Meteorologische Zeitschrift, Vol. 18, No. 2, 155-162 (April 2009) Open Access Article
c© by Gebru¨der Borntraeger 2009
Doppler lidar observations of sensible heat flux and
intercomparisons with a ground-based energy balance station
and WRF model output
JENNY CLARE DAVIS1∗, CHRISTOPHER G. COLLIER1 , FAY DAVIES1 , GUY N. PEARSON1 , RALPH
BURTON2 and ANDREW RUSSELL3
1The University of Salford, Salford, Greater Manchester, UK
2School of Earth and Environment, The University of Leeds, Leeds, UK
3School of Earth, Atmospheric and Environmental Sciences, The University of Manchester, Manchester, UK
(Manuscript received September 9, 2008; in revised form February 12, 2009; accepted February 12, 2009)
Abstract
During the Convective and Orographically induced Precipitation Study (COPS), a scanning Doppler lidar
was deployed at Achern, Baden-Wu¨ttemberg, Germany from 13th June to 16th August 2007. Vertical velocity
profiles (‘rays’) through the boundary layer were measured every 3 seconds with vertical profiles of horizontal
wind velocity being derived from performing azimuth scans every 30 minutes. During Intense Observation
Periods radiosondes were launched from the site. In this paper, a case study of convective boundary layer
development on 15th July 2007 is investigated. Estimates of eddy dissipation rate are made from the vertically
pointing lidar data and used as one input to the velocity-temperature co-variance equation to estimate sensible
heat flux. The sensible heat flux values calculated from Doppler lidar data are compared with a surface based
energy balance station and output from the Weather Research and Forecasting (WRF) model.
Zusammenfassung
Wa¨hrend der Studie zu konvektiven und orographisch induzierten Niederschla¨gen (Convective and Orograph-
ically induced Precipitation Study - COPS) wurde das 1,5 µm scannende Doppler-Lidar der Organisation
UFAM (Universities’ Facility for Atmospheric Measurement) an seinem Messstandort in Achern, Baden-
Wu¨rttemberg, Deutschland vom 13. Juni bis zum 16. August 2007 von der Universita¨t Salford, UK, betrieben.
Vertikale Windgeschwindigkeitsprofile der atmospha¨rischen Grenzschicht wurden alle 3 Sekunden gemessen.
Aus 30-minu¨tigen Azimut-Scans wurden die Horizontalgeschwindigkeitsprofile abgeleitet. Wa¨hrend der in-
tensiven Beobachtungsperioden wurden zusa¨tzlich Radiosonden vom Messplatz gestartet. Im vorliegenden
Artikel wird eine konvektive Fallstudie am 15. Juli 2007 na¨her untersucht. Vom vertikal gerichteten Lidar wird
die Eddy-Dissipationsrate abgescha¨tzt. Sie wird in der Kovarianzgleichung zwischen Windgeschwindigkeit
und Temperatur zur Abscha¨tzung des fu¨hlbaren Wa¨rmeflusses verwendet. Die verwendeten Annahmen wer-
den explizit erwa¨hnt. Der fu¨r die verwendete Methode beno¨tigte Grad der atmospha¨rischen Instabilita¨t wird
durch den Vergleich mit den Radiosondendaten besta¨tigt. Die abgeleiteten Ergebnisse stimmen gut mit den
Daten der Energiebilanzstation und des WRF Modells u¨berein.
1 Introduction
The Convective and Orographically-Induced Precipita-
tion Study (COPS) field trial was conducted in the
Black Forest region of Germany during the summer of
2007. Its aim was to advance the quality of forecasts of
orographically-induced convective precipitation using
extensive observations and modelling (COPS, 20071).
The University of Salford own and operate a scan-
ning 1.5 µm Doppler lidar system, and were funded by
the Universities’ Facility for Atmospheric Measurement
(UFAM) through the UKNatural Environment Research
Council to participate in the project. The Doppler lidar
was mounted in a mobile laboratory and has a full hemi-
∗Corresponding author: Jenny Clare Davis, The University of Salford, Sal-
ford, Greater Manchester, M5 4WT, UK, e-mail: C.Davis@salford.ac.uk
1Convective and Orographically-Induced Precipitation Project 2007, avail-
able at www.cops2007.de
spheric scanning capability using a dual-mirror scan-
ning system. Additionally, a 14 channel microwave ra-
diometer and a Campbell Scientific automatic weather
station (AWS) were deployed at the Achern site. All
instruments were set up to run continuously from 13th
June to 16th August 2007. The lidar, built by Halo Pho-
tonics, was deployed and, being autonomous, was left
unattended and fully controlled over the internet. It had
been previously deployed during the World Weather Re-
search Project (WWRP) Helsinki Testbed (BOZIER et
al., 2007).
The Salford Autonomous Doppler Lidar System, op-
erating at a wavelength of 1.5 µm, employs novel fi-
bre optic technology and the design approach has led
to a new type of eye-safe Doppler lidar providing a high
level of performance and exhibiting exceptional stabil-
ity, which was demonstrated by this successful deploy-
ment. A detailed analysis of wind measurements pre-
0941-2948/2009/0367 $ 3.60
DOI 10.1127/0941-2948/2009/0367 c© Gebru¨der Borntraeger, Berlin, Stuttgart 2009

156 Davis et al.: Doppler lidar observations Meteorol. Z., 18, 2009
Figure 1: The Salford University Doppler lidar with antenna (inset).
Table 1: Autonomous Doppler lidar system parameters.
Parameter Value
Operating Wavelength 1.5 µm
Pulse Repetition Frequency 20 kHz
Energy per pulse. 10 µJ
Pulse duration 150 ns
Beam divergence 50 µrad
Range gate length 30 m
Lens diameter 75 mm
Focal length Infinity
Minimum range 100 m
Maximum Range 7 km
Temporal resolution 0.1–30 s
viously made with this lidar system has been given in
PEARSON et al. (2009). Figure 1 illustrates the Univer-
sity of Salford Doppler lidar system in position at the
COPS field site in Achern, Germany.
The Doppler lidar data was selected to test a method-
ology discussed in depth by DAVIS et al. (2008) and
GAL-CHEN et al. (1992) for calculating QH , in an ur-
ban area. This involves using an estimation of the ki-
netic energy dissipation and the vertical gradient of
the third moment of the vertical velocity. During the
COPS field trial, there were few instruments measur-
ing QH , and none of these were located at the Achern
site. However, the conditions and scanning strategy em-
ployed meant that the data were suitable for testing this
methodology in a semi-rural area, and since QH is an
important variable when investigating the development
of thermals (THIELEN et al., 2000) and associated rain-
fall (BENNETT et al., 2006; ROZOFF et al., 2003), the
COPS field trial was considered an good opportunity for
this methodology to be tested.
2 The Salford University Halo
Photonics Doppler lidar
The lidar system was developed to meet the require-
ments of the University of Salford, being capable of
unattended, autonomous operation. The University of
Salford specification required a Doppler lidar system
capable of providing high temporal and spatial resolu-
tion measurements of the wind velocity and backscatter
within the atmospheric boundary layer. The system is
portable and rugged and capable of being used for field
work and long term measurements (BOZIER et al., 2007;
PEARSON et al., 2009). The lidar works by transmit-
ting a short laser pulse, of approximately 1x10−7 s, and
collecting the backscattered signal from the illuminated
aerosol targets along the path of the laser beam – see Ta-
ble 1 for more details of the lidar. The primary scatterers
are small atmospheric aerosol particles whose diameters
are within an order of magnitude of the lidar wavelength.
At optical wavelengths, scattering within the lower at-
mosphere is primarily by particles with diameters less
than 3 µm,which are sufficiently small to be advected by
the wind, and serve as an effective tracer of wind veloc-
ity (DAVIES et al., 2003; HARDESTY et al., 1992); FRE-
LICH, 1995; SCHWIESOW, 1986). Accurate estimates of
the radial component of the velocity (along the line of
sight of the laser beam) are produced as a spatial aver-
age over the sensing volume of the transmitted pulse.
The lidar system has a modular design arranged in
three separate units; the optical base unit, the weather-
proof antenna, consisting of the telescope and associ-
ated commercially sensitive, scanning electronics, and
the signal processing and data acquisition unit. The base
unit has approximate dimensions 56 cm x 54 cm x 18 cm
and contains the optical source, interferometer, receiver
and the electronics. The weather-proof antenna is at-
tached to the base unit via a 1” diameter, 1 m long optical
fibre conduit. The antenna can be deployed permanently

Meteorol. Z., 18, 2009 Davis et al.: Doppler lidar observations 157
Figure 2: Wind vector plot for 15/07/07, 0800–2200 h UTC, arrows
represent relative horizontal wind speed and direction. Due to some
wind velocities being very small, the arrows appear as dots. The
legend (bottom left) shows an arrow representing a 2 m s−1 wind
speed, with westerly direction.
outside whilst the base unit and data acquisition sys-
tem are housed within a mobile laboratory environment.
The signal processing has been developed with a view
to providing a high level of flexibility with respect to the
data acquisition parameters. Users are able to set param-
eters such as the range gate length, maximum range and
number of pulses accumulated for each measurement,
as detailed in Table 1. During the field campaign, mea-
surements were limited only by atmospheric moisture
(rain/fog), a lightning strike and a mains power failure.
The Doppler lidar system is described in greater detail
in PEARSON et al. (2009), HALO PHOTONICS (20082).
3 Measurements
The UFAM pulsed Doppler lidar is capable of measur-
ing:
• Directly: Radial wind velocity, relative backscatter
intensity
• Indirectly: Horizontal velocities, their variances and
covariances, atmospheric backscatter coefficient (β)
and turbulence kinetic energy dissipation rate (ε)
During much of the field campaign, the lidar system
performed a series of scan patterns pre-programmed
into the system software. Errors are given in Table 1
and described in more detail in PEARSON et al. (2009).
Generally, the system carried out:
• 5 minute azimuth scan at 5 different elevations (20◦,
30◦, 40◦, 45◦ and 60◦), but on the case discussed
here, azimuth scans were performed at 60◦
2The Halo Photonics pulsed Doppler LiDAR system, available at www.halo-
photonics.com
Figure 3: Full day view, 15/07/07, showing thermals building
throughout the day.
Figure 4: Doppler lidar and radiosonde horizontal wind speeds to
800 m.
• 25 minute vertically fixed stare consisting of 334
radial velocity ‘ray’ measurements.
The azimuth scan was performed to determine wind
velocity profiles, derived from VAD analysis (BROWN-
ING and WEXLER, 1968) and these data were concate-
nated enabling a half-hourly vector profile, as illustrated
in Figure 2. The vertically pointing stares were concate-
nated to produce a complete overview of vertical veloc-
ities measured by the Doppler lidar each day, as illus-
trated in Figure 3. Both Figure 2 and Figure 3 show
data up to a height of 1100 m. Beyond this range, on
this day there was no signal return. The data illustrated
can be used to calculate a variety of products, includ-
ing mixed layer height (COLLIER et al., 2005; MOK
and RUDOWICZ, 2004) and turbulence statistics DAVIES
et al. (2004), LENSCHOW et al. (2000), FRELICH and
CORNMAN (2002) and BANAKH et al. (1999).
The data from the 15th July 2007 show that thermals
were building throughout the day and the synoptic situa-

158 Davis et al.: Doppler lidar observations Meteorol. Z., 18, 2009
tion indicated that a convergence line passed, from west
to east, to the north of Achern. High convectivity, partic-
ularly at around 1500 UTC, was measured by the lidar.
The convective conditions suggested a suitable day to
use lidar data to calculate (QH ), a parameter important
in monitoring the development of thermals. A method
discussed in detail by DAVIS et al. (2008) is outlined
and tested here.
It was first necessary to confirm the reliability of
the Doppler lidar data. Comparisons were made be-
tween horizontal velocity data measured by the lidar, ra-
diosonde and a 1290 MHz wind profiler and are shown
here.
Figure 4 illustrates similarities between horizontal ve-
locities measured by Doppler lidar and radiosonde: the
radiosonde was launched at 1000 UTC and the azimuth
scan was performed from 1000 UTC to 1005 UTC.
When this data was taken it is considered that the bound-
ary layer top was at around 800 m, and the lidar data be-
comes noisy, and therefore un-useable, above this level.
Another comparison was made between the UFAM
Doppler lidar data and the University of Manchester op-
erated, UFAM funded 1290 MHz wind profiler. This
is illustrated in Figure 5. As with the radiosonde data
(Figure 4), it can be seen that there are similarities be-
tween the two datasets. There are some areas of small
scale differences, but generally the two remote sensing
instruments are providing comparable data. Having es-
tablished that the Doppler lidar is a suitable instrument
to make atmospheric measurements, and that the ambi-
ent conditions were appropriate, more complex calcula-
tions could be performed to investigate other parameters
such as QH .
The chosen method assumes unstable conditions, so to
confirm whether this was the situation for the 15th July
2007 case, potential temperature profiles were derived
from two radiosonde ascents launched from the Achern
site. These profiles, suggesting unstable conditions are
shown in Figure 6.
4 Methodology
Having established unstable conditions, it was possible
to calculate QH from the vertical velocity-potential tem-
perature covariance term (w′θ′) in (4.1) following the
procedure outlined in GAL-CHEN et al. (1992):
g
θ0
w′θ′ = 1
ρ0
w′
∂p′
∂z
+ ε3 +
∂
∂z
(1
2w
′3
)
(4.1)
WYNGAARD and COTE´ (1971) and DAVIS et al.
(2008) found that the pressure term, ∂p′∂z , was small com-
pared with the other terms of (4.2) for unstable condi-
tions and will therefore be ignored in the subsequent
analysis, which can be applied only to cases of convec-
tion, hence:
w′θ′ ≈
θ0
g
[
∂
∂z
(1
2w
′3
)
+ ε3
]
(4.2)
Figure 5: Vector plot from UFAM 1290 MHz wind profiler showing
similar features to the lidar (Figure 2), with easterlies early in the
morning, becoming southerly as the morning progresses and veering
westerly in the afternoon.
Figure 6: Potential temperature profiles on 15/07/07 suggesting
unstable conditions.
The mean vertical velocity, w, is calculated for each
range gate and averaged over the 25 minute scan period.
This is done for each of the nineteen 30 m-long range
gates, from 135 m to 705 m, using data from a verti-
cally pointing stare scan. The w’ is the deviation from
the mean vertical velocity. Then, w’3 is calculated for
each point and averaged over the 25 minute scan dura-
tion to form a profile of w′3.
In order to use (4.2) to calculate w′θ′, it is also neces-
sary to estimate ε. One way of estimating ε is to exam-
ine the line spectra of the longitudinal velocity correla-
tion. In the inertial subrange, the expected relationship
is (BATCHELOR, 1967):
f(κ) = αε2/3κ−5/3 (4.3)
where κ is the wave number, α is a universal constant
(0.5) and f(κ) is the Fourier transform of the longitudi-
nal velocity correlation. A -5/3 slope indicates the pres-

Meteorol. Z., 18, 2009 Davis et al.: Doppler lidar observations 159
Table 2: Errors associated with Doppler lidar calculations of ε and w′2.
Error type and extent
Vertical velocity variance,w′2 Bias = 0.02 m2 s−2 PEARSON et al., 2008
Random =±0.68 m2 s−2
Turbulent kinetic energy Error = 10 % FRELICH and CORNMAN, 2002
dissipation rate , ε
Figure 7: Spectrum from the GAL-CHEN et al. (1992) spatial
method. A -5/3 gradient indicates the presence of the inertial sub-
range.
Figure 8: Temporal spectrum as reported by CHAMPAGNE et al.
(1977). The -2/3 slope highlights the presence of the inertial sub-
range.
ence of an inertial subrange and is shown in Figure 7.
This will be referred to henceforth as the spatial spec-
tra method. We calculate the spectra for each ray from
135 to 705 m and average the spectra over the 25 minute
time period.
An alternative method for calculating spectra is pro-
posed by CHAMPAGNE et al. (1977). Here, Taylor’s Hy-
pothesis (STULL, 1988) is assumed and is used to cal-
culate the wave number. The u is calculated from the li-
dar data using VAD analysis. The u is the average mean
wind over the 135–705 m height range. The spectrum
can be calculated from:
nS (n) = 0.68ε2/3
(2pin
u
)
−2/3 (4.4)
where S(n) is the spectral energy of frequency n and
u is the mean wind speed. Here, the inertial subrange
is characterized by a –2/3 gradient and is shown in Fig-
ure 8. This will be referred to henceforth as the temporal
spectra method.
When performing spectral analysis to obtain ε, the
data were detrended to remove any nonstationary be-
haviour. However, errors are still expected, and these are
listed in Table 2.
With unstable conditions, QH can thus be calculated
from:
QH = ρ0CPw′θ′ (4.5)
taking CP , the heat capacity of air at constant pressure,
as 1004 J k−1 kg−1 K−1, ρ0, the air density, as 1.275
kg m−3 and where is the potential temperature-vertical
velocity covariance calculated in (4.2) (GAL-CHEN et
al., 1992). (4.3) also assumes unstable conditions, which
were present on this day as illustrated in Figure 6.
5 Results
The Salford Autonomous Doppler Lidar System was de-
ployed for COPS in Achern, Germany, where it col-
lected data almost continuously for 3 months. A case
study of convective development is described here and
the results include turbulence spectra and some time-
series of ε and QH . Figure 7 shows a spectrum produced
from a vertically-pointing stare taken at 1100 UTC on
the 15th July 2007 in order to obtain a single value of ε.
The spectrum in Figure 7 was calculated using the spa-
tial method presented by GAL-CHEN et al. (1992). In
addition, in order to confirm the results shown in Fig-
ure 7, spectra were also plotted using the same dataset
and the method proposed by CHAMPAGNE et al. (1977)
as shown in Figure 8. The points deviating from the ex-
pected –2/3 gradient at high wavenumbers are consid-
ered to be due to noise (MAYOR et al., 1997).

160 Davis et al.: Doppler lidar observations Meteorol. Z., 18, 2009
Figure 9: Eddy dissipation rates calculated from Doppler lidar data
using both spatial and temporal methods on 15/07/07.
Figure 10: QH timeseries calculated for 15/07/07, showing an esti-
mation of the expected errors. Half-hourly averages of QH , as mea-
sured by the IMK-FZK energy balance station for that day are also
shown.
The time series in Figure 9 illustrates ε, derived from
both temporal and spatial methods, developing through-
out the day as would be expected – increasing towards
noon, peaking at 1500 UTC and then decreasing towards
the evening, as convection is developing in the morn-
ing and then dissipating in the evening (STULL, 1988).
With the estimates for ε and vertical velocity fluctua-
tions (w′3), QH was calculated, as illustrated in Figure
10. It was decided that although the ε values were sim-
ilar for both spectra, the values derived from the spatial
spectra would be utilised to calculate QH as per GAL-
CHEN et al. (1992). Figure 10 also shows a timeseries
of QH , measured using an Energy Balance Station at
the COPS operation centre, Baden Airpark, 10 km north
of Achern where the Doppler lidar was located, but still
in the Rhine Valley.
Figure 11: QH from Doppler lidar data and WRF model data.
When considering the results achieved using the data
collected with the Doppler lidar, certain factors need to
be considered, for example, how did the results com-
pare with other measurements? Figure 10 shows the li-
dar data plotted against data collected from an energy
balance station, located at Baden Airpark, 10 km to the
north of the Doppler lidar. The energy balance station
made point measurements of QH , at a single point in
time, at the surface and averaged over half an hour. The
measurements made by the lidar are averages over the
depth of the boundary layer up to 705 m and while show-
ing a general trend, cannot be the same for the following
reasons:
• The two instruments were not collocated;
• The lidar, as a remote sensor, provides a volume
average over a pencil-shaped beam, over a range of
120 m to 705 m above the surface.
The QH values measured by the lidar are higher than
those measured at Baden Airpark. It is considered that
the relatively high values of QH calculated from the
lidar data compared with those from the energy bal-
ance station result from the nature of the instruments
and their associated ‘footprints’ (SCHMID, 1994). Li-
dar measurements are averaged over the lowest ∼700
m of the boundary layer and so have larger footprints
than ground based instruments, in the order of several
kilometres. WOOD and MASON (1993); BELCHER and
WOOD (1996) and WOOD et al. (2001) discuss the ef-
fects of increasing form drag and roughness length when
flow is directed across orography such as the mountains
to the east of the Achern site. Since the mountains are
some 8 km away, within the fetch of the lidar it is con-
sidered that it the high eddy dissipation rates are due to
this orography. These high values greatly influence the
magnitude of the QH . The instruments at Baden Air-
park are at surface level so have lower fetch and are un-
likely to be affected by the orography. It should also be

Meteorol. Z., 18, 2009 Davis et al.: Doppler lidar observations 161
noted that, on this occasion, the synoptic situation indi-
cated that the convergence line mentioned in section 3
was more active to the north of Achern.
Despite these differences, the results are comparable,
having a reasonable order of magnitude and showing a
diurnal trend as expected.
Output from the NERC WRF model runs for this day
is shown in Figure 11. These data also show a diurnal
trend, similar to those shown in Figure 10. It is not real-
istic to expect remotely sensed data to replicate the re-
sults from a computer model, but as with the surface val-
ues, the results are within the same order of magnitude,
there is a similar trend in the model output, with values
rising towards noon and dropping towards sunset. It is
interesting to note that where the model output suggests
high heat flux values at 0800 UTC, the lidar does not.
Although the measured QH values were comparatively
high, at around 1500 UTC these values were unrealisti-
cally so. It is thought that this may be due to a mesoscale
event that occurred at about 1500 UTC that day as men-
tioned previously. Investigations into this are ongoing.
6 Conclusions and future work
It has been shown that by using a method outlined by
DAVIS et al. (2008), GAL-CHEN et al. (1992), it is pos-
sible to calculate values of QH and it is considered that
these values fall within an acceptable range. It is noted
that the diurnal cycle of the lidar-derived QH is closer to
the diurnal cycle of ε, whereas both the model and sur-
face measurements of QH peak earlier in the day. QH
calculated from Doppler lidar data using the method de-
scribed here would be expected to differ from that cal-
culated using a surface based ‘point’ sensor such as an
energy balance instrument or a sonic anemometer; since
the data collected with a Doppler lidar is integrated over
a ‘volume’ of atmosphere aloft, advecting through the
laser beam. However, these measurements are a useful
addition to the other measurements provided by the li-
dar, and require no extra equipment.
It is considered that further investigations of employ-
ing this method to calculate QH are needed to establish
the overall applicability of the method and build on the
preliminary calculations. It is expected that such inves-
tigations will include:
• Calculation of ε using alternative methods;
• investigation of ε at different heights and atmo-
spheric conditions;
• verification of Doppler lidar estimations of ε and w′3;
and
• investigation over different surface types.
Acknowledgments
The authors would like to acknowledge Dr. N. KALT-
HOFF at IMK FZK Karlsruhe for supplying QH data
from their energy balance station located at Baden Air-
field, Germany, collected as part of COPS, July 2007.
Also Dr. A. GADIAN from the University of Leeds, for
his help in securing the WRFmodel output; Dr. E. NOR-
TON from the University of Manchester, for making the
UFAM 1290 MHz wind profiler quicklook plots avail-
able online; H.P. SCHMID for the use of the flux source-
area model (FSAM); finally, UK COPS, for funding
through NERC.
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