The 1 and 20 Hz data are examined from the Electra flights made on July 5, 1987. The flight legs consisted of seven horizontal turbulent legs at the inversion, midcloud, and below clouds, plus 4 soundings made within the same period. The Rosemont temperature sensor and the top and bottom dewpoint sensors were used to measure temperature and humidity at 1 Hz. Inversion structure and entrainment; local dynamics and large scale forcing; convective elements; and decoupling of cloud and subcloud are discussed in relationship to the results of the Electra flight

Baker, M. B.

Bretherton, C. S.

Siems, S. T.

English

NASA Technical Reports Server

N90-28243
Structural Analysis of Stratocumulus Convection
S.T. Siems*, M.B. Bakert and C.S. Bretherton*
*Applied Mathematics Department, _Geophysics Program
University of Washington, Seattle, WA 98195
I. Introduction
In an earlier study (Siems et al, 1989) we found that explosive cloudtop entrainment instability
(CTEI) is possible only when a parameter defined as D is of order unity, where
D = - A0v(Z*)/A0v. (1)
Here Z* is the fraction of environmental air in the exactly saturated mixture of cloudy and environmen-
tal air. A0,(Z* ) is the virtual potential temperature difference of this mixture relative to the unmixcd
cloud, while A0v is the difference between the unmixed fluids.
Our examination of data from the FIRE project and other data sets leads us to conclude that the
enhancement of D is unlikely to ever be sufficient to bring about explosive CTEI under stratocumulus
conditions. It therefore appears that cloud breakup occurs via other processes, possibly related to
decoupling of the cloud and subcloud layers. To better understand this latter possibility, we have inves-
tigated the nature of the turbulent elements and convective motions involved in transport of heat and
moisture in cloudtopped boundary layers. We have sought in particular to test the simple conceptual
picture of the turbulence which has emerged indirectly or by assumption in previous studies of radia-
tively driven Sc in which surface fluxes are weak. According to this picture, negatively buoyant thermal
or plume like structures descend from the bottom of the radiatively cooled layer near cloudtop, merging
to form downdrafts, presumably convective cell edges, within which heat and moisture are transported
down. The return flow is broader and pushes up the cloud-clear inversion into hummocks, creating
baroclinic torques and rebound momentum at the stratified interface. In the absence of overall shear,
these processes should be responsible for entrainment, which is maximum in the intermittent valleys
between hummocks. The descending streams are aided in their downward propagation until cloudbase
by evaporative cooling, to the extent they remain saturated. Purely evaporatively cooled parcels, how-
ever, can proceed downward once they become unsaturated only at the expense of TKE within the
layer. This conceptual model has been explored by Nicholls (1989). The situation in the case that
shear and/or surface fluxes are important has been documented (Brost et al, 1982) but a similar con-
ceptual picture is not available. Since both were important sources of TKE during the FIRE project, we
have investigated the structure of the small scale variability in dynamic and thermodynamic properties
in order to construct such a picture. At the time of writing this abstract we have not had time to com-
pare our results to those of Nicholls (1989), but those comparisons will be presented at the FIRE
workshop. The emphasis of the work at present has predominantly been on small scale features; how-
ever, larger scales are noted throughout.
In this abstract we focus on the following questions:
1) What processes are important in entrainment, where is it maximum and what scales are important?
What is the nature of this mixing across the inversion?
2) To what extent are the local dynamics organised by large scale fluctuations in cloud properties?
(where here large means greater than ten kilometers or so)
3) Which parcels form the roots of the upward moving plumes/thermals at the top of the lower surface
layer, and which form the initial downdrafts at the base of the radiatively cooled layer at cloudtop?
What are the roles of radiative cooling, evaporative cooling and surface fluxes relative to mechanical
forcing in driving these parcels?
4) Is decoupling evident and to what extent does this affect the circulation?
II. Research Methods
We have examined 1 and 20 Hz data from the Electra flights made on July 5, 1987. The flight legs
consisted of seven horizontal turbulent legs at the inversion, midcloud and below cloud, plus 4 sound-
ings made within the same time period. The cloud deck was thin but solid, for the most part, with
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three dimensional structure intermittently noted by the flight scientist. Cloudtop was flat, sloping
upward to the south west. Cloudbase was quite ragged, with intermittent small cumulus clouds below.
We used the Rosemount temperature sensor and the average of the top and bottom dewpoint sen-
sors, lagged by two seconds, for preliminary temperature and humidity measurements at 1 Hz. The
FSSP was working poorly on this day. We therefore used the Johnson-Williams sensor for the 1 Hz
liquid water readings. This data was interpolated to 20 Hz data creating a source of error in the liquid
water content; however, this error this induces in the total water content and 0v is quite small. The
noted drift of the JW sensor is also on this order of magnitude. The Lyman-alpha hygrometer was cali-
brated following the method of Paluch (personal communication 1989) for 20 Hz and corresponding 1
Hz measurements. This gave satisfactory agreement with the dewpoint sensors in cloud, but the cali-
bration is dependent on the relative humidity; extremely dry environmental parcels require special
adjustment. Ozone measurements are useful when crossing the inversion but lose importance in the
cloud layer as the noise exceeds possible shifts.
III. Results
a) Inversion Structure and Entrainment
A typical 20 Hz sounding near the inversion is shown in Figure 1. There is clear evidence of
several individually well-mixed regions, of vertical extent h= 50 meters or less, through which
Qr and 03 are quite constant and between which there are very sharp gradients over less than 1 mb. A
study of the conserved variables shows that these layers (hereafter referred to as intermediate inversion
layers or IILs) are not the product of direct mixing between the cloud and environment at this instant.
Interestingly, the rather homogeneous nature of an individual IIL suggests that it did not arise from a
uniform or gradient mixing process, but rather from a discrete process similar to that of Broadwell &
Breidenthal (1982). Indeed even the transition between IlLs is nonuniform. The IlLs persist for hours
during which they radiatively cool to equilibrium and are sorted by buoyancy. The layers are distinctly
subsaturated, which could not arise from the removal of drops alone.
In examining the overall nature of this inversion region, we find that the velocity jump is approxi-
mately 8 m/s, A0_ about 8 K, and thus the Richardson's number, Ri=g'h/AU z, where g'=gAO_/Ov, is
less than ¼ for h less than 60 m. These regions are thus probably Kelvin Helmholtz vortices forming
near the tops of the cloudy hummocks. Note that from vertical soundings it is impossible to distinguish
localised Kelvin Helmholtz vortices from horizontally extended layers.
We can roughly estimate the entrainment rate into this shear layer due to these vortices from
laboratory and theoretical studies of turbulent mixing in free shear layers (Dimotakis, 1989). These
results show that the entrainment into a shear layer of horizontal velocity difference AU is determined
by two parameters, namely, s=p2/pl and r= UJU1, where the label 2 is associated with the more slowly
moving fluid. (i.e., the upper air, in the July 5 case study). In the presence of density stratification
one would expect the shear layer thickness to be fully developed near hmax=(AU)2/g'. The fraction of
fast moving air flowing into the shear layer, according to these studies, is
C =s'/2( 1+ .68( 1- r)/( 1+ r)) (2)
Thus for the free shear layer we can estimate an entrainment velocity
We = UavehmaxL-1/(l+C) (3)
where L is the distance it takes for the shear layer thickness to grow to saturation. This entrainment
rate would be characteristic of those portions of newly created surface over which h/hmax< 1; as the
surface ages the shear layer thickness approaches hma x and entrainment stops, creating intermittency in
the entrainment. Using parameters characteristic of the inversion on July 5 we have
AU=8 re s, Ua_,=8 re s, g'=.2, s=.98, r=0.33, C= 1.3 (i.e., there is 30% more cloudy than noncloudy
air in the shear layer). For the laboratory free shear layer the thickness of the molecularly mixed shear
layer grows at a rate hmax/L =.075 at s = 1. Thus we estimate at, entrainment velocity of .3 m/s in
regions of scale L = 60/.075 = 800 m. This entrainment velocity would destroy the cloud rapidly, if
prolonged; thus the problem is to determine what fraction of the surface is active at any given time and
the rate of removal of the lowest IIL. This could occur through the lowest IIL cooling until this layer
I08
alone becomes unstable to Kelvin-Helmholtz instability. Entrainment via shear is clearly much more
efficient locally than the baroclinic torque mechanism (Breidenthal and Baker, 1985) or the rebound
mechanism (Linden, 1973), both of which are proportional to the inverse Richardson's number for the
layer, yielding entrainment velocities of several tenths of a centimeter per second.
b) Local Dynamics and Large Scale Forcing
Two flight legs were examined at the inversion, passing in and out of cloud turrets. A two-stream
radiative transfer model estimates the cloud turrets on these legs are approximately 40 m deep if we
assume uniform liquid water mixing ratio .3 g/m 3. This depth is consistent with the lidar measure-
ments. These variations are far greater than can be explained on the basis of turbulent velocities carry-
ing cloudy air into the stratified interface, and must result from a larger scale forcing.
Another symptom of the local effects of larger scale forcing appears to be the presence of upper
level fluid below cloudtop in mixed parcels of scales 100 m and more. According to the work of Dimo-
takis & Brown (1976), and Broadwell & Breidenthal (1982), molecular scale mixing of two fluids in a
turbulent eddy occurs only after the two fluids have been in contact over a time comparable to an eddy
revolution time. That is, the vortex Richardson's number for eddies responsible for molecular scale
mixing must be of order unity. From the observed velocity spectrum it can be shown that for a parcel
100 m in scale to meet this criterion the maximum fraction of upper layer fluid it can contain is on the
order of 8%. We have shown earlier that evaporative cooling does not substantially modify this picture.
One possible mechanism by which the unbalanced mixing ratios might be created is that small bits of
upper level air are drawn down by radiatively cooled cloud parcels, or by the cloud circulations on larger
scales, around the edges of the cloud top undulations.
Cloudtop radiative cooling modifies the properties of the upper 50 meters or so of the cloud. If
this dominates in driving local dynamics, we expect to see descending, negatively buoyant, liquid water
rich parcels whose scales are determined by the requirement that they remain coherent long enough to
be substantially cooled. However, the descending parcels are usually relatively dry and tend to be
grouped in thinner liquid water regions, indicating significant entrainment is involved in the downdrafts.
To understand this better, we note that for a longwave cooling rate,
dO/dt = (F/pcp)'1-1 (4)
in a parcel of scale l, with F the net LW flux from the parcel. Assuming a persistence time x = (/2/e)l/3
(assuming an inertial subrange characterised by TKE dissipation rate e), we find the cooling possible in
a parcel of scale l is
_0/0 = w,/w(l) (5)
where w,= F/pct, O is a measure of the cooling rate and w(l)=(le) 1/3. For typical values of the cloudtop
parameters F=80 W/m 2, E=10 -3 m2/s 3 as estimated from the vertical velocity spectrum midcloud, we
find that w,= 10 -4 re s, so only very small parcels can cool several tenths of a degree at cloudtop before
losing their coherence. Thus the descending parcels which are several hundred meters or more in hor-
izontal scale are not driven directly by their own radiative cooling, but are rather responding to larger
scale forcing. This conclusion is supported by the fact that they are not always the coolest parcels, as
will be shown below.
c) Convective Elements
There were two flights at midcloud levels; one flying upwind and the other flying cross wind. The
downward solar flux ranged from 860 W/m 2 to 650 W/m 2 during this leg, which, by our simple radia-
tion model, would imply that the plane was between about 100 and 200 m below cloudtop. This is
roughly consistent with upward flux observations based on the soundings. The trend is consistent with
the observation that cloudtop sloped upward moving out to sea.
We have conditionally sampled the data in the horizontal flight legs at the inversion, midcloud
and below cloud, to determine the characteristics of the up- and downdrafts. Figures 2 and 3 show the
20 Hz histograms of 0, and QT (a) for a 45 second subcloud section; (b) for the parcels for which w is
in the upper 10% of the values measured, and c) for those parcels for which w was in the lowest 10%
of the values measured. While this is not a sophisticated method to isolate up- and downdrafts, it is a
109
conservative first cut. We see that average values of 0, and Q_ are found in all parcels, independent of
w, whereas the uppermost values of Qr and 0, are found only in updrafts and lowest values of Qr and
0, are found only in the downdrafts. The distribution of values of these parameters is tighter in the
updrafts than in the downdraft data in the midcloud segments. We have looked at similar information
for all the flight legs, and find broadly similar patterns within and below cloud. We do not see organisa-
tion either in the spacing or location of the up- and downdrafts activity in the subcloud legs, whereas
there is a suggestion of roughly 5 km spacing in the downdrafts in the midcloud legs, consistent with
convective cell geometry. Moreover, the correlations of thermodynamic properties with extremes in
vertical velocity are fairly weak suggesting that buoyancy is not dominating the structure. We find the
cutoffs defining the up- and downdrafts change markedly on entering cloudbase; that is, the upper ten
per cent of the positive velocity excursions are much higher below cloud than in cloud, while the lowest
ten per cent of the velocities have small w below cloud and much larger in cloud. Thus buoyancy
differences are probably not driving these parcels continuously up to the inversion. An interesting note
is that the average velocity is positive in the subcloud layer, contrary to the classical picture of sub-
sidence. Simple parcel calculations show the buoyancy differences existing in this situation are so small
that minor excursions in initial vertical velocity (at top or bottom), due to initial forcing, can have sub-
stantial impact on velocities of parcels in the middle of the layer.
Horizontal wind variations are correlated with updrafts at low levels, in the sense that the air com-
ing from below has less horizontal momentum than that from above. These correlations are lost above
cloudbase suggesting that it should not be used as a horizontal tracer.
d) Decoupling of Cloud and Subcloud
As seen from above, it is not necessarily the warmest or the most buoyant parcels which rise the
fastest from low levels to mix with the air above. In fact, the strong updraft regions do not even
penetrate the cloud layer. This is seen in the Paluch diagrams (see Figure 4) which show two regions
for a given sounding. The first is the from near ocean surface to approximately cloud base. We see a
rather uniform mixing line. Note that moist, warm parcels correspond with the updrafts of the previ-
ous section. This mixing line can support the notion of mixing with the SST (Boers & Betts, 1988).
We next examine the cloud region only. We see that the warm, moist parcels of this section do indeed
mix with the air above the inversion but these updrafts do not correspond to the updrafts of the sub-
cloud region. Thus we find that the sounding is decoupled. This height-dependent variation is far
greater than has been observed in the course of longer level flights of the plane indicating that horizon-
tal motion is not believed to be accountable for the evident decoupling.
IV. Discussion
Our data suggest that larger scale forcing, both by shear at cloudtop and by surface fluxes, deter-
mine the small scale motions within clouds on July 5. Direct correlation of buoyancy fluctuations and
vertical motions on small (100 m to several kilometer) scales is weak. Analysis suggest that shear layer
mixing across the inversion dominates the entrainment.
Acknowledgments
We are grateful to R. Breidenthal for very useful conversations. P. Austin has been a tremendous help
throughout all the data difficulties. We also thank R. Pincus for his time and effort. This research was
supported by NSF grant ATM-862-0165.
References
Boers, R. and A.K. Betts (1988). J.Atmos.ScL 45, 1156-1175.
Breidenthal, R. and M. Baker (1985). J.Geophys.Res. 90, 13055-13062.
Broadwell, J. and R. Breidenthal (1982) J.FluidMech. 125, 397-410.
Brost,R., D.Lenschow and J. Wyngaard (1982). J.Atmos.Sci. 39, 800-817.
Dimotakis, P. and G. Brown (1976). J.FluidMech. 93, 535-560.
Dimotakis, P. (1989). 27th Aerospace Sciences Meeting, Reno
Nicholls, S. (1989). Q.J.Roy.Met. Soc. 115,487-513.
Siems, S., C. Bretherton, M. Baker, S. Shy and R. Breidenthal (1989). submitted to Q.J.Roy.raet.Soc.
110
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Figure 1. Sounding through cloudtop: 20:16:00-
20:17:00.
Figure 2. Histogram for 0, and Q, for (a) all
parcels of a 45 second segment at 20 Hz, (b) in
updraft parcels (c) and in downdraft parcels.
Figure 3. 20:14:30-20:18:30 sounding denoted by
pressure to highlight decoupling. * 1000-980
mb; + - 980-960 mb; x - 960-940 mb; V 940-
920 mb.
b)
updrafts
e)
downdrafts
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111



Structural analysis of stratocumulus convection

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