We present the derivation of turbulent energy dissipation rate

Turbulence is an essential atmospheric motion over a wide range of length
scales and timescales. It plays an important role in determining the
evolution and structure of the free atmosphere as well as the trace gases and
pollutants in it; this role is, however,
far from being fully understood

Atmospheric turbulence is normally characterized by the energy dissipation rate

Triggered by the pioneering work by

MST radars have been widely used to study turbulence in the lower and middle
atmosphere based on the conversion of spectral width to the dissipation rate

The MST radar echoes are caused by scattering or reflection from
irregularities of the atmospheric refractive index. Details of these
mechanisms are described by, for example,

MAARSY is a monostatic radar
operating at a frequency of 53.5 MHz in coherent scatter mode

Basic parameters of MAARSY.

The data sets presented in this study were obtained with MAARSY for
tropospheric experiments during the period of 2010–2013 (a total of
522 days) consisting of three sequences based on different experimental
configurations. The data acquisition and data analysis of raw data were
routinely carried out with a commercial software package. The histogram in
Fig.

Length of data set in different months available for the current study during the period of 2010–2013.

MAARSY has the capacity to steer the beam on a pulse-to-pulse basis allowing
us to measure the radial velocities for several different beam directions in one
experiment. Here we make use of the Doppler beam swinging (DBS) technique to estimate horizontal wind
fields (both zonal and meridional) from five beams (one in the vertical
direction and four at an off-zenith angle of 10

Figure

Height–time cross sections of echo power from the radar measurements with MAARSY and temperature derived from the ECMWF reanalysis data as well as horizontal winds and spectral widths with MAARSY from the uppermost to lowermost panels, respectively, during the period of 13 July–10 August 2013. The lines (in the upper two panels) indicate the tropopause height according to temperature profiles from ECMWF: red line for lapse rate tropopause (LRT) and black for cold point tropopause (CPT).

In this section, the

There are several ways to derive estimates of the turbulent energy
dissipation rate from clear-air radar observations. These methods include

Spectral widths have been estimated from the correlation time

Profiles of spectral width (

In the left two panels of Fig.

The data presented here were analysed with a commercially available software
package, which does not provide statistical uncertainties to the estimated
parameters, i.e. the spectral width or radial velocity. As already described, these parameters are derived from the ACF of the measured time series.
Typically 256 or 512 points are recorded after some coherent integrations
(CI), which range between 64 and 256 CI for the data analysed here. In order to
obtain an estimate of the statistical uncertainties, we applied a more
sophisticated approach by fitting a truncated Gaussian to the measured
spectra. The fitting routine is based upon the concept presented in

Basic information of the 14 radiosondes including the launch and end times (UTC), the maximum height (m), the simultaneous radar measurements for comparison, and the measurement noise (mK).

During the WADIS sounding rocket campaign in 2013

Meteorological RS provide measurements of pressure (

The Thorpe analysis consists of rearranging an observed profile of potential
temperature

Vertical profiles of the atmospheric parameters inferred from the
radiosonde on 29 June 2013 at Andøya:

Vertical profiles of the derived dissipation rates from radiosondes
(significant layers in black and non-significant layers in grey) with the
median profile (in blue) and from radar (in red). Here all turbulent layers, including both significant and non-significant ones, from radiosondes were
calculated as median for the comparison with the radar results. Please note
the different height resolution of both instruments: 5 m for radiosondes
and 300 m for radar. In order to compare the radar and radiosonde values
one-to-one, we infer the median of radiosonde

The analysis in this study is performed according to

The basic information of the 14 radiosondes including measurement noise is listed in Table

In Fig.

Scatter plots of the turbulent energy dissipation rates derived from
the simultaneous measurements with radiosondes and radar. Left panel: the
results derived based on the measurements during two flights on 1 July 2013
(i.e. the profiles shown in blue and red in
Fig.

As mentioned above, the comparisons between the remote sensing observations with radar and the in situ measurements are desirable in order to ensure their reliability. With the simultaneous measurements of collocated radar and balloon-borne radiosondes in hand, we are able to validate the radar estimates of turbulent energy dissipation rate by a comparison between both techniques.

Histograms of the derived dissipation rates from radiosondes (left
panel) and radar (middle panel) based on the simultaneous measurements during
the WADIS campaign in 2013. All turbulent layers, including both significant
and non-significant ones, from radiosondes are taken into account. In order to
compare the

Histogram of the logarithm of the derived

Scatter plots of turbulent energy dissipation rate derived from the radar observations with MAARSY in the years of 2011–2013 for different months and the corresponding median values shown in red (solid lines).

Before going into detail, we should note that the two instruments do not
measure the same volume (i.e. they have a different horizontal coverage) and
their height resolutions are quite different: 5 m for radiosondes and 300 m
for radar. In Fig.

We further show scatter plots of the derived

Vertical profiles of the seasonal medians of

Given the large variability of turbulent energy dissipation rates and the
difference between the two techniques (see the caveats mentioned above), the
only fair method is to compare their statistical results. There are 9 flights
of radiosondes out of 14 during the WADIS sounding rocket campaign in 2013
with simultaneous radar measurements. The histogram of the

In a nutshell, the comparison is very encouraging in that the derived

In this section, we apply the analysis described in Sect. 3.1 to all the data
available to derive a preliminary climatology of turbulent energy dissipation
rate

Histograms of energy dissipation rates

Scatter plot of energy dissipation rates

Further, we show scatter plots of

In order to illustrate the seasonal variation of the energy dissipation
rates, we show the vertical profiles of the

Due to the importance of turbulence in atmospheric dynamics, a wealth of
theoretical and experimental efforts has been carried out to identify the
generation mechanisms, which are not fully quantified or understood

Number density of the derived turbulent energy dissipation rate

As mentioned above, a classical approach to analysing the relation between
turbulence and the atmospheric background condition is to determine the
Richardson number

Histograms of the derived turbulent energy dissipation rates

Wind field also plays a role in the generation of turbulence
(indirectly), since there is a strong interaction between gravity waves (GWs)
and the background wind field

Scatter plot of the turbulent energy dissipation rates

Same as Fig.

Same as Fig.

According to Eq. (

In the current paper we have presented the derivation of the turbulent energy
dissipation rate

From a total of 522 days of observations with MAARSY during the period of
2010–2013, we derived a preliminary climatology of turbulence in the free
atmosphere. The derived

With the derivation of wind shear from radar and the Brunt–Väisälä
frequency

In order to study the influence of background wind fields on turbulence, we
presented the number densities of

Last but not least, we compared the derived

The data sets with the MAARSY radar used in this study are stored in the Leibniz-Institut für Atmosphärenphysik (IAP) repository and are available upon request (contact email: chau@iap-kborn.de). The radiosonde data sets can be requested by contacting the first author of this paper.

In homogeneous (isotropic) turbulence, the turbulence intensity is usually
represented as the turbulent kinetic energy per unit mass (

For stationary turbulence, i.e.

The authors would like to thank J. L. Chau for support in MAARSY data handling. Q. Li and M. Rapp acknowledge support by the German Ministry for Education and Research (BMBF) in the scope of the ROMIC-GWLCYCLE Project. Support for A. Schön and G. Stober was provided by the BMBF ROMIC-METROSI Project and for A. Schneider by the International Leibniz Graduate School for Gravity Waves and Turbulence in the Atmosphere and Ocean (ILWAO) funded by the Leibniz Association (WGL).The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association.The topical editor, V. Kotroni, thanks two anonymous referees for help in evaluating this paper.