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Sodar retrieval of vertical acceleration, and implications for the determination of temperature and fluxes in the convective boundary layer
Atmospheric Research, 20 (1986) 199--212 Elsevier Science Publishers B.V., Amsterdam - - P r i n t e d in The Netherlands
199
SODAR RETRIEVAL OF VERTICAL ACCELERATION, AND IMPLICATIONS FOR THE DETERMINATION OF TEMPERATURE AND FLUXES IN THE CONVECTIVE BOUNDARY LAYER
GIORGIO FIOCCO 1, MARIA G R A Z I A CIMINELLI 1 and GIANGIUSEPPE MASTRANTONIO 2
Dipartimento di Fisica, Universitb "La Sapienza", 00185 Roma (Italy) 2IFA/CNR, 00044 Frascati (Italy) (Accepted for publication May 1, 1986)
ABSTRACT Fiocco, G., Ciminelli, M.G. and Mastrantonio, G., 1986. Sodar retrieval of vertical acceleration, and implications for the determination of temperature and fluxes in the convective boundary layer. Atmos. Res., 20: 199--212. With an array of acoustic Doppler sounders it is possible to retrieve a Lagrangian description of the air motions in the boundary layer: with adequate signal-to-noise and data processing, vertical profiles of the vertical acceleration can be obtained. In addition, by application of the buoyancy equation, the temperature and the heat flux in convective conditions can be inferred. Results of experiments carried out with three vertically pointing sodars, but with the horizontal velocity information independently provided, are shown, compared with profiles obtained with tethered balloons, and discussed. RESUME Avec un syst~me de sondeurs acoustique Doppler, il est possible de composer une description Lagrangienne des mouvements de l'air dans la couche limite: pour un signal sur bruit ad~quat et un programme de calcul ~labor~, on peut estimer un profil vertical de l'acc~l~ration verticale. De plus, en appliquant l'~quation des forces de flottabilit~, la temperature et le flux de chaleur sensible dans des conditions convectives peuvent ~tre calculus. Les r~sultats d'exp~riences conduites avec 3 sodars pointant verticalement, associ~s avec une information sur la vitesse horizontale du vent sont montr~s et compares ~ des profils obtenus par ballons captifs: une discussion est entreprise.
INTRODUCTION
The vertical acceleration is a most important quantity in geophysical fluid dynamics. In general, due to its relative smallness, the vertical c o m p o n e n t of the velocity of air, w, is a quantity difficult to measure with adequate accuracy, in comparison with the horizontal components. A direct measurement of the total derivative dw/dt is even more difficult, and it is not c o m m o n l y attempted. 0169-8095/86/$03.50
© 1 9 8 6 Elsevier S c i e n c e Publishers B.V.
200 In this paper we report some progress on the application of acoustic sounding techniques to the study of boundary layer dynamics: we show that with an array of Doppler sodars it is possible, through a Lagrangian description of the air motions, to retrieve vertical profiles of the vertical acceleration and, based on the buoyancy equation, also of the temperature in conditions of convection. Preliminary results were given in the Proceedings of the Remote Sensing Retrieval Methods Workshop (Fiocco et al., 1985). PROCEDURES Measurements of the wind velocity vector U(u,v,w), which are often carried out with fixed sensors, give rise to the distinction between Lagrangian and Eulerian descriptions of the motion. The vertical component of the acceleration following the fluid motion is expressed by the total derivative, d w / d t , of the vertical velocity component and is the sum of the partial (or local) derivative 5 w/6 t and of the advective term U.grad w: d w / d t = 5 w / S t + U.grad w.
(1)
Doppler sodars permit the measurement of the radial velocity component of the fluid motion {Brown and Hall, 1978): the time and space integration necessary to obtain a profile with the required accuracy and precision, and the a m o u n t of additional information that can be gathered, depend not only on the sensitivity of the sodar and the environmental conditions at the time of the measurement, but also on the data processing adopted (see e.g. Mastrantonio and Fiocco, 1982; Fiocco and Mastrantonio, 1983). With a vertically pointing sodar, the quantities that can be retrieved as a function of the height z, are w, 5w/St, 5w/6z, which are insufficient to reconstruct the advective term and thus obtain dw/ dt . With a three-axes Doppler sodar system, having one of the axes vertical and the other two at oblique angles, the three components of velocity u, v, w, can be retrieved, with the caveat however that the three beams do not generally observe the same volume. A measurement of grad w can be obtained with the use of three horizontally displaced, vertically pointing Doppler sodars; suppose the three sodars to be located at positions A, B, C, on the ground along two orthogonal directions x and y, as in Fig. 1. The two horizontal components of the gradient can be taken as: 5 w / 6 x = (wA - WB)/(XA - X B )
(2)
5 wl~y = (Wc -- WB)I(Yc --YB)
Thus by the use of five sodar beams, with three vertical and two oblique axes, a complete determination of the velocity and acceleration profiles, within the limitations previously mentioned and those imposed by the resolution, may be obtained.
201
Fig. 1. Geometrical layout of the three sodars. Vertical acceleration and gravity can be mathematically related through the buoyancy equation. In its simple form this is easily obtained by the standard analysis of the vertical motions of a parcel of air moving in an atmospheric region with a given profile of temperature Tatm (z), neglecting entrainment: d w / d t = g A T / T , t m ~- g A T / T p
(3)
where g is the gravitational acceleration, Tp is the temperature of the parcel and AT = Tp
-
Tat m
(4)
Since d w / d t can be measured, the difference A T can be determined. In order to reconstruct the temperature profile Tatm it will be necessary to provide an independent measurement, To, of the air temperature at a level z0, accessible to the sodar, where AT = 0, and to assume, e.g., an adiabatic profile for Tp, so that: Tatm (z0, $)
=
Tp (z0, t) = To (t)
Tp (z, t) = To (t) + [dTp (z, t ) / d z ] , a dz
(5) (6)
In this way, by application of exp. 4, since ( d T p / d z ) a a is known, T,t m (z, t) can be obtained. However, an important point should be raised: the notion of an infinitesimal parcel moving through an undisturbed medium, thus acting as a tracer, is largely idealized, but it is the accepted basis of a considerable a m o u n t of analysis and practical observing procedures. In the following, vertical profiles of AT obtained through the application of eq. 3, will be compared with temperature profiles measured with a t h e r m o m e t e r raised with a tethered balloon. As far as the fluxes are concerned, if the velocity field is known in detail, the m o m e n t u m fluxes can be readily computed as the product of the relevant quantities. Similarly, knowledge of w and T a t m makes it possible to provide measurements of the vertical heat flux as the product: cp = ~v T, tn~
(7)
202 THE EXPERIMENTS
The experiments were carried out in the period 11--15 September 1979, at Turbigo, near Milan, during an intercomparison campaign sponsored by the Commission of European Communities and by the Ente Nazionale Energia Elettrica. Many groups participated in the campaign, and various quantities of correlative interest were measured. Our group deployed an array of three vertically pointing sodars, which were operated continuously, and in addition made frequent determinations of the horizontal wind field by tracking pilot balloons. Several temperature profiles were obtained daily with a tethered balloon thermosonde by a group from Universit~ Catholique de Louvain, which operated at a location close to the sodars. Traces of the echoes from the ascending and descending balloon are sometimes present in the sodar data. These temperature measurements were carried out in situ with a single sensor progressively displaced in space and time depending on the motion of the balloon, with resulting lack of simultaneity in the profile. It should be pointed out also that while the proximity of the balloon to the sodar beams may be an advantage, since the volumes explored are close and often coincide, the presence of the balloon echoes in the sodar returns have sometime made the retrieval of w difficult. The three sodars, located with the geometry of Fig. 1, were operated simultaneously: each system emitted a 0.1 s duration burst with a cadence of 6 s at a slightly different frequency, namely, fA = 2000 Hz; fB = 1818.18 Hz; fc = 1616.6 Hz. The echoes for the three channels were filtered, combined and recorded on the same track of an analog magnetic tape: later in the laboratory the records were sampled, Fourier analysed and, for each sodar, profiles of the intensity and the Doppler shift of the echoes were retrieved. The lowest altitude at which those determinations were possible, due to the initial receivers' blackout, was 36 m and the height resolution was 29 m. The distances IxA - xB I=lyc - yBI = 100m. The subsequent analyses were concentrated at first around those intervals when, according to the sodar facsimile records, convection was active from the ground level to an identifiable inversion layer, and was successfully extended to other cases when convection was present and for which independent measurements of the horizontal wind and of the temperature fields, carried out within approximately one hour, were available. RESULTS
In the following a detailed description of the results for a 40 min interval of September 11 will be given first; successively a more concise description of other cases of interest will be presented. Fig. 2 is a height vs time facsimile display of the echo intensity for the
203
600,
A
E ~oo, IIO tlJ T
200
0 11h15
3"0
4"5
12"00
TIME
Fig. 2. Typical facsimile representation of the intensity of the sodar echoes as a function of time and height: data taken on September 11, 1979 at Turbigo.
11h19--12h00 interval of September l l t h , obtained with the sodar operating at 1818 Hz; darker traces indicate regions of more intense thermal turbulence corresponding to upward convection. The patterns of different darkness follow the alternation of the ascending and descending branches of the convective cells. The record also shows the presence, in the sodar field of view, of the tethered balloon and its evolutions. The horizontal wind speed was in the vicinity of I m s-1, and the meteorological conditions were fair. The successive analysis of the data was based on sampling the combined analog records for the three sodars at the frequency f, = 1500 Hz, applying the Fast Fourier Transform algorithm to stretches of the digitised data, and obtaining the three vertical velocity values, namely WA, WB, WC, with the procedures described by Mastrantonio and Fiocco (1982). Fig. 3 gives the vertical velocity as a function of height and time, obtained from the Doppler analysis of the echoes for the sodar in location B, whose intensity is shown in Fig. 2. While Fig. 3A represents the instantaneous value at intervals of 6 s, i.e. after every sodar pulse, Fig. 3B shows its running average over 9 successive pulses. It should be pointed o u t that the determination of the vertical velocity is carried o u t only when the signal-to-noise ratio of the measurement exceeds an assigned threshold: for this reason the series of instantaneous values of w may have gaps, which disappear in the smoothed series. From the smoothed vertical velocity values for the three sodars, the derivatives 6 w/5 t, a w/6 x, 8 w/8 y, 8 w/a z, were computed: the spatial derivatives were multiplied with the available values of the wind velocity corn-
204
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:, i ms
600.
E 400.' A
z~O0
I L9 UJ 200 I
11"15
200
30
4'5 TIME
12'00
11h15
. . 30 . .
A
'
' 12h}}0
TIME
Fig. 3. Vertical velocity, w, as a f u n c t i o n o f t i m e at d i f f e r e n t h e i g h t levels: A. i n s t a n t a n e o u s values; B. s m o o t h e d values. D a t a as in Fig. 2.
ponents in order to obtain the product U.grad w and the total derivative dw/dt. As already pointed out, throughout the series of experiments, the horizontal velocity components u and v, were not measured by sodar, since the system only had three vertical axes, but were obtained at unequally spaced time intervals by tracking pilot balloons, with a difference in time of as much as 1 h. Fig. 4. shows the various terms entering the computation, namely the partial derivative 5 w/6 t, and the advective terms u. 6 w/6 x, v. 5 w/5 y, w. 6 w~ 5z, for the same time interval shown in Fig. 2: these terms were c o m p u t e d using smooth values of the vertical velocities, as shown in Fig. 3B for one of the sodars. It should be pointed out that the advected terms are of a magnitude comparable to the local time derivative, even at the very modest values of the horizontal velocity components. The total derivative dw/dt, obtained summing the various terms, is given in Fig. 5. Fig. 6 is a running average for d w / d t based on 10 scans (1-min interval). Of the data utilised in the averaging process, those taken in temporal proximity (+ 1 min) of the presence of the balloon at the relevant height level, may be contaminated by its echoes as evidenced in Fig. 2" the trace and the Doppler "signature" of the balloon are clear and could (but have not) been removed. Another strong noise burst around 11h54 is automatically removed from the analysis after S/N determination. In this respect the echoes from the balloon have a very high S/N ratio. The retrieved vertical acceleration can be expressed in terms of a temperature difference AT by the application of eq. 3. Fig. 7 shows successive profiles of AT taken between 11h40 and 12h00: each is representative of an average over 50 scans (15 min). Throughout the record, the updrafts are decelerated just below 500 m, which points to the presence of a modest inversion, n o t detectable, by the
205
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Fig. 4. Values o f the terms entering the c o m p u t a t i o n o f the vertical acceleration as a f u n c t i o n o f t i m e at different height levels: A. 8 u/~ t; B. u.5 w / ~ x ; C. v.6 w/~ y; D. w.6 w/Sz. Data as in Fig. 2.
way, on the facsimile intensity record. The downdrafts, as shown in particular by the profiles obtained in the interval around 11h34, are characterised by an almost complete lack of vertical acceleration. It would be interesting to follow the dynamical behavior of the plumes to a level closer to the ground than presently accessible, and observe the region where positive acceleration occurs. This is presently denied by the receivers' blackout interval f o l l o w i n g t h e burst emission. Fig. 8 shows the two temperature profiles obtained by the UCL group during ascent and descent within the same time period; the altitude of the balloon as a function of time can be followed in Fig. 2. The ascent took place between 11h24 and 11h33, and the descent between 11h35 and 11h42. During ascent the balloon finds itself within an ascending plume up to a
206
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as a f u n c t i o n
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levels, derived from s m o o t h e d values for w. Data as in Fig. 2.
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Fig. 7. Successive vertical profiles of AT. Each profile represents a 5-min average. Data as in Fig. 2.
GO[ OScent, . . . .
11h2~* 11h33
descent, 11h35÷ 11hl.2
Z,OC
\\ e~ -r
20{
18
20
22 Temperature
2& (°C)
Fig. 8. Vertical temperature profiles obtained with a tethered balloon by the UCL group on September 11, 1979.
height of approximately 450 m, and the temperature profile thus obtained is close to being adiabatic up to that height. During descent instead the balloon finds itself in subsiding air for the upper part of its trajectory, progressively getting into the warmer, ascending plume in the lower part. It is thus natural that the resulting profile appears strongly superadiabatic within the height region 150--320 m. The comparison with the results in Fig. 7 is satisfactory considering that the balloon profiles are not the result of instantaneous point measurements.
208 Fig. 9 shows again the potential temperature profile obtained by the UCL group during ascent as well as two profiles for T obtained by averaging all sodar records between l l h 1 9 and 11h39, and between 11h39 and 11h59. Although these records contain small contributions due to the presence of the balloon, they confirm the presence of the inversion around 500 m. 600' 11r 2L, mi~ ~1h33min •
~
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Potential tcmpcroture, K
Fig. 9. The dotted lines show two profiles of AT obtained by averaging all results of September 11, 1979 between two successive time intervals; the continuous line is a potential temperature profile with respect to an arbitrary origin obtained during a balloon ascent.
Another sequence of interest, obtained on September 12, is depicted in Fig. 10, showing in the b o t t o m part the echo intensity and on the t o p the vertical velocity, as observed by antenna B, in the interval 1 0 h 0 0 - 1 2 h 0 0 . The resulting profiles for AT, limited to the second hour are given in Fig. 11; the profiles are running averages over a 5-~in interval. Well defined trends are apparent in the lower height region between l l h 0 0 and l l h 1 6 , corresponding to the developing plume. A balloon measurement, whose evolution is apparent between l l h 2 1 and 11h43 in Fig. 10, confirms the absence of any well defined inversion up to 400 m (see Fig. 12) with strong accelerations in the lower levels. Again towards the end of the sequence, after 11h45, the acceleration/temperature profile is characterized by the existence of moving trends inside the plume with excursions of + 0.5 K. Everywhere else the atmosphere is neutral. DISCUSSION AND CONCLUSIONS
The significance of these preliminary results, in the present simple formulation, points to the possibility of extracting temperature information in convective conditions. The situations that we have been able to analyse were unfortunately limited in time, due to the occasional character of the experiments during which the sodars were working in that configuration. The possibility of temperature retrieval is in the present, elementary analysis, to a large extent based on assuming the validity of the parcel theory,
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~
.
=-
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tJ
.
.
.
.
.
:
1140
1138
!
;
11,~4
11L8
-s
1150
6%
1154 Time
Fig. 11. Successive vertical profiles of AT. Each profile represents a 5-min average. Data as in Fig. 10.
600-
.....
ascent
11h2]
- -
descent
11h32 11~t,3
1727
~ 2110. Turbige 12 S e p t e m b e r ' 7 9
0
. -1
1 Poter~ticli
Temperature, K
Fig. 12. Profiles of potential temperature with respect to an arbitrary origin, obtained with the tethered balloon on September 12, 1979.
and several i n c o n s i s t e n c i e s m a y arise in its a p p l i c a t i o n , specially w h e n t h e advective t e r m s prevail. T h e a n a l y t i c a l a p p r o a c h c o u l d be c o n s i d e r a b l y i m p r o v e d . T h e a p p l i c a t i o n o f We parcel t h e o r y a p p e a r s m o r e justified w h e n t h e a t m o s p h e r e e x h i b i t s a well p r o n o u n c e d feature, s u c h as an inversion:
211
decelerations and accelerations are then of such a magnitude as to be clearly above the smaller fluctuations which are found in a neutral atmosphere. In this respect the important questions of entrainment and dissipation have not been considered. In the application of these procedures, it is essential that the velocity retrievals be accomplished in a time shorter than or at the most comparable with the observed evolution of the convection process, that is a few minutes at most. For this purpose both the signal-to-noise ratio of the sodars and the techniques of data analysis require adequate attention. In all conditions analysed, a large source of uncertainty appeared to be related to the horizontal velocity measurement. We assume that a fiveaxes sodar system would overcome this difficulty, being able to provide simultaneous, essentially colocated, measurements of the various dynamical quantities. With this proviso the results obtained appear very encouraging. The horizontal resolution of the technique depends to a large extent on the divergence of the sodar beams, being, progressively with distance, more difficult to resolve small eddies. To some extent a detailed spectral analysis may help in providing information within the scattering volume (Fiocco and Mastrantonio, 1983), b u t the analytical difficulties and the ambiguities in interpretation may be severe. It appears feasible, however, to utilize narrower beams, should the requirement of better resolution arise. It should be pointed out also that the existence of a minimum range below which the receivers were gated o u t prevented the observation of the lowest layers were the air is heated in contact with the ground and large positive accelerations are expected. It is possible, mainly by the use of higher frequencies and shorter bursts, to lower considerably the minimum range. We hope to be able sometime to carry out appropriate series of measurements with a multi-axial system, in the hope of clarifying these and other points mentioned above. It should be pointed o u t that the experiments were n o t planned with this application in mind, but rather to study the possibility of horizontal wind velocity retrieval by a study of the conservation of the features of turbulence (Berico et al., 1981). Again, the amount of theory which has been mobilised is indeed very limited and a more consistent model should be used to analyse, define the significance, and finally take advantage of the measurements. At least the present results indicate the potential of a relatively more detailed experimental approach.
REFERENCES Berico, M., Fiocco, G., Mastrantonio, G. and Ricotta, A., 1981. Spatial and temporal correlations of the intensity and of the vertical velocity field obtained with a tri-axial Doppler sodar. Proc. Int. Symp. Acoustic Remote Sensing of the Atmosphere and Oceans, Calgary, Alta. Brown, E.H. and Hall, F.F., 1978. Advances in atmospheric acoustics. Rev. Geophys. Space Phys., 16: 47--109.
21 2
Fiocco, G., Ciminelli, M.G. and Mastrantonio, G., 1985. Determination of vertical acceleration and potential temperature in the presence of convection with an array of Doppler sodars. In: A. Deepak, H.E. Fleming and M.T. Chahine (Editors), Advances in Remote Sensing Retrieval Methods. A. Deepak Publ., Williamsburg, VA. in press. Fiocco, G. and Mastrantonio, G., 1983. Characters of the air flow inferred from detailed spectral analysis of acoustic sounder echoes. J. Acoust. Soc. Am., 74: 1861--1865. Mastrantonio, G. and Fiocco, G., 1982. Accuracy of wind velocity determinations with Doppler sodars. J. Appl. Meteorol., 21 : 823--830.
199
SODAR RETRIEVAL OF VERTICAL ACCELERATION, AND IMPLICATIONS FOR THE DETERMINATION OF TEMPERATURE AND FLUXES IN THE CONVECTIVE BOUNDARY LAYER
GIORGIO FIOCCO 1, MARIA G R A Z I A CIMINELLI 1 and GIANGIUSEPPE MASTRANTONIO 2
Dipartimento di Fisica, Universitb "La Sapienza", 00185 Roma (Italy) 2IFA/CNR, 00044 Frascati (Italy) (Accepted for publication May 1, 1986)
ABSTRACT Fiocco, G., Ciminelli, M.G. and Mastrantonio, G., 1986. Sodar retrieval of vertical acceleration, and implications for the determination of temperature and fluxes in the convective boundary layer. Atmos. Res., 20: 199--212. With an array of acoustic Doppler sounders it is possible to retrieve a Lagrangian description of the air motions in the boundary layer: with adequate signal-to-noise and data processing, vertical profiles of the vertical acceleration can be obtained. In addition, by application of the buoyancy equation, the temperature and the heat flux in convective conditions can be inferred. Results of experiments carried out with three vertically pointing sodars, but with the horizontal velocity information independently provided, are shown, compared with profiles obtained with tethered balloons, and discussed. RESUME Avec un syst~me de sondeurs acoustique Doppler, il est possible de composer une description Lagrangienne des mouvements de l'air dans la couche limite: pour un signal sur bruit ad~quat et un programme de calcul ~labor~, on peut estimer un profil vertical de l'acc~l~ration verticale. De plus, en appliquant l'~quation des forces de flottabilit~, la temperature et le flux de chaleur sensible dans des conditions convectives peuvent ~tre calculus. Les r~sultats d'exp~riences conduites avec 3 sodars pointant verticalement, associ~s avec une information sur la vitesse horizontale du vent sont montr~s et compares ~ des profils obtenus par ballons captifs: une discussion est entreprise.
INTRODUCTION
The vertical acceleration is a most important quantity in geophysical fluid dynamics. In general, due to its relative smallness, the vertical c o m p o n e n t of the velocity of air, w, is a quantity difficult to measure with adequate accuracy, in comparison with the horizontal components. A direct measurement of the total derivative dw/dt is even more difficult, and it is not c o m m o n l y attempted. 0169-8095/86/$03.50
© 1 9 8 6 Elsevier S c i e n c e Publishers B.V.
200 In this paper we report some progress on the application of acoustic sounding techniques to the study of boundary layer dynamics: we show that with an array of Doppler sodars it is possible, through a Lagrangian description of the air motions, to retrieve vertical profiles of the vertical acceleration and, based on the buoyancy equation, also of the temperature in conditions of convection. Preliminary results were given in the Proceedings of the Remote Sensing Retrieval Methods Workshop (Fiocco et al., 1985). PROCEDURES Measurements of the wind velocity vector U(u,v,w), which are often carried out with fixed sensors, give rise to the distinction between Lagrangian and Eulerian descriptions of the motion. The vertical component of the acceleration following the fluid motion is expressed by the total derivative, d w / d t , of the vertical velocity component and is the sum of the partial (or local) derivative 5 w/6 t and of the advective term U.grad w: d w / d t = 5 w / S t + U.grad w.
(1)
Doppler sodars permit the measurement of the radial velocity component of the fluid motion {Brown and Hall, 1978): the time and space integration necessary to obtain a profile with the required accuracy and precision, and the a m o u n t of additional information that can be gathered, depend not only on the sensitivity of the sodar and the environmental conditions at the time of the measurement, but also on the data processing adopted (see e.g. Mastrantonio and Fiocco, 1982; Fiocco and Mastrantonio, 1983). With a vertically pointing sodar, the quantities that can be retrieved as a function of the height z, are w, 5w/St, 5w/6z, which are insufficient to reconstruct the advective term and thus obtain dw/ dt . With a three-axes Doppler sodar system, having one of the axes vertical and the other two at oblique angles, the three components of velocity u, v, w, can be retrieved, with the caveat however that the three beams do not generally observe the same volume. A measurement of grad w can be obtained with the use of three horizontally displaced, vertically pointing Doppler sodars; suppose the three sodars to be located at positions A, B, C, on the ground along two orthogonal directions x and y, as in Fig. 1. The two horizontal components of the gradient can be taken as: 5 w / 6 x = (wA - WB)/(XA - X B )
(2)
5 wl~y = (Wc -- WB)I(Yc --YB)
Thus by the use of five sodar beams, with three vertical and two oblique axes, a complete determination of the velocity and acceleration profiles, within the limitations previously mentioned and those imposed by the resolution, may be obtained.
201
Fig. 1. Geometrical layout of the three sodars. Vertical acceleration and gravity can be mathematically related through the buoyancy equation. In its simple form this is easily obtained by the standard analysis of the vertical motions of a parcel of air moving in an atmospheric region with a given profile of temperature Tatm (z), neglecting entrainment: d w / d t = g A T / T , t m ~- g A T / T p
(3)
where g is the gravitational acceleration, Tp is the temperature of the parcel and AT = Tp
-
Tat m
(4)
Since d w / d t can be measured, the difference A T can be determined. In order to reconstruct the temperature profile Tatm it will be necessary to provide an independent measurement, To, of the air temperature at a level z0, accessible to the sodar, where AT = 0, and to assume, e.g., an adiabatic profile for Tp, so that: Tatm (z0, $)
=
Tp (z0, t) = To (t)
Tp (z, t) = To (t) + [dTp (z, t ) / d z ] , a dz
(5) (6)
In this way, by application of exp. 4, since ( d T p / d z ) a a is known, T,t m (z, t) can be obtained. However, an important point should be raised: the notion of an infinitesimal parcel moving through an undisturbed medium, thus acting as a tracer, is largely idealized, but it is the accepted basis of a considerable a m o u n t of analysis and practical observing procedures. In the following, vertical profiles of AT obtained through the application of eq. 3, will be compared with temperature profiles measured with a t h e r m o m e t e r raised with a tethered balloon. As far as the fluxes are concerned, if the velocity field is known in detail, the m o m e n t u m fluxes can be readily computed as the product of the relevant quantities. Similarly, knowledge of w and T a t m makes it possible to provide measurements of the vertical heat flux as the product: cp = ~v T, tn~
(7)
202 THE EXPERIMENTS
The experiments were carried out in the period 11--15 September 1979, at Turbigo, near Milan, during an intercomparison campaign sponsored by the Commission of European Communities and by the Ente Nazionale Energia Elettrica. Many groups participated in the campaign, and various quantities of correlative interest were measured. Our group deployed an array of three vertically pointing sodars, which were operated continuously, and in addition made frequent determinations of the horizontal wind field by tracking pilot balloons. Several temperature profiles were obtained daily with a tethered balloon thermosonde by a group from Universit~ Catholique de Louvain, which operated at a location close to the sodars. Traces of the echoes from the ascending and descending balloon are sometimes present in the sodar data. These temperature measurements were carried out in situ with a single sensor progressively displaced in space and time depending on the motion of the balloon, with resulting lack of simultaneity in the profile. It should be pointed out also that while the proximity of the balloon to the sodar beams may be an advantage, since the volumes explored are close and often coincide, the presence of the balloon echoes in the sodar returns have sometime made the retrieval of w difficult. The three sodars, located with the geometry of Fig. 1, were operated simultaneously: each system emitted a 0.1 s duration burst with a cadence of 6 s at a slightly different frequency, namely, fA = 2000 Hz; fB = 1818.18 Hz; fc = 1616.6 Hz. The echoes for the three channels were filtered, combined and recorded on the same track of an analog magnetic tape: later in the laboratory the records were sampled, Fourier analysed and, for each sodar, profiles of the intensity and the Doppler shift of the echoes were retrieved. The lowest altitude at which those determinations were possible, due to the initial receivers' blackout, was 36 m and the height resolution was 29 m. The distances IxA - xB I=lyc - yBI = 100m. The subsequent analyses were concentrated at first around those intervals when, according to the sodar facsimile records, convection was active from the ground level to an identifiable inversion layer, and was successfully extended to other cases when convection was present and for which independent measurements of the horizontal wind and of the temperature fields, carried out within approximately one hour, were available. RESULTS
In the following a detailed description of the results for a 40 min interval of September 11 will be given first; successively a more concise description of other cases of interest will be presented. Fig. 2 is a height vs time facsimile display of the echo intensity for the
203
600,
A
E ~oo, IIO tlJ T
200
0 11h15
3"0
4"5
12"00
TIME
Fig. 2. Typical facsimile representation of the intensity of the sodar echoes as a function of time and height: data taken on September 11, 1979 at Turbigo.
11h19--12h00 interval of September l l t h , obtained with the sodar operating at 1818 Hz; darker traces indicate regions of more intense thermal turbulence corresponding to upward convection. The patterns of different darkness follow the alternation of the ascending and descending branches of the convective cells. The record also shows the presence, in the sodar field of view, of the tethered balloon and its evolutions. The horizontal wind speed was in the vicinity of I m s-1, and the meteorological conditions were fair. The successive analysis of the data was based on sampling the combined analog records for the three sodars at the frequency f, = 1500 Hz, applying the Fast Fourier Transform algorithm to stretches of the digitised data, and obtaining the three vertical velocity values, namely WA, WB, WC, with the procedures described by Mastrantonio and Fiocco (1982). Fig. 3 gives the vertical velocity as a function of height and time, obtained from the Doppler analysis of the echoes for the sodar in location B, whose intensity is shown in Fig. 2. While Fig. 3A represents the instantaneous value at intervals of 6 s, i.e. after every sodar pulse, Fig. 3B shows its running average over 9 successive pulses. It should be pointed o u t that the determination of the vertical velocity is carried o u t only when the signal-to-noise ratio of the measurement exceeds an assigned threshold: for this reason the series of instantaneous values of w may have gaps, which disappear in the smoothed series. From the smoothed vertical velocity values for the three sodars, the derivatives 6 w/5 t, a w/6 x, 8 w/8 y, 8 w/a z, were computed: the spatial derivatives were multiplied with the available values of the wind velocity corn-
204
6ooI
:, i ms
600.
E 400.' A
z~O0
I L9 UJ 200 I
11"15
200
30
4'5 TIME
12'00
11h15
. . 30 . .
A
'
' 12h}}0
TIME
Fig. 3. Vertical velocity, w, as a f u n c t i o n o f t i m e at d i f f e r e n t h e i g h t levels: A. i n s t a n t a n e o u s values; B. s m o o t h e d values. D a t a as in Fig. 2.
ponents in order to obtain the product U.grad w and the total derivative dw/dt. As already pointed out, throughout the series of experiments, the horizontal velocity components u and v, were not measured by sodar, since the system only had three vertical axes, but were obtained at unequally spaced time intervals by tracking pilot balloons, with a difference in time of as much as 1 h. Fig. 4. shows the various terms entering the computation, namely the partial derivative 5 w/6 t, and the advective terms u. 6 w/6 x, v. 5 w/5 y, w. 6 w~ 5z, for the same time interval shown in Fig. 2: these terms were c o m p u t e d using smooth values of the vertical velocities, as shown in Fig. 3B for one of the sodars. It should be pointed out that the advected terms are of a magnitude comparable to the local time derivative, even at the very modest values of the horizontal velocity components. The total derivative dw/dt, obtained summing the various terms, is given in Fig. 5. Fig. 6 is a running average for d w / d t based on 10 scans (1-min interval). Of the data utilised in the averaging process, those taken in temporal proximity (+ 1 min) of the presence of the balloon at the relevant height level, may be contaminated by its echoes as evidenced in Fig. 2" the trace and the Doppler "signature" of the balloon are clear and could (but have not) been removed. Another strong noise burst around 11h54 is automatically removed from the analysis after S/N determination. In this respect the echoes from the balloon have a very high S/N ratio. The retrieved vertical acceleration can be expressed in terms of a temperature difference AT by the application of eq. 3. Fig. 7 shows successive profiles of AT taken between 11h40 and 12h00: each is representative of an average over 50 scans (15 min). Throughout the record, the updrafts are decelerated just below 500 m, which points to the presence of a modest inversion, n o t detectable, by the
205
I ~o5 ms'z
600'
600
I
0,05ms"2
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.
.
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.
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11
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ill z 200
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11h!
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4"5
"
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11h;5
"
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-.,,=~
45
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12%0
Fig. 4. Values o f the terms entering the c o m p u t a t i o n o f the vertical acceleration as a f u n c t i o n o f t i m e at different height levels: A. 8 u/~ t; B. u.5 w / ~ x ; C. v.6 w/~ y; D. w.6 w/Sz. Data as in Fig. 2.
way, on the facsimile intensity record. The downdrafts, as shown in particular by the profiles obtained in the interval around 11h34, are characterised by an almost complete lack of vertical acceleration. It would be interesting to follow the dynamical behavior of the plumes to a level closer to the ground than presently accessible, and observe the region where positive acceleration occurs. This is presently denied by the receivers' blackout interval f o l l o w i n g t h e burst emission. Fig. 8 shows the two temperature profiles obtained by the UCL group during ascent and descent within the same time period; the altitude of the balloon as a function of time can be followed in Fig. 2. The ascent took place between 11h24 and 11h33, and the descent between 11h35 and 11h42. During ascent the balloon finds itself within an ascending plume up to a
206
T
600 •
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..... _,.
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.,r,~.liiTiLf v
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'
,,k'*'i,.
I.L~
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45
L.J. i
12h00
TIME F i g . 5. V a l u e s
of the vertical
acceleration
d~/dt,
as a f u n c t i o n
of time at different
levels, derived from s m o o t h e d values for w. Data as in Fig. 2.
600' I 0.05
ms "2
A
E
4oo
IZ 0 W 2O0 I
0 11h15
4"5
30
12";0
TiME Fig. 6. S a m e as in Fig. 5, but smoothed through a 10-point running average.
height
207 o
II~.0
II~,~,
E 6001 "t~ ~' ' - ~ 300
II~
-.... -
"~
~
0. 1150
115~,
1158
Time
Fig. 7. Successive vertical profiles of AT. Each profile represents a 5-min average. Data as in Fig. 2.
GO[ OScent, . . . .
11h2~* 11h33
descent, 11h35÷ 11hl.2
Z,OC
\\ e~ -r
20{
18
20
22 Temperature
2& (°C)
Fig. 8. Vertical temperature profiles obtained with a tethered balloon by the UCL group on September 11, 1979.
height of approximately 450 m, and the temperature profile thus obtained is close to being adiabatic up to that height. During descent instead the balloon finds itself in subsiding air for the upper part of its trajectory, progressively getting into the warmer, ascending plume in the lower part. It is thus natural that the resulting profile appears strongly superadiabatic within the height region 150--320 m. The comparison with the results in Fig. 7 is satisfactory considering that the balloon profiles are not the result of instantaneous point measurements.
208 Fig. 9 shows again the potential temperature profile obtained by the UCL group during ascent as well as two profiles for T obtained by averaging all sodar records between l l h 1 9 and 11h39, and between 11h39 and 11h59. Although these records contain small contributions due to the presence of the balloon, they confirm the presence of the inversion around 500 m. 600' 11r 2L, mi~ ~1h33min •
~
tethered bQlioon
"
lb, 19m,~ +11h39~
"~,-.,.
700.
this work
~
.""
~-"~--~......
11h 39r,,." +lhS9r.in'~- - ' ~ ..........
. . . . . . ,.. ~
"~"~
\
j.\ /
rb,.go September'?9
a .~
_.g
-.i
:}
~
?
:
~
i
Potential tcmpcroture, K
Fig. 9. The dotted lines show two profiles of AT obtained by averaging all results of September 11, 1979 between two successive time intervals; the continuous line is a potential temperature profile with respect to an arbitrary origin obtained during a balloon ascent.
Another sequence of interest, obtained on September 12, is depicted in Fig. 10, showing in the b o t t o m part the echo intensity and on the t o p the vertical velocity, as observed by antenna B, in the interval 1 0 h 0 0 - 1 2 h 0 0 . The resulting profiles for AT, limited to the second hour are given in Fig. 11; the profiles are running averages over a 5-~in interval. Well defined trends are apparent in the lower height region between l l h 0 0 and l l h 1 6 , corresponding to the developing plume. A balloon measurement, whose evolution is apparent between l l h 2 1 and 11h43 in Fig. 10, confirms the absence of any well defined inversion up to 400 m (see Fig. 12) with strong accelerations in the lower levels. Again towards the end of the sequence, after 11h45, the acceleration/temperature profile is characterized by the existence of moving trends inside the plume with excursions of + 0.5 K. Everywhere else the atmosphere is neutral. DISCUSSION AND CONCLUSIONS
The significance of these preliminary results, in the present simple formulation, points to the possibility of extracting temperature information in convective conditions. The situations that we have been able to analyse were unfortunately limited in time, due to the occasional character of the experiments during which the sodars were working in that configuration. The possibility of temperature retrieval is in the present, elementary analysis, to a large extent based on assuming the validity of the parcel theory,
i-
LJ
15
,~
.JI
30
3"o
~,,,
-
&5
;s
-
_
11h00 TIME
1~'oo
i . . , , . . ~
15
~
~
30
io
~
&'S
~
.~.-~,..-~-~---~
2. m s -~
Pig. 10. B o t t o m : facsimile r e p r e s e n t a t i o n o f t h e i n t e n s i t y o f t h e e c h o e s . T o p : vertical t e l o c i t y w. D a t a w e r e t a k e n o n S e p t e m b e r 1 2 , 1 9 7 9 w i t h a n t e n n a B.
10h0
!00
,00
~o~oo
i00.
9
0.i,,,..-.-.------..
r
E
,00-
z%
12¢oo
D
O
210
1100
l!0z.
11!0
1114
600-
600"
I
1~]~
1118 :
1120
1124
1130
1134
~
.
=-
:
11'28
30e
tJ
.
.
.
.
.
:
1140
1138
!
;
11,~4
11L8
-s
1150
6%
1154 Time
Fig. 11. Successive vertical profiles of AT. Each profile represents a 5-min average. Data as in Fig. 10.
600-
.....
ascent
11h2]
- -
descent
11h32 11~t,3
1727
~ 2110. Turbige 12 S e p t e m b e r ' 7 9
0
. -1
1 Poter~ticli
Temperature, K
Fig. 12. Profiles of potential temperature with respect to an arbitrary origin, obtained with the tethered balloon on September 12, 1979.
and several i n c o n s i s t e n c i e s m a y arise in its a p p l i c a t i o n , specially w h e n t h e advective t e r m s prevail. T h e a n a l y t i c a l a p p r o a c h c o u l d be c o n s i d e r a b l y i m p r o v e d . T h e a p p l i c a t i o n o f We parcel t h e o r y a p p e a r s m o r e justified w h e n t h e a t m o s p h e r e e x h i b i t s a well p r o n o u n c e d feature, s u c h as an inversion:
211
decelerations and accelerations are then of such a magnitude as to be clearly above the smaller fluctuations which are found in a neutral atmosphere. In this respect the important questions of entrainment and dissipation have not been considered. In the application of these procedures, it is essential that the velocity retrievals be accomplished in a time shorter than or at the most comparable with the observed evolution of the convection process, that is a few minutes at most. For this purpose both the signal-to-noise ratio of the sodars and the techniques of data analysis require adequate attention. In all conditions analysed, a large source of uncertainty appeared to be related to the horizontal velocity measurement. We assume that a fiveaxes sodar system would overcome this difficulty, being able to provide simultaneous, essentially colocated, measurements of the various dynamical quantities. With this proviso the results obtained appear very encouraging. The horizontal resolution of the technique depends to a large extent on the divergence of the sodar beams, being, progressively with distance, more difficult to resolve small eddies. To some extent a detailed spectral analysis may help in providing information within the scattering volume (Fiocco and Mastrantonio, 1983), b u t the analytical difficulties and the ambiguities in interpretation may be severe. It appears feasible, however, to utilize narrower beams, should the requirement of better resolution arise. It should be pointed out also that the existence of a minimum range below which the receivers were gated o u t prevented the observation of the lowest layers were the air is heated in contact with the ground and large positive accelerations are expected. It is possible, mainly by the use of higher frequencies and shorter bursts, to lower considerably the minimum range. We hope to be able sometime to carry out appropriate series of measurements with a multi-axial system, in the hope of clarifying these and other points mentioned above. It should be pointed o u t that the experiments were n o t planned with this application in mind, but rather to study the possibility of horizontal wind velocity retrieval by a study of the conservation of the features of turbulence (Berico et al., 1981). Again, the amount of theory which has been mobilised is indeed very limited and a more consistent model should be used to analyse, define the significance, and finally take advantage of the measurements. At least the present results indicate the potential of a relatively more detailed experimental approach.
REFERENCES Berico, M., Fiocco, G., Mastrantonio, G. and Ricotta, A., 1981. Spatial and temporal correlations of the intensity and of the vertical velocity field obtained with a tri-axial Doppler sodar. Proc. Int. Symp. Acoustic Remote Sensing of the Atmosphere and Oceans, Calgary, Alta. Brown, E.H. and Hall, F.F., 1978. Advances in atmospheric acoustics. Rev. Geophys. Space Phys., 16: 47--109.
21 2
Fiocco, G., Ciminelli, M.G. and Mastrantonio, G., 1985. Determination of vertical acceleration and potential temperature in the presence of convection with an array of Doppler sodars. In: A. Deepak, H.E. Fleming and M.T. Chahine (Editors), Advances in Remote Sensing Retrieval Methods. A. Deepak Publ., Williamsburg, VA. in press. Fiocco, G. and Mastrantonio, G., 1983. Characters of the air flow inferred from detailed spectral analysis of acoustic sounder echoes. J. Acoust. Soc. Am., 74: 1861--1865. Mastrantonio, G. and Fiocco, G., 1982. Accuracy of wind velocity determinations with Doppler sodars. J. Appl. Meteorol., 21 : 823--830.