We present the first measurement of the sensible heat
flux (
The energy reaching the earth surface in form of solar radiation during
the daytime is partly reflected as outgoing radiation, partly conducted into the
ground and partly transported into the atmosphere by turbulent eddies of
various scales forming the convective boundary layer (CBL) during the daytime
(LeMone, 2002). The latter energy flux partitions into sensible heat flux
The variance of humidity and temperature at the CBL top determines cloud formation (Moeng and Sullivan, 1994). Weckwerth et al. (1996) found strong variability in the moisture structure in the CBL due to the presence of horizontal convective rolls. The coherent perturbations of temperature and moisture in these rolls influence the formation of deep convection (Weckwerth et al., 1999). Also, surface flux partitioning is an important parameter for studying convection initiation (e.g., Gantner and Kalthoff, 2010; Adler et al., 2011; Behrendt et al., 2011; Kalthoff et al., 2011) and land–atmosphere feedback (Santanello et al., 2018). Clearly, not only the mean structure of moisture in the CBL is important but also the variance profiles due to their contribution to the variance budget (Lenschow et al., 1980). At the same time, variations in the humidity structure also influence precipitation patterns (Dierer et al., 2009).
It is difficult to parameterize these sub-grid-scale moisture variations in
cloud, convection, and turbulence-resolving models (Moeng and Sullivan,
1994). Shallow cumulus parameterizations (e.g., Bretherton and Park, 2009;
Neggers, 2009; Berg et al., 2013) are used in mesoscale models which do
not resolve the turbulent eddies to approximate their effects. These schemes
are decisive for the correct simulation of clouds and precipitation. To
verify these parameterizations in weather prediction models, not only
monitoring of the mean CBL thermodynamic structure (e.g., Milovac et al., 2016), but also measurements of higher-order moments of turbulent
fluctuations of the thermodynamic variables (like variances, skewness,
kurtosis) and their covariances (like
It is clear that in situ measurements performed from airborne platforms (e.g., Grunwald et al., 1996, 1998; Bange et al., 2002) can only sample the atmosphere stepwise. Recently unmanned aerial vehicle systems were used for the estimation of water-vapor fluxes in the CBL (Thomas et al., 2012). However, in situ measurement systems cannot obtain the total vertical profile simultaneously and continuously over longer measurement periods, though it is very important to derive the flux divergence.
In recent years, it has been demonstrated that lidar, a laser remote-sensing technique covering the CBL, is capable of not only determining mean profiles and gradients in the daytime CBL, the interfacial layer, and the lower free troposphere above but also higher-order-moment profiles of turbulent fluctuations for more and more variables: vertical wind (e.g., Frehlich et al., 1998; Lenschow et al., 2000, 2012; Lothon et al., 2006, 2009; Hogan et al., 2009; O'Connor et al., 2010; Lenschow et al., 2012), humidity (Kiemle et al., 1997; Wulfmeyer, 1999a; Wulfmeyer et al., 2010; Lenschow et al., 2000; Couvreux et al., 2005, 2007; Turner et al., 2014a, b; Muppa et al., 2016; Di Girolamo et al., 2017), aerosol backscatter (Pal et al., 2010), and – most recently – also temperature (Behrendt et al., 2015; Di Girolamo et al., 2017). Consequently, large-eddy-simulation (LES) models can be evaluated with the synergy of temperature, humidity, and wind lidar systems (Heinze et al., 2017) and new parameterizations can be developed (Wulfmeyer et al., 2016, 2018).
First measurements of virtual heat flux with a remote-sensing technique,
were presented by Peters et al. (1985) by combining a sodar for vertical
wind measurements and a radio acoustic sounding system (RASS) for virtual
temperature measurements reaching heights of up to 188 m above ground level (a.g.l.). With the
combination of a radar wind profiler and a RASS, the range of virtual heat
flux measurements could later be extended up to a few hundred meters
(Angevine et al., 1993a), and comparisons with aircraft measurements were
made for the average of a 7 d period reaching up to 0.8
First
While all the abovementioned measurements were made in the CBL – which
means in the daytime – Rao et al. (2002) presented nighttime water-vapor Raman
lidar measurements in combination with sodar measurements estimating
Lidar flux measurements of other trace gases than water vapor were
discussed, e.g., by Senff et al. (1996), who combined an ozone DIAL and a
RASS for measuring turbulent ozone fluxes, and by Gibert et al. (2011), who
combined a
While there has been great progress for measuring all these different types
of fluxes in the atmospheric boundary layer in recent years, profiles of
An overview of the instruments is given in Sect. 2. The methodology is described in Sect. 3. The results are presented and discussed in Sect. 4. Finally, a summary and an outlook are given.
Rotational Raman lidar makes use of Raman signals of atmospheric molecules
(mainly
Doppler lidar measures the radial wind velocity via the Doppler shift of
laser radiation scattered in the atmosphere (e.g., Werner, 2005). In this
study, we used data of the heterodyne Doppler lidar Wind-Tracer WTX of
Lockheed Martin Coherent Technologies, USA, operated by the Karlsruhe
Institute of Technology (KIT) (Träumner et al., 2014). The lidar
transmitter is a Er:YAG laser that emits laser pulses at a wavelength of 1.6
In the following, we also introduce briefly the WVDIAL of the University of Hohenheim (UHOH) because we show latent heat flux profiles for comparison. WVDIAL provides absolute humidity profiles with high temporal and spatial resolution in the lower troposphere (Wulfmeyer and Bösenberg, 1998). During the HOPE campaign (see Sect. 4.1 below for definition; Macke et al., 2017), the scanning water-vapor WVDIAL of the University of Hohenheim (Wagner et al., 2013) was operated in vertical mode during clear-sky conditions and in scanning mode during cloudy periods (Späth et al., 2016). The operational wavelength of the UHOH WVDIAL is near 818 nm. The laser transmitter was switched shot by shot between the online and offline frequencies. The backscatter signals were recorded for each laser shot (250 Hz) with a range resolution of 15 m. The measured absolute humidity has typical temporal and spatial resolutions of 1 s to 1 min and 15 to 300 m, respectively, depending on the range of interest. Due to the instrument's high laser power (about 2 W) in combination with a very efficient receiver (0.8 m telescope), the data have low noise uncertainties up to the CBL top. When deriving absolute humidity from the UHOH WVDIAL data used in this study, 10 s averages and a gliding window length of 135 m for the Savitzky–Golay algorithm (Savitzky and Golay, 1964) were used, resulting in a triangular weighting function with a full width at half maximum of about 60 m.
Lenschow et al. (2000) introduced a procedure for the estimation of higher-order moments of turbulent fluctuations that accounts for random instrumental noise. We follow this method for resolving the turbulent moments of temperature, vertical wind, and humidity for estimating instrument noise uncertainties. Further, important refinements were presented in Wulfmeyer et al. (2016) such as automated spike detection and the proper choice of lags used in the autocovariance analyses.
The flux profiles in the CBL were calculated using the eddy covariance method (see, e.g., Senff et al., 1994; Wulfmeyer, 1999b). The data processing procedure is described in detail in Wulfmeyer et al. (2016). In the following, we explain the method with the sensible heat flux as an example; the measurement of the latent heat flux works in an analogous way. First, temperature and wind data measured by the TRRL and Doppler lidar, respectively, were despiked. This means that histograms of the data at each height were calculated for the selected period, and then all data outside of 4 standard deviations from the median were removed. Other authors (Turner et al., 2014a, b) refined the despiking of noisy lidar data by also considering non-Gaussian distributions and asymmetric despiking thresholds on either side of the histogram, but we found that for the case shown here such further refinements do not change the results significantly. A despiking procedure is required because the lidar data analysis algorithms are non-linear and noise in the data may result in large (non-linear) outliers in some cases.
In a second step, the despiked temperature data were detrended using a
linear fit at each height level. This procedure is required in order to
focus on the turbulent fluctuations by removing influences of large-scale
advection, synoptic processes, and the diurnal cycle. Detrending means that
the time series of the scalar observations
In case of the wind data
In practice, both despiking and detrending has to be performed with caution
in order not to eliminate real atmospheric features. This means that the
time series of data should be investigated first and only quasi-stationary
time series with small trends in the scalar (
Before the scalar and wind time series can be combined, one must ensure in a third step that the time and height for each data point are as close as possible. For this, we gridded the data to closest neighbors.
The correlation of the temperature fluctuations
For the lidar data, which are discrete in time, Eq. (2) results in
The instrumental noise uncertainty and the representativeness uncertainty play a major role when deriving the statistics of turbulent fluctuations in the atmosphere with noisy data (Lenschow et al., 1994, 2000). The noise uncertainty is due to the instrumental noise of the lidar data. The uncertainty due to sampling only a limited period of time covering a limited number of turbulent eddies is referred to as representativeness uncertainty or sampling uncertainty.
Fortunately, when
This can be understood by splitting the fluctuations into an atmospheric part
and into a noise part according to
Inserting Eqs. (4) and (5) in Eq. (3) yields
But even though there is no noise term to be subtracted when determining
fluxes from noisy data, of course, there still remains an uncertainty of the
flux value due to noise: because the real atmospheric data set is always of
a finite length, the noise terms do not cancel fully. This noise uncertainty
of the covariance of the fluctuations of a scalar
Equation (8) can be further approximated and rearranged so that the relative noise of the covariance is expressed with the relative noise variances according to
In order to identify these atmospheric variances of the temperature and
vertical wind fluctuations, we use the method of Lenschow et al. (2000) to
separate the noise variance from the total variance: the atmospheric
variance
After the noise uncertainty profiles have been determined from the variance
analysis for both the temperature and vertical wind measurements,
The representativeness uncertainty or sampling uncertainty of the flux
expressed as a variance is the square of the difference of the mean flux
An upper limit of the representativeness uncertainty can be obtained from
the minimum of the integral timescales of vertical wind
The vertical divergence of the sensible heat flux can be related to a
temperature tendency via
With the lidar data, we obtain the fluxes in the lower part of the CBL and
at the CBL top simultaneously. Thus, we get the temperature trend due to
flux divergence in the observed part of the CBL with
In a similar way, the divergence of the latent heat flux is related to the
moisture tendency in the CBL via
The data used in this study were collected during the HOPE campaign (Macke
et al., 2017). HOPE stands for the HD(CP)
In this study, we use data collected on 24 April 2013, the HOPE intensive observation period (IOP) 6. The HOPE domain was under the influence of an anticyclone located over central Europe on this day (see also Behrendt et al., 2015; Muppa et al., 2016). At the lidar site, the CBL was well developed by 10:00 UTC (Muppa et al., 2016). We selected the period from 11:05 to 11:50 UTC around solar noon at 11:32 UTC for the analysis of fluxes. Similar periods have been used regarding separate analyses of higher-order moments of the turbulent wind, temperature, and humidity fluctuations (Behrendt et al., 2015; Maurer et al., 2016; Muppa et al., 2016; Wulfmeyer et al., 2016).
As discussed in Behrendt et al. (2015), the mean of the instantaneous CBL
heights
Figure 1 shows the fluctuations of temperature, humidity, and vertical wind
Time–height cross sections of the measurements of the detrended and despiked fluctuations of
It is interesting to now compare the simultaneous fluctuations of
temperature, humidity, and wind with each other. Updrafts (
The products of vertical wind fluctuations with temperature and with humidity fluctuations are shown in Fig. 2. Positive instantaneous latent heat flux values are dominant throughout the CBL, while the instantaneous sensible heat flux values are dominantly positive in the lower half of the CBL but negative in the upper half.
Time–height cross sections of the fluctuation products
For completeness, Fig. 2 also shows the product of temperature and humidity fluctuations. Apart from noise, the data show partly positive and partly negative values. Positive values indicate that warmer air was moister, while cooler air was drier in the CBL. The fact that there are also negative data points reveals that cooler and moister as well as warmer and dryer fluctuations also appeared simultaneously here.
For the variance data and noise uncertainties presented here, 20 data points
of the structure function were used for the fit, giving a period of 200 s with 10 s resolution
of the data. This is a reasonable number because the first
zero crossing of the autocovariance function
The temperature variance profile in this case shows the typical peak near
the CBL top (Fig. 3b). The value at
The correlation coefficients (Eq. 10) of the lidar data (Fig. 1) are shown
in Fig. 4. Figure 5 shows the sensible heat flux profile
Profiles of the correlation coefficients of the lidar data.
Sensible heat flux
Figure 5 also shows the latent heat flux profile
We have presented the first measurements of sensible heat flux profiles
The data are available from the corresponding author upon request.
AB, SKM, FS, DL, NK, and AW collected and analyzed the lidar data; AB, VW, and CS developed the codes; AB prepared the manuscript, which was improved by all co-authors.
The authors declare that they have no conflict of interest.
This project was funded by the German Federal Ministry of Education and Research within the framework program “Research
for Sustainable Development (FONA)”,
This paper was edited by Laura Bianco and reviewed by three anonymous referees.