observations of the turbulence structure within two stratocumulus-topped, marine boundary layers

OBSERVATIONS OF THE TURBULENCE STRUCTURE WITHIN TWOSTRATOCUMULUS-TOPPED, MARINE BOUNDARY LAYERS

PIERRE DURAND and THOMAS BOURCYCentre National de Recherches Météorologiques, URA Météo-France-CNRS 1357, Toulouse, France

(Received in final form 22 August 2000)

Abstract. Two situations observed during the second Aerosol Characterization Experiment (ACE-2)are analysed from aircraft measurements in the broken stratocumulus (Sc)-topped marine boundarylayer. The first one (26 June 1997), characterized by a non-polluted, oceanic air mass, presents adecoupling between the Sc layer (1400–1520 m) and the turbulent mixed layer, this latter extendingfrom the surface up to 580 m. In contrast, the second case (9 July 1997), during which continentalair had been advected over the experimental area, presents a well-coupled layer extending from thesurface up to the top of the Sc layer (910 m). This coupling, uncommon in this area in the middle ofthe day, is related to the relative shallowness of the boundary layer. For both situations, it is shownthat the turbulent fluxes can be computed with reasonably good accuracy (better than 10%), takinginto account both the random and the systematic errors involved in the eddy-correlation technique.Estimation of random error is based on the computation of the integral scale of the covariance, andsystematic error is estimated from the parameterization of Mann and Lenschow. The fluxes show thatthe buoyancy, as a source of turbulence, is due to latent heat flux rather than sensible heat flux, withvalues comparable to previous experiments in the Azores-Canaries basin. In addition, we propose amethod to analyse, for coupled situations, the relationship between the fractional cloudiness and theorganization of the turbulent field below the clouds. This method is based on a conditional samplingtechnique. It is shown that this organization cannot be deduced from the analysis of the velocitysignal, which is dominated by turbulence. However, when the signals are conditionally sampledaccording to the presence or absence of clouds, a weak cloud-related organization can be shown, andthe cloud-related transports quantified; the values found are of the order of 10% of the total transfers,i.e. the same order of magnitude as the errors on the total flux computation. The method developedis therefore promising, provided that the uncertainties can be reduced by analyzing a high amount ofdata.

Keywords: Atmospheric boundary layer, Conditional sampling, Decoupled cloud-layer, Turbulence.

1. Introduction

The Azores–Canaries region, like the eastern part of the Northern Pacific, is oftencovered by boundary-layer clouds, whose impact on weather and climate is of con-siderable importance. The meridional variation of this cloud layer generally obeysthe following scheme: from north to south, it evolves from a homogeneous, stra-tocumulus (Sc) layer, to broken Sc with interactions with some underlying cumuli(Cu), and to trade Cu. Over the eastern North Atlantic, the mid-latitude area, ap-proximately ranging from 30◦ to 40◦ in latitude, generally presents an intermediatesituation, i.e. the boundary layer is topped with a broken Sc layer. Such situations

Boundary-Layer Meteorology99: 105–125, 2001.© 2001Kluwer Academic Publishers. Printed in the Netherlands.

106 PIERRE DURAND AND THOMAS BOURCY

have been widely studied in the Azores region during campaigns like ASTEX(Atlantic Stratocumulus Transition Experiment) (Albrecht et al., 1995), SOFIA(Surface of the Ocean: Fluxes and Interaction with the Atmopshere) (Réchou et al.,1995) and SEMAPHORE (Structure des Echanges Mer-Atmosphère, Propriétésdes Hétérogénéités Océaniques: Recherche Expérimentale) (Lambert and Durand,1999, hereafter LD99). During SEMAPHORE, aircraft measurements were re-peatedly performed around midday, during mostly anticyclonic conditions south ofthe Azores archipelago. The average fractional cloudiness was estimated at about26% for the Sc capping the boundary layer, whereas the underlying Cu cloud coverwas on average only 6%. The vertical structure of the boundary layer was extens-ively studied by LD99, and can be summarized as follows: the whole boundarylayer, which extends from the surface up to the top of the Sc layer, can be dividedinto three distinct layers: the mixed layer, driven by surface fluxes, is decoupledfrom the broken Sc layer; this decoupling is associated with an intermediate layer,between the mixed layer and the Sc layer, which presents a weak stable stratifica-tion. Some broken Cu can appear at the top of the mixed layer, which is turbulent.The Sc layer is also turbulent, and topped by a sharp temperature inversion anddrying aloft.

It is important to define what is meant by a ‘decoupled layer’. Stevens et al.(1998) underline the importance of a precise definition of this concept. Nicholls(1984, p. 810), one of the first authors to discuss this, presented diurnal aircraftobservations of a layer of ‘minimum of activity’ (i.e., where the terms of the turbu-lent kinetic energy budget are small) situated below the Sc base and above a clearmixed layer. As mentioned by, for example, Garratt (1992, p. 200), the turbulentlayer composed by the cloud and its prolongation just below the cloud, which isalso turbulent, is a detached layer whose base is separated from the surface-driven,mixed layer. We agree with this definition, in the sense that the decoupled Sc layeroriginates from an initially well-coupled boundary layer. Without strong advectionor subsidence, this detachment is associated with the diurnal cycle (stabilization ofthe cloud layer by absorption of solar radiation).

Such a boundary-layer structure seems to have prevailed during SEMAPHOREin the middle of the day. In a few situations, however, the intermediate decouplinglayer does not exist, and the Sc layer is connected to the surface through the tur-bulent activity in the mixed layer. In this case, the mixed layer and the boundarylayer are the same, extending from the ocean surface up to the top of the Sc layer.The boundary layer often evolves from a coupled to a decoupled situation, andvice versa, with the diurnal cycle: during the daytime, the absorption of shortwaveradiation in the upper part of the Sc compensates, at least in part, for the longwaveradiative cooling; furthermore, the profile of the net shortwave radiation throughthe cloud layer tends to stabilize the air. The downward buoyancy, and the associ-ated source of turbulence, is therefore inhibited, the Sc becomes decoupled fromthe surface-layer turbulence, and it tends to dissipate (and therefore the fractionalcloudiness decreases) since the loss of moisture by entrainment of drier air at the

OBSERVATIONS OF THE TURBULENCE STRUCTURE 107

top of the Sc is no longer compensated for by moisture from surface evaporation.Conversely, at the end of the afternoon, incoming shortwave radiation vanishes andthe downward buoyancy source, due to longwave cooling, becomes strong enoughto establish the communication between the cloud and surface moisture. The cloudcover increases accordingly, as observed in the diurnal cycle of the oceanic Sclayers (Betts et al., 1995).

The diagnosis of the coupling of the Sc layer is of fundamental importancefor boundary-layer parameterization: if coupled, the relevant length scale is thethickness of the whole boundary layerZi (from the surface up to the top of theSc layer), whereas, in the other case, it is the mixed-layer thickness,h, which ismuch lower thanZi . LD99 developed a method to diagnose whether the Sc layer iscoupled or not, based on the computation, from aircraft slant ascents or descents,of the continuous profile ofε, the dissipation rate of the turbulent kinetic energy(TKE). In this paper, the method is used to analyse two situations described inthe CLOUDYCOLUMN project (Brenguier et al., 2000), which was a part of thesecond Aerosol Characterization Experiment (ACE-2) (Raes et al., 2000).

The cloud structure and evolution are strongly dependent on the turbulence fieldin the sub-cloud layer, and on the connections between these two layers. For frac-tional cloudiness, an intuitive scheme is to associate the cloudy areas with upwardvelocities, and the cloud-free areas to downdrafts. Such an organization was, inpart, verified in fair-weather Cu fields (e.g., Attié et al., 1997). For decoupledSc boundary layers, it is not true, because the cloud layer is detached from theunderlying turbulent mixed layer, and the cloud evolves towards dissipation. Thequestion, however, remains open for coupled, broken Sc layers. We will analysethis for a situation in ACE-2.

The first section of this paper will be devoted to the analysis of the verticalstructure of the boundary layer observed during the 26 June and 9 July 1997. In thefollowing section, we will analyse the turbulent transfer computed from the aircraftmeasurements, with a special emphasis on the various errors involved in the eddy-correlation technique. The third section is an attempt to rely on, through conditionalsampling techniques, the observed fractional cloudiness with the structure of theturbulence field below this cloud layer. The cloud-related transport will then bequantified.

2. Boundary-Layer Structure

2.1. MEASUREMENTS

The measurements were performed using the Merlin IV aircraft of Météo-France,which was equipped forin-situ turbulence measurements. A detailed descriptionof the instrumentation, and of the computational methods and performances of themeasurement systems, can be found in Lambert and Durand (1998) and Durand


et al. (1998). The instruments used for this work are those described in the abovepapers, but the sampling rate of the fast sensors was significantly increased duringACE-2, with respect to previous campaigns: it varied from 50 to 200 s−1. How-ever, the turbulence calculations (fluxes and variances) are performed on detrendedtime series at a rate of 25 s−1, after averaging the raw data. Average horizontalwind, temperature and specific humidity, as well as the turbulent fluctuations ofthe three wind components, temperature and specific humidity, were available overthe whole flight. The cloud structure along the aircraft track could be deduced fromradiation measurements, including an upward-looking PRT5 Barnes radiometer todetect the fine cloud structure just above the aircraft.

2.2. 26 JUNE AND 9 JULY

On 26 June, the Merlin flight number 21 (between 1130 and 1430 UTC) was usedto explore an area, 60-km square, whose centre was located at 29.4◦ N, 16.6◦ W.The boundary layer was topped by Sc whose fractional coverage varied from 6 to 8oktas, and whose top average altitude was about 1500 m (see the satellite picture inBrenguier et al., 2000). Well below the Sc layer, 1 to 2 oktas of Cu were observed inthe flight area. The wind direction in the boundary layer was from east–northeast,with speed increasing with altitude from 4 to 6 m s−1. Above the boundary layer,the flow was weak and disorganized, at least up to 2200 m. Although the flow inthe boundary layer suggests a continental origin of the air mass, analysis of backtrajectories at a greater scale has shown that the air mass was of oceanic origin, andwas therefore classified as non-polluted (Brenguier et al., 2000).

On 9 July, the Merlin (flight number 30, between 1215 and 1530 UTC) mademeasurements along a square of identical size, but centered at 29.4◦ N, 17.0◦ W,i.e. slightly shifted to the West with respect to the 26 June flight. This time, theboundary layer only extended up to 910 m, the Sc fractional coverage at the topof the boundary layer varied from 3 to 7 oktas (see Brenguier et al., 2000), andno Cu were observed within the boundary layer. The wind in the boundary layerwas homogeneous from east–northeast, with a strength of 7 m s−1. In contrast tothe 26 June, the wind above the boundary layer remained east–northeast oriented,with speed of about 5 m s−1, at least up to 1500 m. This suggested advection fromcontinent, and the situation was classified as polluted (Brenguier et al., 2000).

The vertical structure of the boundary layer was characterized following themethod developed by LD99, i.e., by simultaneously analysing the profiles of po-tential temperature, specific humidity, and the dissipation rate (ε) of the turbulentkinetic energy. The variableε was computed from the time series of the turbulentvertical velocity of the air, computed along the slant ascent or descent of the aircraftthroughout the boundary layer. After a high-pass filtering of the signal to retainfrequencies in the inertial subrange, the Kolmogorov relation is used to relate thevariance of the filtered signal toε. This is done in a time window moving throughthe time series, so a continuous profile ofε can be obtained in this way. Such a


technique was already used, for example, by Shaw and Businger (1985) on straightand level runs, or by Tjernström and Smedman (1993) on aircraft slant profiles.This technique, as shown by LD99, is an excellent means to determine if theturbulence is continuous from the surface up to the Sc layer or not, in other wordswhether the Sc layer is coupled or not by turbulent mixing with the surface layer. Asmentioned above, the decoupling appears as an intermediate layer of low turbulentactivity, i.e., a low level of TKE. Numerous studies in the atmospheric boundarylayer have shown that its top is marked by an important decrease in TKE, andin ε (see, for instance, the schematic profiles presented by Kaimal and Finnigan,1994, p. 22). Such decreases in TKE andε should therefore appear at the top of themixed layer (i.e., well below the cloud layer in the decoupled case). The traditionalestimation of TKE profiles requires stacked horizontal runs, long enough to takeinto account the various turbulent scales. In contrast, the technique used here tocomputeε only requires inertial subrange scales, which can be sampled over shorttime series on slant profiles. This is the reason whyε was used in the diagnosis ofthe decoupled boundary layer. For the soundings analysed in this paper, the aircraftascends (or descends) at a rate of about 5 m s−1. Given the sampling rate of the data(25 s−1), a vertical resolution of 0.2 m is reached. To computeε, the time seriesof the vertical velocity are filtered in a frequency band ranging from 0.5 s−1 to theNyquist frequency (12.5 s−1), which, given the airspeed of the aircraft, correspondsto horizontal wavelengths of 200 and 8 m, respectively. Then,ε is computed onoverlapped time series of 20 s (about 2000 m in the air mass), during which thealtitude variation of the aircraft is about 100 m. We therefore assume thatε varieslittle in this range of altitude.

The profiles of the potential temperature (θ), specific humidity (q) andε, for the26 June, are presented in Figure 1. Theε profile shows two layers with high valuesof turbulent energy: the Sc layer, which extends from 1400 to 1520 m, and below400 m. Above 800 m, there is a significant decrease inε values, which are oneorder of magnitude smaller than those below 400 m. This indicates a decoupling ofthe Sc layer. The problem is to determine the height of the top of the mixed layer(driven by surface fluxes), which is somewhere between 400 and 800 m in altitude.It cannot be precisely determined from theε profile, since the profile is somewhatsmoothed by the time required to compute the variance; furthermore, since one ortwo small Cu were probably present in this area, there is a local but significantincrease in the turbulent energy at 700 m. However, with the decoupling beingestablished, the altitude of the top of the mixed layer can be accurately determinedfrom the profiles ofθ andq: a small but significant variation of+0.5 ◦C and−1 gkg−1 can be seen at 580-m altitude, which marks the top of the turbulent mixedlayer. It should be noted that the diagnosis of decoupling could not have been estab-lished from the thermodynamical profiles only, because the small variations at thetop of the mixed layer are not much greater than the r.m.s. of the temperature and

moisture fluctuations in the mixed layer (for example, we computedθ ′21/2 ≈ 0.4 ◦C


Figure 1.Profiles of the potential temperature, specific humidity and dissipation rate of the turbulentkinetic energy for the 26 June 1997.

andq ′21/2 ≈ 0.4 g kg−1 on a straight and level run at 180-m height). The weakness

of the buoyancy flux computed at 740-m altitude (see below, Section 3) supportsthis conclusion, indicating that the mixed layer could not reach this altitude.

The case of 9 July is notably different: the profile ofε, shown in Figure 2,does not exhibit any significant variation in energy throughout the mixed layer; theprofiles of θ andq are also very continuous. This is characteristic of a coupledsituation: in this case, the mixed layer and boundary layer are the same, with atop at an altitude of 910 m. This situation is somewhat uncommon in this area– the coupled boundary layers are mostly associated with solid Sc layers. LD99showed that, in the Azores–Canaries basin, the daily Sc layer was, most of thetime, broken and decoupled. The observed coupled case on the 9 July is probablydue to the thickness of the whole boundary layer; the synoptic trade inversion thistime appears at an altitude (910 m) that is much lower than that observed on the 26June (1520 m), and even generally in this area during anticyclonic conditions. Forexample, LD99 reported 12 Sc cases observed during SEMAPHORE, with inver-sion heights ranging between 1140 and 2216 m. These situations were decoupled,with the mixed-layer thickness ranging from 500 to 1300 m (880 m on average).Given that the surface sensible and latent heat fluxes of LD99 are comparable tothe present cases (see below), we could expect comparable thickness for the mixedlayer during ACE-2. As a consequence, if the trade inversion (and therefore thetop of the Sc layer) is only at 910 m (probably due to strong subsidence), it is notsurprising that the mixed layer driven by surface flux would reach the cloud layer,leading to a coupled situation.


Figure 2.Same as Figure 1, but for the 9 July 1997.

3. Turbulent Fluxes

The fluxes were computed with the eddy-correlation technique, on straight andlevel runs of about 60 km in length. As discussed, for example, by Mann andLenschow (1994), Lambert and Durand (1998) and LD99, two types of errors areinvolved in the computation of the covariance: the first one is a random error, whichis associated with the fluctuating character of the time series; and the second is asystematic error that appears when a high-pass filtering is applied to the time series.Increasing the cut-off frequency of the filter reduces the random error, becauseit removes the greatest length scales that are poorly resolved along the run, butdramatically increases the systematic error because it removes part of the signal.As demonstrated by Lambert and Durand (1998) for the marine boundary layer, acut-off frequency corresponding to a wavelength of 5 km was found to be a goodcompromise between these two competing effects, and this was thus adopted forthe data processing of ACE-2.

The random errorσwX on the covariance ofw andX can be expressed as(Lumley and Panofsky, 1964),

σwX

w′X′=[2λwX

L(1+ r−2

wX)

]1/2

, (1)

whereλwX is the integral scale of the instantaneous covariancew′X′, L is thelength of the run andrwX is the correlation coefficient betweenw andX. λwXwas computed from the autocorrelation of the signalw′X′, integrated up to its firstzero, as suggested by, for example, Lenschow and Stankov (1986). Consideringthat the relation given by (1) represents a random error, its value can be reducedby averaging the results obtained on several runs, provided that we can assume ho-rizontal homogeneity and steady-state conditions for these runs. We hypothesized


this was true for consecutive runs performed on the various sides of the squareat approximately the same altitude. The final random error was thus estimated asσwX/√n, where the overbar denotes the average on then runs.

The systematic error could be estimated from the low-frequency range removedby the high-pass filtering, but this requires a run of great length (or several runs)to obtain an accurate estimation. This was not possible from our data set, but analternative way was to compute this error from the relationship proposed by Mannand Lenschow (1994),

δwX

w′X′= w′X′ − w′X′f

w′X′= 1.2h

( zh

)1/2(

1

Lc− 1

L

), (2)

where the subscriptf refers to the filtered flux,h is the mixed-layer thickness,z themeasurement altitude andLc is the cut-off wavelength of the filter. Lambert et al.(1999) tested this expression against direct computations in the marine boundarylayer, and found good agreement, mainly for cross-wind runs. Thus, we decided touse the right side of (2) for ACE-2 data. For the 9 July,h is the altitude of the topof the Sc (910 m); for the 26 June,h is the top of the mixed layer (580 m) for theruns inside the mixed layer, whereas for the runs between h and the top of the Sc,(z/h) in (2) was replaced by (Zi − z)/(Zi − h), i.e., the distance of the run to thetop of the Sc, normalized by the thickness of the layer extending from the top ofthe Sc to the base of the decoupled layer (just above the mixed layer).

The best estimate of the flux is thus obtained as

w′X′ =[

1

n

∑n

(w′X′f )i

]+ δwX ± σwX√

n. (3)

The covariancesw′θ ′ andw′q ′ (respectively proportional to the sensible andlatent heat fluxes) are presented in Figures 3 and 4 for the 26 June and 9 July,respectively. At each level of measurement, we have plotted the mean filtered value(the first term on the right side of Equation (3)), the estimate of the non-filtered flux(the sum of the first two terms on the right side of Equation (3)), and the error bar(the last term on the right side of Equation (3)). The error bars, as well as thedifference between the filtered and non-filtered values, are small (in the order of10%, except when the flux vanishes). This is significantly better than the valuesobtained by Lambert and Durand (1998) for the SEMAPHORE experiment, andcan be explained by the length of the runs, which is greater for ACE-2 (60 kminstead of 27 km), and the averaging of several runs.

Although the precise shape of the profiles cannot by inferred from the fewlevels analysed in the boundary layer, we see that the sensible heat flux is weakfor both cases. Except in the Sc layer, the predominant term is the latent heatflux, for both the surface energy budget and the source of buoyancy. In terms ofenergy, the sensible heat flux is expressed asH = ρ̄Cpw′θ ′ and the latent heat


Figure 3.Turbulent fluxes for the case of 26 June:w′θ ′ (left) andw′q′ (right). The open circles rep-resent the value computed after high-pass filtering of the time series. The solid diamonds correspondto the filtered values increased by the difference between non-filtered and filtered values computedaccording to (2). The error bars are computed according to (3) (see text for precise explanation). Thedashed lines indicate the Sc base and top, and the dash-dotted line the top of the mixed layer.

Figure 4.Same as Figure 3, but for the 9 July 1997. The dash-dotted line indicates both the top ofthe mixed layer and the top of the Sc layer.


flux asLvE = ρ̄Lvw′q ′, in whichρ is the air density,Cp the specific heat of airat constant pressure, andLv the latent heat of vaporization of water (note thatq

must be dimensionless, ifLv is expressed in J m−3). Assumingρ̄Cp ≈ 1200 J m−3

K−1, andρ̄Lv ≈ 3× 106J m−3, we can see that the latent heat flux is at least oneorder of magnitude greater than the sensible heat flux. For example, the 26 Juneprofiles suggest surface values of about 140 W m−2 for LvE, and 4 W m−2 forH . The buoyancy flux, which is the major source of turbulence in the mixed layer(except close to the surface where friction becomes important), can be expressedasw′θ ′v ≈ w′θ ′ + 0.61T w′q ′, whereθv is the potential virtual temperature andTthe absolute temperature, andq is dimensionless. It can be seen from the values offluxes that the contribution of the latent heat flux to buoyancy is at least as high asthat of the sensible heat flux, a frequent occurrence in the marine boundary layer(Lambert et al., 1999). For the case mentioned above, the TKE source due to totalbuoyancy flux is(g/T )w′θ ′v = 4.2× 10−4 m2 s−3, of which 1.4× 10−4 m2 s−3 isdue to the kinematic heat flux, and 2.8×10−4 m2 s−3 is due to the moisture flux. Ifwe consider the fluxes computed at the altitude of 740 m on June 26, the moistureflux represents a TKE source of 7×10−5 m2 s−3, whereas the heat flux represents aTKE sink of−10−4 m2 s−3. The global contribution to TKE is a sink of−3×10−5

m2 s−3, a very small value, confirming the decoupling between the mixed layer andthe Sc layer.

4. Conditional Sampling

4.1. THE TECHNIQUE

In the case of the decoupled Sc layer (case of 26 June), some connections betweenthe Sc layer and the mixed-layer turbulent field may exist via the few Cu observedat the top of the mixed layer, which could penetrate into the Sc layer. However,these connections are weak, and cannot establish a high correlation between thebroken Sc geometry and the velocity field in the mixed layer. Conversely, for thecoupled case, we can analyze whether the cloud structure (and, in particular, thespatial distribution of the clouds) is related to the organization of the underlyingturbulent field in the mixed layer into updrafts and downdrafts. This was done inthe case of the 9 July using a conditional sampling technique.

The conditional sampling technique consists in selectively sampling the timeseries according to a specified criterion, which is generally a threshold defined onone or several variables. For our purpose, the criterion chosen was the presenceof cloud just above the aircraft. The corresponding threshold was a value of thelongwave radiation (or radiometric temperature) measured by the upward lookingBarnes radiometer: when the measured value exceeded this threshold value, it wasassumed that the aircraft flew below cloud.

Another criterion was applied to the vertical velocity signals: in order todetermine the characteristic length-scales of the organization into updrafts and


downdrafts, we conditionally sampled the segments with values of w greater than

the standard deviation(w′21/2). This threshold enables the detection of movements

greater than the turbulent background. Given that we are only interested in theenergy-containing scales, the signal was previously smoothed, in order to attenu-ate the small-scale fluctuations, and to prevent too-fast changes on both sides ofthe threshold. This smoothing, which consists of a repeated weighted average onthree consecutive values, resulted in a reduction of variance of 10%. The distancebetween two consecutive updrafts,Lw, was computed to characterize the field ofw.

Four runs, performed at an average altitude of 480 m (i.e., at about half of themixed layer, and about 300 m below the cloud base) and whose lengths were about20–30 km, were chosen because they were made below fractional cloudiness withalternating cloud-free and cloudy areas. The results presented below represent theaverages of these four runs.

We examined two questions relative to the conditional sampling ofw: (1) whatis the influence of the threshold on the result? and (2) what could be inferred fromthe field of w on the relation between the velocity and cloud fields? The histograms

of w according to the threshold chosen (from 0.6 to 1.8 timesw′21/2

) are presentedon Figure 5. As the threshold increases, the histogram moves towards higher val-ues, which implies that the turbulent character of the signal (although smoothed) ispredominant on the coherent velocities linked to the clouds. The average distancebetween two consecutive updrafts also regularly increases (from 630 m to 1430 m)according to the threshold. These values are coherent with the wavelengths com-puted from the spectral peak ofw (1320 m, 940 m, 570 m and 1300 m on thefour runs, respectively). The conclusion is that the possible connections betweenclouds and velocity field in the boundary layer cannot be deduced from the statisticsonw. This is confirmed on the (w – cloud) diagram (Figure 6), which shows animportant scatter. The criterion used in the following is therefore the cloud presencediagnosed on the Barnes radiometer signal.

The average fractional area covered by cloud is 0.57. The cloud criterion is usedto determine the lengths of the cloudy segmentsLc, of the cloud-free segmentsLf , and the characteristic wavelength of the cloud fieldL1 (distance betweentwo consecutive clouds,L1 = Lc +Lf ). The histograms of these parameters arepresented in Figure 7. The most probable values ofLc lie between 75 and 300 m,whereas forLf they range from 150 to 600 m.L1 lies generally between 300 to1200 m. The average values areL1 = 910 m,Lc = 520 m andLf = 390 m.

The study thus proceeded with the cloud criterion, and the time series weredivided into two sub-samples (cloudy and cloud-free) to determine, (1) whetheran organization related to the fractional cloudiness exists and to what extent itcontributes to the total transfers, and (2) what is the respective contribution of the


Figure 5.Histograms of the horizontal distance between consecutive updrafts, for various values ofthe threshold on the vertical velocity signal.


Figure 6. Vertical velocity vs. radiometric temperature measured by the upward looking Barnesradiometer. The dashed line represents the threshold chosen to discriminate between cloudy andcloud-free areas. Only one value per second is displayed on the graph (the complete data set contains25 times more values).

cloudy and cloud-free areas to the transfers. The time series of the various signalswere decomposed, according to the following method, on each of the four runs:

X = X̄ + X′, (4)

whereX is the average ofX over the whole run (including cloudy and cloud-freeareas), whereX could be either vertical velocity, temperature, specific humidity orhorizontal velocity. Let us now consider the sub-sample composed of cloudy areas;we can write

Xc = X̄ +X′c +X′′, (5)

whereX′c is the average of the fluctuations in the cloudy areas, andX" = X′ −X′c.Hereafter, subscriptc refers to cloudy areas, and subscriptf to cloud-free areas.A similar equation can be written for the cloud-free areas. A non-zero value ofX′c(and therefore ofX′f ) indicates a coherent structure of the field in relation to thespatial distribution of clouds. The average turbulent flux ofX in the cloudy areascan thus be written as

w′X′c = w′c X′c + w′′X′′c . (6)

A similar equation can be written for the cloud-free areas, with the subscriptf used instead ofc. In the above equation, the first term of the right-hand side


Figure 7.From top to bottom: histograms of the lengths of the cloud-free paths, of the clouds, and ofthe characteristic length of the cloud field (cloud + adjacent cloud-free length).


represents the transfer due to the organization linked to the clouds, and the secondrepresents the turbulent transfer. Note that the average flux on the total run can bewritten as

w′X′ = Lc

Lw′X′c +

Lf

Lw′X′f , (7)

whereL,Lc andLf are the total, cloudy and cloud-free lengths of the run, respect-ively (L = Lc+Lf ). The average fractional cloudiness of the four runs (i.e.Lc/L)was 0.57. Combining Equation (6) (and the similar equation for cloud-free areas)and Equation (7) leads to

Lc

L

w′c X′cw′X′

+ Lc

L

w′′X′′cw′X′

+ Lf

L

w′f X′f

w′X′+ Lf

L

w′′X′′fw′X′

= 1.

(A) (B) (C) (D)

(8)

Here, (A), (B), (C) and (D) terms represent the four contributions to the totaltransfer on the whole run, whereas(A)L/Lc, (B)L/Lc, (C)L/Lf and(D)L/Lfrepresent the average flux on each sub-sample.

4.2. VARIOUS CONTRIBUTIONS TO THE TRANSFERS

The average fluctuations are presented in Table I. Although weak, they are non-zero, and imply the following organization in the mixed layer: the clouds are linkedwith updrafts in the mixed layer, with an average velocity of 0.045 m s−1 and anaverage specific humidity 0.02 g kg−1 higher than average, whereas the potentialtemperature and the longitudinal wind were found to be 0.004◦C and 0.007 ms−1 lower than average. The air parcels below cloud-free areas are drier, becauselatent heat flux is slightly lower than in cloudy areas (see below), and because thedowndrafts between the clouds incorporate upper, drier air into the mixed layer.The difference between a cloudy cell and its neighbouring cloud-free cell is 0.10m s−1 in vertical velocity and 0.05 g kg−1 in specific humidity.

In order to determine whether these differences are significant or not, we have toevaluate the two possible sources of errors: instrumental and statistical. The first isdifficult to estimate, because it involves various factors like sensor accuracy, hous-ing and pressure contamination due to the airflow around the sensor (Lenschow,1986; Lambert and Durand, 1998). Furthermore, calibration against ground-basedmeasurements cannot be considered as satisfactory because the sampled areas andthe sampling time are different for the two platforms, and ground-based platformscannot be used over the open ocean. So, only indirect estimations can be made,such as, for example comparison between various aircraft, as performed by Lam-bert and Durand (1998) in the marine boundary layer in the Azores region duringSEMAPHORE, i.e., for conditions comparable to the present. They found a total(instrumental + statistical) error on the rms ofw, θ , q andu of 0.05 m s−1, 0.003◦C,


TABLE I

Average values of the fluctuations in the cloudy(X′c)and cloud-free(X′f ) areas, for the vertical velocity, po-tential temperature, specific humidity and horizontal wind(along the mean wind). The statistical errors (σX) are alsoindicated.

w (m s−1) θ (◦C) q (g kg−1) u (m s−1)

X′c +0.045 −0.004 +0.022 −0.007

X′f −0.061 +0.006 −0.030 +0.009

σX 0.033 0.006 0.027 0.039

0.017g kg−1 and 0.08 m s−1, respectively. For our data, we computed the statisticalerror on these estimates as (Lumley and Panofsky, 1964)

σX =[2X′2

λX

L

]1/2

, (9)

whereX could be eitherw, θ , q or u. The integral scale of the vertical velocityλwwas computed from the time series ofw, as explained above, whereas for the otherparametersλX was estimated from the relationships proposed by Lenschow andStankov (1986) (these authors proposed simple parameterizations for the integralscales of the variancesλX2, and suggested thatλX = λX2/0.67). The results (forthe cloudy area) wereσw = 0.033 m s−1, σθ = 0.006 ◦C, σq = 0.027g kg−1 andσu = 0.039 m s−1. These values, although slightly different, present a reasonableagreement with those of Lambert and Durand (1999), and can be used as a roughestimate of the accuracy. Given the values presented in Table I, we can see thatthe signal is significant forw, ambiguous forq, probably not significant forθ , andcertainly not foru.

The contribution of these coherent motions to the total transfers is presentedin Table II, and represents less than 10%. Furthermore, the contribution to themomentum flux is opposed to the total transfer. This is notably different from theresults found by Attié et al. (1997), who performed a similar study below Cu cloudsover the equatorial rain forest (the data were measured at 750-m altitude, whereasthe cloud base was estimated from the lifting condensation level at 970± 110 mby Delon (1999)). They found that the average values of the organized verticalvelocity, moisture and temperature were one order of magnitude greater than ours,and contributed to the transfers by up to 50% in the cloudy area.

In terms of flux (i.e., the terms(A)L/Lc,. . . ), the results presented in Table IIIdemonstrate that latent heat flux is significantly greater below the clouds than else-where. This is also true for momentum flux, at least for its turbulent contribution.Sensible heat flux is probably too weak to exhibit a characteristic feature.

OB

SE

RVA

TIO

NS

OF

TH

ET

UR

BU

LEN

CE

ST

RU

CT

UR

E121

TABLE II

Contribution (in %) to the total transfer of sensible heat, latent heat and momentum, on the whole run, of the cloudyand cloud-free areas, and, for each of them, the contribution of the coherent and turbulent signals. Note that the variouscontributions can be summed, because they are expressed as the fractional contribution to the total transfer.

Transfer of sensible heat Transfer of latent heat Transfer of momentum

Coherent Turbulent Total Coherent Turbulent Total Coherent Turbulent Total

Cloudy 4 52 56 2 65 67 −3 66 63

Cloud-free 5 39 44 3 30 33 −2 39 37

Total 9 91 100 5 95 100 −5 105 100

122P

IER

RE

DU

RA

ND

AN

DT

HO

MA

SB

OU

RC

Y

TABLE III

As in Table II, except that the various contributions are expressed as the ratio of the flux of the sub-sample (i.e. quantitytransferred by unit of area) to the total flux. Thus, the values in the cloudy and cloud-free columns cannot be summed up,because the fractional areas of each sub-sample are not identical.

Sensible heat flux Latent heat flux Momentum flux

Coherent Turbulent Total Coherent Turbulent Total Coherent Turbulent Total

Cloudy 7 91 98 4 114 118 −5 116 111

Cloud-free 12 91 103 7 70 77 −5 91 86


The signals of the relationship between fractional cloudiness and the organ-ization of the turbulent field in the underlying mixed layer are therefore weak.However, they could considered as significant, because similar behaviour wasfound on the four runs analysed.

5. Conclusion

Methods able to characterize the vertical structure and the dynamics of the marineSc-topped, boundary layer observed during ACE-2 have been presented. Thesemethods were based on aircraft in situ measurements, and were applied to twosituations, the 26 June and 9 July 1997 cases, corresponding to air masses ofoceanic and continental origin respectively.

Both situations present a broken Sc layer at the top of the boundary layer, ina moderate easterly wind. First of all, we have shown how the vertical structurecan be characterized using a simultaneous analysis of the profiles of the dissipationrate of the turbulent kinetic energy and of the thermodynamical parameters. The26 June case shows a mixed layer extending from the surface up to 580 m, whichis well below the level of the Sc base. This situation is therefore decoupled, that isto say there is little turbulent connection between the cloud layer and the surfacefluxes. In contrast, the 9 July case presents a mixed layer extending from the surfaceup to the top of the Sc layer, which only reaches 910-m altitude. The low altitudeof the trade inversion explains this uncommon daytime coupling of the broken Sclayer.

The turbulent fluxes of sensible heat and latent heat were computed for thesetwo situations, with special attention given to estimating and reducing the errorslinked to the eddy-correlation technique. A method was proposed to keep theseerrors below 10% (except if the flux vanishes). In this method, the random errorin flux estimates is computed from the integral scale of the instantaneous flux, andthe systematic error is deduced from the parameterization proposed by Mann andLenschow (1994). The sensible and latent heat fluxes indicated that the buoyancyflux, as a source of turbulence in the mixed layer, is mainly due to the latent heatflux rather than the sensible heat flux, which is a peculiarity of the marine boundarylayer with respect to the continental one.

For the coupled situation (9 July), we showed with a conditional sampling tech-nique that there is a weak relationship between the fractional cloudiness and theorganization of the turbulent field in the underlying mixed layer, into updrafts anddowndrafts. The fractional cloudiness in this case was 0.57. We showed that theturbulent signal predominates in the time series of the vertical velocityw, and thatthe cloud-related organization cannot be deduced from thew signal itself. Thetime series were thus conditionally sampled according to the presence or absenceof cloud, as indicated in the signal of the upward-looking, Barnes radiometer. Thecharacteristic length scales of the cloud field ranged from 300 to 1200 m. The


time series was decomposed into a signal correlated with the cloud structure, anda turbulent signal. Estimations of the statistical error in the signals showed thatsuch an organization of the turbulent field is of the same order as the random fluc-tuation. The contribution of this weak signal to the vertical transfer only reaches9% for sensible heat and 5% for moisture. This is considerably lower than thevalues observed below continental, fair-weather Cu clouds by Attié et al. (1997),and of the same order of magnitude as the errors in the flux estimates, as shownin the first part of this paper. This difference is probably due to the life-time ofthe clouds, which is much shorter for Cu than for Sc; the former therefore remainsconnected to the updrafts from which it originates, and could form and disappear ina few minutes, whereas the latter has its own life cycle, often several days. Lambert(1997) analysed a decoupled broken Sc layer during SEMAPHORE and showedthat it was transported by the mean flow without strong modification during severalhours.

Although the dataset used in this paper was limited, we showed that the method-ology presented is able to describe the cloud-related transport in the boundary layertopped by broken Sc. Further investigations would require a more complete dataset,in order to reduce the uncertainties in the estimates of the cloud-related transport.The study of the variation with height of this transport would also require muchdata. As shown in this paper, a 40-min run, performed at the same flight level, isjust sufficient to estimate the cloud-related transport with an accuracy comparableto the uncertainty in the total fluxes. We cannot repeat such superposed runs in theboundary layer without violation of the steady-state assumption. Many flights incomparable conditions would be needed to achieve a complete study, but it wouldprobably be difficult to obtain, because diurnal coupled Sc are mostly uncommonover the ocean (Lambert and Durand, 1999). Two approaches could thus be ex-plored: the first one would be the analysis of the nocturnal Sc boundary layer (moreoften coupled than the diurnal case); and the second would be to analyze large-eddy simulations of the coupled, broken Sc boundary layer, in order to quantify thecloud-related transport in the underlying mixed layer.

Acknowledgements

Special thanks are due to Jean-Louis Brenguier who allowed this study to be con-ducted and provided us with the aircraft data, and to Bruno Piguet and his team fortheir help in data processing.

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observations of the turbulence structure within two stratocumulus-topped, marine boundary layers

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