TURBULENCE STRUCTURES IN A NON - STATIONARY
MARINE ATMOSPHERIC BOUNDARY LAYER
Ulf Andrm
Supervisor: Michael Tjernstrom
Department of Meteorology UppsaIa University
Abstract
The vertical structure in the coastal marine atmosphere has been investigated using data from aircraft measurements performed along the Blekinge coast. The present data are from the third of October 1990. The main feature is fairly homogeneous horizontal conditions and a subceeing boundary layer which lowers from 600 meters down to about
50 meters during the day. The turbulence were found to be in a decreasing state.
The turbulence parameters were normalized using normal stationary scaling, in order to compare with other results.
ERRATA
Now side 5, line 7 surface difference side 13, line 15 wind side 14, line 10 9 2 2000side 14, line 5—6 from bottom
Aloft we the warming.
side 24, text to fig. 20
easterly part (—1—)
side 24, line 3 Lat 15.8side 28, nonations, add:
g Magnitude of gravity frequency a1 Constant 0.55 Ua True airspeed BL Boundary layer Change
surface temperature difference
Wind speed
9 2 1800
aborted
easterly part (X)
Contents 1 Introduction 2 The Experiment 2.1 The Area 2.2 The Measurements 2.3 The Case 3 Results 3.1 Average conditions 3.2 Turbulence structure 4 Some turbulence applications 5 Conclusions
Notations
1 Introduction
The atmospheric boundary layer (ABL) is one of the most important parts of the
atmosphere for the human environment and therefore also one of the most interesting
parts. However, the boundary layer is difficult to describe from a purely theoretical
approach, compared with the free atmosphere. Therefore most of our knowledge about the ABL comes from numerous field experiments, from masts and from aircraft measurements. As computers has grown more powerful, numeric simulations has become useful tools in
investigating and understanding the ABL. The development of different closure models is
fundamental for the forthcoming BL research.
When we are studying the boundary layer we like to have as ideal conditions as possible. Assumptions about stationarity in time and an upstream horizontal homogeneity are important to study isolated effects. Here the Marine Atmospheric Boundary Layer
(MABL) is useful and interesting because of the homogeneous fetch, the small diurnal
variations and also the importance for the human environment. It has been shown,however, by cf.eg. Tjernstrom [1991] that especially the coastal MABL is far from as
homogeneous as often assumed.
An interesting feature in the MABL is the frictional decoupling. It occurs when the lowest layer is stabilised when the air blows out from land and out over cold water so that the shearing stress is ”turned of”, completely or partially. This is a source to low level jets
[Hogstrom and Smedman 1990], which occurs frequently in the Baltic sea. Even in cases
of frictional decoupling there can, however, still be turbulence. This is sometimes called ”inactive turbulence” and is assumed to be transported from other parts of the boundary
layer [Smedman et. a1. 1994].
The most important vertical transport processes in the ABL are the turbulence flux. The transport of momentum down to the surface and sensible and latent heat up from, or down to, the surface is essential for the heat and momentum balance in the ABL. The conversion of energy from the mean flow to turbulence quantities by shear and buoyancy production may be expressed with the turbulent kinetic energy (TKE) equation [ Kaimal
and Finnigan 1994 ]. Here in the mean wind direction form:
g, : wry/mg?) + %(W) ._
figm) ._ gar) ... E
(1)
The two first terms on the right side are the shear and buoyancy production, the
third term describes how the energy redistributes by pressure fluctuations, the fourth term spreads the energy vertically and the last term is the dissipation.
a = iiw'e'i
<2)
<W>l a}
This is the flux Richardson number (Rf) and it is an important stability parameter.
The flow is turbulent when R; is less than a critical value (RC) of 0.25. There may be some
hysteresis effect, which means that there can still be turbulence left on values higher than
R; when going from turbulent to laminar flow. When going from laminar to turbulent flow, however, the change is at 11620.25 [ Stall 1994 l The height Where the buoyancy production and the shear production becomes equal is often referred to as the MoninObukhov length (L). In the surface layer where the flux is assumed to be constant we
introduce a characteristic velocity 21* a characteristic temperature T, and a characteristic specific humidity Qras:ui : ~~(ii—’73")
(3)
u*T* : ~(W) (4)
“*Q* 2 ”(W)
(5)
Using these characteristic parameters in the production terms along with surface layer similarities we may write Monin Obukhovs length as:
“W“ETO
gk(w’9’)<6)
In the boundary layer we often use these parameters to generalise observations, in order to compare results from different measurements. For the surface layer we have parameters as Zi, L, ur, Q*, T*. Similar to this we have u; and Tf for convective scaling
and w,, and 6* for mixed layer scaling [ Hogstro'm and Smedman 1989 ] We use this
scaling parameters to form expressions for the turbulence flux in quantities of gradients as universal functions of z/L were 2 is the height above surface. For example:
®u(z/L) :- ~33??? (7)
To understand the conversion of mean kinetic energy to turbulence kinetic energy it is important to separate the different scales of the turbulence. This can be done using Fourier spectra and cospectra which gives the turbulent energy as a function of wavenumber or
frequency. To transform the spectra from wavenumber to frequency we use Taylor’s
hypothesis which assumes that the eddies are passively advected with the mean wind. We may divide the spectra in to three regions: the energy containing range, where the
turbulent energy is produced by shear and buoyancy, the inertial subrange, where large eddies is broken into smaller, and the viscous subrange where the eddies is broken into internal energy. It is only in the inertial subrange that we can find a theoretical expression
for the spectra [ Kaimal and Finnigan 1994 ]
nSu(n) ___ 011 ©2/3(¥)~2/3 (8)
ugt ~— (27rk)3/3 6 an
If we multiply eq. 8 with 712/3 we can determine 143$?” for each level. If ”S" n is use? 3
. ~2/3 . .
plotted versus the normalized frequency (34) all spectra Will fall off With a ~2 / 3 slope
in the inertial subrange. The dissipation, 6, may then by estimated from the definition of
<I>€ as:
[€26 2: (D511? (9)
In the present paper we have studied a situation with a non - stationary BL in order to compare the results with the ones given in the literature. The understanding of the processes in the BL is very much connected to the different turbulence variables introduced here. Due to the importance and common use of numerical simulations some turbulence closure applications have also been studied to test the validity of the approximations done.
2 The Experiment
2.1 The Area
The measurements were taken off the coast of Blekinge between Lat 55~570N, Long 15—16.5°E, in autumn 1990. The coast is orientated in E — W direction for about 80 km
and then with a more 8 - N direction in the western and eastern part, fig. 1. There is
a small archipelago in the eastern part with quite shallow water. The E — W orientated coastline is exposed to a good undisturbed fetch on winds from E—SW.
During the autumn (beginning of October) the sea has a temperature around 1044
0C [ SMHI 1990 l. The land can still get warm during daytime in clear conditions which
gives a positive land—sea surface difference. However, the main feature is that we have sea surface temperatures higher than land temperatures. This gives unstable conditionswhen the land air is advected out over sea.
56.6 56.4 * First profile 55.2 -U? U) l Latitude (deg) Straight paths
Profile two and four 55.8
SEER
Fig. 1. The measurement area at Blekinge coast with the profiles and the straight paths.
Third profile
14.5 15 15.5 16 16.5
Longitude (deg)
2.2 The Measurements
The measurements were taken with an Sabreliner 40 A aircraft on 3 October 1990. The aircraft is equipped with an inertial navigation system (lNS) which provides the aircraft’s acceleration. A step by step integration of the acceleration then gives the aircraft’s speed relative the ground and another integration gives the position [ Lenschow 1986 l. The wind measurements are performed with the ”radome gust probe” technique [ Brown eta]. 1983 ]. This technique uses five holes in a cruciform pattern at the tip of the radome. The differential dynamic pressure is measured over the five holes which gives the true airspeed (airspeed relatively aircraft). With the knowledge of the aircraft’s speed the wind
speed can then be estimated. The use of an INS is somewhat uncertain for longer flights
because of the step by step integration of speed and position which gives an increasing
error. For shorter flight times the mean horizontal airspeed is accurate to less than
+/- 0.5 m/s [ Tjernstro'm and Friehe 1991 1 Since the Gulf war the commercial use of Global Positioning System (GPS) has been common and provides a good possibility to
minimise this error (not used here). The equipment for measuring temperature, humidity, short / longvawe radiation and the calibration process are described in detail in Tjernstro'm
and Friehe [1991].
When probing the ABL with aircrafts it is desirable to have a relatively low true airspeed to get as high resolution as possible. A low true airspeed, however, necessitate
a large attack angle which gives a rise of large flow distortion around the fuselage. The
Sabreliner is not built for low speed flights and the relatively high true airspeed of about
100 m/s still gives an attack angel of about 4-5 0. The high true airspeed, however,
makes Taylor’s hypothesis better fulfilled because the eddies do not have time to change
significally when the aircraft flies through them. The measurements are also sensitive to
accelerations and large course changes [ Tjemstro'm and Samuelsson 1995 1. Therefore
the probing has to be done with constant vertical and horizontal velocity. Slant profiles
flown in spiral motions are therefore impossible to do, even if it would be desirable in order to minimise horizontal differences.The advantage with airborne measurements compared with masts etc. is that large areas, and depths, can be covered in a short time. The problem on the other hand is that it can never be really stated if the variations seen are spatial or temporal. On
this
flight no straight path takes more than 10 minutes and the seven straight paths all
together takes about an hour. Even in diurnal varying conditions each flight leg may be considered as reasonable short. With this circumstances in mind and with a fairly stationary weather situation the picture we get when we make a vertical cross section of the BL is approximately a snapshot of the state of the atmosphere.
The data used for the mean values were sampled at 6 Hz and the turbulence data were sampled at about 50 Hz and then filtered to the Nyquist frequency to avoid aliasing. The mean values were used to estimate a vertical cross section of the atmosphere and analyse the tendency for the different parameters. The data has been smoothed by averaging over blocks and then using a cubic interpolation to obtain a smoother picture. The numbers of blocks chosen may differ between the profiles but are selected to fit each profile as good as possible. In the turbulence dataset the profiles is high and low~pass filtered at 0.1 Hz and the leg data is high—pass filtered at 0.02 Hz. The choice of the cut off frequencies is, as with the mean values, subjective. The filter frequency for the straight paths has
been chosen after examination of the spectra and cospectra and for the profiles it has been chosen to get reasonable data. The analysis in this paper mostly follows the one
presented in Tjemstro'm and Smedman [1993].
2.3 The Case
m ”Taro if" ""” ”V”
L3/iomomm..
+. “J.“ . ”Ll l010 '020
Fig. 2. The synoptic weather analysis for the third of October.
The synoptic weather analysis [ SMHI ], fig. 2 for the day in question shows
a low pressure between Iceland and Great Britain, moving slowly towards NE. The corresponding warm front is located over middle part of Sweden and has passed the measurement area since the day before. The cold front is located over the north sea and does not reach the present area until the day after the measurements. There is a high pressure centre over eastern Europe. The wind at the Blekinge coast is SSW7 about 6
m/s. In the southern part of Sweden the surface temperatures are around 13 0C but
over northern Germany, where the air comes from, the temperature lies around 20 0C.
At the beginning of the first flight there was 7/8 Sc at 300 meters and some haze over the sea and at the end of the second flight there was less than 4/8 Sc over sea but still
a lot of haze, see the flight log. The fewer clouds on the second flight is an indication of subsidence. The sea surface temperature was about 130C (30/9) over whole southern part of the Baltic sea, fig. 3. The small temperature difference between sea and land indicates
that we could expect no clear thermal mesoscale circulations as described in Tjernstro'm
11991t
Fig. 3. Sea surface temperature for 30th of September.
The SSW wind and the homogeneous sea surface condition indicates that we have a
upstream fetch of about 100—150 km (distance to German coast) which hopefully leads to
a horizontally homogeneous MABL. The relatively small distance to the Swedish coast may cause some 77downstream problems” with effects mentioned in section 3.1.
There were two flights flown this day. The first flight started at 11.20 with a slant profile flown from 1800 down to about 30 meters. After that seven straight paths were flown at: 50, 100, 150, 200. 300, 450 and 600 meters, between 11.30 and 12.40. The first flight ended with a slant profile which was finished at 12.50. The second flight follows the same pattern and started with a profile at 14.25. After that follows seven straight
a slant profile was flown and the measurements ended at 16.05. Both the profiles and straight paths were flown at a true airspeed of 100 m/s and the vertical velocity for the
profiles were about 4-6 m/ s. This gives a horizontal resolution of 4 meters and a vertical
3 Results 3.1 Average conditions 1800 . . Z 1800 . 1000 . . . 1800 I.‘ -\\ (I; 1600- 1000- \y « 1500- 1600~
‘31
1400» 1400— 31 « 1400— 1400-1200— 1200~ _.-,- "1.. _ 1I ~ 1200- 1200-A f. 15,1000m 1000- ‘1:‘ i - 1000» 1000-U a . g 800- 800- 800~ 800~ 600- 800— 600» 600-400- 400» 400~ 400~ 200~ 200» \\1‘. — 200— 200-O1o 15l t 0 I O i l I O L l 1 20 25 o 5 10 0 5 1o 15 20 100 180 200 220 240Potential temp (deg) Specific humidity (g/kg) Mean wind (W3) Wind direction (deg)
Fig. 4. Mean values from the four profiles. Profl. (lined), prof.2. (dashed), prof.3. (dashdotted). profA. (dotted).
The essential observation on the potential temperature and the specific humidity
profiles is the lowering of the inversion, fig. 4. Inside the BL we have near neutral
conditions, though on the last profile it is hard to say because the whole flight is above the BL. Above the inversion the stratification is stable with a cooling of about 4 0C above
1500 meters from the two first to the two last profiles. Between 300 and 500 meters there
is a warming of about 4 0C between the first and the second profile. See discussion below.
There is a specific humidity of about 8 g/kg in the lowest levels and above that it is fairly
constant except for the first profile which has a clear minima at 1500 meters. The wind
speed is about 9 m/s for the lowest levels and then shows a great variability aloft. There
is an obvious differens between the first profile and the coming. On the first flight the
wind at the surface is from S and both the wind speed and direction are nearly constant up through the BL. After that the wind is turning more to SW above the surface and we also have an increasing wind speed upward. The warming around 400 meters between
the two first profiles is more rapid than the later tendency. The difference is probably
due to the dissipating cloud layer, see flight log. As long as the Sc are left we will have a
well defined BL top and below the clouds the BL will be well mixed. When we have less
clouds we get a clockwise turning of the wind direction and an increasing vertical wind
600 600 r [we .4 _. 220 500 500‘ 220 ETE> 400 Altitude (m) 23O % Altitude (m) OJ0O 200 200 ~ 190 195 ~ 100 100 ’ 190 X 85 O I l l l J 0 l l I l i 15.6 15.7 15.8 15.9 16 16.1 16.2 15.6 15.7 15.8 15.9 16 16.1 16.2
Longitude (deg) Longitude (deg)
600 1 . . . . 600 15.5 500 - ~ 500 M 400 M r 400 A "‘ 12.5 "‘ M mm
2?;
‘2
7.:
E 300 WW 3 300 g W 3.: 11.4 200 ~ 200 100* 100 l l I l l I O l l l l 1 105.6 15.7 15.8 15.9 16 16.1 16.2 15.6 15.7 15.8 15.9 16 16.1 16.2Longitude (deg) Longitude (deg)
Fig. 5. Vertical structure for the first flight. Wind speed (m/s) (upper left), wind direction (deg) (upper right), potential
temperature (0C) (bottom left), specific humidity (g/kg) (bottom right).
Vertical cross sections for the straight paths are shown in fig. 5—6. They are made in an E—W direction which differs about 200 from the flight track. From E to W they cover a distance of about 60 kilometres and with the S - SW wind, the cross sections are
almost crosswind. In the first flight we have near neutral conditions in the lowest 200
meters and the sharpest gradient just above 300 meter. The specific humidity is approx. constant up to 300 meters Where there is a sharp gradient. The constant value in potential
temperature and specific humidity below the inversion indicates a well mixed BL. The
wind speed increases up through the whole area although more above 300 meters and there is a sharp change in the wind direction just above 300 meters. The well defined BL top is probably an effect of the cloud layer. There is a reasonably good horizontal homogeneity for all parameters, at least in BW direction.
600 500 400 CO O O Aflfl ude(n0 200 100 15] 158 Longitude (deg) 15B 16 1Ei2 500 600 500-400* Altitude (m) w 8 200 100 210 O 156 15£ 15$? Longitude (deg) 600 500 400 400 E E o 3 300 3 300 a if 2:” 200 ‘ 12.5 ‘ 200 12.2 100 — — 100 — 0 l l 1 l l O l l l l .I 15.6 15.7 15.8 Longitude (deg)15.9 16 16.1 16.2 15.6 15.7 15.8 15.9 16 16.1 Longitude (deg) 162
Fig. 6. Vertical structure for the second flight. Wind speed (In/s) (upper left), wind direction (deg) (upper right), potential temperature (0C) (bottom left), specific humidity (g/kg) (bottom right).
On the second flight the potential temperature has increased and there is no longer
a sharp boundary layer top, which is consistent with less amount of clouds. The specific humidity has also increased in the lowest layers, which is probably an effect on the diurnal heating of the surface and an upward transport of moisture. It may also be an effect of the decreasing BL. A simple approx. gives that:
«m
Q53 ~ sit-(Wt)
(10)
Or in a bulk formulation, assuming zero flux at the BL top:
it ~ Li?)
(11>
With a fairly constant upward humidity flux7 fig. 9, and a decreasing A2 i.e. BL depth the humidity must increase in time.
The largest vertical gradient is just below 200 meters and might indicate the top the boundary layer. The wind direction is S in the lowest layers with just a small turning toward SSW aloft. These three parameters are still reasonable homogeneous in the E ~ W direction. The wind speed, however, varies clearly from E to W. In the eastern part we have a local jet maxima of 13 m/s at 300 meters, but in the western part the wind is nearly constant with height. The reason for this maxima is difficult to explain. It might be an effect of the sharp change on the Blekinge coast when it changes from E ~ W to N —
S direction, fig. 1. The change in the Wind lies just where the coast changes direction. In
the western part theflow maybe blocks by the land and the Wind speed decreases. 1n the
eastern part the wind has free way and can continue to flow. It will even increase some, probably due to convergence. A small tendency of this phenomena can be seen even in
the first flight.
A comparison between the twoflights shows that the variations in the E ~ W direction
are overall small except for the wind on the second flight. If we neglect this deviation and
assumes that the variations that can be seen between the profiles are functions of time, and not of space, it is possible to make a time composite of the profiles. It is difficult to say anything about the variations in the N—S direction. It is, however, difficult to believe that the large temporal variations would be in the streamwise direction alone, in particular when we have in mind the fetch mentioned in section 2.3.The vertical time structures are build up from the four profiles, which means that fig. 7. are made with observations from about 11.30, 12.50, 14.30 and 16.00. It is important to have in mind that this time cross sections does not cover all changes and that they
sometimes differs from the cross sections made from the straight paths.
1800 1 1 . . . , 1800 M \1205\ M 20 1600 — .. 1600 ~— 1.5 1 20.5 19 5 1400 ”‘ 19 ‘1 1400 h 1 200 1200“ m .-m A - w1000— ‘000 W a)m E 7?; 17 3 g800— W — {(1 800“ ‘ 16 600" v soo~ . f 400_ _ 400~ 7.5 7 15 \%\ 8 — ' ' - 200— 200 “.5 12
-O
was
11 11.5 12 12.5 13Time (hows)13.5 14 14.5 15 15.5 16 11 12 13‘ 14 15 Txme (hours)Fig. 7.a Vertical structure based on the profiles. Potential temperature (left), specific humidity (right). 13
Altitude
(m)
E 180 W
11.5 12 12.5 13 13.5 14 14.5 15 15.5 16 Time (hours) Time (hours)
Fig. 7.b Vertical structure based on the profiles. Wind speed (left), Wind direction (right).
On the potential temperature tendency plot, the decreasing boundary layer depth is discernible as an area with the sharpest vertical gradient lowering from 600 meters to below 200 meters. Fig. 8 shows a subceding ABL from about 500 to 30 meters in 4 hours
which gives a subsidence speed of about 80 meters/ hour. The top of BL for the straight
paths has been chosen between the two levels where the potential temperature and/orthe specific humidity has the greatest vertical gradient and are marked with large cross
in fig. 8. giving the uncertainty in space and time. The lower subceding velocity between
13 and 15 hours could be an effect of the warming from the surface, which should reduce the effect of the subsidence.
Above the BL the thickness of the layer between (-9 :2 15.5 and 9 2 20 0C has increased from 400 to 800 meters. That is due to the adiabatic warming caused by the subsidence.
The vertical wind has been calculated, fig. 8, using [Holton 19.92] :
Qi- : “Wit?
(1?)
Here we have assumed absence of strong diabatic warming. The vertical gradient has be calculated from the profiles and the time gradient has been calculated using linear
interpolation between the profiles. We can see, in addition to fig. 7 that inside the BL we
have a small but clear subsidence. Aloft we have rising motions which may be coupled to the warming.
The specific humidity changes are small below 1000 meters, but it increases rapidly
above 1400 meters between 11.00 and 12.00 and after that it is quite constant. With the same discussion as former we can use eq. 11 to make it plausible that the increase
800 meters increases the first one and a half hour. During that time it also turns more to SSW. After that it is nearly constant in the lowest layers but decreases aloft. The
wind direction follows the same pattern with clear change during the first hours and after
that a relatively constant direction. As discussed earlier this is an effect of the rapidly dissipating cloud layer, generating vigorous mixing. As long as the cloud layer is left it holds back the subsidence, but when it has dissipated the subceding speed increases.
From the discussion above, with the z,- tendency, the calculated vertical motions and the dissipating cloud layer we can be reasonable sure that the decreasing BL is caused by synoptic subsidence. Of course other effects may influence but this is dominating.
500 450 _ 1600 400 _ 1400 350 r 1200 52300 $1000 (I) d) 'O ‘0 3‘3 0 .3 800 :r 25 2: 200 ~ 600 150 r 400 100 ~ 200 50 1 1 I 1 11 12 13 14 15 16 11.5 12 12.5 13 13.5 14 14.5 15 15.5 16
Time (hours) Time (hours)
Fig. 8. Left: Height to inversion as a function of time. Right: Vertical motions estimated from eq. 12.
3.2 Turbulence structure
Table l: The Monin Obukhov length and the friction velocity. The friction velocity for Leg. 1 and 2 is taken from the
lowest straight paths.
Profl Legl Prof. 2. Prof. 3 Leg. 2 Prof. 4
L «142 216 483 ~l26 ~190 34
u...
0.28
0.32
0.34
0.23
0.22
0.15
The Monin Obukhov length has been calculated for the bottom value for each profile and the two lowest straight paths, Tab. 1. We see that there is clear unstable conditions for all but the last one. The friction velocity has got a decaying tendency indicating a smaller surface shear production.
At the first profile’s vertical turbulence structure there is a peak at 400 meters in
the turbulence fluxes, fig. 9. These high values in fluxes and variances are due to the
cloud layer that was flown trough, and discussed earlier. The filter technique used has a
tendency to overshot near large gradients and therefore the values will look higher than
they really are, however, most of the increase is real. These fluxes differs from normalBL flux and might therefore contaminate the normalised flux so that the already small
amount of data will scatter even more. Therefore the majority of the normalised plots for
the profiles are made without the first profile and will be named ”no cloud data”.
1800 . 1800 1800 1300 . \(1 1. i 1600- .“1 1600" 1600» ‘5 1600~ "-4; 2" l I (x '1 1400" \,‘-_ 1400' 1400— .3 1400» -j {5 :l1 l 1200* ’\ 1200* 1200— 1200» ' E1000~ 1000- -§1ooo- 1000-0 o E .5 g 800' 800*- ~fi 800- 4 300. 600~ 600— 600- 600~ 400“ 400' 400- 400» 200~ 200* 200- 200» 0 o A I? 1 l —15 «10 -5 O 5 10 Sensibel Heatflux (W/mA2)
O l 1 1
—15 -10 —5 0 1O
Latent Heamux (W/mAZ) Streamwise Momentum«0.1 —-0.05 0 0.05flux ("1021302)0.1 0.15 -O.1Lateral Momentum~0.05 0 flux (NZ/952)0.05 0.1
0.15
Fig. 9. Turbulenceflux from the profiles. Profi. (lined), prof. 2. (dashed), prof.3. (dashdotted), prof.4. (clotted).
1300 r 1300 . 1800 1000 y I ’ .1 lg .’ . / ' _ / .'~ /‘ t. / [ I 1600 H 1600-,' 1600 Ly 1500 ~, 1.‘ E E1 1400 .. 1400 7». 1400 , 1400 13i: 1 3 ‘-. ' I? l ' -1200 1.; 1200 p 1200 1200 1" E1000- 1000~ - Ewoo- 1000-8 1‘3 3 3: g 800 «fi 800L 000 0.2 0.3 0.4 u variance (m’\2/s"2) 0.5 0 0.1 0.2 0.3 0.4 v variance (mAZISAZ) 0.5 0 0.1 0.2 0.3 0.4 0.5 w variance (NZ/$02) I l I r >\ \ 600>\‘ I_ . 0.1 0.2 0.3 0.4 0.5 TKE (WE/5"?)
Fig. 10. Variances and TKE for the profiles. Prof.1. (lined), prof. 2. (dashed), prof.3. (dashdotted). prof.4. (dotted).
The sensible heat flux is positive (upward) for the first three profiles. with the largest
values near the surface and decreasing against zero near BL top. It gets smaller from
profile to profile and on the last one the flux has reversed sign. The latent heat flux. shows
the same pattern as the sensible heat flux with decreasing values in time. Above the
negative (downward) and is largest near surface with decreasing values near BL top. It
differs from the idealised flux for the mixed layer given by Stall [1994] and is more like
the stable boundary layer. The lateral momentum flux is small for all profiles.
The variances of the wind components has got the same tendency as the other
turbulence variables. Large values near surface and with a decreasing tendency in time. None of the turbulence wind components gives example of the jet structure above BL mentioned by Tjernstro'm and Smedman [1993]. There is an unexplained increase in TKE
for the third profile above 1600 meters.
3 I I I I I 3 I I I I 2.5 ~ - 2.5 ~ + + 2 — - 2 — < )6 X g 1 5 — g 1 5 — + + X X 1 ~ ~ 1 -0.5 ~ - 0.5 ~ +-+ x + X 0 0 l i 0 6 O 0.5 1 1.5 2 2.5 3 Normalized u variance Normalized v variance 2.5~ + 2.. X § 1.5 + X 1-—1 + X 0.5~ x + O I l l 0 0.5 1 1.5 2 Normalized w variance
Fig. 11. Normalised variances for the straight paths. Stars denotes first flight and crosses the second flight. The solid lines
are from Brost eta]. [1982].
The variances and flux for the straight paths have been normalised with Zi, uf, uiq.
and uiT... While all parameters are changing in time the interpolated z,- in fig. 8. and a linear tendency for 113 have been used for the straight paths to minimise time effects.
The tendency for uiq... and u...T.,. was difficult to find, therefore the value from the lowest straight path was taken. A comparison between these tendency values and mean values for Z. and 113 showed that the effect might have been negligible.
The normalised variances for the straight paths are shown in fig. 11. In spite of the small amount of data the variances follows the expected line given by Brest eta].
[1982] quite well, but of course it is difficult to see any tendencies. The scaled streamwise
momentum flux follows the expected appearance unlike the lateral momentum flux which has no clear tendency.3 i i 3 i 2.5 ~ - 2.5 ~ -+ + 2 - — 2 -x x § 1 5 ’ 3g 1.5 ~ -+ + x as 1 1 -+ + x x 0.5 - x * 0.5 -he an x + x x 0 l ‘ 0 l
—1 Normalized Streamwise Momentum Flux~05 0 0.5 ~i «0.5 0 Normalized Lateral Momentum flux
3 T I 3 I 2.5 - ~ 2.5 ~ — + + 2 - - 2 — -X 36 § 1.5 § 1.5 + as x 1 — - 1 ~ + 0.5 ~ - 0.5 ~ + ~ X x X 0 l l 0 l I
—0.5 O Normalized Heat Flux0.5 1 1.5 ~O.5 0 0.5 1 1.5 Normalized Latent Heal Flux
Fig. 12. Normalised turbulence fluxes for momentum and heat for the straight paths. Stars denotes first flight and crosses
the secondflight.
The scaled sensible and latent heat flux also follows the expected lines. One could expect a difference from the momentum flux because the use of constant u...q... and uiT... instead of tendency values, but this seems to have none or at least a very small effect.
1 6 i x I 1 6 . + + 1.4 ;+ + 1 4 ~ + + ~ + + 1 2 * + ~ 1.2 of + + + + + + + 7:. 1 _ c 1 - + 3 g1 + g 0.8 — + — g 0 8 — ++ + 3 3 + 1:3 E + < < 0-6 “ 0.5 — + + + + 0.4 — ~ 0.4 ~ + + 0.2 ~ ~ 0.2 — + + ~ + O 0 l l l l 0 1 2 3 4 5 6 0 0.5 1 1.5 2 2.5 3
Normalized u variance. No cloud data Normalized v variance. No cloud data.
1.6 l T I I I T I + + 1.4 — ++ « + I. 12 4- + ~1 + + + A 1 - ~ 7:: h + g 0 8 — + + ~ .2 + + fi + 0.6 - _ 0.4 — 0.2 — O l l I I l O 0.5 1 1.5 2 2.5 3 3.5 4 Normalized w variance
Fig. 13. Normalised variances for the profiles.
The scaling parameters for the profiles has been determined with extrapolation from
the lowest layers down to the surface for each profile. The variances from the profiles follows the expected appearance but with a tendency to lover values. This might be an effect of an overestimation of the surface values used for scaling when extrapolating down to the surface or an effect of the averaging method used. However, it would then appear on the momentum flux to, but they seem to be unaffected. It could also be a real effect but then it would appear in the straight paths to.
The scaled streamwise and lateral momentum flux follows the expected appearance
quite well and the lateral flux has got a better correspondence to the expected values than
the straight path had. The sensible heat flux has got a good agreement but the latent
heat flux differs from the expected values.
nut {1; 0.8 g 0.8 + E; .2 fi 2 0.6 0.6 + + 0.4 - 0.4 + 0.2 0.2 o l 1 O I l l i l l I j
-l.5 Normalized streamwlse momentum flux. No cloud data.A —0.5 O 0.5 -0.5 —0.4 —0.3 ~02 ~01 O 0.1 0.2 0.3 0.4 0.5 Normalized lateral momentum flux. No cloud data.
1 6 i i 1 6 l l + + + + i 4 - ++ - l 4 ~ ++ + + + i 2 - + + + — 1 2 - ++ -+ + + + + 1 + 1 ~ ’3? + 3—3 a J E g 0 8 + g 0 8 — 3. ++ + g 2 + 2E 0 6 - + - 0 6 - « + + + O 4 - + 4. - O 4 *-+ + 0.2 - + 0.2 — 0 ‘ ' O
—0.5 Normalized sensible heat0 flmi.0 5 1 ~05 0 0.5 1 1.5 Normalized latent heatflux. No cloud data.
Fig. 14. Scaled momentum and heat flux for the profiles.
Scaled non — filtered spectra for the longitudinal, lateral and vertical components are
showed in fig. 15—16. These spectra follows the —2/3 slope in the inertial subrange, given by eq. 8, quite well, although less for the second flight. A comparison between the two flights shows a decreasing TKE for the upper levels. That is rather expected because they are above the inversion and the profiles, fig. 10, shows of a small amount of TKE there.
On the first flight the streamwise wind spectra up to 200 meters falls of clearly for lower
frequencies, indicating that the energy are concentrated to turbulence variations. Above 300 meters, however, there are energy at smaller frequencies indicating variations on a
larger scale. On the second flight the two lowest levels contains only turbulence and the
larger scale variations are now covering all the other levels, which are consistence with the decreasing BL.
nSu(n)/phi
f=(riz/Ua) f=(nz/Ua)
Fig. 15. Scaled streamwise wind spectra for thefirst flight (upper left) and the second flight (upper right) and scaled lateral
wind spectra for thefirst flight (bottom left) and the second flight (bottom right). The scaling parameter phizzuECPE/S is
used. The solid straight line marks the —2/3 slope. The lines are marked from bottom level and upward: solid, dashed. dashed—dotted, dotted, solid-cross, solid~star, solid—circle.
The lateral Wind spectra has got the same appearance as the strearnwise spectra. The
small scale variations covers a deeper layer on the first flight than on the second flight.
and there are variations on a larger scale above the BL.
The vertical Wind spectra falls of as the other ones, with a better correspondence to
the 2/3 slope on the first flight than on the second one. The two layers on top on the first
flight are clearly influenced by larger scale variations. The 300 meters level, (solid—cross).
however, clearly contains less energy than the other ones. This tendency can be seen on the streamwise and lateral spectra to but it is most apparent here. On the second flight it looks as if the large scale vertical circulations has been suppressed.
nSw(n)/phi nSw(n)/phi
10
f:(n2/Ua)
Fig. 16. Scaled vertical wind spectra for the first flight (left) and the second flight (right). Notation as former
The non - filtered cospectra for streamwise and lateral momentum flux and for the
heat flux are plotted in fig. 17-19. Here we see that the major part of the momentum
are transported at approximately equal (normalised) length scales for all levels. It is, however, possible to see a tendency to smaller eddies for the second flight which should be a effect of the decreasing BL depth and that the transport is clearly concentrated to the lower levels.
The eddies transporting the heat are more scattered in size. On the second flight there is a downward flux at lower frequencies for the 150 and 200 meters levels, fig. 19.
That is, according to fig. 8, above or at least at the top of the BL. This downward flux is
caused by the stable stratification and generated by variations larger than the turbulence
scale.
0.5 ~ ‘ 0.5
-nCwu(n)/U"\2 nCwu(n)/U*A2
—-1 ...| l .1..‘.l . A1....11 . . lallll L A1111‘] _1 i .1“..| .‘AAtll. . i.. i..l I . ,A l A ..
10" f=(nz/Ua)10° 10 10 10“ 10' 10': 10" 10° 10‘ 102 103 f=(nz/Ua)
o_4 ... m, ..., ,... ...,
nCvN(n)/U'/\2
.03 »- ..
_O.4 ‘ l .11.“! J ;1....ul ‘ .‘AlAAAl A .‘..-.al All . 1 A”;
10‘3 10‘2 10" 10° 10' 102 103 f=(nz/Ua) nv(n)/U"\2 0.4 —0.3~ — .0.4 .1] 1.1 ....I AA1] .l An 10”3 10’2 1o“ 10" 10 1o 10 f=(nz/Ua)
Fig. 18. Scaled wv cospectra. Firstflight left, second flight right. Notation as former. 0.5 ~
nt(n)lu"T‘
1 A 1...l . A..‘...I . ..1.;‘l . x.“..d
10 1o 10‘ 10° 10
f=(nz/Ua)
Fig. 19. Scaled wt cospectra. First flight left,
10 1O
nt(n)/u'T*
0.5
-1 10
secondflight right. Notation as former.
1 0° f=(nz/Ua)
4 Some turbulence applications 600 500 ~ 400 *-600 500 ~ 400 ~ E E a) - a) + E 300 3 300 g *0 X g GEEK 200 ‘ 200 ~ + X! K) O X NE 0 100 ~ 100 ~ 0 )6 x 0 as X + + O l l l I 1 0 l I i I 1
——2 -15 «1 ~05TKE budget (mAZ/sAZ)0 0.5 1 1.5 2 -2 ~15 —1 «0.5 0 0.5 1 1.5 2
x 10—3 TKE budget (mA2/sA2)
x 10-3
Fig. 20. TKE production for the straight paths. First flight left, second flight right. Notation: Buoyancyprod.: *, shearprod.: x, dissipation: +, turbulent transport: 0. On the second flight the shearproduction are splitted in one easterly
part (+) and one westerly part (H)
The terms in the TKE budget, eq. 1, has been calculated for the two straight flights
and are shown in fig. 20. The dissipation has been calculated with eq. 9. As shown in
fig. 20 the east and the west side has been separated at Lat 15.8 0E for the second flight due to the difference in wind, fig. 6. The difference in vertical wind speed gradient from E to W clearly affects the shearproduction in the TKE equation. The momentum flux, however, showed out to be reasonable homogeneous and was not separated. In Tjemstré’m
and Smedman [1993] the dominating terms are the dissipation and the shear production
terms. The same pattern can be seen here for these values. On the first flight both
buoyancy and shear are producing terms and the dissipation is the dominant sink. On
the second flight the buoyancy is small and there is a substantial scatter between the E
and W shear producing terms. The vertical transport term is small for both cases. If we add all the terms in eq. 1 we get the time change of TKE and the pressure correlation term. Measuring during stationary conditions the time change of the TKE are often assumed to be zero, and since the pressure correlation term is difficult to measure it is often referred to as residual in the TKE equation. If we look at the TKE calculated
from the profiles, fig. 10. it looks as if we have a clear tendency of decreasing TKE. The
residual calculated from the TKE budget, fig. 21, has no such clear tendency. On the first flight there is a positive residual and on the second flight the scatter between the east and the west part is substantial, however, with and advantage on the negative side. This lack of tendency might be an effect of a large pressure transport or just an effect of the
uncertainties we have when we calculate the TKE terms in the ”bulk” form that must be used with only seven levels. It may also be so that we have a short period of increasing TKE in the lowest layers around noon.
600 500 x 450 ~ 0 + 500 ~ -0+ 400 *-x o 400- 350 ~ + X "‘ G 300
-f;
s
g 300 '3; 250 + x 0 5 O + * E < 200 — 200 _ ~ x O + + x O 150 _ O *+ 3K 0 + 100 — 100 -+ O x O * + 50 _ 01 0'5 0 o 5 i 1 5 0 ‘ ‘ ‘ ‘ '" ‘ ' TKE budget Imbalance (mA2/sA2). ' x 10 3y —1.5 ~1 Richardson-o.5flux number 0 0.5
Fig. 21. Left: TKE budget imbalance. First flight are marked with stars, second east with crosses and second west with circles. Right: The Richardsonflux number for the straight paths. First flight is denoted with stars, second E with circles and second W with cross. The straight line marks R620.25. One point from the first flight with Rf :—19 has been left out.
The Richardson flux number mentioned in the introduction has been calculated for
the straight paths, fig. 21. As there is decaying turbulence here we could expect to have
turbulence even though the Rf is larger then RC. Taking the TKE calculated from the
profiles, fig. 10, as a reference we see that we have turbulence up to 600 meters on the
first flight which agrees with the estimated Rf values which are all lower than RC. On the second flight we have Rf over the critical value on levels that we have small, but still
some, turbulence. The E and W Rf differs from each other with lower values for the B side as we could expect.
When modelling the BL turbulence closure models of varying types are used
to describe the flux and variances. When describing the dissipation a common
parameterization is [Tjernstrcim 1993 l:
6: W (13)
Celt
where C. is a constant, characteristic for the dissipation, and l. is a characteristic length scale. It is often assumed that the same length scale can be used for momentum and dissipation. Tjernstro'm [1993], however7 showed that the relation between the length scales are depending on the Richardson number. The length scale are then related to
their turbulence parameters through different constants. The master length scales for
momentum have been calculated from the vertical wind spectra for each level. If theselength scales are used in eq. 13 we get a mean C6 of about 2.8. This value can be compared
with Andrén [1990] who uses 14.3 and Tjemstro'm [1993] who got 13. Both though uses
another way to calculate the length scale. Wamser and Muller [1977] suggest a value of
3.13, also using the peak of the vertical wind spectra for the length scale. It is clear that the choice of way to determine the length scale is important for the value of the constant.
5 Conclusions
The vertical structure of a MABL is investigated using airborne measurements. The
data was collected on third of October 1992. The dominating feature is a decreasing BL top during the day. The average conditions were found to be fairly homogeneous over the measured area, maybe excluding the wind speed. With small horizontal differences and a small sea—land surface temperature difference we can assume that the variations we see are functions of time, not of space. A time composite of the slant profiles could then be made to get a better picture of what was happening. These composite plots together with the straight paths indicates the fact that the BL depth is decreasing during the day, and that it is caused by synoptic subsidence.All turbulence parameters have got a decaying tendency following the lowering of the inversion, i.e. the BL top. The turbulence parameters, and the corresponding spectra and cospectra, where scaled with normal surface layer scaling. The spectra and cospectra shows a superimposed variation of larger scale on the levels above the BL tOp. This could be effects of mesoscale circulations or buoyancy waves generated by some unknown reason. Most other investigations are done during stationary conditions and the theories are made up on those assumptions. Therefore it is valuable to test this theories on a case where the variability in time is a dominant feature. Both the scaled turbulence parameters from the straight paths and from the profiles follows the values estimated on other, more stationary, experiments and investigations reasonable well.
A comparison with a common dissipation parameterization is done. The result was found to be well in the same domain as the other ones. Also in this case, the other investigations are done during stationary conditions.
This is interesting when modelling the turbulence. Some turbulence closures, has turned out to give bad results in cases of increasing turbulence and is often exchanged with other more complicated, and computer power demanding closures [ Andrén 1990 ] Hence, however, the turbulence statistics from this clearly non — stationary case does not
differ significantly from stationary cases, which indicates that normal, low level, closures
can me used.
Acknowledgements: I would finally like to thank my supervisor Michael Tjernstrom
for all good ideas, help, and time spent. 1 would also like to thank all PhD. students at MIUU for all your help and engagement.
Notation
k Von Karmans constant. 0.4
u... friction velocity
T... Characteristic temperature
6 Dissipation of TKE
uf
Characteristic velocity for free convection
Tf Characteristic temperature for free convection
w... Characteristic velocity for mixed layer
6... Characteristic temperature for mixed layer
L The Monin Obukhov length
ABL Atmospheric Boundary Layer
TKE Turbulence Kinetic Energy
2,- Height to inversion, boundary layer depth
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