observations of turbulence in cirrus clouds

ELSEVIER Atmospheric Research 43 (1996) 1-29

ATMOSPHERIC RESEARCH

Observations of turbulence in cirrus clouds

Samantha A. Smith, Peter R. Jonas Department of Physics, UM1ST, PO Box 88, Manchester, M60 1QD, UK

Received 16 August 1995; accepted 4 December 1995

Abstract

Three daytime flights of the UK Meteorological Office's C-130 aircraft through thick frontal cirrus have been analysed with the aim of determining the length scales at which energy is produced, and which mechanisms are responsible. The data was obtained as part of the EUCREX campaign.

It will be shown that the occurrence of turbulence is patchy, weak and rather 2-dimensional with most turbulent kinetic energy being contained in the horizontal wind components. Evidence for the production of turbulence by the breaking of Kelvin-Helmholtz waves is found for all of the flights analysed. In one case there also seems to be turbulence production at a scale of 2 km by convection set up by radiative cloud top cooling.

1. Introduction

Cirrus clouds form in the upper troposphere and are composed mainly of ice. They can cover extensive areas, and are important because they play a major role in the ear th 's radiation budget. Small-scale turbulence has an important influence on the cloud structure and therefore on the spatial distribution of the optical properties. Turbulence is directly linked to the life cycles of the clouds through internal mixing and entrainment processes. It is therefore necessary to better understand the dynamics of these clouds, as well as the microphysics and radiation effects, in order to improve their representation in general circulation models.

Previous observational studies of cirrus clouds (e.g. Dmitriev et al., 1984; Quante and Brown, 1992) point out that the occurrence of turbulence is patchy and that the velocity field is anisotropic, leading to a two-dimensional character of the flow. In general, turbulence is weak, except for patches where there is a strong wind shear.

In the upper troposphere the thermal stratification is stable, and therefore consumes turbulent kinetic energy (TKE). The sources of turbulence are instabilities associated

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2 S.A. Smith, P.R. Jonas/Atmospheric Research 43 (1996) 1-29

with gravitational waves and the vertical shear of the horizontal wind, which are neither continuous in time nor spatially homogeneous. Turbulence in the free atmosphere thus occurs intermittently. In the presence of clouds, however, turbulence is also generated by the release of latent heat and radiation effects.

Dmitriev et al. (1984) looked at the structure of wind and temperature fields in jet stream cirrus over the northern part of Russia using aircraft measurements. They noted the intermittency of the turbulent zones, the inhomogeneity of the wind and temperature fields and the weakness of the turbulence. The mean turbulence intensity was largest in the middle of the clouds, while the mean intensity above the cirrus was somewhat larger than at the cloud base level.

In each horizontal run, 75-90% of the regions within the cirrus were turbulent compared with only 10-20% of the clear air regions. The mean length of turbulent zones in the clouds was 40 km, while in clear air it was 60 km.

The microscale (100's of metres to a kilometer) vertical velocity power spectra exhibited the - 5 / 3 power law. They found that the energy dissipation rate at small scales was smaller than the turbulent energy scale-to-scale transformation found from the "mesoscale" spectra (scales of a kilometer to tens of kilometers), due to the work done against the thermal stratification. It was found that the vertical velocity spectral densities at inertial subrange scales was higher in cross-stream flights than along stream flights. This was also true for the spectra of the horizontal wind component, where there was an order of magnitude difference, and of temperature T. This demonstrates the spatial anisotropy of the wind pulsation intensity.

More recently, Quante and Brown (1992) looked at the turbulence characteristics of different types of cirrus clouds, including frontal cirrus and jet stream cirrus, also using aircraft measurements. They found that the bulk Richardson numbers calculated for entire layers between flight legs were in general larger than the critical value of 0.25, below which Kelvin-Helmholtz instabilities will create turbulence. It is probable that averaging over thick layers will bias the estimates towards higher values. The Richard- son number profile calculated from the composited aircraft ascents from one flight showed a large variation with height, with values below 0.25, indicating the existence of several turbulent layers in the cloud field.

Above the top of the jet stream cirrus, the vertical velocity time-series exhibited wavelike behaviour with extremely weak turbulence, and the spectrum had a slope of - 3 down to scales smaller than 190 m. The velocity field above cloud was therefore two-dimensional, with most energy in the horizontal wind components. Within the cloud top, very active regions (with standard deviations in the horizontal velocities with cut-off wavelength 500 m, ~r .... of around 0.4 m s -~) occur together with less intense ones (with ~ of around 0.1 m s -~) and regions of wavelike motion. Turbulence is obviously not homogeneous, and the flow is complex. The transitions between the turbulent and non-turbulent regions were found to be abrupt, especially in cases of strong wind shear. The turbulence was most intense at certain locations in the jet stream cirrus (associated with the largest shear), with the vertical velocity variance being an order of magnitude larger than was observed in the more turbulent regions of the frontal cirrus over a large range of scales.

Typical turbulence length scales varied substantially between different cases and even

S.A. Smith, P.R. Jonas~Atmospheric Research 43 (1996) 1-29 3

between different regions in any one case. Also, the degree of anisotropy in the velocity field varied from turbulent to calm regions. The ratio of cr w to ~u,v in the turbulent regions was 0.8, while it was 0.5 in the calm regions for scales smaller than 500 m. Energy dissipation rates were around 2 × 10 -4 m 2 s -3 for turbulent regions and an order of magnitude smaller for calm regions.

In general, vertical motions were suppressed due to the stability of the atmosphere, leading to the 2-dimensional character of the flow. Scales of energy containing eddies were found to vary between a few tens of metres to a few hundred metres. Linear gravity waves were probably present at a wavelength of about 3.8 km.

Gultepe and Rao (1993) studied the moisture and heat budgets of a cirrus cloud associated with a jet stream using aircraft observations over Wisconsin. This cloud was fairly homogeneous compared to other cirrus clouds observed. In contrast to the results of Dmitriev et al. (1984), they found that the standard deviation of the vertical velocity was at a maximum at cloud top and cloud base, where there was moderate turbulence. The standard deviation of the potential temperature was small except close to cloud top, indicating that there was little convective activity in the bulk of the cloud.

The horizontal advection of moisture into, and heat out of, the lowest layer of the cloud and the radiative fluxes were found to be important in the formation and maintenance of cirrus layers. Ice crystal growth is significant in the upper layers. Maintenance of cirrus was attributed to relatively warm and moist air advection, radiative cooling at upper levels, and moisture advection in the vertical. Turbulent heat and moisture fluxes were found to be significant in the low levels of cirrus.

Francis et al. (1994) reported aircraft observations of microphysical and radiative properties of two relatively thick (5 km) frontal cirrus clouds, and used several radiative transfer models to estimate the layer-averaged heating rates. One case was relatively homogeneous compared to the other. There was net radiative cooling in the upper half of the clouds, and a small amount of heating in the lower half. The shapes of the heating rate profiles were qualitatively similar to those for stratocumulus and supercooled altocumulus clouds, despite the fact that the ice water content (Ql) profiles were totally dissimilar to commonly observed liquid water content (QL) profiles in the water clouds. In cirrus, the highest Ql was found near the base of the clouds, but there was still enough optical thickness at cloud top to produce marked cloud top cooling. These radiation profiles act to make the cloud layers convectively unstable, so that some degree of overturning is expected (though not to the same degree as in stratocumulus and altocumulus).

Starr and Cox (1985a) described a cirrus model with which they simulated a thin cirrus layer between 6.5 and 7.5 km, which was typical of a weakly forced, midlatitude springtime cloud. Large-scale ascent of 2 cm s-~ gave ice water contents and vertical motions which agreed with observations for similar cases, and predicted the formation of layers of cirrus below the original layer as is often observed. Two simulations were run - - a nighttime case and a daytime case.

Modelled up- and downdraughts were of comparable intensity to each other and to typically observed values (10-20 cm s - l ) . The ice crystal fall speeds were much larger than this (80 cm s - 1 ), so they tended to fall out of the cloud base quite rapidly, where

4 S.A. Smith, P.R. Jonas~Atmospheric Research 43 (1996) 1-29

they eventually evaporated, cooling the subcloud layer. In the generator region, the formation of ice heated the cloud.

The magnitudes of the horizontal average heating rates due to radiative transfer were comparable to those due to latent heat effects, demonstrating the importance of radiation. The net radiative heating profile for the daytime case showed weak heating near cloud top, net cooling through most of the cloud, and sometimes weak heating below the cloud. The vertical structure of the radiative effects modified the static stability structure of the layer, which had a cumulative effect. The radiative stabilization of the upper part of the generator region in the daytime case resulted in the cloud becoming less energetic than the nighttime case by the end of the simulation.

The nighttime simulated cirrus had 20% more cloud ice than the daytime case. However, the daytime cirrus was more cellular, as seen in the ice water field, and the maxima of cloud water in the convective cells was greater. Some of these cells persisted throughout the simulation, in association with organised and persistent updraught regions. The cells became vertically elongated in time, due to the effects of the ice fall speeds and the weakness of the updraughts. The initial horizontal scales of these cells were 1-1.5 km, which is characteristic of observed convective elements.

Due to the optical thinness of the cloud, infrared cooling was distributed in the vertical, and not concentrated at cloud top. The horizontal structure of the radiative heating rates directly modified the local production and destruction of vorticity and turbulent kinetic energy (TKE) through the buoyancy forces. Infrared cooling increases with increasing Q~, which partially offsets the warming from the latent heat of fusion. Thus, infrared acts as a negative feedback mechanism to decrease the buoyancy in the convective cells. The absorption of solar radiation during the day increases with increasing QI, and this additional heating enhances the convection. Thus the daytime cirrus were more cellular and more convective. There was significant horizontal structure in the radiative and latent heating and cooling, and the generation of TKE continued locally in association with these patterns.

Starr (1987) compared cirrus simulated at a low level (from Starr and Cox, 1985a) with a subtropopause cirrus layer (between 10 and 11 km). The subtropopause cirrus cloud had several differences from the lower level cloud. The Ql was about 7.5 times smaller, and the maximum QI was at cloud top, with only a weak relative maximum near cloud base. The subtropopause case was more cellular, and the domain averaged TKE was 5 times greater. Maximum updraughts were of the order of 1 m s -1 . A consequence of more intense circulations was that entrainment of overlying air which was relatively drier in this case was enhanced. The resulting evaporative cooling contributed to the formation and maintenance of relatively strong downdraught. Adia- batic warming in the downdraughts resulted in further evaporation and a midcloud region of net ice destruction. The nighttime subtropopause case was more energetic than the daytime case. There were thus two generation regions (release of latent heat) separated by a midcloud layer of net ice destruction. Infrared cooling was large in the ice generation regions (due to the high concentration of large ice particles).

Previous studies therefore suggest that radiative processes strongly regulate the cloud ice water budget and the structure of convective thin cirrus clouds. Turbulence within a cirrus cloud is intermittent and weak, and the velocity field is usually anisotropic. The

S.A. Smith, P.R. Jonas/Atmospheric Research 43 (1996) 1-29 5

aim of the current research is to investigate the length scales involved in the turbulence within cirrus clouds, and to see how these relate to the microphysical characteristics of the cloud. We also investigate the origins of the fluctuations on the various length scales found.

2. Observations

Observations were made in relatively thick cirrus during the daytime using the instrumented Hercules aircraft of the Meteorological Research Flight, as part of the EUCREX (European Cloud and Radiation Experiment) project. The standard instrumen- tal performance has been described by Nicholls (1978), Nicholls et al. (1983), and Slingo et al. (1982). The frequency with which the important parameters were measured and their accuracy are described in Table 1.

The air velocities relative to the aircraft were found from the pitot-static system (speed) and the freely rotating wind vanes (direction) located on the tip of the noseboom. The inertial navigation system (INS) was used to transform these into the stationary earth based coordinate system. Although the accuracy of absolute value of the vertical velocity measurements is poor as indicated in Table 1, the variations in w are reliable.

Temperature was measured using data from the Rosemount 102BL platinum resis- tance thermometer. The accuracy quoted in Table 1 is for clear air and is lower for in-cloud regions, but is still used because the in-cloud temperature probe is too noisy at these low temperatures.

The Lyman-alpha absorption hygrometer (total water probe) was used to find the total water content (QT). This gives reliable fluctuations in QT. However, the drift in the offset of the Lyman-alpha is removed by calibration with the General Eastern hygrometer, which is not very reliable at these low humidities and temperatures. Therefore the long term trend in the Lyman-alpha data is unreliable.

Cloud microphysics data were obtained using the PMS 2D-C optical array probe, which samples ice crystals in the size range 25 to 800 ixm (see Brown, 1993). The 2D-P probe, which measures larger ice particles (size range 200 to 6400 p~m), was noisy and failed near the end of one of the cases, flight A290.

Particles are classified on the basis of the projected area of the images using a fast Fourier transform technique. The ice water content (QI) is then found by using empirical

Table 1

Paramete r F requency Absolu te accuracy Resolut ion

Horizonta l wind componen t s 32 Hz + 0.5 m s - l +__ 0.06 m s 1

Vertical wind componen t 32 Hz + 0 . 1 m s -1 ___0.03 m s

Tempera ture 32 Hz _+ 0.3°C _ 0.06°C Total water content 64 Hz + 0.15 g kg i _ 0.005 g kg - i

2D-C concent ra t ions 1 Hz depends on condi t ions 25 I-~m


relations between the shape and size of the each crystal and its mass. The QI estimated from these probes is accurate to within a factor of 2 to 3. This does not concern us because only relative values are of importance here. Uncertainties are due to the use of empirical relationships between the mass and size of the crystals and, to a lesser extent, due to particles which are too small to be detected.

Linear interpolation was used to replace any bad or missing data in the time series.

2.1. Flight A283

Flight A283 took place between 9:05 and 16:40 on 24 September 1993. A waving cold front, associated with a low pressure system north of Iceland, was moving slowly from west to east across the British Isles. Surface winds were roughly southwesterly during the period.

The flight was carried out in the leading edge of a thick sloping sheet of cirrus in the region of Wick in Scotland. There was thick cirrus in the west of the operating region and the leading cirrus edge was to the east of the region. For the most part, there was no significant mid-level cloud (although there was some mid-level cloud in the west of the region). The main cirrus layer was between 6.4 km and 10.4 kin, although there were some patches of cirrus extending even above 11 km in places. The heights of cloud base and cloud top varied along a line from west to east, but the cirrus deck was between 3 and 4 km deep. The very top of the cirrus was unattainable by the aircraft.

Two fixed ground positions A and B were selected, orientated west to east, with B just east of the leading edge of the cirrus. The aircraft performed straight and level runs at several heights between A and B, travelling at its optimum air speed of between 120 and 145 m s 1 (depending on height). The lengths of these horizontal runs were typically 100 km. Profiles were carried out before (ascent) and after (descent) the horizontal runs.

Only the first nine horizontal runs and the first six profiles are used in the subsequent data analysis (before 14:00 GMT), as the INS data was erroneous in the second half of the flight, resulting in unreliable vertical velocity data.

Fig. la shows profiles of 2D-C ice water content (QI), equivalent potential temperature 0 e and the horizontal wind components u (eastward) and v (northward) at the start of the flight. The level at which each level run was flown is indicated on the fight axis by lines labelled by the run numbers. The ice water content in the diagram goes down to zero at the top of the profile sooner than expected because the aircraft flew out of the east edge of the cirrus before reaching cloud top.

2.2. Flight A290

Flight A290 took place between 9:30 and 16:40 on 9 October 1993. A low pressure system was situated over southwest England. An occluded frontal system associated with this was present to the northwest of Scotland, giving rise to a large amount of cirrus and mixed phase clouds.

The flight was carried out in a thick cirrus layer lying to the north of Scotland. Initially, cirrus cloud base height was 6.2 km and cloud top height was 9.2 km, with


10000 . . . . . . . . . i . . . . . . . . .

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North wind ( m / s )

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• 2D-C ,W%'~(Wr~3) 0.8 295 Eqo~v P~O~emp (K) 320 -30 Eost w ~ (m/~) 3O -30 Noah ~,i~Od (m/s)

Fig. 1. (a) Conditions encountered during flight A283. The variation of 2D-C IWC (g m-3), equivalent potential temperature (K), the eastward wind component u and the northward wind component u (m s- l ) with height at the beginning of the flight are shown. The height at which each run was flown is marked on the fight-hand axis of the last profile. (b) Conditions encountered during flight A290. The variation of 2D-C IWC (g m-3), equivalent potential temperature (K), the eastward wind component u and the northward wind component u (m s 1) with height at the beginning of the flight are shown. The discontinuity at 8.5 km in the profiles is due to combining the main profile with a shorter one at higher levels. The height at which each run was flown is marked on the fight-hand axis of the last profile. (c) Conditions encountered during flight A288. The variation of 2D-C IWC (g m-3), equivalent potential temperature (K), the eastward wind component u and the northward wind component v (m s- 1 ) with height at the beginning of the flight are shown. The height at which each run in stack A was flown is marked on the fight-hand side of the last profile. (d) As for Fig. lc but for the end of flight A288. The height at which each run in stack C was flown is marked on the fight-hand side of the last profile.

some lower level cloud. Howeve r , the c loud deepened and by the end of the flight, the

base was at a he ight o f 3.5 km. It s eemed to have merged with the lower level cloud.

Therefore , on average, the depth o f the main cirrus layer was approximate ly 4 kin. The

main cirrus layer appeared hor izonta l ly un i fo rm through most o f the flight.

A prof i le ascent was f lown at the start of the f l ight f rom 50 m up to 9000 m, but there

was still thin cirrus above this level . Straight and level runs were then carr ied out at a

number o f levels wi th in and be low the cloud. These runs were not a lways f lown direct ly

above each other, but the general direct ion o f the runs was west to east. A final profi le

descent was carr ied out f rom 10000 m (above the cirrus) to 50 m.

Fig. l b shows the variat ion o f Q~, 0 e, u and u wi th height for the first prof i le of

f l ight A290. There are discont inui t ies in some of the profi les because a shorter, h igher

prof i le is shown above the main profile. The level at which each level run was f lown is

indicated on the r ight axis by l ines label led by the run numbers . The cirrus is above

6300 m, with thicker cirrus above 7100 m.

2.3. Flight A288

Fl ight A288 took place be tween 12:40 and 18:40 on 6 October 1993. A low pressure

system was situated over southwest England. A complex occ luded frontal system


associated with this was present to the north of Scotland, giving rise to reasonable amounts of cirrus and mixed phase cloud. These conditions are very similar to the conditions on the day flight A290 was flown.

The flight took place through a thick cirrus layer lying to the north of Scotland (as for A290). From the initial profile ascent, the cirrus cloud base was situated at a height of 4.8 km and the top was at 8 km. There was still some thin cirrus above the top of the profile. The depth of the cloud was therefore 3.2 km. The cirrus was split into two layers, with the top of the lower layer situated just below 6 km. The cirrus was horizontally uniform. There was a lower cloud layer between 650 m and 4.4 km. By the end of the flight, there was no discernable break between the cloud layers and the cirrus had dissipated a great deal.

Three stacks of straight and level runs were flown after the initial profile at a number of levels through the cirrus cloud layer between two chosen ground points, the orientation of which was at 25 ° to the eastward direction. The first stack consisted of runs at consecutively higher levels between 3.9 km and 7.6 kin. The second stack descended again to 2.4 km (only 2 runs). The final stack ended with a run above cloud top at 8.8 km after the sun had set. (The sun set at about 17:40, around the time of run 17). Most of these runs lay more or less above each other. For the last stack it was decided to drift with the wind, although this did not affect the pattern (with respect to the ground) too much, and the aircraft stayed fairly close to the original track although runs 15, 16 and 17 are very slightly north of the other runs.

A final profile descent was carried out from 9 km (above the cirrus) to 1.4 km. Fig. lc shows the variation of Q~, 0 e, u and v with height for the first profile of

flight A288. The level at which each level run of stack A was flown is indicated on the right axis by lines labelled by the run numbers. Also, Fig. ld shows the variation of QI, 0~, u and v with height for the last profile, with the level at which each level run of stack C was flown indicated on the right axis.

3. Data analysis

3.1. Calculation of power spectra

The power spectra of the vertical velocity variations were calculated for each horizontal run and also for 100-s sections of each run which corresponded to 14 km (minimum frequency 0.01 Hz). In this way we could examine what happened in different regions of each run. Each run lasted on average 800 s (minimum frequency 0.0013 Hz). Spectra were also calculated for variations of temperature (T), total water content (TWC or QT) and the horizontal velocity components eastwards (u) and northwards (v). The best fit straight line was removed from the initial time series, as mean vertical velocities are unreliable. Then 10% of the data was tapered at both ends using the split cosine bell, to reduce leakage to neighbouring frequency bins. The NAG Fortran Library routine G13CBF was utilized to calculate a smoothed sample spectrum using spectral smoothing by the trapezium frequency (Daniell) window. To obtain smoother spectra for the entire runs (subsequently referred to as averaged spectra),


averaging was performed over all spectral estimates within frequency intervals over a factor of 2 (frequency bins 16-8 Hz, 8 -4 Hz . . . . ).

Any frequency f in Hz corresponds to a scale k given by k = U/f, where U is the wind speed relative to the aircraft (true air speed or TAS). The air speed varies with height from 100 m s -1 at low levels to 145 m s -1 at the highest levels.

The coherence functions for the vertical velocity w and the potential temperature 0 were estimated using

abs( Pwo )2 coherence

Pw w Poo

where Pwo is the complex cross-spectral density of w and 0 and Pww and P00 are the power spectral densities of w and 0 respectively. The phase was found from the phase angle of Pwo

= tan- 1 [ imag( Pwo ) real( Pwo ) )

phase t

3.2. Spectral noise

When taking aircraft measurements in the upper troposphere, care has to be taken when analysing the vertical velocity power spectra due to the low energy densities encountered at such high levels. Quante et al. (1996) examined the differences between the data obtained by the 3 aircraft which participated in the EUCREX campaign. These were the Falcon (from Germany), the Merlin (France) and the Hercules. The vertical velocity spectra for weak turbulence from each aircraft showed evidence of different types of noise at higher frequencies. All of the w spectra in weak turbulence segments inspected from the Hercules data appeared to be affected by red noise at frequencies higher than about 0.1 Hz, the origin of which was unknown. Most of the spectral densities observed during these cases were larger than the values seen in Quante et al. (1996).

In addition, Nicholls (1978) showed that the longitudinal gust component was affected by noise at frequencies above 3 Hz even in the boundary layer where there is much more TKE.

No corrections were made to the data to eliminate the noise, but it was kept in mind during the spectral analysis.

3.3. Results

3.3.1. Flight A283 To examine what happens within different regions at each level, each horizontal run

was split into several 100-s long sections of data (approximately 14 km). Fig. 2 shows the time series of the vertical velocity (w) and the 2D-C ice water content (Q0 from run 1 at a height of 8900 m. Five sections A through to E each of 100 s are taken from the region between 10:39:10 and 10:48:20 GMT. These are indicated on the time series by


3

2

I

0

-I

- 2

- 3 I03

E A C 8

900 I( Time (G~AT)

A C E

=_- ~ D

)48

0.20

~" 0,15 E

0,10

(J I

0.05

0 O0 10,3 O0

Time (GMT) 10 )48

Fig. 2. Time series of the vertical velocity (w) and the 2D-C IWC (QI) for run 1 (8900 m) of flight A283. The time period of each of the selected 100-s long sections is indicated by horizontal lines labelled A through to E.

the horizontal lines marked A to E. The vertical velocity power spectra for each of these sections are shown in Fig. 3. Fig. 4 shows the vertical velocity spectrum for region D, along with the spectra of temperature T, the Lyman-alpha total water content QT and the horizontal velocities u (the eastward component) and v (the northward component). Note that the limits of the logarithmic y-axis in Fig. 4 are - 5 and 2, rather than - 6 and 1 as for the previous spectrum.

It can easily be seen that there is a great difference in the turbulent kinetic energy (TKE) between different parts of the same horizontal run at high levels in cloud. The most energetic region is D followed by C, and this can also be seen from the trace of w in Fig. 2. The spectral densities for region D are up to two orders of magnitude greater than the spectral densities in region A, which is a relatively calm region within the cloud. The length of the turbulent region seen in the vertical velocity trace is approximately 40 km, comparable to the lengths of turbulent regions observed by Dmitriev et al. (1984). This turbulent region corresponds to relatively low ice water contents. Both the vertical and the horizontal air velocity power spectra follow the - 5 / 3 power law in sections C and D with the spectral densities of w being similar to those of u and v (only very slightly smaller), showing that the turbulent energy is contained in all three components and the turbulence is fairly isotropic. In the calmer regions, the spectral densities of all three wind components are similar over mid-frequencies (0.1 to 3 Hz), but the spectral density of w falls at higher frequencies. This may be a result of the small scale vertical motions not being strong enough to overcome local stable stratifica-


- 2

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" ~ \ ~ ' ~ , D! - : ~ \:~ ~, "'~',,,, , .......... El

• . . ~ ' ,: ~' ,1'~,,~ '

0 1 - 2 - 1Log( Frequeney/Hz )

Fig. 3. Spectra for the lO0-s sections of the vertical velocity time series marked in Fig. 2. Frequency is in Hz and power is in m 2 s -2

tions. However, this is similar to the red noise effect described by Quante et al. (1996) and so may not be real. Whichever is the true cause, the turbulence in these calmer regions is anisotropic.

L -1 0

Q..

" ~ - 2 2

- 4 -

- 5

v A .

f

I . . . . . . . .

w

. . . . . . . -f

. . . . . Q t

0 -1Log( Frequency/Hz )

Fig. 4. Spectra of vertical velocity (w) , temperature (T), total water content (QT) and the horizontal velocities u (eastward) and u (northward) from section D of run I (8900 m), flight A283. Note that the limits of the y-axis are - 5 and 2 rather than - 6 and 1 as for the spectral plot in Fig. 3.


The calm regions do not exhibit any spectral peaks. The more energetic w spectra for regions C, D and E seem to peak at a scale of about 2 km (frequency 0.07 Hz), which is also seen in the T spectra and sometimes in the Qx spectra. There is a possibility that this peak is due to the fact that this scale is approaching the length of the time series analysed. However, 2 km is only a sixth of the length of the 100-s section so it is likely that this peak is real. It can also be seen in the vertical velocity spectra for each entire r u n .

Several peaks are noticeable in the vertical velocity spectrum for section D other than the main peak at 2 km. These correspond to scales of 580 m (0.25 Hz), 380 m (0.35 Hz), 220 m (0.66 Hz) and 187 m (0.8 Hz). The peak at 380 m is also seen in the T and Qv spectra.

Power spectral estimates vary about the actual long-term average values, which would be given by the - 5 / 3 power law in the inertial subrange for isotropic turbulent regions. In order to check that the peaks in the raw spectra were real peaks and not just due to the natural variation of the spectral estimates, the method described in Blackman and Tukey (1958) was used to estimate the expected limits of the variation of the spectral estimates about the actual (or average) spectrum.

A convenient description of the stability of the estimate is its equivalent numbers of degrees of freedom, k, which can be found from

2(average) 2 k =

variance

The value of k is 11 for these spectra. The lower 95% confidence limit is 0.5018 and the upper limit is 2.8828. Using the long-term average value at the frequency in question, then there is a 95% chance that the calculated value will actually fall within the values given by

lower value = average X lower confidence limit

and

upper value = average X upper confidence limit

In all of the peaks in the raw spectra mentioned above, the peak value of the spectral density is greater than the upper 95% confidence limit. This makes it very likely that these peaks are real.

Run 3 was flown at 9160 m, in the thin cirrus above the main deck. Again there are large differences between the energy contained in the vertical component for the different regions. All of the w spectra for 100-s time series have slopes of - 5 / 3 in mid-frequency ranges (0.1 to 3 Hz) and - 3 at high frequencies, similar to the lower energy regions described in runs 1 and 2. Wether this is due to the low energy of the small eddies or to noise effects is again not clear. However, there is a local region of high stability at this height as can be seen in Fig. la. The w spectra from several sections have peaks at 2 km (0.07 Hz), and one section also has a second peak at 360 m (0.4 Hz). A w spectrum from a relatively calm region has a peak at 1.5 km, but which is not seen in any other section or run.

The lower level runs yield w power spectra with lower energy densities than from the


(a) 3

2 A C E

B D

1

E 0 v

- 1

- 2

--3 1041 ,%0 105(

Time (Gk4I)

v~E 0'15 F

o O. 10 Iz-

344

e~ 0.05

0 ~I00041 Time (GMT) 105044-

Fig. 5. Time series of the vertical velocity (w) and the 2D-C IWC (Q1) for run 1 (9150 m) of flight A290. The time period of each of the selected 100-s long sections is indicated by horizontal lines labelled A through to E.

higher level runs. Peaks occur often at scales of 2 km, with smaller scale peaks of a few hundred metres. Inertial subranges characterised by spectral slopes of - 5 / 3 are present at frequencies higher than that of the smallest peak in each case.

From the run-averaged spectra (not shown), the levels with the most kinetic energy are runs 1 and 2, which at 8900 m are in the upper regions of the cirrus. This is true for scales smaller than 5 km (or frequencies larger than 0.03 Hz). Run 9 at 4540 m, below the main cirrus deck, is the next most energetic for scales smaller than 150 m (0.97 Hz).

In summary for this case, the turbulence is obviously intermittent, with some sections within a run being much more energetic than other calmer regions. The flight track was plotted with coordinates which advect with the mean wind, so that the relative positions in the cloud are plotted. The most turbulent regions, defined as having standard deviations of w, ~r w, greater than a threshold value of 0.3 m s -1 , were marked on the flight track (20-s sections are used for this purpose). From this it could be seen that the most turbulent regions at each height were located above each other. A peak is commonly seen in both the spectra from the 100-s sections and from entire runs at a scale of around 2 km in the spectra of all the parameters. This is particularly evident high in the cloud, in the more energetic regions. Other smaller scale peaks in the vertical velocity spectra vary between scales of 500 and 100 m for different regions of the cloud.

3.3.2. Flight A290 Fig. 5 shows a time series of the vertical wind component (w) and the ice water

content (QI) for run 1, with the sections A to E indicated as before. At 9150 m, run 1


. . . . . . . ~ . . . . . . . . . . . . T

0 " , . . . . . Qt

~ ....... v

\,!' af,,

- + , ,,,,, ,, ,, , . ; , , : ~ ~ "

Log( Frequency/Hz )

Fig. 6. Spectra of vertical velocity (w), temperature (T), total water content (Qx) and the horizontal velocities u (eastward) and v (northward) from section D of mn 1 (9150 m), flight A290.

was still in thin cloud but above the main cloud top. It is obvious from the w time series that there is not much TKE in w. The variation in energy between the 100-s sections selected for this run is not as great as some of the variations observed between spectra for flight A283, the difference between the largest and smallest spectral densities at any frequency being less than an order of magnitude. Some of the sections seem to have peaks between scales of 1 and 2 km (frequencies between 0.145 and 0.073 Hz). In Fig. 6 are the spectra of w, T, QT, u (east wind component) and v (north wind component) for section D from run 1. The spectra of the horizontal wind variations u and v have slopes of - 5 / 3 , showing that they are turbulent at all scales. On the whole they are much more energetic than the vertical velocity spectra, indicating that the turbulent flow is essentially 2-dimensional (anisotropic). In the w and u spectra, there is a clear spectral peak at 1.5 km with a slight bump in the temperature spectrum. However, the temperature peak appears to be below the maximum value expected from the natural variation of the spectral estimates.

All of the vertical velocity spectra exhibit broad peaks between 100 m and 50 m (between 1.45 Hz and 3 Hz) as seen for section D, where the spectral density of the w spectrum approaches that of the u and u spectra. At smaller scales, the vertical velocity loses energy rapidly and decreases down to the noise level. The rapid fall in spectral density between the peaks at 1.5 km and 100 m and at very high frequencies is probably due to energy being consumed by the stable stratification as energy is handed down to lower scales from the scale at which it was produced. There is a slight peak in the spectrum of u at 5 Hz, corresponding to a scale of 30 m. This is due to noise. In Nicholls (1978), it was seen that the longitudinal gust component was affected by noise at frequencies above 3 Hz.


Run 3 was flown at a height of 8220 m, in the upper part of the main cloud. The ice water contents were much larger here than for run 1 and there was also more energy in the vertical velocity component. The energies of the different regions at this level vary by an order of magnitude.

Some spectra exhibit the noise effects described by Quante et al. (1996), with no apparent peaks. Other sections at this height are similar to that shown in Fig. 6, with small scale peaks in the w spectra from 100 to 50 m, and with spectral densities much lower than that for u or v.

Spectra obtained from lower level runs in this case do not deviate much from the described behaviour, either having small-scale peaks or demonstrating the red noise effects. Below the base of the cirrus deck, the 100-s spectra are similar to each other. They are energetic and exhibit the - 5 / 3 power law. Overall, various other peaks were observed at wavelengths varying between around 200 m (0.7 Hz) and 2 km (0.07 Hz).

The vertical velocity power spectra averaged over each horizontal run were also analysed. It was observed that runs 3 and 4 at a height of just above 8200 m were the most energetic. The least energetic were those runs near cloud base.

To summarise for flight A290, the vertical velocities contain less energy than for A283, and the turbulence is more anisotropic. Most energy is in the horizontal components. The flight track was plotted with coordinates which advect with the mean wind as for flight A283. There were very few regions marked as turbulent if the same threshold for ~r w was used. Instead a threshold value of 0.2 m s - l was used. There was not so much vertical coherence in the positions of the most turbulent regions in this case, with turbulent regions scattered across the operating region.

3.3.3. Flight A288

The spectra obtained from higher runs taken during stack A behaved in a very similar manner to that described for flight A290, with some spectra showing peaks between 100 and 50 m while others seemed to be affected by red noise. Other peaks at scales of a few hundred metres were sometimes seen.

The runs at or below 5.5 km in the lower cirrus cloud layer (runs 4 and 5) yield significantly different spectral behaviour. All 3 components are turbulent at scales smaller than 120 m (frequencies larger than 1 Hz), the scale at which energy appears to be produced.

The last stack, stack C, took place between 16:50 and 18:04, by the end of which the sun had set and the cirrus had dissipated a great deal. However, the run averaged spectral densities are not significantly different from the earlier runs.

Run 16 was flown in the upper part of the thin cirrus at 7.6 km. The spectra from the sections are shown in Fig. 7. Three of the four sections analysed for this run have wide peaks in the w spectra between 100 and 50 m and very little energy at high frequencies. The exception to this rule is section C, the most energetic spectrum, which appears to follow a - 5 / 3 slope at all scales below 420 m, where there appears to be a peak.

Runs at 5.1 km and 6.4 km have sections which behave in a variety of ways, including spectral peaks in the w spectra between 100 and 50 m and at 400 m (run 15).

Sections from run 13 (4.2 km) at cloud base is similar to the earlier run at cloud base,

S.A. Smith, P.R. J o n a s / A t m o s p h e r i c Research 43 (1996) 1 - 2 9 17

A

0 . . . . C

. . . . . . . D

-1

o_

- 4

_5 ~

--6iL --I ' /_ --.[ I Log( Frequency/Hz )

Fig. 7. Spectra for the 100-s sections of the vertical velocity time series from run 16 (7600 m) of flight A288. Frequency is in Hz and power is in m 2 s -2.

with u, t, and w energies similar at small scales. There are peaks in the w spectra at scales of between 330 and 100 m (0.36 Hz and 1.2 Hz).

In summary therefore, the spectra obtained during flight A288 behave similarly to the spectra in flight A290, with similar peaks and anisotropic flow on the whole, particularly in calmer regions. The exceptions to this rule occur in the lower parts of the cirrus, where peaks are found at scales of a few hundred metres with 3-dimensional turbulence at high frequencies. Again, the flight track was plotted with coordinates which advect with the mean wind. There were very few regions marked as turbulent if a threshold for ~r w of either 0.3 or 0.2 m s-~ was used. There seemed to be no organization in the positions of the more turbulent regions.

3.4. D i s c u s s i o n

There are a variety of atmospheric processes which may contribute variations in the vertical velocity at certain scales. These include gravity waves, Ke lv in -Helmhol tz waves and buoyancy effects.

The first mechanism to be discussed is that of gravity waves, which form if air is displaced from its equilibrium level in a statically stable environment.

Gravity waves may enter the cirrus from other levels or be produced in the region of the cirrus clouds. Gravity waves are produced by numerous mechanisms. These include excitation by convection or an undulating surface. They also include instabilities due to the wind shear. According to Lalas and Einaudi (1976), an atmospheric shear layer can support a number of unstable modes. The Ke lv in -He lmhol tz wave is the wave with the shortest wavelength excited by the shear layer and is the most unstable wave. It is


evanescent above and below the shear layer. The additional waves of much larger wavelength, which are possible due to the presence of a solid lower boundary (the surface of the earth), may propagate out of the layer. (The growth rates of these additional modes are smaller because energy is propagating away).

The Brunt-Vaisala frequency, N, the angular frequency with which an air parcel would oscillate if displaced vertically from its equilibrium position in a statically stable environment, is given by

g

0v N 2 = _ _

30,.

~z

where g is the acceleration due to gravity, z is the height and 0 v is the virtual potential temperature. The frequency given by N / 2 r r gives an upper limit to the frequency of oscillation of a gravity wave in the limit of a horizontally propagating gravity wave. The wavelength h is found by dividing the phase speed of the wave by the frequency. In general the phase speed will not be equal to the mean background wind speed and will not be in the same direction due to the vertical shear in the horizontal wind, except for at the critical level of the wave at which it was produced. However, an estimate of the

7500

P! ,G, nd, P294:,4-! ~5,z1,1,: ! 4:26

_ 3 _ 1 / 2

v

Z 5000 .,~ T

2500

o (9,1

I t l ~ l l l l l l l l l l l q l

_ 4 - / 5

_ 6/7 8

9

A E

I

~fd~e P! ,qqd, P ,2 ,93:,5,0i1,_1,0: ,23, :28 GN

_ ~/2

~ / 4

7 5 0 0 5 / 6

J 7/8

911o 5 0 0 0 ~

11/~2

13/14

2500 ~ 15/16

16

Fig. 8. Variation of the Brunt-Vaisala frequency N with height at the start of flights A283 and A290, obtained using the data from the profiles. (a) Flight A283, (b) flight A290.


scale involved can be found using the horizontal wind speed as it should be of the same order of magnitude as the phase speed.

The variations of N with height calculated using the initial profiles is shown in Fig. 8 for flights A283 and A290 in which larger scale peaks were observed. The profiles of virtual potential temperature 0, were low-pass filtered to remove small-scale variations (frequencies greater than 0.1 Hz or scales smaller than 50 m). The differentials were calculated over 3-s periods, which corresponds to 15-m deep layers at a typical ascent rate of 5 m s-1.

For flight A283, it can be seen that N varies throughout the profile between values of 0.01 Hz and 0.03 Hz. Therefore only gravity waves with frequencies lower than 0.03 Hz are able to propagate through the cirrus. This corresponds to wavelengths on the scale of a few kilometres assuming that the phase speed is of similar magnitude to the observed wind speeds.

If gravity waves are present, the cross-spectra of w and 0 are expected to show a stable phase relation of 90 ° (with the oscillation in w leading 0) at the observed frequency with a correspondingly high coherence approaching 1 (as seen in Axford,

A285 R I D wtheta raw 1.2 I r a ) ' . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

f' 1.0

o.8

~ 0.6

~ o.4 /

: i 0.0 . . . . . . . 0.01 . . . . . . Oi I1 CI 1.0(] 10.00 100 .00

frequency (Hz)

A 2 8 5 R 1 0 w t h e t G row 180 (b ) . . . . . . . . . . . . . . . . . . . . . . . . . . .

9o

C k

- 9 0

, . . . . . *1 . . . . - 1 80001 6, 10 1,00 10,OO 100.O0 frequency (Hz)

Fig. 9. Coherence and phase spectra of w and 0 for section D of run 1, flight A283.


1971). However, this can only be expected to be observed in regions where only gravity waves are present. If turbulence is present, this phase relation will not hold. Instead, phase angles are likely to vary about 0 °.

Fig. 9 shows the coherence and phase spectra of w and 0 for section D from run 1 high in the cirrus from flight A283 at 8900 m. It can be seen that there is high coherence and a phase relation oscillating around 90 ° at frequencies around 0.07 Hz, corresponding to scales of about 2 km. This is possible evidence of gravity wave activity, possibly forced by convection below. The variations in the phase are due to turbulence. The lack of evidence for gravity waves elsewhere may be due to the presence of a significant level of turbulence in comparison to the level of gravity wave activity.

The observed vertical velocity spectral peaks at scales of around 2 km may be due to

( a ) 0 .20

~" o.15 E -....

,u 0 1 0

(D I

0 , 0 5

0 , 0 0 1 1 4

(b) o.2o~

!°o::E

4 5

A C

B D

T i m e (GMT) 1 ;

A C

119

B D

0 , 0 5

O.OOF . [/ ' l~If I r . . . . I , . 11111dl~! ~ ~ q 1 1 4 8 2 0 T i m e (GMT) 1 1 5 7 5 2

o.2o[ : ,~ c , ~- ( c ) - ~ - o

~--E 0 15 - - _ _

r

? o.o5

, J

0"1040 851 Time (GMT)

Fig. 10. Time series of the 2D-C ice water content (g m -3) obtained from mid-cloud runs. (a) Flight A283, run 4 (7900 m), (b) flight A290, run 5 (7300 m), (c) flight A288, run 4 of stack A (4800 m).


gravity waves, to convective activity or to both, as they also occur in the spectra of T and QT- They could also be due to Kelvin-Helmholtz waves, although these wavelengths are not the most unstable and are therefore unlikely to break to form turbulence.

Similarly for flight A290, on the basis of values of N taken from the earliest profile P1, only gravity waves with wavelengths of the order of 10 km or more will be able to propagate. There is no convincing evidence for the presence of gravity waves in flight A290, but this may just be due to the presence of turbulence.

At lower levels in the cirrus layer encountered during flight A283, the peaks at scales of around 2 km appear to be due to convective activity rather than gravity waves. Fig. 10a shows the 2D-C ice water content time series for run 4 at 7900 m from A283. It can be seen that there is a cellular structure in the ice water content (in this and other runs), with large peaks in Q1 divided by regions of lower values. In updraught regions, large local concentrations may be due to new crystal nucleations in regions of enhanced supersaturation. The higher ice water contents can be correlated with higher number concentrations. In downdraught regions, crystals may have grown by vapour deposition or aggregation as they fall. This is supported by the findings of Spice (1994). Cellular structures in cirrus layers were simulated by Starr and Cox (1985a). Those described by Start and Cox for thin cirrus cloud layers (1 km deep) were on scales of 1 to 1.5 km. Cells occurred on larger scales for the present cases due to the larger depth of the cirrus layer (approximately 4 km). The higher ice water contents in the convective cores meant that both infrared emission and solar absorption were enhanced. Start and Cox (1985b) found that their daytime simulated cirrus was more cellular than the nighttime cirrus, indicating that the increase in solar absorption in the cells is at least as large as the increase in infrared emission. In this way, the horizontal structure of the radiative heating rates directly modifies the local production and destruction of vorticity and TKE through the buoyancy forces.

On the other hand, the cirrus sampled during flight A290 did not seem to have much cellular convection occurring. It was noted in the flight log that the cloud looked extremely uniform in the horizontal, and the time series of QI shown in Fig. 10b for run 5 at 7300 m does not show any large peaks.

The cirrus of flight A288 did not have much cellular activity either. Fig. 10c shows a time series of Q~ for run 4 at 4800 m. (The cirrus formed at a lower level than the other two cases). The values of QI do not have the large peaks observed in A283. The variation of Q~ along the other runs are even more homogeneous than the run shown.

The difference between these two flight and flight A283 is most probably due to the differences in the vertical ice water content profiles which affects the radiation profiles. In optically thin clouds, the infrared cooling is distributed in the vertical rather than being concentrated at cloud top (Starr and Cox, 1985a). As a result there is net radiative heating near cloud top and net cooling through most of the cloud. This makes the upper regions of the cloud convectively stable. There is evidence that the cirrus observed during flight A283 was optically thicker than the other cases, particularly at the highest observation levels. This can be seen for A283 in Fig. 2 (run 1) and for A290 in Fig. 5 (run 1). It can also be seen from the profiles shown in Fig. 1, which show that the ice water contents are higher in flight A283 than in the other two cases at all heights, and so the radiative cooling is more likely to be concentrated at cloud top.


Another mechanism for the creation of turbulence is instability due to the vertical shear of the horizontal wind. Kelvin-Helmholtz waves form in a layer with a stable lapse rate and a vertical wind shear. Whether these waves break and produce turbulence depends on the relative strengths of the density gradient, which tends to damp vertical motions, and the shear, which creates them. This is measured by the Richardson number,

N 2 R i =

~z] +(az] where N is the Brunt-Vaisala frequency described above. N 2 is a measure of stability. The air is stable locally if N 2 is positive, and unstable if N 2 is negative.

Consider a layer of the atmosphere of thickness h in which there is wind shear and a stable density gradient. The profiles of both density and wind velocity vary smoothly across the layer. While Ri is above the critical value of 0.25, disturbances of all wavelengths are stable. As it falls below 0.25 some wavelengths become unstable. The "most unstable" wavelength is defined as that which becomes unstable first as Ri falls below 0.25, and it varies between (6.3 × h) and (7.5 × h) depending on the variation of the density and velocity profiles within the layer (Turner, 1973).

The profiles of virtual potential temperature 0 v and the horizontal air velocities were low-pass filtered to remove small-scale variations as for the Brunt-Valsala frequency calculations. The differentials were calculated over 3-s periods, which corresponds to 15-m deep layers at a typical ascent rate of 5 m s - t . Fig. 11 shows the variation of the Richardson number with height.

In all three cases, the Richardson number varies greatly within the cloud layers. There are large values in excess of 10 and small values of less than 0.25, which is the critical Richardson number below which some K - H waves may become unstable and break to produce turbulence. Therefore it is likely that within some cloud layers, Kelvin-Helm- holtz instabilities are leading to the creation of turbulence as observed previously by Quante and Brown (1992).

Unfortunately, the aircraft was never entirely above cloud top in any flight, and therefore we can not examine the effect of K - H instabilities in that region, which is likely to be strongly sheared.

The regions in which the Richardson number is below its critical value of 0.25 may be due to the effect of gravity waves. If a gravity wave propagates through a stable atmosphere it alters the local value of the Richardson number. This may cause the Richardson number to fall below the critical value of 0.25 in localized regions due to the enhancement of shear by the wave within certain phases of the wave cycle. Patches of turbulence are widely believed to be produced in this manner in stable environments with depths ranging from 10's to 100's of metres as determined by the vertical wavelength, and which are elongated in the horizontal due to the horizontal wavelength usually being longer than the vertical wavelength. The depth of the layer over which Ri is less than 0.25 in turn determines the size of the largest eddies produced. This mechanism is described by Weinstock (1987), Finnigan et al. (1984) and by Fua et al. (1982).


10000 L . . . . . . . I '

8000 [ . - _~4,15

I. i]]][-- [ I 16/'7 a, 6000

5000~

4-000

8000 ~ _

o ooo , oo 4 RTchardson nunqber Unstable K-H Wavelengths

10000

9000

(b) 8 0 0 0

7O0{ %-

2 600(

I

5000

4000

5000

2000

L i i i i i i i i ] i i i i i i i i i

m

~---=~ ,.-.,

F- - - . . . .

~ i . . . . I . , . i i i i I

0 2 4- Richardson number

[ l l l l l lH I I I I I I I I I I l I l l l l l t l f l l ~ l l l l l l l l

1 t/2 n

- s/4

:--'_ - s / ~

- 7/'8

- ,9 110

I I I /i~L I

i

- 13/14

15116 ...... .,,IH,HJ,,d ......... I ......

0 400 800 1200 1§00 Unstable K-H Wavelengths [m)

Fig. 11. Profile of the Richardson number (with the critical value shown by the vertical dashed line) and the most unstable Kelvin-Helmholtz wavelengths for each flight. The flight level of each horizontal run is marked on the right-hand axis of the last plot. (a) Start of flight A283, (b) start of flight A290, (c) start of flight A288, (d) end of flight A288.


10000

9000

(°)

: E

8000 I

7000 I 6000

5000

# 0 0 0

3000

2 0 0 0 o

L

2 4 Richardson number

i l l 1 ~ ~ p n i~ i i i i i i i i i f i i ] i r i i ~ ] i1 ~ ~ l l l l l

° - m

m D

m

m

0 400 800 1 2 0 0 150Q Unstable K-H Way_lengths [.m)

E

I

10000

9000

8000'

7000

6000

5000 #000[ 3000 2000 o

b I I I I I I ~ I I I I I I I I I I I

2 Richordson number

I I { I I ~ I I I I I I I I I ~ H I [ ~ T I I ~ I I I I I I I I I I I I I ¸

, , , , , , , h , , , , , , , , I , , , , , , , , , I . . . . . .

17

16

15

400 800 1200 1G00 Unstable K-H Wavelengths (m)

Fig. 11 (continued).

Fig. 11 also shows the magnitudes of the wavelengths which are likely to become unstable first within each layer for which the Richardson number was smaller than 0.25. The level at which each run was flown is indicated on the right-hand axis of the last plot. However, we must use these profiles as a guide to the expected wavelengths only.


We cannot say exactly which wavelengths correspond to which levels because the atmosphere has probably evolved to some extent between the time of the profile and the time of each run (up to 3 h). Also the profiles contain some horizontal variation due to the horizontal motion of the aircraft during a profile. It can be seen from comparing the profiles in Fig. 1 lc and 1 ld for flight A288 that although the expected wavelengths are similar, the exact values change with time.

In the cirrus cloud of A283, typical wavelengths are of the order of 50 to 500 m, as can be seen from Fig. 11. Values as high as 1 km are occasionally seen for the deeper layers. Therefore it is possible that the peaks observed in the vertical velocity spectra between 100 and 500 m are due to these Kelvin-Helmholtz instabilities.

In the cirrus cloud of A290, typical wavelengths are again around 50 to 500 m, with occasional values up to 1 km. It is likely that the peaks observed between 50 and 100 m is due to this mechanism. Other peaks at scales of a few hundred metres to a kilometre may also be due to Kelvin-Helmholtz waves.

Similar values to those for flight A290 are again seen for A288, implying that the peaks seen in this flight are mostly due to the breaking of Kelvin-Helmholtz waves.

3 :

lO000Iir 7500

5 0 0 0

- - w

~ t

Y

4

10000

7500 Lr-<'..

iL. ,.'"

5 0 0 0

2500

o (b) 0 . 0

i * , , I , , , i , , , , , , . . . . . , , , I . . . . 2 5 5 0 2.5

Standard Deviations Stondurd Deviations

W 1

. . . . . U

. . . . . V

4 q

q !

5 0

10000 . . . . . . . . . , . . . . . . . ~w' 10000 . . . . . . . . . , . . . . . . . . w ' T T

. . . . . . v . . . . . v

7500 " ~ . . 7500 '" "~" /

v " . . ' ~ " v

~= 5000 ' " . ~ 5000 (,-~

2500 ~ 2500

% (C) '0( ) . . . . S t a n d a r 2 # e . . . . . . . . . . . . . . . . . . . o o ° d . . . . . . . . . . . . . 5.0

Standard2 Dev at o n s v l a b o n s

Fig. 12. Profiles of the standard deviations in the wind components (m S - 1 ) and in the temperature (K), calculated using the data from each horizontal run after high-pass filtering to remove variations due to scales larger than 5 km. (a) Flight A283, (b) flight A290, (c) flight A288, stack A, (d) flight A288, stack C.


4. Standard deviations

Standard deviations of the vertical velocity cr w, the temperature ~r r and the horizontal wind velocities tr, and ~r, were calculated for data obtained during the straight horizontal runs, after it had been high-pass filtered to remove variations at frequencies smaller than 0.03 Hz, (scales larger than 5 kin). The variation of these with height are shown in Fig. 12. The lines join the average values from each horizontal run. In all three cases, cr, and cr~ are both much greater than cr w. Fig. 13 shows the ratio of tr w to or, and ~. for all of the flights.

For flight A283, the velocity standard deviation ratios vary between 0.06 and 0.25, with Crw/Cr . smaller than crw/cr . within the cirrus layer. For flight A290, Crw/~ . varies between 0.1 and 0.3, while trw/Cr ~ reaches a maximum of 0.7 at a height just above 7000 m. This is due to the very low values of ~r, at this level corresponding to a maximum value of t%. This is true in all of the mid-cloud sections. At this level v is small and there is not much variation with height below this level, resulting in small variations in v along a run. For stack A of flight A288, Crw/Cr . and t rw/~r . vary between 0.1 and 0.45, with the highest values of both at cloud top due to low tr, and c%. For stack C, the values vary between 0.05 and 0.35.

1 O0 O0

7500

5000

2500

W:U

. . . . . W:V

(a)

10000

7500

5000

2500

. : ~ . . ............

(b)

W:U W:V

. . . . . I . . . . . . . . . 0 . . . . . . . . . i . . . . . 0.5. 1.0 0.0 0.~ , StandardDevlatlonRatios StandardDevlahonRatios

10000

7500

E 5000

32

2500

W:U

W;V

(c)

10000

7500

~o~ 5000

2500

W:U W N

(d) . . . . . . . . . t . . . . . . . . . 0.~ 1.0 0..5 10 C~ . . . . . . . . . , . . . . . . . . .

Standard Dewatian Ratios ' Standard Deviation Ratios

Fig. 13. Profiles of the ratios of the standard deviations in the vertical wind components to those in the horizontal wind components. (a) Hight A283, (b) flight A290, (c) flight A288, stack A, (d) flight A288, stack C.


The profile of cr w for flight A283 has a maximum well below the main cirrus deck, and the maximum in-cloud value is 0.39 m s-1 in the upper half of the cloud. The maximum updraughts and downdraughts are + 2 m s -~. ~w for flight A290 has a maximum below cloud base which is larger than any other value (0.45 m s - ~ ). In-cloud, the maximum of 0.23 m s - ~ appears in the upper half of the cloud. This value is smaller than for A283 by almost half. The maximum updraughts and downdraughts are only ± 1 m s -1 . The profile of cr w for flight A288 also has a maximum of almost 0.2 m s-1 in the upper parts of the cirrus for stack A. The maximum updraughts and downdraughts are only + 1 m s - l . This is comparable to flight A290.

The values of (rr for flight A283 are twice as large as those for A290 and A288, consistent with the greater convective activity.

Values of ~r u and ~r~ also are larger for flight A283 than for flights A290 or A288. In the cases of A290 and A288, neither cr u nor or, exceed 2.5 m s - 1. For A283, however, cru reaches 2.3 m s - 1 at the second highest sampled level and g,, reaches 4 m s- I in the upper half of the cloud layer.

5. Conclusions

Three daytime flights of the Hercules aircraft through thick frontal cirrus layers have been analysed in this paper. It has been observed that the occurrence of turbulence is patchy and weak in comparison with TKE found in the boundary layer. It is also on the whole rather 2-dimensional, with more turbulent energy possessed by the horizontal wind components. This is in agreement with previous observations, e.g. Dmitriev et al. (1984) and Quante and Brown (1992). Also in agreement with Quante and Brown (1992), it was found that more turbulent regions were associated with a more 3-dimensional isotropic flow field.

In cirrus clouds, there are a number of possible sources of turbulent kinetic energy (TKE). One mechanism for the production of TKE is instability due to the vertical shear of the horizontal wind. Kelvin-Helmholtz waves form in a layer with a stable lapse rate and a vertical wind shear. If the Richardson number Ri is below its critical value of 0.25 (the strength of the shear is large enough to overcome the damping effect of the stable density stratification), then these waves will break and become turbulent. This appears to occur within shallow layers of the cirrus in all three flights investigated. The turbulence is produced in this way at scales of between 50 m and 600 m (depending on the depth over which the Richardson number is below its critical value).

The observed peaks for flights A290 and A288 were on the whole at smaller scales than the peaks observed during A283, due to the high shear regions being concentrated in more shallow layers.

The observation of layers in which turbulence is produced by the Kelvin-Helmholtz mechanism is in agreement with Quante and Brown (1992).

The occurrence of these regions in which the Richardson number falls below its critical value of 0.25 may partly be due to the modification of the atmosphere by gravity waves propagating through the cloud. In certain phases of the wave cycle the local shear


will be enhanced by that due to the gravity wave. This can lead to complex interactions between gravity waves and the turbulence thus produced.

Another source of turbulence is buoyancy produced by latent heat effects or radiation. As an air parcel rises, ice crystals form which release latent heat, giving the parcel more buoyancy so that it continues to rise, producing TKE. Also, the vertical radiative heating profile can produce TKE. In optically thick cirrus layers, there is usually net radiative cooling in the upper parts of the cloud and net warming at lower levels (Francis et al., 1994). This makes the cloud convectively unstable and is a source of TKE.

Convective cells with a horizontal scale of 2 km were observed only during flight A283, for which there appeared to be enough optical thickness at cloud top to produce marked cloud top cooling. The ice water content time series exhibited large peaks which corresponded to higher ice crystal concentrations, probably due to new crystal nucleations in regions of enhanced supersaturation (updraughts). The convection would have been enhanced by the increased radiative heating within the convective cores due to higher ice water contents.

Spice (1994) came to the conclusion that the cirrus in another flight (A108) showed signs of convective activity, and cellular structures were observed in the simulated cirrus layers of Starr and Cox (1985a).

The cirrus clouds sampled during the other two flights did not seem to have much cellular convection occurring. The ice water contents were much more horizontally homogeneous. The smaller optical depth of these cirrus clouds resulted in the radiative cooling occurring throughout the cloud rather than being concentrated at cloud top.

Gravity waves were possibly observed in the upper regions of the cirrus in flight A283, as shown by peaks in the vertical velocity spectra at 2 km and by the coherence and phase cospectra of w and 0. These were probably forced by the convective cells at lower levels. Gravity waves were also observed in jet stream cirrus by Quante and Brown with similar wavelengths.

Acknowledgements

The authors are indebted to the aircrew and scientists of the Meteorological Research Flight for their dedication in making the measurements and for their assistance in the post-flight analysis of the data. Support for this work from the CEC and the NERC is gratefully acknowledged.

References

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observations of turbulence in cirrus clouds

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