- Email: [email protected]
University of Saskatchewan MF radar
Journal q/‘Amospheric
Pergamon
andSolar-Terreswial
PI1 : S1364-6826(97)00124-7
Physrcs, All rights
Vol. 60, No. 4, pp. 437-440, 1998 G 1998 Elsev~er Science Ltd reserved. Punted in Great Britain 136+6626/98 $19.@0+0.00
Rapid Communication Turbulent energy dissipation rates from the University of Tromse/University of Saskatchewan MF radar C. M. Hall,‘* C. E. Meek’ and A. H. Manson’
’Department
of Physics, University of Tromsa. N-9037 Tromss, Norway ; ’Institute of Space and Atmospheric Studies, University of Saskatchewan, Saskatoon, SK 57N 5E2, Canada (e-mail; [email protected])
(Receioed 17 March 1997, in ret’isedforms 21 July and 17 October 1997, and accepted 29 October 1997) Abstract-Improvements to the University of Tromser/University of Saskatchewan joint MF radar in northern Norway have enabled new estimations of the kinetic energy dissipation rate to be made. This parameter, E’, is then taken to be an indicator of E, the turbulent energy dissipation rate. We shall address the derivation of E’for the mesosphere and present a method which we hope will prove well suited to future geostatistical studies. The methodology presented here will form the basis for continual monitoring of the mesosphere and therefore its seasonal and climatic variability. 0 1998 Elsevier Science Ltd
1. INTRODUCTION
Estimates of turbulent energy dissipation rates, E, in the mesosphere above northern Scandinavia are quite numerous and consist of both in situ and groundbased measurements using a variety of methods. Liibken (1996) is a starting point for references to in situ observations while Hall (1997) describes a new method for investigating turbulence using a 224 MHz radar (EISCAT VHF). Although the 2.78 MHz MF radar at Ramfjordmoen (69.58”N, 19.22”E) has been in existence for around 3 decades, no results quantifying turbulent parameters have been published hitherto, the system having been used to estimate either electron densities or, more recently, winds (e.g. Manson and Meek, 1991). Recent improvements (in late 1996) to data acquisition, antennae and transmitter have prompted the authors to re-address the problem of determining E. The means of using such a radar have been discussed in depth by Hocking (1996) and more particularly with a system similar to ours by Vandepeer and Hocking (1993). In these references, the concepts of beam- and shear-broadening are examined, exposing the potential disadvantages of several methods. The vertical structure function which forms the basis of the method of determining E described by Briggs (1980) has potentially fewer
*Author to whom correspondence
should be addressed. 437
pitfalls, provided that a suitable frame of reference (moving with the wind) is used. Indeed Vandepeer and Hocking (1993) show that turbulence parameters derived from this “radar-echo-fading-rate” method compare well with those derived from a “Dopplerradar-scattering-beamwidth” method which has been corrected for all possible contamination by the horizontal wind field. The work of Vandepeer and Hocking (1993) has reawakened our interest in this first method, described elegantly by Briggs (1980), and easily available from the spaced antenna full correlation analysis (FCA) method of wind measurement. We used this in Manson and Meek (1980) and Manson et al. (1981) to obtain profiles of E and u’ (turbulence velocity), and compared these with the same parameters found from the variance of the horizontal wind. The latter is associated with gravity waves (GW). The agreement was good. At that time the E values (typically 0.1 W/kg, with peaks of 0.2-0.3 W/kg) were comparable with rocket and meteor estimates (e.g. Roper, 1977). Since then much refinement of analysis has occurred, leading to changes in magnitude for preferred values. However, we used these two methods in Manson and Meek (1987) to provide energy dissipation rate climatologies (60-100 km, monthly resolution) for Saskatoon (52”N). The E values from the “radar-echo-fading-rate” method showed a strong semi-annual oscillation. with a maximum in summer
C. M. Hall et al.
438
and a secondary, lesser, maximum in winter. This is consistent with larger GW variances in summer and winter months than at the equinoxes, and also the observed stronger radar scattering. Such a scenario of semi-annual variation is mentioned by Vincent (1990), whereas, if one considers only the lower mesosphere, an annual variability is evident (Hirota, 1990). It should be noted, however, that these earlier observations were from rather different geographical locations. Our interest is now in re-visiting this work and applying similar but updated analyses to the Tromss data giving results which may be compared with the wealth of measurements from nearby (e.g. Ltibken, 1997). Quantification of turbulence is fraught with uncertainty and differences of opinion regarding methodologies and constants of proportionality. Here, therefore, we present yet another approach to the problem : we shall not invest time in making estimates that are as accurate as possible but, rather, we make assumptions which are plain to see and which yield estimates of c which are suited more to geostatistical studies of variations in turbulence than case studies at particular times. This was also the philosophy behind the study of Hall (1997) who employed an intuitive approach based on the work of Blamont (1963), and we shall use the results of this reference as a comparison.
2. METHOD
Descriptions of the experimental set up of the University of Tromsar/University of Saskatchewan joint MF radar may be found in Manson and Meek (199 1). Subsequently, the loop antennae described in this reference have been replaced with inverted-V antennae. Essentially, the system consists of a 4 x 4 crossed dipole transmitter array and three spaced receivers, the operating frequency being 2.78 MHz. The signal fading times, rc, are determined by the FCA mentioned earlier and an example is shown in Fig. 1. Full details of the FCA, including a discussion of errors in the method, may be found in the references given. Subsequently, velocity fluctuations, v’, appropriate to an observer moving with the background wind, are computed according to Briggs (1980), and as used by Manson et ul. (1981), at a height resolution of 3 km and time resolution of 5 min. via n&J= 47X,
(I)
where I is the radar wavelength. In an idea1 situation, the radar beamwidth would be infinitely narrow and
970129
sol
0
I”““’
I
” ”
2
3
”
4
4
d
Fading time (second.)
Fig. I. Average fading times, in seconds, at different altitudes for 29 January 1997. See text for discussion of this parameter.
exactly vertical. This is not the case, however, and in order to allow for this we shall consider the measured P’ to be the total component of the fluctuation. We have to assume that the fading time determined by the FCA is indeed the characteristic decay time of neutral atmosphere structures. Furthermore, although a structure seen by the radar is dissipating with a time constant z,, we cannot assume apriori that it is exclusively the vertical (or horizontal) dynamics which are responsible. The energy dissipation rate may be arrived at by dividing the kinetic energy of the turbulence. related to c’*, by a timescale (Blamont, 1963). In previous studies (e.g. Manson et al., 1981), the Brunt-V&ala period has been identified as a suitable timescale, the fluctuation is the vertical component, U=, and the expression s = 0.4 lJ:w, has been used (ws being the Brunt-V&ala frequency). Here, however, we have assumed a total velocity fluctuation and thus use E’= 0.8 v”/TB
(2)
where T, is the Brunt-V&ala period in seconds. Note that we recognise that the spatial scale inherent in the experiment cannot preclude buoyancy-scale fluctuations, because the outer scale of turbulence, L,, can be expected to be as little as 200 m in the mesosphere. We therefore choose to introduce 8’ to distinguish our measurement from E. Furthermore, eqn (2) implicitly assumes that there is no motion of the observer relative to the background wind; we have not attempted to compensate for departures from this. Our approach contrasts somewhat with that of Blamont (1963) (used by Hall, 1997), who identify a timescale as L/v’, where L is a length scale charac-
Turbulent energy dissipation rate for the mesosphere teristic of the experiment. To use a formulation for E which assumes a radar completely free from beam broadening would be clearly inappropriate, and we attempt to address the warnings of Hocking (1983) (somewhat weakened by Vandepeer and Hocking 1993) by accepting that U’is an estimate of total velocity perturbations within the scattering volume and choosing a time scale accordingly. It should be pointed out, however, that a disadvantage of incorporating the Brunt-V&sglg period in the time scale is that we must use a model with an implicit seasonal variation. The Brunt-V&31% period is determined from the Mass Spectrometer and Incoherent Scatter (Extended) (MSISE90) model (Hedin, 1991).
3. RESULTS
Apart from occasional interruptions, the current radar system delivers profiles of signal fading times every 5 min. Since the database from this radar is growing continually we shall initially restrict our presentation of the data to January 1997 and take this period to be representative of the winter mesosphere. In Fig. 2, we show the average profile of E’ for 29 January 1997. Figure 2 represents a typical profile, and in practice data may be available right down to 60 km or missing altogether, depending on the state of the ionosphere. The horizontal bars indicate the standard deviations, the number of contributions varying as a function of height up to a maximum of 288 values per height. The dotted line shows the result
970129 90.
T”,’ /
,
/ 80 :
I
’ ,’
”
“7
I’ I
1
\ E .x
:
,
:
,’ 70; _ __
0.450.
0.8T. 60 I
IO
100
1oao
mw/kg
Fig. 2. Average energy dissipation rate E’as a function of altitude for 29 January 1997 (solid line). The horizontal bars indicate the standard deviation of the underlying 5 min. profiles. The dotted line indicates the result of assuming the derived velocity fluctuation to be the vertical component for inertial subrange turbulence (Manson and Meek. 1981), a method considered inappropriate by this paper.
eot
439
I
Fig. 3. Average energy dissipation rate E’ as a function of altitude for January 1997 (solid line). The horizontal bars indicate the standard deviation of the underlying day-average profiles. The dotted line indicates the estimate for 20 January 1993 given by Hall (1997) from the EISCAT VHF system nearby.
of using the method of Manson and Meek (198 1) not attempting to make corrections for beam- and shear-broadening as prescribed by Hocking (1983), and simultaneously assuming the measured velocity fluctuations to be vertical components. Taking all available data for January 1997 we arrive at Fig. 3. Here the horizontal bars show the standard deviations derived from the daily averages, and therefore indicate the day-to-day variability. The dotted line, in this case, shows the profile obtained from the EISCAT VHF radar, situated only a few hundred meters from the MF system, for 20 January 1993 as published by Hall (1997). Considering both the uncertainties implicit in any derivation of mesospheric E and also real variability in this parameter itself, we assert that there is good agreement between these results. The values also compare favourably with recent in situ measurements (Liibken, 1993) in which E is indicated to be around 20 mW kg-’ at 90 km and at 69”N in winter. We have also concentrated on winter data hitherto because the radar gating does not take the group retardation due to the ionosphere into account. In other words, the heights given are virtual heights; the true heights of the observations may be less. This phenomenon is relatively unimportant during aurorally quiet conditions at night, but the difference between virtual height and real height may amount to several kilometres during the summer, especially at heights over 90 km. Bearing this limitation in mind, we nevertheless present, in Fig. 4, the results for 1997 up to the time of writing. The figure
440
C. M. Hall et al.
with both radar and in situ measurements lend encouragement ; we have presented the tentative beginnings of a study of seasonal variation of turbulent intensity, indicating a semi-annual nature at 90 km. The method will be used over a longer time, allowing seasonal and inter-annual variations to be explored. AcknoM;ledgements-The authors wish to thank Bjornar Hansen and Bjarn-Ove Hussy for technical support. We are indebted to the reviewers of this paper for constructive comments. REFERENCES 2
1
3
7
6
5
4 month
Fig. 4. Time series of E’for 90 km for the first half of 1997 (solid line) and total horizontal windspeed (dotted line). Units of E’are mW kg-’ and those of windspeed are mss’. The digits on the horizontal axis denote the ends of months (i.e. “1” corresponds to 31 January 1997). Day averages, like that shown in Fig. 2, have been used and a 4-day boxcar filter applied.
shows the kinetic altitude
energy
as a function
1997. Also indicated
dissipation of time
is the total
from
rate,
a’, for 90 km
February
horizontal
wind
to July speed,
curves have been smoothed with a 4-day boxcar. There is a suggestion of minima in both parameters around the time of the reversal from winter to summer dynamics near the equinox ; the maximum E’ occurs in summer, in reasonable agreement with Ltibken (1997). and
both
4.
CONCLUSION
We have employed what might be described as a heuristic and pragmatic argument for the derivation of an energy dissipation rate because of the uncertainty in interpretation of the measured fluctuation velocity v’. We have called this dissipation rate E’as distinct from E, the turbulent energy dissipation rate. We have nevertheless been able to derive results from the University of Tromso/University of Saskatchewan joint MF radar for the winter mesosphere which plausibly indicate that E’may be representative of E. We therefore propose this strategy as a means of studying long-term variability of turbulence in the height regime 60 to 90 km in the future. The presence of a model atmosphere in our method unfortunately risks masking a true seasonal variation, though, but the assumptions involved are based on well-known theory, thus facilitating comparisons with similar results from other instruments. Initial comparisons
Blamont, J.-E. (1963) Turbulence in atmospheric motions between 90 and 130 km of altitude. Planet. Space Sci. 10, 89-101. Briggs, B. H. (1980) Radar observations of atmospheric winds and turbulence: a comparison of techniques. J. Atmos. Terr. Phys. 42, 823-833. Hall, C. M. (1997) Kilometer scale kinetic energy perturbations in the mesosphere derived from EISCAT velocity data. Radio Sci. 32,93-101. Hedin, A. E. (1991) Extension of the MSIS thermosphere model into the middle and lower atmosphere. .I. Geophys. Res. 96, 1159-l 172. Hirota, I. (1990) Seasonal and latitudinal variations of gravity waves. Adt. Space Res. 10, (12)103-(12)109. Hocking, W. K. (1983) On the extraction of atmospheric turbulence parameters from radar backscatter Doppler spectra-I. Theory. J. Atmos. Terr. Phys. 45, 89-102. Hocking, W. K. (1996) An assessment of the capabilities and limitations of radars in measurements of upper atmosphere turbulence. Ado. Space Res. 17, (11)37-(11)47. Ltibken, F.-J. (1996) Rocket-borne measurements of small scale structures and turbulence in the upper atmosphere. Adv. Space Res. 17, (11)25-(11)35. Ltibken, F.-J. (1997) Seasonal variation of turbulent energy dissipation rates at high latitudes as determined by in situ measurements of neutral density fluctuations. J. Geophys. Res., in press. Manson, A. H. and Meek, C. E. (1980) Gravity waves of short period (5-90 min) in the lower thermosphere at 52-N (Saskatoon, Canada). J. Atmos. Terr. Phys. 42, 1033113. Manson, A. H. and Meek, C. E. (1987) Small scale features in the middle atmosphere wind field at Saskatoon, Canada (52”N, 107”W) : an analysis of MF radar data with rocket comparisons. J. Atmos. Sci. 44,3361&3367. Manson, A. H. and Meek, C. E. (1991) Climatologies of mean winds and tides observed by medium frequency radars at Trams (70”N) and Saskatchewan (52”N) during 1987-1989. Can. J. Phys. 69,966975. Manson, A. H., Meek, C. E. and Gregory, J. B. (1981) Gravity waves of short period (5-90 min) in the lower thermosphere at 52”N (Saskatoon, Canada) : 1978/1979. J. Atmos. Terr. Phys. 43, 35-44. Roper, R. G. (1977) In Studies in Geophysics: The Upper Atmosphere and Magnetosphere. The Geophysics Research Board, National Academy of Sciences, Washington D.C., pp. 117-129. Vandepeer, B. G. W. and Hocking, W. K. (1993) A comparison of Doppler and spaced antenna radar techniques for the measurement of turbulent energy dissipation rates. Geophys. Res. Left. 20, 17-20.
Pergamon
andSolar-Terreswial
PI1 : S1364-6826(97)00124-7
Physrcs, All rights
Vol. 60, No. 4, pp. 437-440, 1998 G 1998 Elsev~er Science Ltd reserved. Punted in Great Britain 136+6626/98 $19.@0+0.00
Rapid Communication Turbulent energy dissipation rates from the University of Tromse/University of Saskatchewan MF radar C. M. Hall,‘* C. E. Meek’ and A. H. Manson’
’Department
of Physics, University of Tromsa. N-9037 Tromss, Norway ; ’Institute of Space and Atmospheric Studies, University of Saskatchewan, Saskatoon, SK 57N 5E2, Canada (e-mail; [email protected])
(Receioed 17 March 1997, in ret’isedforms 21 July and 17 October 1997, and accepted 29 October 1997) Abstract-Improvements to the University of Tromser/University of Saskatchewan joint MF radar in northern Norway have enabled new estimations of the kinetic energy dissipation rate to be made. This parameter, E’, is then taken to be an indicator of E, the turbulent energy dissipation rate. We shall address the derivation of E’for the mesosphere and present a method which we hope will prove well suited to future geostatistical studies. The methodology presented here will form the basis for continual monitoring of the mesosphere and therefore its seasonal and climatic variability. 0 1998 Elsevier Science Ltd
1. INTRODUCTION
Estimates of turbulent energy dissipation rates, E, in the mesosphere above northern Scandinavia are quite numerous and consist of both in situ and groundbased measurements using a variety of methods. Liibken (1996) is a starting point for references to in situ observations while Hall (1997) describes a new method for investigating turbulence using a 224 MHz radar (EISCAT VHF). Although the 2.78 MHz MF radar at Ramfjordmoen (69.58”N, 19.22”E) has been in existence for around 3 decades, no results quantifying turbulent parameters have been published hitherto, the system having been used to estimate either electron densities or, more recently, winds (e.g. Manson and Meek, 1991). Recent improvements (in late 1996) to data acquisition, antennae and transmitter have prompted the authors to re-address the problem of determining E. The means of using such a radar have been discussed in depth by Hocking (1996) and more particularly with a system similar to ours by Vandepeer and Hocking (1993). In these references, the concepts of beam- and shear-broadening are examined, exposing the potential disadvantages of several methods. The vertical structure function which forms the basis of the method of determining E described by Briggs (1980) has potentially fewer
*Author to whom correspondence
should be addressed. 437
pitfalls, provided that a suitable frame of reference (moving with the wind) is used. Indeed Vandepeer and Hocking (1993) show that turbulence parameters derived from this “radar-echo-fading-rate” method compare well with those derived from a “Dopplerradar-scattering-beamwidth” method which has been corrected for all possible contamination by the horizontal wind field. The work of Vandepeer and Hocking (1993) has reawakened our interest in this first method, described elegantly by Briggs (1980), and easily available from the spaced antenna full correlation analysis (FCA) method of wind measurement. We used this in Manson and Meek (1980) and Manson et al. (1981) to obtain profiles of E and u’ (turbulence velocity), and compared these with the same parameters found from the variance of the horizontal wind. The latter is associated with gravity waves (GW). The agreement was good. At that time the E values (typically 0.1 W/kg, with peaks of 0.2-0.3 W/kg) were comparable with rocket and meteor estimates (e.g. Roper, 1977). Since then much refinement of analysis has occurred, leading to changes in magnitude for preferred values. However, we used these two methods in Manson and Meek (1987) to provide energy dissipation rate climatologies (60-100 km, monthly resolution) for Saskatoon (52”N). The E values from the “radar-echo-fading-rate” method showed a strong semi-annual oscillation. with a maximum in summer
C. M. Hall et al.
438
and a secondary, lesser, maximum in winter. This is consistent with larger GW variances in summer and winter months than at the equinoxes, and also the observed stronger radar scattering. Such a scenario of semi-annual variation is mentioned by Vincent (1990), whereas, if one considers only the lower mesosphere, an annual variability is evident (Hirota, 1990). It should be noted, however, that these earlier observations were from rather different geographical locations. Our interest is now in re-visiting this work and applying similar but updated analyses to the Tromss data giving results which may be compared with the wealth of measurements from nearby (e.g. Ltibken, 1997). Quantification of turbulence is fraught with uncertainty and differences of opinion regarding methodologies and constants of proportionality. Here, therefore, we present yet another approach to the problem : we shall not invest time in making estimates that are as accurate as possible but, rather, we make assumptions which are plain to see and which yield estimates of c which are suited more to geostatistical studies of variations in turbulence than case studies at particular times. This was also the philosophy behind the study of Hall (1997) who employed an intuitive approach based on the work of Blamont (1963), and we shall use the results of this reference as a comparison.
2. METHOD
Descriptions of the experimental set up of the University of Tromsar/University of Saskatchewan joint MF radar may be found in Manson and Meek (199 1). Subsequently, the loop antennae described in this reference have been replaced with inverted-V antennae. Essentially, the system consists of a 4 x 4 crossed dipole transmitter array and three spaced receivers, the operating frequency being 2.78 MHz. The signal fading times, rc, are determined by the FCA mentioned earlier and an example is shown in Fig. 1. Full details of the FCA, including a discussion of errors in the method, may be found in the references given. Subsequently, velocity fluctuations, v’, appropriate to an observer moving with the background wind, are computed according to Briggs (1980), and as used by Manson et ul. (1981), at a height resolution of 3 km and time resolution of 5 min. via n&J= 47X,
(I)
where I is the radar wavelength. In an idea1 situation, the radar beamwidth would be infinitely narrow and
970129
sol
0
I”““’
I
” ”
2
3
”
4
4
d
Fading time (second.)
Fig. I. Average fading times, in seconds, at different altitudes for 29 January 1997. See text for discussion of this parameter.
exactly vertical. This is not the case, however, and in order to allow for this we shall consider the measured P’ to be the total component of the fluctuation. We have to assume that the fading time determined by the FCA is indeed the characteristic decay time of neutral atmosphere structures. Furthermore, although a structure seen by the radar is dissipating with a time constant z,, we cannot assume apriori that it is exclusively the vertical (or horizontal) dynamics which are responsible. The energy dissipation rate may be arrived at by dividing the kinetic energy of the turbulence. related to c’*, by a timescale (Blamont, 1963). In previous studies (e.g. Manson et al., 1981), the Brunt-V&ala period has been identified as a suitable timescale, the fluctuation is the vertical component, U=, and the expression s = 0.4 lJ:w, has been used (ws being the Brunt-V&ala frequency). Here, however, we have assumed a total velocity fluctuation and thus use E’= 0.8 v”/TB
(2)
where T, is the Brunt-V&ala period in seconds. Note that we recognise that the spatial scale inherent in the experiment cannot preclude buoyancy-scale fluctuations, because the outer scale of turbulence, L,, can be expected to be as little as 200 m in the mesosphere. We therefore choose to introduce 8’ to distinguish our measurement from E. Furthermore, eqn (2) implicitly assumes that there is no motion of the observer relative to the background wind; we have not attempted to compensate for departures from this. Our approach contrasts somewhat with that of Blamont (1963) (used by Hall, 1997), who identify a timescale as L/v’, where L is a length scale charac-
Turbulent energy dissipation rate for the mesosphere teristic of the experiment. To use a formulation for E which assumes a radar completely free from beam broadening would be clearly inappropriate, and we attempt to address the warnings of Hocking (1983) (somewhat weakened by Vandepeer and Hocking 1993) by accepting that U’is an estimate of total velocity perturbations within the scattering volume and choosing a time scale accordingly. It should be pointed out, however, that a disadvantage of incorporating the Brunt-V&sglg period in the time scale is that we must use a model with an implicit seasonal variation. The Brunt-V&31% period is determined from the Mass Spectrometer and Incoherent Scatter (Extended) (MSISE90) model (Hedin, 1991).
3. RESULTS
Apart from occasional interruptions, the current radar system delivers profiles of signal fading times every 5 min. Since the database from this radar is growing continually we shall initially restrict our presentation of the data to January 1997 and take this period to be representative of the winter mesosphere. In Fig. 2, we show the average profile of E’ for 29 January 1997. Figure 2 represents a typical profile, and in practice data may be available right down to 60 km or missing altogether, depending on the state of the ionosphere. The horizontal bars indicate the standard deviations, the number of contributions varying as a function of height up to a maximum of 288 values per height. The dotted line shows the result
970129 90.
T”,’ /
,
/ 80 :
I
’ ,’
”
“7
I’ I
1
\ E .x
:
,
:
,’ 70; _ __
0.450.
0.8T. 60 I
IO
100
1oao
mw/kg
Fig. 2. Average energy dissipation rate E’as a function of altitude for 29 January 1997 (solid line). The horizontal bars indicate the standard deviation of the underlying 5 min. profiles. The dotted line indicates the result of assuming the derived velocity fluctuation to be the vertical component for inertial subrange turbulence (Manson and Meek. 1981), a method considered inappropriate by this paper.
eot
439
I
Fig. 3. Average energy dissipation rate E’ as a function of altitude for January 1997 (solid line). The horizontal bars indicate the standard deviation of the underlying day-average profiles. The dotted line indicates the estimate for 20 January 1993 given by Hall (1997) from the EISCAT VHF system nearby.
of using the method of Manson and Meek (198 1) not attempting to make corrections for beam- and shear-broadening as prescribed by Hocking (1983), and simultaneously assuming the measured velocity fluctuations to be vertical components. Taking all available data for January 1997 we arrive at Fig. 3. Here the horizontal bars show the standard deviations derived from the daily averages, and therefore indicate the day-to-day variability. The dotted line, in this case, shows the profile obtained from the EISCAT VHF radar, situated only a few hundred meters from the MF system, for 20 January 1993 as published by Hall (1997). Considering both the uncertainties implicit in any derivation of mesospheric E and also real variability in this parameter itself, we assert that there is good agreement between these results. The values also compare favourably with recent in situ measurements (Liibken, 1993) in which E is indicated to be around 20 mW kg-’ at 90 km and at 69”N in winter. We have also concentrated on winter data hitherto because the radar gating does not take the group retardation due to the ionosphere into account. In other words, the heights given are virtual heights; the true heights of the observations may be less. This phenomenon is relatively unimportant during aurorally quiet conditions at night, but the difference between virtual height and real height may amount to several kilometres during the summer, especially at heights over 90 km. Bearing this limitation in mind, we nevertheless present, in Fig. 4, the results for 1997 up to the time of writing. The figure
440
C. M. Hall et al.
with both radar and in situ measurements lend encouragement ; we have presented the tentative beginnings of a study of seasonal variation of turbulent intensity, indicating a semi-annual nature at 90 km. The method will be used over a longer time, allowing seasonal and inter-annual variations to be explored. AcknoM;ledgements-The authors wish to thank Bjornar Hansen and Bjarn-Ove Hussy for technical support. We are indebted to the reviewers of this paper for constructive comments. REFERENCES 2
1
3
7
6
5
4 month
Fig. 4. Time series of E’for 90 km for the first half of 1997 (solid line) and total horizontal windspeed (dotted line). Units of E’are mW kg-’ and those of windspeed are mss’. The digits on the horizontal axis denote the ends of months (i.e. “1” corresponds to 31 January 1997). Day averages, like that shown in Fig. 2, have been used and a 4-day boxcar filter applied.
shows the kinetic altitude
energy
as a function
1997. Also indicated
dissipation of time
is the total
from
rate,
a’, for 90 km
February
horizontal
wind
to July speed,
curves have been smoothed with a 4-day boxcar. There is a suggestion of minima in both parameters around the time of the reversal from winter to summer dynamics near the equinox ; the maximum E’ occurs in summer, in reasonable agreement with Ltibken (1997). and
both
4.
CONCLUSION
We have employed what might be described as a heuristic and pragmatic argument for the derivation of an energy dissipation rate because of the uncertainty in interpretation of the measured fluctuation velocity v’. We have called this dissipation rate E’as distinct from E, the turbulent energy dissipation rate. We have nevertheless been able to derive results from the University of Tromso/University of Saskatchewan joint MF radar for the winter mesosphere which plausibly indicate that E’may be representative of E. We therefore propose this strategy as a means of studying long-term variability of turbulence in the height regime 60 to 90 km in the future. The presence of a model atmosphere in our method unfortunately risks masking a true seasonal variation, though, but the assumptions involved are based on well-known theory, thus facilitating comparisons with similar results from other instruments. Initial comparisons
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