Furthermore, we also extract the default TM5 BLH (both at the InGOS and IGRA station) and the BLHs from ECMWF reanalyses. In general, the difference between the BLH based on Seidel et al. (2012) and the TM5 default and ECMWF BLHs are very small. Therefore, the latter are only shown in the Supplement (Figs. S2–S11).

We use the new 222Rn flux map developed by Karstens et al. (2015) within the InGOS project (called hereafter “InGOS 222Rn flux map”). This map is based on a parameterisation of 222Rn production and transport in the soil, using a deterministic model based on the equations of continuity and diffusion (Fick's first law) to compute the transport of the 222Rn flux from the soil to the atmosphere. The modelled radon flux is dependent on soil porosity and moisture, with the latter obtained from two different soil moisture data sets, i.e. from the Land Surface Model Noah (driven by NCEP-GDAS meteorological reanalysis and part of the Global Land Data Assimilation System (GLDAS); Rodell et al., 2004) and from the ERA-Interim/Land reanalysis, respectively. Karstens et al. (2015) found that the flux estimates based on the GLDAS Noah soil moisture model on average better represent observed fluxes. Therefore, we apply in this study the 222Rn flux map version based on the Noah soil moisture data set. Furthermore, the 222Rn flux map considers the water table (from a hydrological model simulation), the distribution of the 226Ra content in the soil, and the soil texture. For comparison, we also apply the commonly used constant emission maps with uniform continental 222Rn exhalation of 21.98 mBq m-2 s-1 between 60∘ S and 60∘ N; uniform continental 222Rn emissions of 11.48 mBq m-2 s-1 between 60 and 70∘ N (excluding Greenland); and zero flux elsewhere (Jacob et al., 1997). The InGOS 222Rn flux map provides monthly 222Rn fluxes over the 2006–2011 period, aggregated to a 0.5∘ × 0.5∘ grid for Europe and complemented by the constant emissions for the regions outside Europe. Figure 2a and b illustrate the spatial and mean seasonal variations of the 222Rn fluxes from the InGOS 222Rn flux map over Europe. The modelled 222Rn flux is found to be larger in the areas where the 226Ra activity concentration in the upper soil is very high, such as the Iberian Peninsula, areas in Central Italy and the Massif Central in southern France (Fig. 2a). The mean seasonal variations of the 222Rn fluxes are mainly driven by the soil moisture. On average, the InGOS 222Rn emissions over Europe are smaller than the constant emission (except July–September; Fig. 2b).

We simulate 222Rn activity concentrations using either the InGOS 222Rn flux map based on Noah soil moisture data, or constant 222Rn fluxes (see Sect. 3.3). Furthermore, we also apply the revised slopes scheme and the updated convection scheme based on ECMWF reanalyses (see Sect. 3.1) for the InGOS 222Rn flux-map-based simulations only. These different simulations are labelled by the following acronyms:

FC_CT: constant 222Rn fluxes, and default convection scheme in TM5 based on Tiedtke (1989)

The model simulations are 3-D linearly interpolated (i.e. horizontally and vertically) to the location of the station, and averaged over 1 h.

We focus the analysis on the InGOS stations (measuring CH4 and N2O, and/or 222Rn activity concentrations; Fig. 1) at low altitudes (i.e. excluding mountain stations) and compare the modelled BLHs with observations at the closest IGRA stations. Figures 3 and 4 show the mean seasonal variation for the nocturnal (00:00 UTC) and daytime (12:00 UTC) BLH, respectively (2006–2010 average). The nocturnal BLHs show a clear seasonal cycle at most stations, with typically higher nocturnal BLHs during winter (but also larger range between 25 and 75 % percentile) compared to summer. This seasonal pattern is very consistent between measurements and model simulations. However, at some continental stations (e.g. Heidelberg, Gif-sur-Yvette) the IGRA data show very low nocturnal BLHs (median value below 100 m) during summer, which are not reproduced by the model. In general, the whisker plots (Fig. 3) show a skewed (non-normal) distribution for most monthly data (observations and model simulations) with the median value being usually significantly lower than the mean. The daytime BLHs show a very pronounced seasonal cycle at most continental stations (opposite in phase with the seasonal cycle of the nocturnal BLH), with typical values around 500 m during winter, and ∼ 1000–2000 m during summer. The daytime BLH is in general relatively well simulated at most stations, as further illustrated by the ratios between modelled and observed BLHs, which are close to 1 (see Fig. 8). An exception, however, are coastal sites (e.g. Angus, Mace Head), where apparently the model representation errors (e.g. transition between land and sea) are a limiting factor. In general, it should be expected that the model BLH extracted at the location of the IGRA station should agree better than that extracted at the InGOS station (see Sect. 3.2 for the definition of the model BLHs). However, e.g., at Egham, the opposite is the case, since the IGRA station (Herstmonceaux) is closer to the coast, and the corresponding model BLH has more “marine” character (and the transition zone between sea and land is not resolved by the model). For most stations far from the coast, however, the difference between the BLH at the InGOS station and the IGRA station is usually very small (Figs. 3, 4, and S2–S11). Compared to the data for the nocturnal BLH, the daytime BLHs show much smaller difference between median and mean value, indicating a less skewed frequency distribution (Figs. 3 and 4).

In the Supplement (Figs. S2 to S11) we show the full time series for the 10 stations in 2009, illustrating that also the synoptic variability of the BLH is relatively well reproduced by the models (for both nocturnal and daytime BLH). Furthermore, we extend the analysis by using all IGRA stations over Europe (about 130 stations; see Figs. 1, S12, and S13). This extended analysis confirms the major findings discussed above, especially (1) the good agreement between simulated and observed BLH during daytime, (2) the tendency for the simulated nocturnal BLHs to be too high during summer, and (3) larger differences between TM5 and IGRA BLHs for stations located close to the coasts.

In the following we include the ceilometer and lidar derived BLH at Cabauw and Traînou, respectively, in the analysis. As clearly visible from the correlation plot between ceilometer and IGRA data for Cabauw (Fig. S1), the ceilometer BLHs during midday are usually lower than the IGRA data (especially for the period March to September), while modelled BLHs fall in between the two observational data sets (Fig. 5). Part of this difference is likely due to the different methodologies. Hennemuth and Lammert (2006) pointed out that inconsistencies between the atmospheric thermal profile and the aerosol concentration profile can result in differences between radiosonde and lidar/ceilometer BLH retrievals. In addition, the spatial separation between Cabauw and De Bilt (∼ 23 km) combined with different surface characteristics (wetter soils in Cabauw and different large scale surface roughness) may play some role. While the correlation between IGRA BLHs and the ceilometer BLH retrievals at Cabauw is reasonable (r=0.63) during daytime, it is very poor during night (Fig. S1), probably due to the issues of ceilometers to detect the shallow nocturnal BLH, as mentioned in Sect. 2.1.2. The lidar daytime data at Traînou for 2011 agree relatively well with the model BLHs (except May) (Fig. 5). While no IGRA data are available for this period, the comparison between model simulations and IGRA for 2006–2010 at Traînou (Fig. 4) shows a similar (or slightly better) agreement as the comparison between lidar and model for 2011.

Figures 6 and 7 show the mean seasonal variations of observed and simulated 222Rn activity concentrations at each of the studied InGOS sites at 05:00 UTC (time around which typically the daily maximum 222Rn activity concentration occurs) and at 14:00 UTC (222Rn daily minimum), respectively. For most stations, TM5 simulated 222Rn activity concentrations based on the InGOS 222Rn flux map show significantly better agreement with observations than the simulations based on the constant 222Rn flux, especially regarding the average seasonal variations. The improvement is largest during winter months, when TM5 simulations based on the constant 222Rn fluxes often overestimate observations, while simulated concentrations based on the InGOS 222Rn flux map are significantly lower owing to the lower 222Rn fluxes (Figs. 6 and 7). This, in turn, is driven mostly by the higher soil moisture and consequently lower permeability of the soil in winter. Furthermore, large differences are visible at many northern European sites close to the coast (Angus, Lutjewad, Mace Head, Cabauw), where the water table can be very shallow, significantly reducing the 222Rn fluxes (Karstens et al., 2015). Model simulations based on the InGOS 222Rn flux map (which include modelled water table in the parameterisation of 222Rn fluxes) agree much better with observations than the control runs with constant 222Rn fluxes. Despite the larger 222Rn fluxes during summer, daily minimum 222Rn concentrations in the model and observations are usually lower at continental stations (e.g. Heidelberg, Gif-sur-Yvette) due to the much higher daytime boundary layer in summer compared to winter.

Figures S14 to S24 in the Supplement show the full time series of simulated and observed 222Rn concentrations at the 10 studied InGOS stations (with 222Rn activity concentration observations available) for 2009.