Planetary boundary layer (PBL) CO

Anthropogenic activity can influence the global climate in the long term through
the emission of greenhouse gases, most notably carbon dioxide (CO

Until the late 1990s surface-based measurements (typically at 2–20 m
above ground) were available almost exclusively for the estimation of the
characteristic CO

In this study, combining tall-tower and aircraft measurements, we estimate
the uncertainty with which measurements on a tower characterize the CO

Carbon dioxide mole fraction data used in the present study derive from
western Hungary, where the Hungarian Meteorological Service and the
Department of Meteorology, Eötvös Loránd University, Budapest,
operate a tall-tower greenhouse gas (GHG) monitoring site
(Hegyhátsál, 46

The Hegyhátsál tall-tower GHG monitoring site is located in a fairly
flat region, in a rural environment, with low levels of anthropogenic CO

The tower also hosts an eddy covariance system at 82 m above the ground for
the continuous monitoring of the vertical flux of CO

Airborne in situ carbon dioxide mole fraction measurements were performed
over the Hegyhátsál tall-tower GHG monitoring site on board a small
aircraft (Cessna 210) between 10 February and 12 November 2006, and
between 8 November 2007 and 18 January 2009 as part of a European
Commission-sponsored research project (CarboEurope-IP –

The comparability of the tall-tower-based and the airborne measurements is
guaranteed by the calibration standards traceable to the same primary ones
at WMO CCL, the uncertainty of which is < 0.1

The airborne measurements did not provide the meteorological data needed for the direct determination of the height of the PBL. Therefore, data on the height of the planetary boundary layer were retrieved from the Meteorological Archive and Retrieval System (MARS) database of the European Centre for Medium-Range Weather Forecasts (ECMWF). PBL height data were calculated by the deterministic model in forecast time steps with 3 h temporal resolution (Beljaars et al., 2001). For the actual time of the flight (late morning–early afternoon) the PBL height was linearly interpolated between the model time steps, but occurrent decrease in the PBL height was not taken into account.

As the present study focuses on the PBL, airborne profiles could only be
used when the PBL was at least 300 m high. This leaves a total of 136
CO

The airborne and tall-tower in situ measurements record the vertical distribution of carbon dioxide in the lower troposphere. The mole fraction values measured aloft, representing the levels simulated by an atmospheric transport model (called “estimation height” in this paper), can be compared with the values measured below, simulating the top of a hypothetical tower (called “tower height” in this paper). In other words, the deviation of the constant vertical profile determined by the measurement at the top of the tower from the real one is determined at each estimation height. For a given tower height–estimation height pair this mole fraction deviation can be calculated for each measured mole fraction profile. These deviations form the empirical frequency distribution of the bias between the true mole fraction and the estimated one for each tower height–estimation height combination. The value of this bivariate function at any given tower height–estimation height point is a frequency distribution function; therefore, the graphical presentation of this bivariate function is hardly possible. Instead, mean, median, standard deviation and other statistical characteristics of the bias between the measured and assumed (constant) mole fraction profiles can be presented as the function of the tower height and the estimation height.

The comparison of the measured and estimated profiles gives information on
how well a tower of height

For the study the airborne in situ measurements were layer-averaged with 25 m vertical resolution from 225 m a.g.l. up to the top of the measurements, usually about 3000 m a.g.l. Any data gap in the layer-averaged profile caused, for example, by calibration or baseline check of the instrument was filled by linear interpolation between the neighboring layers as long as the gap was not wider than 50 m (two layers).

For the specific study on the mid-PBL CO

In this study the height-dependent performance of the hypothetical tall tower is primarily expressed on a relative scale: the estimation height is expressed as percent of the PBL height. The reason for this is the fact that a given absolute elevation can represent rather different relative ones within the PBL depending on the actual PBL depth, and gradients are functions of depth within the PBL, not absolute elevation above ground. It should also be noted that the gradient function may be different in shallow and deep PBLs, but the limited number of the available measurements does not make possible the resolution according to PBL height. The use of relative elevation scale may cause inconvenience for certain applications because the results may need to be transformed using the actual PBL height.

The virtual tall-tower concept was first presented by Davis (2005). Using
the mixed-layer similarity theory of Wyngaard and Brost (1984) and
Moeng and Wyngaard (1984), theoretical (idealized) scalar profiles
can be estimated for the entire PBL, taking into account surface fluxes,
convection and entrainment processes. In our case, CO

Following the work of Wyngaard and Brost (1984) and Moeng
and Wyngaard (1984), the CO

In Eq. (

In Eq. (

Theoretically,

Here

At a monitoring site, where eddy-covariance-based CO

The proposed forms of

In order to find the most appropriate functional form for the application of
the VTT concept, we tested all three gradient functions mentioned above and
identified those that best matched the data (see the Supplement).
The integrated form of the gradient function that proved to be the most
appropriate is the following:

The median bias between the true CO

The gradient function may depend on local environmental conditions (e.g.,
on-site heterogeneity); therefore further studies on this topic are desirable.
We used Eq. (

Convective velocity scale and surface fluxes were calculated using the results of the eddy covariance measurement the closest in time to the middle time of the airborne measurements. In order to provide more robust estimation of simulated gradients, convective velocity scale and surface flux data available in 1 h resolution were averaged for 3 h starting 3 h before the middle time of the airborne measurements. The averaging is also useful as it decrease the random flux error inherently present in the eddy covariance measurements.

Empirical frequency distribution of the differences between
the CO

The simplest approach to using tower CO

Theoretically, a monotone increase of median bias is expected with increasing elevation. The variable internal structure of the PBL and the limited number of data cause the more complex picture seen in Fig. 1. The bottom panels of the figure also show the frequency distribution of the PBL height at 12:00 UTC for the days considered. Comparing the PBL-height statistics of the flight days and those of all days for the period of 2006–2008, the fair-weather bias of the flight days can be noticed, which should be kept in mind while interpreting of the results. Bad weather conditions, usually accompanied by shallow PBL, prevented the aircraft measurements. The number of flights was 56 in summer and 80 in winter half year.

As mentioned in Sect. 2.2., the “value” of the bivariate tower
height–estimation height function at any given point in altitude space
is a frequency distribution, which cannot be presented in a figure. For
practical reasons Fig. 1 shows only the median of the distributions that is
a single value per point. The other statistical characteristics of the
frequency distributions are also important for the interpretation of the
results. To give an impression of the frequency distribution, Fig. 2 shows
how accurately a tower of height

Empirical probability of the cases when the bias between the
true CO

An empirical cumulative density function of the biases can be calculated for
any tower height–estimation height combination. As an example Fig. 3
shows the probability with which a tower of

The median bias between the true CO

Tall-tower and airborne measurements revealed that persistence of surface
sources/sinks and systematic differences between free-tropospheric and
boundary layer mole fractions cause the formation of non-constant vertical
CO

For those cases when the VTT concept could be applied the biases between the
measured and estimated CO

The gradient functions utilized here are not able to simulate the true
vertical mole fraction profile without bias, but Fig. 4 shows that the bias
is generally somewhat lower than without the application of the VTT method,
especially in summer. Figure 5 shows how much closer our estimated mole fraction gets
to the real one if the VTT concept is applied, relative to the simple
extrapolation of the tower-top mole fraction (constant profile), again as a
function of the tower height and estimation height. A positive sign indicates
that the application of the VTT concept improves the estimation of the real
vertical distribution of the CO

Figure 5 shows that improvement can be achieved in both summer and winter, but there are characteristic differences between the seasons.

Difference of the median biases of the estimations applying
and not applying the VTT concept (

There are characteristic differences between the plots presented in Fig. 1.
In summer (top-left panel in Fig. 1) the shorter the tower, the higher the
underestimation of the mole fraction above the tower, especially close to
the top of the PBL. Essentially it is caused by two facts: (1) in summer
daytime the surface is usually a net CO

In winter (top-right panel in Fig. 1) the shorter the tower, the higher the
overestimation of the mole fraction above the tower, especially in the case
of shallow PBL. In winter the surface is a net CO

The characteristic differences between the summer and winter half years can
also be recognized in Fig. 2. The frequency distribution of the deviation
from the mid-PBL mole fraction is rather skewed, especially in the case of
short towers. In winter, it has a long right tail (significant
overestimation), while in summer it is skewed in the opposite direction.
In winter, when the vertical mixing is limited, a high amount of carbon
dioxide may accumulate close to the surface. Consequently, short towers
sampling the air in this frequently CO

In summer, in the case of surface measurements or short towers the
application of the VTT concept improves the CO

If we wanted to know the CO

Given a criterion for the maximum median bias, the minimum height of the
tower satisfying the criterion can be determined. Figure 1 shows what is
possible without the application of the VTT method. The detailed data behind
Fig. 1 (see the Supplement) show that a median bias lower than
0.5

A 170–180 m tall tower can also estimate the CO

The chaotic nature of the atmosphere, the vertical mixing variable in both time and space and the ever-changing advection keep the planetary boundary layer heterogeneous even if it is usually considered “well mixed” (Stoy et al., 2013). As a result, the deviations of the measurements at a given elevation from another one scatter in a wide range, as could be seen in Fig. 2. Figure 3 shows the probability with which the bias remains below a given accuracy demand as a function of the height of the tower.

If we aspired after mid-PBL CO

In winter, due to the shallower PBL, 1

Applying the VTT method, even with imperfect gradient functions, reduces the
bias considerably. The lower-than-0.5

In winter, the application of the VTT concept does not help much except for
the top region of the PBL, as can be seen in the right panel in Fig. 5.
The reason for the better estimation of the upper PBL mole fraction is that
the VTT model handles the free-tropospheric entrainment, which may influence
the mole fraction here significantly due to the frequently large CO

Generally, the VTT concept improves the performance of the relative short
towers (Fig. 5). Tall towers with a height of 400–800 m required for low maximum bias at
high probability do not perform better when applying the VTT method. However, the
more common towers of 100–300 m can provide < 1

Empirical probability of the cases when the bias between the
true CO

Usually scientists are not in the position to construct monitoring towers
according to theoretical accuracy criteria. In most cases existing
meteorological or telecommunication towers can be equipped with CO

In winter the tower can estimate the daytime CO

For taller tower of 200–300 m the improvement is smaller (summer) or negligible (winter, Fig. 5).

In addition to the tall towers there are also ground-based monitoring
stations in the GHG monitoring networks. Typically they sample air at
5–20 m elevation above the ground. According to our study these stations
can estimate the daytime mid-PBL CO

As shown in Fig. 5, the VTT method providing theoretical information on the
vertical gradient of the CO

Applicability of the VTT concept requires sensible heat and CO

As a test of the theoretical considerations on the height above the ground of the eddy covariance system, the calculations were repeated using the available data set of another eddy covariance system located 3 m above the grass-covered ground at the bottom of the Hegyhátsál tall tower (Barcza, 2001; Nagy et al., 2011). Although the overlapping operation time of the two systems (82 and 3 m) was too short to draw a sound conclusion, we got comparable results. This is most likely caused by the covariance of NEE and sensible heat flux between the low- and high-elevation eddy covariance systems. Covariance of NEE is the result of the fact that the functioning of both the mixed croplands sampled by the high-elevation eddy covariance system and the grassland sampled by the low-elevation one is driven by the same environmental factors (radiation, temperature, precipitation). Due to footprint considerations, we recommend using the highest-possible elevation for the eddy covariance measurements.

In the present study we analyzed how well towers of different heights could
estimate the vertical distribution of CO

Our results are primarily valid for relatively homogeneous, flat regions.
The data in this study reflect only the daytime conditions. The nighttime
boundary layer is typically shallower over a continental site than the
daytime PBL and is often stably stratified, making it difficult to simulate
in transport models. On 70 % of the nights (00:00 UTC) at the Hegyhátsál
tall-tower greenhouse gas monitoring station, the base of the present study,
the height of the PBL is below 200 m according to the MARS database of
ECMWF. A tower satisfying the daytime requirements may encompass the entire
nocturnal PBL and provide a directly measured, PBL-integrated mole fraction
if CO

As was shown, application of the VTT concept may improve the performance
of the shorter tower, especially in summer. The extra benefit of the
operation of an EC system is the information on the local
biosphere–atmosphere carbon budget. Technological development in recent
years has also made the EC flux measurement of certain non-CO

The monitoring program at and above the Hegyhátsál tall-tower site was
supported by the 6th R&D Framework Programme of the European Commission
(CarboEurope-IP – GOCE-CT-2003-505572, IMECC – RII3 026188), by the
Hungarian Ministry of Economy and Transport (GVOP-3.2.1.-2004-04-0107/3.0)
and by the Hungarian Scientific Research Fund and the National
Development Agency (KTIA-OTKA CK77550, OTKA K104816, K109764). The study
could not have been realized without Martin Simon (Air Taxi Ltd.), pilot of the
aircraft hired for the airborne measurements, and his crew operating the in
situ CO