COMPARISON OF AGGREGATED AND MEASURED
TURBULENT FLUXES IN AN URBAN AREA
Ekaterina Batchvarova1,2
, Sven-Erik Gryning3, Mathias W. Rotach
4 and
Andreas Christen5
1. INTRODUCTION
Most of the parameters commonly used to describe the turbulence in the
atmospheric boundary layer represent conditions of atmospheric turbulence near the
ground and therefore have a small footprint. For a mast of 10 meters above ground the
footprint is few hundred meters. A 40-50 meter mast looks over some kilometers in
upwind direction. The height of the convective boundary layer is typically 1-2 kilometers
in middle latitudes and reflects the conditions several tens of kilometers upwind. The
footprint of meteorological characteristics is essentially dependant on atmospheric
stability and wind speed (Gryning and Batchvarova, 1999; Kljun et al., 2003). The
mixing height determination based on surface data is much more demanding in terms of
requirements of homogeneous conditions because it overlooks a large area. It is still
commonly accepted practice to use parameterisations for homogeneous terrain, even
under inhomogeneous conditions. The results are not always good when compared to
measurements.
The sub-grid variability of the mixed-layer height, momentum and sensible heat
fluxes is believed to be an important but not yet settled issue for many model
applications. Models for long-range transport and dispersion of atmospheric pollutants,
Numerical Weather Prediction models, and Climate Models are all characterised by large
grid cells that often enclose regions of pronounced non-homogeneities. The estimation of
the regional or aggregated momentum and heat fluxes over non-homogeneous surfaces is
1 National Institute of Meteorology and Hydrology, Sofia, Bulgaria (permanent);
2 Hertfordshire University, Hatfield, UK (visiting November 2003 – June 2004);
3 Risø National Laboratory, Roskilde, Denmark;
4 Swiss Federal Office for Meteorology and Climatology, MeteoSwiss, Zürich,
Switzerland; 5 University of Basel, Institute of Meteorology, Climatology and Remote sensing, Basel,
Switzerland.
therefore a central issue when the boundary conditions in models with large grid cells
have to be specified.
The size of the grid determines the features that models can resolve. The larger the
grid the more of the small scale features in the flow field will not be resolved. A
multitude of well established models have their roots in parameterisations of surface
fluxes that have been developed for homogeneous terrain. The effect of their use in
simple aggregation schemes over typical European areas characterized by a patchy
structure of villages, towns, various types of agricultural fields and forests is not clear.
Consequently the estimation of the regional or aggregated momentum and heat fluxes
over non-homogeneous surfaces is a central issue when the boundary conditions in
models with large grid cells have to be specified. Here we consider the heterogeneity of
an urban area and its surroundings. Therefore the complex structure of the urban
boundary layer is sketched in Figure 1.
Figure 1. Schematic of the boundary layer structure over an urban area. The vertical and horizontal patterns represent the underlying surface of the neighbourhoods of tall and low buildings, respectively. Broad spaced
patterns represent the urban internal boundary layers where advection processes are important. Fine spaced
patterns show the inertial sub-layers that are in equilibrium with the underlying surface and where Monin-
Obukhov scaling applies. The forward slash pattern represents the roughness sub-layer that is highly
inhomogeneous both in its vertical and horizontal structure. The dotted pattern represents adjustment zones
between neighbourhoods with large accelerations and shear in the flow near the top of the canopy. Above the height where the internal boundary layers are intermixed the effects of the individual neighbourhoods cannot be
distinguished any more – the so-called blended layer.
In this paper we consider the use of boundary layer parameterisations for
homogeneous conditions when applied for heterogeneous land cover areas. We consider
the actual (measured) convective boundary layer height as formed by the forcing of the
surface conditions tens of kilometers upwind. We use a method that is based on the
height and the growth rate of the convective layer (Gryning and Batchvarova, 1999) to
estimate aggregated surface sensible heat flux values. Further we use in situ turbulence
measurements at 40 meters height on a urban meteorological tower to compare the
results.
2. THE METHOD
The required information for use of the method to aggregate fluxes can be derived
from wind speed and temperature profiles obtained by radio soundings when performed
frequently enough to provide a reasonably detailed structure of the mixed-layer
development. Alternatively data from remote sensing technique like combined wind
profiler and radio acoustic sounding systems can be used.
The method was used first over a sub-Arctic area with rather large patches of forest,
fields, mires and lakes. The aggregated heat flux was found to be in general agreement
with the land-use-weighted average heat flux. Thus, rough aggregation of the heat flux is
simple, but it is not known if this can be extended to small patches as in an urban area.
Batchvarova et al. (2001) and Gryning and Batchvarova (2002) show that this is not the
case for the momentum flux. It is desirable to continue to investigate the blending of
fluxes over patchy terrain, and extend the research to include aggregation for the urban
area that today is virtually unknown. The urban area is far more complicated that the
forest (Figure 1) and research in the formation of the local fluxes and the way they
interact and finally forms the blending layer is very relevant for a better understanding of
the urban climate (Rotach et al., 2002).
The framework is the mixed-layer growth model by Batchvarova and Gryning
(1991) and (1994).
eff
sseff
eff
eff
ww
dt
dh
LBhAg
TuC
LBhA
h ''
)1(
)(
2)21(
2
*
2
. (1)
The potential temperature gradient, in the free atmosphere, the large scale vertical
air velocity, s
w , the height of the boundary layer, h its growth rate, dtdh and the rate
of warming, t¶¶q of the free atmosphere above the mixing layer can be extracted from
i.e. radio soundings. The warming rate at height z in the free atmosphere is connected to
the vertical velocity sw and the potential temperature gradient at the same height
through:
)()(
zwt
zsg
q-=
¶
¶. (2)
Equation (1) can be solved numerically for the effective vertical turbulent kinematic
sensible heat flux at the surface, ( )effsw ''q , that is forcing the growth of the boundary
layer. The coupled momentum and heat flux solution is discussed in Batchvarova et al.
(2001).
A comprehensive discussion on the applicability of this approach is given in
Gryning and Batchvarova (1999). Based on footprint analysis, the blending height
hypothesis and internal boundary layer theory, the height at which the surface
heterogeneities do not influence the flow any more can be determined. For typical values
of the meteorological parameters and landscape patchiness, this height is 100-200 meters.
The method is applicable when the mixed layer is deeper than the layer where the flow
features are blended, the so-called blending height.
3. THE SOFIA EXPERIMENT
Data drawn from a recent urban boundary layer experiment (September/October
2003) in Sofia, Bulgaria, that comprised high resolution boundary layer radiosoundings
to determine the mixing height and mixed layer growth and measurements with sonic
anemometers at two heights in a sub-urban area of the city of Sofia are used for the
analysis. The two sonic anemometers and a fast hygrometer were mounted on the
research tower of NIMH at 20 and 40 m height agl (above ground level) and 10 and 30 m
above roof, respectively on booms 4 m away of the tower in direction west, Figure 2.
Figure 2. The meteorological tower with sonic anemometers and a Krypton hygrometer(left) and a view from
the tower to the west (right)
High resolution radiosoundings were performed with Vaisala equipment. Typical
convective conditions were chosen for the campaign when 7 soundings per day were
performed providing data for the growth of the mixed layer with 2 hours time interval.
Five days with such conditions were identified in the period 18 September – 8 October
2003.
NIMH
Figure 3. Map of Sofia and close rural areas (56 by 28 km approximately). The position of the
measurement tower at NIMH is marked.
0 3 6 9 12 15 18 21 24
29 September 2003, LST
-50
0
50
100
150
200
250
300
350
400
450
500
Sensib
le h
eat flux [W
m-2
]
29 September 200320 m
40 m
Aggregated
12 16 20 24 28 32 36
Potential Temperature [deg C]
500
1000
1500
2000
2500
3000
He
ight
ab
ove s
ea
le
ve
l [m
]
29 September 20037 LST
9 LST
11 LST
13 LST
15 LST
17 LST
19 LST
0 3 6 9 12 15 18 21 24
29 September 2003, LST
0
1
2
3
4
5
6
Win
d s
peed [m
s-1
]
29 September 200320 m
40 m
0 3 6 9 12 15 18 21 24
29 September 2003, LST
0
45
90
135
180
225
270
315
360
Win
d d
irection [degre
es]
29 September 200320 m
40 m
Figure 4. Turbulence and radio sonde measurements on 29 September 2003.
Following the understanding of aggregation of fluxes over heterogeneous areas,
(Gryning and Batchvarova, 1999 and Batchvarova et al., 2001) the observed convective
boundary layer was considered forced by the blended thermal and mechanical fluxes over
the area. The measuring site (NIMH) is in the south east part of the city and the urban
characteristics for it are spread over 3 km to south and east, about 10 km to north and
about 20 km to the west. Depending on wind direction, the aggregated fluxes represent
different percentages of urban and rural conditions, Figure 3.
4. RESULTS OF MODELLING
In Figure 4 the comparison of measured and aggregated sensible heat fluxes is
presented (upper left panel) for 29 September 2003. The aggregated and measured values
are close, suggesting that blended fluxes are representing urban conditions for western
and north-western weak winds, Figure 4 (lower panels). At 13.00 local summer time
(LST) the mixed layer-height reaches some 1000 meters above the ground (Figure 4,
upper right panel).
Figure 5. Turbulence and radiosonde measurements on 1 October 2003.
On 1 October 2003 the aggregated fluxes are smaller than those measured on the
tower (Figure 5 upper panel). On this day the wind is easterly (Figure 5, lower panel),
thus leading to the conclusion that the footprint of the profile observations contains large
rural areas in upwind direction (Figure 3). These are apparently influencing the blended
(i.e., modeled) values as obtained from the soundings. On the other hand, the tower
remains within the roughness sub-layer of the urban atmosphere and exhibits larger
(urban only) surface heat fluxes. The depth of the convective boundary layer is again
about 1000 meters above ground, Figure 5.
It can be seen from the upper left panels of Figures 4 and 5 that the measured heat
fluxes at 40 meters are slightly higher as compared to the 20 meters level. This feature is
connected to the structure of the urban surface layer, Figure 1, and is discussed on data
from several experiments such as BUBBLE (Rotach et al. 2004), Copenhagen (Gryning
and Lyck 1984) and Sofia in Batchvarova et al. (2004), Batchvarova and Gryning (2004
& 2005).
5. DISCUSSION
One immediate implication of the results presented here is the caution needed when
applying pre-processors based on local measurements in urban areas. In the case of 1st
October 2003 the use of the turbulence measurement for estimation of the mixing height
with the use of a meteorological pre-processor will give a much deeper mixed layer than
is actually observed. Under such circumstances air pollution concentrations could be
under-predicted. The representativeness of measuring sites is wind direction dependant.
The same considerations are valid if mesoscale model results are compared to
measurements. The area over which the modelled parameters are averaged can be
different from that represented by measurements. Considering the representativeness of
airport stations for urban meteorological and air pollution studies is therefore a complex
issue.
Acknowledgements
The study reports results from ongoing work that aims further understanding of the
complex layer structure and turbulence regime over a city and is a part of Swiss-
Bulgarian collaboration project (7IP 065650), COST 715 Working group 1 and a NATO
CLG grant (979863). The Sofia experiment was also in the frame of the BULAIR Project
EVK2-CT-2002-80024. The input in the experimental work of Ivan Lanzov, Plamen
Videnov, Nedialko Valkov and Alexander Gamanov, researchers from NIMH is kindly
acknowledged.
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