IL NUOVO CIMENTO

VOL. 19 C, N. 4

Luglio-Agosto 1996

A turbulent data analysis in the Antarctic boundary layer(*) G. FICCA(1), M. PANGIA(1), S. PIERINI(2), R: PURINI(1) and E. SANSONE(2) (1) Istituto di Fisica dell'Atmosferc~ CNR - P.le L. Sturzo 33, 00144 Roma, Italy

(2) Istituto di Meteorologia e Oceanografia, Istituto Universitario Navale Corso Umberto I 174~ 80138 Napoli~ Italy

(ricevuto il 27 Novembre 1995; approvato il 2 Febbraio 1996)

Summary. - - Data collected by the Institute of Atmospheric Physics of CNR (Italy) during the 1991 Italian Antarctic expedition are used for the development qf Ea~h-air-sea interaction studies. In this paper wind and temperature data obtained by a digitized~ ultrasonic anemometer-thermometer describe the temporal, statistical and spectral turbulence behaviour in the surface atmospheric boundary layer at different windconditions and in morphologically different sites. The vertical momentum and thermal fluxes, evaluated through the direct method, are found to be strictly dependent on the local stability condition recorded during the measurements. The examination of the velocities and temperature probability density functions conf~rms the Lumley and Panofsky hypothesis on the influence of both velocity components on temperature fluctuations. A multichannel spectral analysis confirms the obtained results for the low-frequency range. PACS 92.60.Fm - Boundary layer structure and processes. PACS 93.30.Sq - Polar regions. PACS 92.60 - Meteorology.

1. -

Introduction

The turbulent fluctuations in the atmospheric boundary layer are of primary importance for several meteorological applications. Near the ground strong wind shears and surface heating continually feed turbulent eddies. Such eddies are v e r y effective mixing agents which serve to transfer heat, momentum and water vapour. This turbulent t r a n s p o r t influences appreciably the motion throughout the planetary boundary layer and therefore in the two sublayers in which it is divided, the surface layer and t h e E k m a n layer. T h e r e are many difficulties in the study of turbulence in the surface layer, where the effect of viscous dissipation becomes v e r y important. H e r e the stratification is strong, and direct measurements of turbulent fluctuations

(*) The authors of this paper have agreed to not receive the proofs for correction. 487

G. FICCA, M. PANGIA, S. PIERINI, R. PURINI and E. SANSONE

4~8

require sensible and fast-response instruments such as the three-axial ultrasonic anemometer-thermometer. Even a v e r y small terrain slope and adiabatic phenomena can radically affect the evolution of heat and momentum flux. Therefore, polar locations offer several advantages since there are v e r y flat snow-covered surfaces and the atmospheric stability is more stationary than elsewhere due to weak daily t e m p e r a t u r e excursions. In this paper we describe the areas of study, the instrument used for velocity and t e m p e r a t u r e measurements, the organization of the recorded data and the technique used to avoid the misalignment of the instrument. H e a t and momentum fluxes are derived and the statistical characteristics of data by means of probability density functions are discussed. The coherence between velocities and t e m p e r a t u r e by means of four-channel spectral estimations are finally presented. 2. -

Materials

methods

and

During J a n u a r y and F e b r u a r y 1991 measurements were taken at two different sites near the Italian base in T e r r a Nova Bay (fig. 1): Campo Icaro located in a rocky coastal zone and Nansen Ice Sheet at (50 • 2 0 ) k m flat glacier. The instrument used for turbulence study is the three-axial digitized ultrasonic a n e m o m e t e r - t h e r m o m e t e r KAIJO D E N K I model DAT-300, which was installed 10 m above the surface. It measured wind velocity components and t e m p e r a t u r e from arrival times of acoustic signals transmitted across a fixed path [1, 2]. It is composed of three couples of sonic probes: two are located horizontally spanning the angle of 120 ~ while the third one is displayed on the vertical axis. Two ultrasonic pulses of 100KHz are alternatively emitted in opposite directions by two lead zirconate 74 ~ 00' *

15' " ,, .-

".~2_:~, vo .,,^,u, ~ , . ,,

x. ~-,

~

-~ ~

\

30' ,,~._

....

_._.

J

,

--'~

r

45' t',

75 ~ 00"

Wool[ ~a,,

,lvleleourne

_

r

A

; ,~o~wnan~{ ~

~

,- . . . ~ . . .

,

,.,.,,_~

"-,

/

~

Antarctica

}

Mt~.

Nansen Ice S h e e t

,__.~.

,,, )~ '~ ~ 'C

Terra Nova Ba-

,.,~)/ x~

163 ~

o

0

164 ~

Y

TO

~0

,/ qan~

f'~'~

~ . l ~ ~_ ~ .... .............! ~

3"Okra

165 ~

166 ~

167 ~

Fig. 1. - Sites of measurements in Antarctica: A: Nansen Ice Sheet, B: Italian base, C: Campo Icaro.

A TURBULENT DATA ANALYSIS IN THE ANTARCTIC BOUNDARY LAYER

489

transducers located 20 cm apart, and the consequent mechanical oscillations are converted into electrical signals. This holds for the three axes of the ultrasonic anemometer-thermometer at a frequency of 20 Hz [2]. The principal characteristics of the instrument are a reduced interference of the acoustic transducers on the air flux and the independence of temperature and humidity variations in the velocity measurements. The final formula obtained for velocity measurements is

VD :

tl

1)

t2

where VD is the instantaneous wind velocity along the acoustic path, D is the distance between the transducers and tl and t2 are the times needed for the acoustic pulses to cover in opposite directions the same path. Note that VD does not depend on the sound velocity, so there is no need for corrections accounting for air temperature, humidity and atmospheric pressure. For temperature measurement the final formula

tl

t2

giving the so-called ~sonie temperature,, (from which the absolute temperature T of air can be obtained) was used, where K is a function of specific humidity and atmospheric pressure. Since fluctuation cycles of humidity and atmospheric pressure are longer than the temperature fluctuation cycle, K can be considered as constant, even though a very small correction on temperature to account for humidity variations might be included [3]. However, given the Antarctic meteo-elimatie conditions, characterized by low values of specific humidity (e.g., about 15% as resulted from a meteorological station at Campo Iearo) we can consider that, to a very good approximation, K is poorly influenced by humidity and Ts is a satisfactory approximation of the instantaneous absolute temperature T of air. Therefore, the i,astantaneous values of the velocity components and the temperature of the air can be reliably obtained from digital measurements of the transit times of the ultrasonic pulses. The velocity range of the sonic anemometer-thermometer is between 0 and 30 m s -1 with a resolution of 0.005 m s -1 and an accuracy of 1%. The temperature range is between - 1 0 ~ and 40 ~ with a resolution of 0.025 ~ and an accuracy of I% [4]. 3. -

Data

collection

The signals were digitized with 15bit resolution for the velocity and 12bit resolution for the temperature. The instrument was connected to a Personal Computer for data recording. The records were divided into 30 minute files for storage capability. Because the measurements were made at a frequency of 20 Hz, there are 36 000 data for each velocity component and for temperature in a single file. This allows to resolve all those frequencies contributing to heat and momentum transfer processes. For the Nansen Ice Sheet the data selected consist of two records of 10h (including 20 files each). The first record, starting from 9.22 p.m. of 8 February 1991 until 7.22 a.m. of 9 February 1991, is characterized by a mean wind velocity of

$90

G. FICCA, M. PANGIA, S. PIERINI, R. PURINI

and

E. SANSONE

5.4 m s -1, while the second, starting from 6.03 p.m. of 9 F e b r u a r y 1991 until 4.03 a.m. of 10 F e b r u a r y 1991, is characterized by a strong wind with a mean velocity of 16.4 m s 1. These data have been used for direct calculation of heat and momentum fluxes.

A single file recorded at Campo Icaro starting from 4.04 p.m. of 6 January 1991 was then compared with two single files of the two different Nansen Ice Sheet recordings. These three records, the first in a rocky place, the second on a flat glacier and the third still on the glacier but with strong wind conditions are characterized by very different stability values. So it has been possible to study the different spectral, statistical and temporal behaviours of the measured physical quantities. The data were elaborated on a MICROVAX 4000. 4. - D a t a

correction

The misalignment of the instrument produces a -tilt error- due to the fact that the measured vertical velocity is contaminated by the horizontal velocity. If the 10.0 7.5" =

5.0 2.5 a)

0.0 0.2

0.1 "-- 0.O

-o.1!

9

b) -0.2 : .,,,i.,.,i,..,itttllt.ttlttt,l,,..i.t.tl,t,,i,..,i,=,,i,,,, -4 -5 -6 -7 --8"

-9 i -10 -11 minutes Fig. 2. - Streamwise component of velocity (a)) vertical velocity (b)) and temperature (c)) low-pass filtered by a moving average of 200 seconds for 10 hours recorded at Nansen Ice Sheet with moderate-wind condition.

491

A TURBULENT I)ATA ANALYSIS IN THE ANTARCTI(' I:tOUNI)ARY LAYER

surrounding area of measurements is uniform and flat like that of the Nansen Ice Sheet, then it is possible to correct the original data. The method used to correct this e r r o r is based on a three-dimensional rotation of coordinate for the wind vector [5, 6j. If (u~, (v~ and (w) are the components of the mean wind vector, where (u) is parallel to the wind and (w) is normal to the surface, the first rotation is chosen in order to satisfy the condition (v) = 0, the second rotation must satisfy the condition (w) = 0 and the third one the condition (v'w')= 0 (the selected averaging time is 30 rain). However, the third rotation is based on a physical constraint and not on a geometrical one like the others. This could affect the turbulence behaviour of the processed data. Therefore, considering the fact that after the first two rotations the detected covariance (v'w') is v e r y little with respect to (u'w'), the third rotation is omitted. The detected angles to satisfy the first two conditions for the coordinate rotations are around 34 ~ and 0.2 ~ for the Nansen Ice Sheet record with moderate wind condition and 38 ~ and 0.6 ~ for the Nansen Ice Sheet record with strong-wind condition. Figures 2a), b) and c) show the mean streamwise component of velocity, the vertical velocity and the mean t e m p e r a t u r e low-pass filtered by a moving average of 200 seconds for the 10 h recorded at Nansen Ice Sheet with moderate-wind condition 252O 15 10 5

,,,,i,i

|,i,,

,,i.,i,i..,,i,,,,i,.,,i.,,.i...,i..,.iii.,i,,

,,

0.2" 0.1 "~ 0 . 0 -0.1 -0.2

b)

--2' --3"

-4 --5"

-6 50 100 150 200 250 300 350 400 450 500 550 minutes Fig. 3. - Streamwise component of velocity (a)) vertical velocity (b)) and temperature (c)) low-pass filtered by a moving average of' 200 seconds for 10 hours recorded at Nansen Ice Sheet with strong-wind condition.

492

G. FICCA, M. PANGIA, S. PIERINI, R. PURINI and E. SANSONE

after the data correction, while fig. 3a), b) and c) show the same graphics as before recorded at Nansen Ice Sheet with strong wind condition. The method described below for the computation of heat and momentum fluxes is based on the computation of the cross-products of the high-pass-filtered components. This allows to partially correct for non-stationarity and any residual sensor misalignment [5]. The ,shadowing effects- due to the obstruction of the flow by the ultrasonic transducers of the instrument are negligible because the detected mean angle between the wind direction and the ultrasonic path is around 36 ~[2].

5. - H e a t

and momentum

flux

In this section the heat and momentum fluxes will be evaluated by the direct correlation method, this being possible thanks to the fast response of the instrument. 5"1.

Definition of derived parameters. -

(1)

u,

= (( -

We define the friction velocity u . as[7]

u' w' )2 + ( _ v' w' }2)1/4.

The momentum flux can then can be calculated as follows[8]: ~2 =

Qu 2 ,

while for the heat flux we have [9] (2)

g = ~)cp(T' w' ).

In these formulas ~) represents the air density, % the specific heat of air at constant pressure and u ' , v', w' e T' are the two horizontal velocity fluctuations, the vertical velocity fluctuation and the temperature fluctuation, respectively, obtained by decomposing the instantaneous quantities as the sum of an average quantity plus a turbulent fluctuation as follows (Reynolds assumption): u = + u ' ,

v = + v ' ,

w = + w ' ,

We can compute only a mean value, for example

T =
,where

to+ T

(UT) = ~1

I

u(t)d(t).

to

The difference between

(UT} and

the true mean value (u} is given by[10] to+T

1

(UT)-(u)=-T

I (u(t)to

t~+T

(u}) dt i

~ I

u'

(t)dt.

to

This equation represents the first central moment and it is an estimate of the accuracy of the average value so as of the selected period of integration. From equations (1) and (2) it is possible to define the Monin-Obukhov length in the

493

A TURBUI,I,]NT DATA ANALYSIS IN THE ANTAI~.CTIC I~OUNI)ARY I,AYER

surface boundary layer I l l ] (3)

L = - (T)

u~

kg (T'w')'

where k is the Von Karman's constant (taken as 0.4) and g is the gravitational acceleration, z/L represents a dimensionless stability parameter, where z is the observation height. 5"2. Spectral analysis. - A spectral analysis was carried out by means of the Fast Fourier Transform [12]. The sampling rate of 20 Hz ensm'es the diminution of aliasing because this frequency is certainly twice any other fi'equency reachable in the frequency domain under investigation. The mean trend was also eliminated. When necessary the leakage effects of the additional fl'equency caused by the time domain truncation are reduced by the Harming temporal window. The Kolmogorov's - 5 / 3 power law for the inertial subrange was recovered. 10 2 10 ~ 10 -2 10 -4 10 ~s !

a) l

,

l.,,,,

I

,

1

. ,T,.,

I

i

!

fiN''

,

I

,

r,,l,.

I

10 2 10 ~ 10-2 10 -4

1 0 -6

..............

', l ,i'2J

102 N

?

i0 ~

10 -2 1 0 -4 1 0 -6 ,

1 0 -3

'

,N.,,l

1 0 -2

.

.

,..,,,I

'

i 0 -I

,,,.,,l

i0 ~

,

,

,.',..I

101

Hz

Fig. 4. - Logarithmic power spectral density and -5//3 slope straight line for the streamwise component of velocity (a)) for the vertical velocity (b)) an(1 for the temperature (c)) of the fourth file recorded at Nansen ice Sheet with moderate wind condition.

494

G. FICCA, M. PAN(;IA, S. PIERINI, R. PURINI

and

E. SANSONE

Measured logarithmic spectra should have a - 5 / 3 slope when plotted against log (f). Figures 4a), b) and c) show the logarithmic power spectral density for the streamwise component of velocity, for the vertical velocity and for the temperature of the fourth file recorded at Nansen Ice Sheet with normal-wind conditions. There is a good agreement with the theory for all the three analysed physical quantities. 5"3. T e m p o r a l analysis. - From the examination of the spectral power density of the Nansen Ice Sheet recordings (e.g., fig. 4) it appears that most of the density energy is always concentrated around 0.005 Hz. The corresponding period of 200 seconds has been selected for the computations of all the time integrals that appear in subsect. 5"1. So for this period several parameters have been calculated, namely: the mean values of velocities and temperature; the first central moment, the standard deviation, skewness and kurtosis of the fluctuations[10]; the frictional velocity according to eq. (1), the covariance ( T ' w ' > , the Monin-Obukhov length (L) according to eq. (3) and the stability parameter z / L (where z = 10 m). Table I shows the values of the means, calculated over 200 s periods moving average, of all such quantities for the 10 hours recorded at Nansen Ice Sheet with a mean wind velocity of 5.4 m s '. Table II shows the same quantities for the ten hours recorded at Nansen Ice Sheet with a mean wind velocity of 16.4 m s- '. Figures 5a) and b) show the heat and momentum fluxes, respectively, computed according to the direct correlation method based on the evaluation of the cross-products of the high-passfiltered components, for the ten hours recorded at Nansen Ice Sheet with moderatewind condition, while fig. 6a) and b) show the same graphs for the ten hours recorded at Nansen Ice Sheet with strong-wind condition. Figures 7a) and b) show the stability conditions for the moderate and strong case, respectively. It can be noticed that for the strong-wind case the momentum flux is very large, especially in the zone of strong gusts of wind. In this zone, located around the 350th minute of the file length, the heat and momentum fluxes are in phase, i.e. an increase of the momentum flux corresponds to an increase (upward) of the heat flux. This situation occurs about after the 250th minute of the file length, whereas heat and momentum fluxes were in phase TABI,E I . - Estimates of turbulent characteristics ]'or 10 hours recorded at Nanse,n Ice Sheet with moderate-wind condition.

Mean value First central moment Standard deviation Skewness Kurtosis Covariance

u

w

T

5.435 m s ~ 0.000 m s-1 0.629 in s-1 0.1 l0 5.395

0.000 m s - ' 0.000 m s ~ 0.168 In s 1 - 0.063 3.486

-7.805 ~ 0.000 ~ 0.665 ~ - 0.205 3.609

u2. = 0.012 me s -'~

(w' T') = -0.017 ~ m s-'

Monin-Obukhov length L Monin-Obukhov stability z/L, z = 10 m

5.037m 1.985

Discrete period of integration Corresponding time Corresponding frequency

4000 samples 200 s 0.005 Hz

495

A T U R t H ' L E N T DATA A N A L Y S I S IN T H E A N T A R C T I C I~()[TNDAIU~ r L A Y E R

TABL~" II. - Estimates of turbulent characteristics for 10 hours recorded at Nansen Ice Sheet

with strong-wind condition.

Mean value F i r s t central moment Standard deviation Skewness Kurtosis Covariance

u

w

T

16.361 m s-1 0.000 m s - I 2.008 m s-1 0.069 3.276

0.000 m s ~ 0.000 m s 1 0.852 m s-1 - 0.057 4.393

-4.209 ~ 0.000 ~

ue, = 0.463 m e s e

0.824 ~ - 1.659 16.233

( w ' T ' } = -0.104 ~ m s -1

Monin-Obukhov length L Monin-Obukhov stability z/L, z = 10 m

206.792 m 0.048

Discrete period of integration Corresponding time Corresponding frequency

4000 samples 200 s 0.005 Hz

o p p o s i t i o n a t p r e v i o u s t i m e s . T h i s c a s e is c h a r a c t e r i z e d on a v e r a g e b y n e a r - n e u t r a l conditions, as w e can s e e in fig. 7b). I n p a r t i c u l a r , t h e s t a b i l i t y is s t r o n g e r w h e n t h e h e a t a n d m o m e n t u m fluxes a r e in p h a s e o p p o s i t i o n a n d it is w e a k e r w h e n t h e h e a t a n d m o m e n t u m fluxes a r e in p h a s e . V e r y d i f f e r e n t is t h e s i t u a t i o n of t h e m o d e r a t e - w i n d 25 0 - 2 5 84 -50: -75 0.100cq

lllll,llllll,,llllll,,,.llllll,.,ll.l~.llllrl,,,,l,l,,lll,l

b)

t

0.075 0.050

0.025 9 0.000 50 100 150 200 250 300 350 400 450 500 550 minutes Fig. 5. - Heat flux (a)) and momentum flux (b)) for 10 horn's recorded at Nansen Ice Sheet with moderate-wind condition.

496

G. FICCA, M. PANGIA, S. PIERINI, R. PURIN1 and E. SANSONE

0: -50

,,,~-1oo.

_t5oi -200 -250 ...,

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

~ . . . . . . . . . .

+

1.000.75

0.50 o.25 0.00:

i ii

,i

i i , , i , , i i i , ,

i i i i i i , i , , i i i

11,,11

i , i i i i i , i i , , " + 1 1

i , , i i i

50 100 150 200 250 300 350 400 450 500 550 9 minutes Fig. 6. - Heat flux (a)) and momentum flux (b)) for 10 hours recorded at Nansen Ice Sheet with strong-wind condition. case where the heat and momentum fluxes appear--on average--in phase opposition, i.e. negative heat flux peaks correspond to positive momentum flux peaks. Sometimes, when the wind is very weak, the heat flux becomes positive, presumably because in such cases the vertical thermal convection prevails. In these cases the instability is very strong, as we can see in fig. 7a), but this moderate-wind case is generally characterized by very strong stability conditions, as we can see in the previous figure. Two extreme situations are analysed in this paper: the first is represented by the fourth of the twenty files recorded at Nansen Ice Sheet with a mean wind velocity of 5.4 m s -1, while the second is a recording at Campo Icaro. In tables III and IV the estimates of the turbulent characteristics are shown. We find a very strong instability at Campo Icaro. This is certainly due to its particular morphological condition. Here the vertical velocity induced and magnified by the roughness and unevenness of the surface causes a strong and positive covariance (T'w'>, so the particular position of Campo Icaro appears to be interested by warm updrafts probably due to the fact that the temperature of the sea surrounding Campo Icaro is warmer then the overhanging air temperature, but we have no oceanographic data to confirm this last hypothesis, and to the fact that the bare rock at this site will absorb solar radiation more strongly than the glacier surface contributing to the observed unstable stratification. The heat and momentum fluxes calculated for the Nansen Ice Sheet recording are in agreement with the standard values for Antarctica [7]. Here the negative heat flux and the strong stability represent important advantages for turbulent measurements on big and flat glaciers.

497

A TI'RI,)UI,FNT DATA ANAI,YSIS IN TIlE ANTAI~CTIC BOI?NDAI~.V I,AYER

15, 10 84

-~

5 84

O -5

,,,,I,'',v

',,v,,,,I,,,,I,',,I,'"v,",l,,,,i,,,,i,,,,i,,,,

0.25 0.20

0.15 0.10 0.05 0.00 minutes Fig. 7. - M o n i n - O b u k h o v stability for 10 h o u r s r e c o r d e d at N a n s e n Ice S h e e t with m o d e r a t e wind condition (a)) a n d with s t r o n g - w i n d condition (b)) ( s t r o n g p e a k s o c c u r r i n g s o m e t i m e s out of t h e selected r a n g e a r e not shown).

In the next section these three situations (Nansen s t r o n g - w i n d c a s e a n d C a m p o I c a r o ) will b e a n a l y s e d multichannel spectral routines.

moderate-wind case, Nansen by means of statistical and

TABLE III. - Estimates of turbulent characteristics Jbr the Jburth file recorded at Nansen Ice Sheet with raoderate-wind condition.

M e a n value First central moment S t a n d a r d deviation Skewness Kurtosis Covariance

u

w

T

5.382 m s - 1 - 0 . 0 0 3 m s -~ 0.5880 m s -I - 0.0306 2.9396

- 0.004 m s - 1 0.000 m s - l 0.1200 m s -1 0.3008 5.3335

- 6.778 ~ 0.003 ~ 0.7385 ~ - 0.1485 2.7456

u ." = 0.010 m 2 s "-

(w ' T ' ) = - 0.031 ~ m s - I

Monin-0bukhov length L M o n i n - O b u k h o v stability z/L, z = 10 m

2.405 rn 4.158

D i s c r e t e period of i n t e g r a t i o n C o r r e s p o n d i n g time Corresponding frequency

4000 s a m p l e s 200 s 0.005 Hz

498

TABLE IV.

(;. FICCA, M. PANGIA, S. PIERINI, R. PURINI

-

and E. SANS()NE

Estimates of turbulent characteristics for the ,file recorded at Campo Icaro.

Mean value First central moment Standard deviation Skewness Kurtosis Covariance

u

w

T

3.130 m s -1 -0.003 m s-1 0.300 m s 1 0.165 3.757

0.006 m s -1 0.000 m s 1 0.414 m s 1 0.646 2.845

-1.103 ~ 0.002 ~ 0.575 ~ 1.248 3.759

u 2 = 0.024 m2 s- 2

(w' T') = -0.176 ~ m s -1

Monin-Obukhov length L Monin-Obukhov stability z/L, z = 10 m

-1.501 m -6.661

Discrete period of integration Corresponding time Corresponding frequency

4000 samples 200 s 0.005 Hz

6. - S o m e s t a t i s t i c a l c h a r a c t e r i s t i c s o f t h e d a t a s e t

Analysis of the principal characteristics of turbulence in the surface boundary layer shows that some of the derived parameters, such as standard deviation, skewness and kurtosis, describe the profile of the probability distribution of the measured physical quantities. The probability density function (hereafter p.d.f.) has been computed from vertical and streamwise components of velocity fluctuations and from temperature fluctuations obtained from high-pass filtering by differencing with respect to a 200 s moving average. These results have been compared with the Gaussian p.d.f, calculated by the standard deviation of velocities and temperature fluctuations [13]. Figures 8a), b) and c) show the p.d.f, of the streamwise and vertical components of velocity fluctuations and temperature fluctuations superimposed on the corresponding normal p.d.f, for a 30 rain period (fourth file) recorded at Nansen Ice Sheet, with a mean wind velocity of 5.4 m s-1. Figures 9a), b) and c) show the same graphics as before corresponding to the seventh file recorded at Nansen Ice Sheet with a mean wind velocity of 16.7 m s -1, and fig. 10a), b) and c) show the Campo Icaro recording. Generally the p.d.f.'s are not Gaussian, but it is evident that for the streamwise component of velocity fluctuations the Gaussian function approximates the p.d.f. quite well, both for weak and strong wind records, and especially for stability conditions. The p.d.f, of the streamwise component of velocity fluctuations is characterized by a larger standard deviation and a smaller kurtosis than the p.d.f, of vertical velocity fluctuations. For strong stability conditions the p.d.f, of vertical velocity fluctuations is characterized by very small standard deviation and large kurtosis, while for neutral conditions it is closer to the Gaussian p.d.f, and for strong instability conditions there is a considerable increasing of skewness. The most interesting aspect is the temperature behaviour. The profile of the p.d.f. of temperature fluctuations is clearly dependent on those of the streamwise and vertical components of velocity fluctuations. For strong stability conditions it is

A

TURIIUI,ENT

DATA

ANALYSIS

IN

THE

ANTARCTIC

~2 d

0

0.0'

....

....

5 ....

i ....

....

m/s

0.6:

~2

,,,,I .... i ,,'~ i,,L,l,,,,l,,,,

-2

-1

0 m/s

1

2

i ,,1,

i ,,,,

.2

i ,,,t

0.0

m/s

i t,,,

i ,,,,

2.5 5.0

7.5

b)

0.5: 0.4: 0.3: 0.20.1: 0.0 . . . . . . . . . -7.5 -5.0 -2.5 0.70.6 ~ c) 0.51 0.41

c)

3:

i,,,,

-7.5 -5.0 -2.5 0.7-

b)

3:

499

I,AYER

0.7 a) 0.6 ~ 0.5: 0.4 0.3 0.2: 0.1:

a)

3:

BOIINDARY

O.3 ~ 0.20"11

,,,1,,.1!

0.0 2.5 m/s

5.0

7.5

0.0 oC

5.0

7.5

#

0.0' .,..,'. . . . .

"':h'"'-'1'"'5

.... i

....

....

-7.5 -5.0 -2.5

~ Fig. 8.

2.5

Fig. 9.

Fig. 8. - Probability density function for streamwise component of velocity fluctuations (thin line) (a)) for vertical velocity fluctuations (thin line) (b)) and for temperature fluctuations (thin line) (c)) with respect to the calculated normal probability density function (thick line) for the fourth ffile recorded at Nansen Ice Sheet with moderate-wind condition. Fig. 9. - Probability density function for streamwise component of velocity fluctuations (thin line) ((a)) for vertical velocity fluctuations (thin line) (b)) and for temperature fluctuations (thin line) (c)) with respect to the calculated normal probability density function (thick line) for the seventh file recorded at Nansen Ice Sheet with strong-wind condition.

nearly Gaussian like that of the streamwise component and, as stability decreases, its shape is more and more influenced by the vertical velocity fluctuations. This behaviour of temperature fluctuations was also observed by different authors [14,15], and shows the importance of the geomorphological and climatic conditions of the areas under investigation on the local turbulence.

500

G. FICCA, M. PANGIA,S. PIERINI, R. PUR1NI and E. SANSONE a)

1.5: 1.0 0.5 0.0

-2

-I

0

1

2

0

i

2

m/s

b)

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-2

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1.51 c) 1.0

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,,

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-2

i

,

,

-1

,

,,1

, , l ,

0

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~ Fig. 10. - Probability density function for streamwise component of velocity fluctuations (thin line) (a)) for vertical velocity fluctuations (thin line) (b)) and for temperature fluctuations (thin line) (c)) with respect to the calculated normal probability density function (thick line) for the file recorded a t Campo Icaro.

7. - Multichannel spectral estimation Four-channel spectral estimations are presented. The four channels include the three velocity components and the temperature measured by the ultrasonic anemometerthermometer. The routine is derived from the classical method of autospectral and cross-spectral estimation based on averaging k segments. We define the multichannel power spectral density matrix P(f) of the multichannel random process [16] as a matrix whose on-diagonal elements are the singlechannel autospectral densities and whose off-diagonal elements are the two-channel cross-spectral densities9 This matrix is Hermitian and positive semidefinite. This implies that every principal minor matrix of P has a non-negative determinant and, therefore, all coherencies of channel pairs have values bounded between 0 and 1~

A TURBUI,I,:NT DATA ANALYSIS IN TtIE ANTARCTIC BOUNDARY I,AYER

501

The coherence function is defined as

P,,,,,(f)

~ ~,,, ( f ) =

We can compute the magnitude squared coherence and the phase coherence from the absolute value and phase of this function calculated averaging k segments. Averaging is not only important for statistical smoothing purposes but also for minimizing the bias in the coherence estimate[16]. The routine was applied to the three files previously analysed, the first and second reeorded at Nansen Ice Sheet with moderate-wind condition and strong-wind condition, respectively, and the third recorded at Campo Iearo. The data are low-pass filtered by a moving average of 200 samples (10 s) in duration in order to filter out the inertial subrange frequency eomponents and to investigate the eharaeteristie periods of turbulent larger eddies. Data decimation by a factor of 100 reduces tile number of samples in such a way that each velocity component and temperature are generated at a rate of 0.2 Hz. The mean trend has also been high-pass filtered. Fourteen segments of 80 samples in duration with 20 samples of overlap have been filtered by the Hamming window. The magnitude squared and phase coherence have been computed by the autospeetral and cross-spectral estimation based on averaging the 14 segments. Figures l la) and b) show the magnitude squared coherence for temperature and 1.00-

0.75 oa

~ 0.50 oa

0.25 0.00. ID

1.00 b)

g 0.75 0.50 0.25 ! .

0.00

0.02

0.04

0.06

0.08

0.100

Hz

Fig. 11. - Magnitude squared coherence for temperature and streamwise velocity component (a)) and for temperature and vertical velocity (b)) of the fourth file recorded at Nansen Ice Sheet with moderate-wind condition.

50"2

G. HCCA, M. PANGIA, S. PIERINI, R. PURINI

and

I,:. SANSONE

1.00 0.750.50' 0J

0.25. "O

0.00 1.00 b)

O

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t~

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0.00

0.02

0.04

0.06

0.08

0.100

Hz Fig. 12. - Magnitude squared coherence for temperature and streamwise veloSity component (a)) and for temperature and vertical velocity (b)) of the seventh file recorded at Nansen Ice Sheet with strong-wind condition. streamwise velocity component and for temperature and vertical velocity recorded at Nansen Ice Sheet with moderate wind condition and stable conditions. A peak of 0.86 at a frequency of 0.0074 Hz appears in the temperature and streamwise velocity component coherence, while a lower peak of 0.72 appears at the same frequency of 0.0074 Hz for temperature and vertical velocity coherence. Figures 12a) and b) show the magnitude squared coherence for temperature and streamwise velocity component and for temperature and vertical velocity recorded at Nansen Ice Sheet in the case of strong-wind condition and near-neutral conditions. A peak of 0.88 at a frequency of 0.055 Hz appears for temperature and streamwise velocity component coherence while other peaks between 0.74 and 0.8 appear in the frequency range 0.017-0.099 Hz. Little weaker peaks between 0.57 and 0.71 appear for temperature and vertical velocity coherence. Figures 13a) and b) show the same graphics as before for Campo Icaro. It can be seen that there are no significant peaks for temperature and streamwise velocity component coherence, while large peaks of 0.92 and 0.91 appear for temperature and vertical velocity coherence at the frequencies of 0.005 Hz and 0.0672 Hz, respectively; other peaks of 0.87, 0.82 and 0.83 are found between these two frequencies. Since the streamwise component of velocity considered so far corresponds to that of the mean wind direction, we have omitted the coherence representations of the transverse velocity component that are similar to the streamwise component behaviour, but with smaller peaks. We find again a spectral temperature behaviour which is dependent on the

A TURBULENT DATA ANALYSIS IN THE ANTARCTIC BOUNDARY LAYER

503

1.00 a)

0.75

r

0.50

~D Q

0.25 o.oo

1.oo 0.75. ~

0.50 0.25 b) 0.00

0.02

0.04

0.06

0.08

0.100

Hz Fig. 13. - Magnitude squared coherence for temperature and streamwise velocity component (a)) and for temperature and vertical velocity (b)) of the file recorded at Campo Icaro. stability conditions. For stable and near-neutral conditions there is a good coherence between temperature and streamwise velocity component; weaker peaks appear in temperature and vertical velocity test coherence. For unstable conditions there is a great coherence between temperature and vertical velocity, while the coherence between temperature and the streamwise component of velocity is very low. The characteristic time scales of turbulent eddies in which coherence is present are between 0.005 Hz and 0.07 Hz, e.g. between periods of 200 and 14 seconds. At these frequencies the turbulent energy is available for the heat and momentum transfer process.

8. -

Conclusions

The results presented in this paper concerning the turbulence behaviour of wind and temperature data collected in Antarctica by means of a three-axial digitized ultrasonic anemometer-thermometer show the potential of this instrument in determining the fundamental characteristics of the planetary boundary layer. Data from three different situations were analysed which clearly imply the fundamental role the stability condition plays in the description of the turbulent dynamics. i) A flat glacier (Nansen Ice Sheet) with moderate wind is characterized by a strong-stability condition. Here the statistical and coherence tests and also the

504

G. FICCA, M. PANGIA, S. PIERINI, R. PURINI and E. SANSONE

temporal recordings show how the horizontal-velocity fluctuations influence the temperature fluctuations, while the vertical velocity remains essentially zero. ii) The same glacier with strong-wind condition is characterized by nearneutral stability condition and strong momentum flux. In the zone of strong gust of wind the increase of momentum flux occurs in phase with the heat flux. iii) A rocky coastal zone (Campo Icaro) is characterized by a strong-instability condition. This situation due to the morphological condition of Campo Icaro is an example of thermally driven instability. Here the heat flux is strong and positive, and significant coherence appears between temperature and vertical velocity.

We thank the National Research Program in Antarctica (PNRA) for partially supporting this study. We are grateful to Dr. J. C. King whose comments helped improve the manuscript. Finally, we would like to thank Dr. C. Cassardo for valuable suggestions about the problem of data correction. REFERENCES [1] KAIMALJ. C., Sonic anemometers, in Air Sea Interaction, edited by F. DOBSON, L. HASSE and R. DAVIS,Vol. 4 (Plenum Press, New York, N.Y.) 1980, pp. 81-96. [2] HANAFUSA T., FUJITANI T., KOBORI Y. and MITSUTA Y., A new type sonic anemometerthermometer for field operation, in Papers in Meteorology and Geophysics, No. 1, Vol. 33 (1982) pp. 1-19. [3] HIGNETT P., Boundary-Layer Meteorol., 61 (1992) 175. [4] Kaijo Denki Co. Ltd., Digitized Ultrasonic Anemometer Thermometer, Model DAT-300. Instruction Manual. [5] McMILLEN R. T., Boundary-Layer Meteorol., 43 (1988) 231. [6] CASSARDOC., SACCHETTID., MORSELLIM. G., ANFOSSID., BRUSASCAG. and LONGHETTOA., Nuovo Cimento C, 18 (1995) 419. [7] KING J. C., Q. J. R. Meteorol. Soc., 116 (1990) 379. [8] HOLTONJ. R., A n Introduction to Dynamic Meteorology (Academic Press, New York, San Francisco, London) 1979. [9] BATCHELORG. K., An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge) 1981. [10] TENNEKES n. and LUMLEY J. L., A First Course in Turbulence (The MIT Press, Cambridge) 1972. [11] MCBEAN G. A., Boundary-Layer Meteorol., 1 (1971) 438. [12] BRIGHAME. 0., The Fast Fourier Transform (Prentice Hall, New Jersey) 1974. [13] OaIvh P. L. and TERRASI F., Elaborazione statistica dei risultati sperimentali (Liguori, Napoli) 1976. [14] LUMLEYJ. L. and PANOFSKYH. A., The Structure of Atmospheric Turbulence (Interscience, New York, N.Y.) 1964. [15] KAIMALJ. C., WYNGAARDJ. C., IZUMIY. and COTE O. R., Q. J. R. Meteorol. Soc., 98 (1972) 563. [16] MARBLES. L., Digital Spectral Analysis (Prentice Hall, New Jersey) 1987.