Pavlos Kollias, Bruce A. Albrecht and Benjamin J. Dow

1
TURBULENCE AND MICROPHYSICAL RETRIEVALS USING
MM-WAVELENGTH DOPPLER SPECTRA

Pavlos Kollias, Bruce A. Albrecht and Benjamin J.
Dow Rosenstiel School of Marine and Atmospheric
Science (RSMAS), University of Miami
INTRODUCTION
TURBULENCE RETRIEVALS
Millimeter wavelength Doppler radars operating at
94 GHz (e.g. Lhermitte 1987) have high temporal
and spatial resolution, extreme sensitivity, and
high velocity resolution. Due to their short
wavelength, millimeter radars are capable of
detecting very small droplets. This capability of
millimeter wave radars has established them as
the ultimate observing systems for the study of
weak meteorological targets undetectable by
conventional weather radars. Parallel with the
development of millimeter wavelength radars,
retrieval techniques for the estimation of cloud
and drizzle drop distributions were developed
(Gossard 1994 Frisch et al., 1995 Babb et al.,
1999). In this paper, some new ideas on the use
of millimeter wavelength Doppler spectra for the
retrieval of turbulence and microphysical
parameters are considered in an attempt to
emphasize the importance of recording the Doppler
spectrum.
In the case of fair-weather cumuli and
non-drizzling stratus layers, cloud droplets are
the main source of backscattering. The terminal
velocity of a cloud droplet is small, (0.3 cm s-1
and 7 cm s-1 for a 10µm and a 50µm droplet,
respectively) so that the droplets vertical
velocity is primarily due to air motion and
turbulence. The cloud droplets inertia is small
so they are good tracers of turbulent air
velocity in the same way that smoke particles
reveal turbulent eddies in a smoke filled room.
The time-height mapping of the mean Doppler
velocity reveals the cloud internal circulation
structure in terms of updrafts-downdrafts
(Kollias and Albrecht, 2000 Kollias et al.,
2001) that can use to analyze the internal
dynamics and the interaction between the cloud
and its environment. Examples of Large-Eddy
Observations (LEO, Figs. 1-3), power spectra of
vertical velocity time series (Fig. 4) and
calculations of fractional area of updrafts and
downdrafts (Fig. 5) using direct sampling or the
statistics of the vertical velocity (Randall et
al., 1992) in a non-drizzling marine stratus are
shown in the above figures.
I/Q AND MICROSHEAR
A variation of 2 ms-1 across the beam cross
section, which is likely to happen in a fair
weather cumulus, will create a very large
spectrum variance. Fair-weather cumuli are highly
turbulent. We often observe Doppler spectrum
bimodality that indicates the presence of sharp
vertical velocity gradients such as those in the
region between adjacent updrafts and downdrafts
(Albrecht et al, 2001).
For a typical cloud droplet distribution, the
expected spread of the droplets terminal
velocities (0.3 to 10 cms-1) and the associated
Doppler spectrum variance will be only a few
cm2s-2. As a result the observed Doppler spectrum
width arises from turbulence and systematic
variation of the vertical wind across the beam.
Depending on the character of the systematic
variation of w across the beam, either wide or
bimodal spectra can be produced.
Fig. 6 Mean Doppler velocity estimates using FFT
calculated using raw I/Q time series in a cirrus
cloud. 2,500 I/Q pairs were used for each FFT.
The data were collected within (black) and above
(red) a cirrus fallstreak. Notice the
high-resolution mean Doppler variability within
the fallstreak caused by micro-shear.
Fig. 7 Examples of FFTs (top) calculated using
raw I/Q time series (2,500 pairs 0.5 sec dwell
time). The data correspond to the time period
26-30 sec in Fig. 6. Bottom The resulting
Doppler spectra if all the I/Q data were used for
the calculation of a single FFT. Notice the
spectra broadening due to the linear variation of
w.
Fig. 8 Simulation of Doppler spectra for
different types (linear (top left) and
step-function (bottom left)) of sub-resolution
volume cross-radial wind variation. Linear wind
fields result in Doppler spectrum broadening.
Discontinuous (step function) wind field profile
results in bimodal Doppler spectrum.
Fig. 9 Time-height mapping of Doppler spectrum
width in a fair-weather cumulus. The white
contour represents the 1.5 ms-1 contour
identified as the updraft boundary. Note the
large spectrum width values near the updraft
boundary.
Fig. 10 Top Cross section of mean Doppler
velocity (blue) and Doppler spectrum width at
1.55 km altitude within the fair weather cumuli.
Note the large values of spectrum width
associated with large wind shear zones at the
updraft boundaries. Bottom Example of bimodal
spectra near the updraft boundaries.
MICROPHYSICAL RETRIEVALS
CONCLUSIONS
Frisch et al., (1995) demonstrate a retrieval
technique for drizzle microphysical parameters
using the Doppler moments. Assuming a lognormal
drizzle size distribution, the parameters
(N-concentration, ro-modal radius and
?x-lognormal distribution width) are retrieved by
the first three Doppler moments. While the
assumption that the drizzle distribution controls
reflectivity and mean Doppler velocity is
plausible, especially if conditional sampling
(threshold values for dBZ and mean Doppler) is
applied to the data set, this is not clear for
the Doppler spectrum width. The width of the
lognormal size distribution is parameterized as
the ratio of the second and first moment of the
Doppler spectrum. Data from the Drizzle and
Entrainment Cloud Study 99 (DECS99) experiment
show that the turbulence contribution to the
second moment is large and has to be removed.
Otherwise, ?x and N will be significantly
overestimated and ro underestimated. Fig. 1 shows
time series of standard deviation of mean Doppler
velocity (dashed line) and Doppler spectrum width
(solid line). The variance of the mean Doppler
velocity ?2w is an indicator of turbulence
intensity at scales larger than the sampled
volume, while the Doppler spectrum variance ?2 is
an indicator of turbulence intensity within the
sampled volume. During non-drizzling periods the
main contributor to Doppler spectrum width is
turbulence and thus ?t R??w (R?1 in our case).
In general, the ratio R ?t/?w can be estimated
theoretically from the Kolmogorov turbulence
theory. During drizzling periods

?2 ?2t ?2DSD.
Therefore we need to correct the Doppler spectrum
width for turbulence broadening. This is done by
using the ?w during the drizzling period and the
estimate of R from non-drizzling periods. In
other words, we assume that the variance due to
the drizzle drop size distribution (DSD) can be
estimated from the difference between the Doppler
spectrum variance and the mean Doppler velocity
variance at the same altitude
The recorded Doppler spectra from millimeter
wavelength radars can be used to obtain critical
information on microphysical processes and their
interaction with updraft and downdraft
structures. As the retrieval techniques for cloud
radar become more sophisticated, it will be
possible to further advance our understanding by
providing critical observations for process
studies and the direct evaluation of cloud
models.
The lognormal size distribution width ?x is given
at the ratio of the ?DSD and the mean Doppler
velocity (Frisch et al., 1995). Our modification
to the original Frisch technique can lead to more
realistic microphysical retrievals since the
turbulence broadening is essentially removed.
Finally, higher Doppler spectra moments can be
incorporated into the retrieval algorithm. The
data have showed a remarkable correlation between
the mean Doppler velocity and the Doppler
spectrum skewness. Although turbulence acts as a
smearing mechanism and partially removes the
asymmetry of the Doppler spectrum caused by the
large drops velocity tail, the skewness of the
Doppler spectrum can be expressed as a function
of the lognormal size distribution parameters and
therefore can be used to enhance the robustness
of the retrievals.
REFERENCES
Albrecht, B. A., P. Kollias and B. J. Dow, 2001.
Millimeter-wavelength radar observations of
updrafts, downdrafts and turbulence in fair
weather cumuli, 30th International Conference on
Radar Meteorology, Munich, Germany, 19-24 July
2001. Babb, D., J. Verlinde and B.A. Albrecht,
1999. Retrieval of cloud microphysical parameters
from 94-GHz radar Doppler power spectra. J.
Atmos. Oceanic Tech., 16, 489-503. Gossard E.
E., 1994 Measurements of cloud droplet size
spectra by Doppler radar. J. Atmos. Oceanic
Tech., 11, 712-726 Frisch, A.S., C.W. Fairall
and J.B. Snider, 1995. Measurement of stratus
cloud and drizzle parameters in ASTEX with a K?
band Doppler radar and microwave radiometer. J.
Atmos. Sci., 52, 2788-2799. Istok, M.J. and R.J.
Doviak, 1986. Analysis of the relation between
doppler spectral width and thunderstorm
turbulence. J. Atmos. Sci., 42,
607-614. Kollias, P. and B.A. Albrecht, 2000.
The turbulent structure in a continental
stratocumulus cloud from millimeter-wavelength
radar observations. J. Atmos. Sci., 57,
2417-2434. Kollias, P., B.A. Albrecht, R.
Lhermitte and A. Savtchenko 2001. Radar
Observations of Updrafts, Downdrafts, and
Turbulence in Fair Weather Cumuli. J. Atmos.
Sci., 58, 1750-1766. Randall, D. A., Q. Shao,
and C-H Moeng, 1992 A second order bulk
boundary-layer model. J. Atmos. Sci., 49,
1903-1923.
Figure 13 Modal radius time series of the
drizzle modal radius (?m) at gate 3, 260 m over
the time interval 1320 UTC to 1430 UTC.
Fig. 11 Time series of the standard deviation of
the mean Doppler velocity (average time 5
minutes) (dashed line) and standard deviation of
the Doppler spectrum (solid). The circles at the
top of the graph show the drizzling periods.
Figure 12 Microphysical retrievals of drizzle
modal radius (?m), number density (lt-1),
logarithmic width (?x), and liquid water content
(gm-3). The data from the radar at each gate are
averaged over the time interval 1340 UTC to
1345 UTC.
Fig. 14 Time series of Mean Doppler velocity and
Doppler spectrum skewness during a drizzling
period.