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Sodar-derived structural functions of the windvelocity fieldTo cite this article L G Shamanaeva 2008 IOP Conf Ser Earth Environ Sci 1 012007

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Sodar-derived structural functions of the wind velocity field

L G Shamanaeva Institute of Atmospheric Optics of the SB RAS 1 Akademicheskii Ave 634021 Tomsk Russia E-mail simaiaoru Abstract The structural functions of the wind velocity field reconstructed from the vertical profiles of the wind velocity vector measured with the Zvuk-2 three-channel monostatic Doppler sodar (1700 Hz) and a commercial minisodar of the Atmospheric Systems Corporation (4900 Hz) are presented in the report The Doppler sodars allow long-term series of instantaneous values of the three wind velocity components in the atmospheric boundary layer to be measured The temporal longitudinal and transverse structural functions of the wind velocity field calculated from these time series in the altitude ranges of 75-535 m with a step of 20 m (Zvuk-2 sodar) and 15-200 m with a step of 5 m (minisodar) are presented With the use of the hypothesis of frozen turbulence the spatial longitudinal and transverse structural functions are calculated

1 INTRODUCTION At present acoustic radars (sodars) are widely used to measure vertical profiles of the wind velocity vector and characteristics of the dynamic turbulence in the atmospheric boundary layer To analyze random wind velocity fields it is expedient to use the velocity structural functions [1] Application of sodars allows long-term data series to be obtained and the velocity structure function for separation distances up to several hundred meters to be calculated The structural functions of the wind velocity field reconstructed for different altitudes from series of vertical profiles of the wind velocity vector measured with the Zvuk-2 three-channel monostatic Doppler sodar (1700 Hz) [2] and a commercial minisodar of the Atmospheric Systems Corporation (4900 Hz) [3] are presented in the report 2 INSTRUMENTATION AND DATA COLLECTION One of the most important characteristics of the random wind velocity field in the atmosphere is the structural tensor of the second rank [4]

( ) ( ) ( )[ ] ( ) ( )ik i i k kD V V V VΔ = + Δ minus times + Δ minusr r r r r r r r (1) where ( )x y z=r specifies the observation point Δr is the increment of r and ( )iV r is the projection of the wind velocity vector V(r) onto the ith coordinate axis In general the tensor

can have 9 independent components In the theory of atmospheric turbulence [4] the wind velocity field is assumed locally isotropic which reduces the number of independent components to two referred to as the longitudinal (

( )Δr rikD

( rrD )Δr r ) and transverse ( )( )ttD Δr r structural functions The Zvuk-2 sodar design and operation were described in detail in [2] The sodar operated at a

frequency of 1700 Hz its pulse repetition period was 115 s and its pulse length was 150 ms One transceiving antenna was pointed vertically and two others were tilted at angles of 20deg from the

14th International Symposium for the Advancement of Boundary Layer Remote Sensing IOP PublishingIOP Conf Series Earth and Environmental Science 1 (2008) 012007 doi1010881755-130711012007

ccopy 2008 IOP Publishing Ltd 1

vertical in the orthogonal planes The instantaneous wind velocity components Vxj(zk) Vyj(zk) and Vzj(zk) were stored every 115 s for 24 successive range gates zk of 20 m each starting from z0V = 55 m where j denotes the serial number of the wind velocity profile in a measurement series j = 1 N N = 53

The vertical profiles of the backscattered signal power proportional to CT2(zl) were stored every

115 s in successive range gates zl 2 m each starting from z0 = 589 m The proportionality coefficient was determined by sodar calibration against CT

2(zt) measured in developed convection with the ultrasonic thermometeranemometer

The temporal longitudinal and transverse velocity structural functions Drr(zk nΔt) and Dtt(zk nΔt) were then calculated in the altitude ranges of 75-535 m with a step of 20 m for each range gate zk with Δt = 115 s n = 1 2 N5 Accepting the hypothesis of frozen turbulence the corresponding spatial velocity structural functions Drr(zk nΔr) and Dtt(zk nΔr) were then calculated where Δr = ΔtltV(zk)gt and ltV(zk)gt is the wind velocity vector for the range gate zk averaged over the entire measurement period T = NΔt

Long-term series of instantaneous values of the three wind velocity components measured with an autonomous AV4000 Doppler minisodar equipped with a solar battery and a 50-element phased antenna array [3] kindly provided by Dr Ken Underwood President of the Atmospheric Systems Corporation were also processed The sodar operated at a frequency of 4900 Hz and measurements were performed in the altitude range of 15-200 m with a step of 5 m 3 RESULTS AND THEIR DISCUSSION Figure 1a shows 10-min vertical profiles of the three components of the wind velocity vector reconstructed from sodar measurements on June 25 1997 from 10 till 1010 Tomsk local time Here crosses indicate Vx(z) squares Vy(z) triangles Vz(z) and the dashed curve shows the average wind velocity profile Vav(z) The wind shear region is clearly seen between 215 and 315 m in which Vav(z) increased from 5 to 15 ms at z = 295 m and then subsequently decreased to 4 ms

The corresponding 10-min vertical profiles of the structural parameters are illustrated by figures 1b and 1c The reconstructed values of CV

2(z) are shown by black squares in figure 1b and their approximation by the least-squares method is shown by the red solid curve The values of CT

2(z) shown in figure 1c were normalized by CT

2(z0) at the first sensing altitude indicated in the figure

100

200

300

400

-12 -8 -4 0 4 8 12 16

06259710 - 1010

V ms

z m

50

100

150

200

250

300

350

400

001 01

06259710 - 1010

z m

CV2(z) m43 sndash2

50

100

150

200

250

300

350

400

01 1

062597

10 - 1010

CT2(z0)=13110-4K2cm-23

z m

CT2(z)CT

2(z0) a b c

14th International Symposium for the Advancement of Boundary Layer Remote Sensing IOP PublishingIOP Conf Series Earth and Environmental Science 1 (2008) 012007 doi1010881755-130711012007

2

50010001500200025003000100

200300

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0

50

100

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250

300D rr (m s) 2

z mΔr m

0 5001000

15002000

25003000

100200

300400

5000

2

4

6

8

10

12

14

Dtt

(ms

)2

z m

Δr m

d e

Z km f g Figure 1 Vertical profiles of the three components of the wind velocity vector (a) velocity (b) and thermal (c) structural parameters and spatial longitudinal (d and f) and transverse (e and g) velocity structural functions reconstructed from measurements with the Zvuk-2 three-channel monostatic Doppler sodar on June 25 1997 from 10 till 1010 Tomsk local time

A wide maximum can be seen in the CT2(z) profile which indicates the presence of an elevated

temperature inversion Below the inversion CT2 follows a zminus43 dependence typical of convection

Above the inversion CT2 becomes small From Fig 1b it can be seen that CV

2 increases with altitude from ~002 m43sminus2 at z = 55 m to ~01 m43sminus2 at z = 375 m that is by a factor of 5 Its altitude dependence is much weaker in comparison with CT

2 which changes almost by two orders of magnitude This is in agreement with the data presented in [5 6] In addition sodar measurements indicated that the main contribution to the refractive index structure parameter Cn

2(z) = CT2(z)(4T)2 + CV

2(z)C02 comes from the dynamic turbulence This is in agreement with the

data presented in [5]

500

50 100 150 200

100

200

300

400

Z km

Δ t s

Drr (97062510) 4813 -- 5500 4125 -- 4813 3438 -- 4125 2750 -- 3438 2063 -- 2750 1375 -- 2063 6875 -- 1375 0 -- 6875

50 100 150 200

500

Dtt (97062510)400 1225 -- 1400

1050 -- 1225 8750 -- 1050 7000 -- 8750

300 5250 -- 7000 3500 -- 5250 1750 -- 3500 0 -- 1750

200

100

t s Δ

14th International Symposium for the Advancement of Boundary Layer Remote Sensing IOP PublishingIOP Conf Series Earth and Environmental Science 1 (2008) 012007 doi1010881755-130711012007

3

The most typical behavior of the spatial longitudinal and transverse structural functions in the morning is illustrated by Figs 1d and e Here the structural functions are shown for separation distances up to 3000 m The longitudinal structure function first increases with the separation distance Δr and then saturates the greater the sensing altitude z the smaller Δr at which Drr saturates This can be explained by larger values of the average wind velocity at these altitudes [6]

The transverse structure function monotonically increases with Δr It also increases with the sensing altitude As expected it is much smaller in comparison with Drr Below the wind shear region Drr and Dtt are strongly suppressed for all Δr Above the wind shear layer the structural functions noticeably increase The similarity and synchronism in variations of Drr and Dtt can also bee seen

Figures 2a and 2b illustrate the temporal and spatial longitudinal structural functions Drr(z Δt) and Drr(z Δr) reconstructed from sodar measurements on October 5 1996 at night hours from 01 till 0110 Tomsk local time It can be seen that the velocity structural functions are spatially inhomogeneous not only in the vertical but also in the horizontal plane with intermittence regions in which they differ significantly

50100

150200

100200

300400

5000

50

100

150

200D rr ( m s) 2

z mΔt s

5001000150020002500

100200

300400

5000

50

100

150

200D rr (m s) 2

z m

Δr m

a b Figure 2 Longitudinal temporal Drr(z Δt) (a) and spatial Drr(z Δr) (b) velocity structural functions reconstructed from measurements with the Zvuk-2 sodar on October 5 1996 from 01 till 0110 Tomsk local time Figure 3a-b shows the longitudinal temporal and transverse spatial structural functions calculated from the vertical profiles of the wind velocity vector measured with the minisodar on May 25 2006 from 16 till 1610 LT Two elevated layers of enhanced turbulence at altitudes of 160-170 m and 140 m are clearly pronounced The horizontal homogeneity of the wind velocity field can be seen from figure 3a Figure 4 shows the vertical profiles of the structural characteristic CV

2(z) of the wind velocity field retrieved from the calculated values of Drr(z Δt) and Dtt(z Δr) shown in figure 3 The model profile of the structural characteristic is also shown in figure 4 It can be seen that the model profile describes well the altitude behavior of the structural characteristics retrieved from the sodar data From figure 4 it can be seen that the CV

2 values retrieved from the longitudinal velocity structural functions are smaller than those calculated from the transverse structure function 4 CONCLUSIONS In conclusion it should be noted that the suggested algorithm of sodar data processing can be used to visualize large-scale inhomogeneities of the wind velocity field in the atmospheric boundary layer thereby providing information about spatial structure and intermittence of atmospheric turbulence in

14th International Symposium for the Advancement of Boundary Layer Remote Sensing IOP PublishingIOP Conf Series Earth and Environmental Science 1 (2008) 012007 doi1010881755-130711012007

4

real time It also allows the structural functions to be calculated for long separations between the observation points An analysis of the structural functions demonstrates a highly inhomogeneous

20 40 60 80 100 120

50

100

150

200

m2s2

Drr(Δt)

Δt s

Z m

102030405060708090100110120130135

5 10 15 20

50

100

150

200

m2s2

Dtt(Δz)

ΔZ mZ

m

004

008

012

016

020

024

028

032

036

040

a b Figure 3 Longitudinal temporal Drr(z Δt) (a) and transverse spatial Dtt(z Δr) (b) velocity structural functions reconstructed from minisodar measurements on May 25 2006 from 16 till 1610 LT

0

50

100

150

001 01

Cv2model

Cv2rr

Cv2tt

Cv2 [m43s2]

H

[m]

Figure 4 Vertical profiles of the structural characteristics of the wind velocity field retrieved from the velocity structural functions Drr(z Δt) and Dtt(z Δr) shown in figures 3a and 3b spatial field structure At night in the presence of a wind shear a decrease in the longitudinal structural functions was observed under the wind shear region together with its significant increase above the shear region Under conditions of daytime convection the structural functions first increased with the separation of the observation points and then were saturated ACKNOWLEDGMENTS The author would like to acknowledge Professor N P Krasnenko and Ph D Ken Underwood for kindly providing sodar data REFERENCES [1] Rytov S M Kravtsov Yu A and Tatarskii V A 1978 Introduction to Statistical Radiophysics

Part 2 (Moscow Nauka)

14th International Symposium for the Advancement of Boundary Layer Remote Sensing IOP PublishingIOP Conf Series Earth and Environmental Science 1 (2008) 012007 doi1010881755-130711012007

5

[2] Gladkikh V A Krasnenko N P and Fedorov V A 1997 Extended Abstracts of the COST-76 Profiler Workshop (Engelberg Switzerland) p 174-177

[3] httpminisodarorg [4] Tatarskii V I 1961 Wave Propagation in a Turbulent Medium (New York Dover) [5] Petenko I V Kallistratova M A and Bedulin A N 1996 Proc 8th Int Symp Acoustic Remote

Sensing and Associated Techniques of the Atmosphere and Oceans (Moscow Russia) p 355-360

[6] Bogushevich A Ya and Shamanaeva L G 1999 Atmos Oceanic Opt 12 54-57

14th International Symposium for the Advancement of Boundary Layer Remote Sensing IOP PublishingIOP Conf Series Earth and Environmental Science 1 (2008) 012007 doi1010881755-130711012007

6

vertical in the orthogonal planes The instantaneous wind velocity components Vxj(zk) Vyj(zk) and Vzj(zk) were stored every 115 s for 24 successive range gates zk of 20 m each starting from z0V = 55 m where j denotes the serial number of the wind velocity profile in a measurement series j = 1 N N = 53

The vertical profiles of the backscattered signal power proportional to CT2(zl) were stored every

115 s in successive range gates zl 2 m each starting from z0 = 589 m The proportionality coefficient was determined by sodar calibration against CT

2(zt) measured in developed convection with the ultrasonic thermometeranemometer

The temporal longitudinal and transverse velocity structural functions Drr(zk nΔt) and Dtt(zk nΔt) were then calculated in the altitude ranges of 75-535 m with a step of 20 m for each range gate zk with Δt = 115 s n = 1 2 N5 Accepting the hypothesis of frozen turbulence the corresponding spatial velocity structural functions Drr(zk nΔr) and Dtt(zk nΔr) were then calculated where Δr = ΔtltV(zk)gt and ltV(zk)gt is the wind velocity vector for the range gate zk averaged over the entire measurement period T = NΔt

Long-term series of instantaneous values of the three wind velocity components measured with an autonomous AV4000 Doppler minisodar equipped with a solar battery and a 50-element phased antenna array [3] kindly provided by Dr Ken Underwood President of the Atmospheric Systems Corporation were also processed The sodar operated at a frequency of 4900 Hz and measurements were performed in the altitude range of 15-200 m with a step of 5 m 3 RESULTS AND THEIR DISCUSSION Figure 1a shows 10-min vertical profiles of the three components of the wind velocity vector reconstructed from sodar measurements on June 25 1997 from 10 till 1010 Tomsk local time Here crosses indicate Vx(z) squares Vy(z) triangles Vz(z) and the dashed curve shows the average wind velocity profile Vav(z) The wind shear region is clearly seen between 215 and 315 m in which Vav(z) increased from 5 to 15 ms at z = 295 m and then subsequently decreased to 4 ms

The corresponding 10-min vertical profiles of the structural parameters are illustrated by figures 1b and 1c The reconstructed values of CV

2(z) are shown by black squares in figure 1b and their approximation by the least-squares method is shown by the red solid curve The values of CT

2(z) shown in figure 1c were normalized by CT

2(z0) at the first sensing altitude indicated in the figure

100

200

300

400

-12 -8 -4 0 4 8 12 16

06259710 - 1010

V ms

z m

50

100

150

200

250

300

350

400

001 01

06259710 - 1010

z m

CV2(z) m43 sndash2

50

100

150

200

250

300

350

400

01 1

062597

10 - 1010

CT2(z0)=13110-4K2cm-23

z m

CT2(z)CT

2(z0) a b c

14th International Symposium for the Advancement of Boundary Layer Remote Sensing IOP PublishingIOP Conf Series Earth and Environmental Science 1 (2008) 012007 doi1010881755-130711012007

2

50010001500200025003000100

200300

400500

0

50

100

150

200

250

300D rr (m s) 2

z mΔr m

0 5001000

15002000

25003000

100200

300400

5000

2

4

6

8

10

12

14

Dtt

(ms

)2

z m

Δr m

d e

Z km f g Figure 1 Vertical profiles of the three components of the wind velocity vector (a) velocity (b) and thermal (c) structural parameters and spatial longitudinal (d and f) and transverse (e and g) velocity structural functions reconstructed from measurements with the Zvuk-2 three-channel monostatic Doppler sodar on June 25 1997 from 10 till 1010 Tomsk local time

A wide maximum can be seen in the CT2(z) profile which indicates the presence of an elevated

temperature inversion Below the inversion CT2 follows a zminus43 dependence typical of convection

Above the inversion CT2 becomes small From Fig 1b it can be seen that CV

2 increases with altitude from ~002 m43sminus2 at z = 55 m to ~01 m43sminus2 at z = 375 m that is by a factor of 5 Its altitude dependence is much weaker in comparison with CT

2 which changes almost by two orders of magnitude This is in agreement with the data presented in [5 6] In addition sodar measurements indicated that the main contribution to the refractive index structure parameter Cn

2(z) = CT2(z)(4T)2 + CV

2(z)C02 comes from the dynamic turbulence This is in agreement with the

data presented in [5]

500

50 100 150 200

100

200

300

400

Z km

Δ t s

Drr (97062510) 4813 -- 5500 4125 -- 4813 3438 -- 4125 2750 -- 3438 2063 -- 2750 1375 -- 2063 6875 -- 1375 0 -- 6875

50 100 150 200

500

Dtt (97062510)400 1225 -- 1400

1050 -- 1225 8750 -- 1050 7000 -- 8750

300 5250 -- 7000 3500 -- 5250 1750 -- 3500 0 -- 1750

200

100

t s Δ

14th International Symposium for the Advancement of Boundary Layer Remote Sensing IOP PublishingIOP Conf Series Earth and Environmental Science 1 (2008) 012007 doi1010881755-130711012007

3

The most typical behavior of the spatial longitudinal and transverse structural functions in the morning is illustrated by Figs 1d and e Here the structural functions are shown for separation distances up to 3000 m The longitudinal structure function first increases with the separation distance Δr and then saturates the greater the sensing altitude z the smaller Δr at which Drr saturates This can be explained by larger values of the average wind velocity at these altitudes [6]

The transverse structure function monotonically increases with Δr It also increases with the sensing altitude As expected it is much smaller in comparison with Drr Below the wind shear region Drr and Dtt are strongly suppressed for all Δr Above the wind shear layer the structural functions noticeably increase The similarity and synchronism in variations of Drr and Dtt can also bee seen

Figures 2a and 2b illustrate the temporal and spatial longitudinal structural functions Drr(z Δt) and Drr(z Δr) reconstructed from sodar measurements on October 5 1996 at night hours from 01 till 0110 Tomsk local time It can be seen that the velocity structural functions are spatially inhomogeneous not only in the vertical but also in the horizontal plane with intermittence regions in which they differ significantly

50100

150200

100200

300400

5000

50

100

150

200D rr ( m s) 2

z mΔt s

5001000150020002500

100200

300400

5000

50

100

150

200D rr (m s) 2

z m

Δr m

a b Figure 2 Longitudinal temporal Drr(z Δt) (a) and spatial Drr(z Δr) (b) velocity structural functions reconstructed from measurements with the Zvuk-2 sodar on October 5 1996 from 01 till 0110 Tomsk local time Figure 3a-b shows the longitudinal temporal and transverse spatial structural functions calculated from the vertical profiles of the wind velocity vector measured with the minisodar on May 25 2006 from 16 till 1610 LT Two elevated layers of enhanced turbulence at altitudes of 160-170 m and 140 m are clearly pronounced The horizontal homogeneity of the wind velocity field can be seen from figure 3a Figure 4 shows the vertical profiles of the structural characteristic CV

2(z) of the wind velocity field retrieved from the calculated values of Drr(z Δt) and Dtt(z Δr) shown in figure 3 The model profile of the structural characteristic is also shown in figure 4 It can be seen that the model profile describes well the altitude behavior of the structural characteristics retrieved from the sodar data From figure 4 it can be seen that the CV

2 values retrieved from the longitudinal velocity structural functions are smaller than those calculated from the transverse structure function 4 CONCLUSIONS In conclusion it should be noted that the suggested algorithm of sodar data processing can be used to visualize large-scale inhomogeneities of the wind velocity field in the atmospheric boundary layer thereby providing information about spatial structure and intermittence of atmospheric turbulence in

14th International Symposium for the Advancement of Boundary Layer Remote Sensing IOP PublishingIOP Conf Series Earth and Environmental Science 1 (2008) 012007 doi1010881755-130711012007

4

real time It also allows the structural functions to be calculated for long separations between the observation points An analysis of the structural functions demonstrates a highly inhomogeneous

20 40 60 80 100 120

50

100

150

200

m2s2

Drr(Δt)

Δt s

Z m

102030405060708090100110120130135

5 10 15 20

50

100

150

200

m2s2

Dtt(Δz)

ΔZ mZ

m

004

008

012

016

020

024

028

032

036

040

a b Figure 3 Longitudinal temporal Drr(z Δt) (a) and transverse spatial Dtt(z Δr) (b) velocity structural functions reconstructed from minisodar measurements on May 25 2006 from 16 till 1610 LT

0

50

100

150

001 01

Cv2model

Cv2rr

Cv2tt

Cv2 [m43s2]

H

[m]

Figure 4 Vertical profiles of the structural characteristics of the wind velocity field retrieved from the velocity structural functions Drr(z Δt) and Dtt(z Δr) shown in figures 3a and 3b spatial field structure At night in the presence of a wind shear a decrease in the longitudinal structural functions was observed under the wind shear region together with its significant increase above the shear region Under conditions of daytime convection the structural functions first increased with the separation of the observation points and then were saturated ACKNOWLEDGMENTS The author would like to acknowledge Professor N P Krasnenko and Ph D Ken Underwood for kindly providing sodar data REFERENCES [1] Rytov S M Kravtsov Yu A and Tatarskii V A 1978 Introduction to Statistical Radiophysics

Part 2 (Moscow Nauka)

14th International Symposium for the Advancement of Boundary Layer Remote Sensing IOP PublishingIOP Conf Series Earth and Environmental Science 1 (2008) 012007 doi1010881755-130711012007

5

[2] Gladkikh V A Krasnenko N P and Fedorov V A 1997 Extended Abstracts of the COST-76 Profiler Workshop (Engelberg Switzerland) p 174-177

[3] httpminisodarorg [4] Tatarskii V I 1961 Wave Propagation in a Turbulent Medium (New York Dover) [5] Petenko I V Kallistratova M A and Bedulin A N 1996 Proc 8th Int Symp Acoustic Remote

Sensing and Associated Techniques of the Atmosphere and Oceans (Moscow Russia) p 355-360

[6] Bogushevich A Ya and Shamanaeva L G 1999 Atmos Oceanic Opt 12 54-57

14th International Symposium for the Advancement of Boundary Layer Remote Sensing IOP PublishingIOP Conf Series Earth and Environmental Science 1 (2008) 012007 doi1010881755-130711012007

6

50010001500200025003000100

200300

400500

0

50

100

150

200

250

300D rr (m s) 2

z mΔr m

0 5001000

15002000

25003000

100200

300400

5000

2

4

6

8

10

12

14

Dtt

(ms

)2

z m

Δr m

d e

Z km f g Figure 1 Vertical profiles of the three components of the wind velocity vector (a) velocity (b) and thermal (c) structural parameters and spatial longitudinal (d and f) and transverse (e and g) velocity structural functions reconstructed from measurements with the Zvuk-2 three-channel monostatic Doppler sodar on June 25 1997 from 10 till 1010 Tomsk local time

A wide maximum can be seen in the CT2(z) profile which indicates the presence of an elevated

temperature inversion Below the inversion CT2 follows a zminus43 dependence typical of convection

Above the inversion CT2 becomes small From Fig 1b it can be seen that CV

2 increases with altitude from ~002 m43sminus2 at z = 55 m to ~01 m43sminus2 at z = 375 m that is by a factor of 5 Its altitude dependence is much weaker in comparison with CT

2 which changes almost by two orders of magnitude This is in agreement with the data presented in [5 6] In addition sodar measurements indicated that the main contribution to the refractive index structure parameter Cn

2(z) = CT2(z)(4T)2 + CV

2(z)C02 comes from the dynamic turbulence This is in agreement with the

data presented in [5]

500

50 100 150 200

100

200

300

400

Z km

Δ t s

Drr (97062510) 4813 -- 5500 4125 -- 4813 3438 -- 4125 2750 -- 3438 2063 -- 2750 1375 -- 2063 6875 -- 1375 0 -- 6875

50 100 150 200

500

Dtt (97062510)400 1225 -- 1400

1050 -- 1225 8750 -- 1050 7000 -- 8750

300 5250 -- 7000 3500 -- 5250 1750 -- 3500 0 -- 1750

200

100

t s Δ

14th International Symposium for the Advancement of Boundary Layer Remote Sensing IOP PublishingIOP Conf Series Earth and Environmental Science 1 (2008) 012007 doi1010881755-130711012007

3

The most typical behavior of the spatial longitudinal and transverse structural functions in the morning is illustrated by Figs 1d and e Here the structural functions are shown for separation distances up to 3000 m The longitudinal structure function first increases with the separation distance Δr and then saturates the greater the sensing altitude z the smaller Δr at which Drr saturates This can be explained by larger values of the average wind velocity at these altitudes [6]

The transverse structure function monotonically increases with Δr It also increases with the sensing altitude As expected it is much smaller in comparison with Drr Below the wind shear region Drr and Dtt are strongly suppressed for all Δr Above the wind shear layer the structural functions noticeably increase The similarity and synchronism in variations of Drr and Dtt can also bee seen

Figures 2a and 2b illustrate the temporal and spatial longitudinal structural functions Drr(z Δt) and Drr(z Δr) reconstructed from sodar measurements on October 5 1996 at night hours from 01 till 0110 Tomsk local time It can be seen that the velocity structural functions are spatially inhomogeneous not only in the vertical but also in the horizontal plane with intermittence regions in which they differ significantly

50100

150200

100200

300400

5000

50

100

150

200D rr ( m s) 2

z mΔt s

5001000150020002500

100200

300400

5000

50

100

150

200D rr (m s) 2

z m

Δr m

a b Figure 2 Longitudinal temporal Drr(z Δt) (a) and spatial Drr(z Δr) (b) velocity structural functions reconstructed from measurements with the Zvuk-2 sodar on October 5 1996 from 01 till 0110 Tomsk local time Figure 3a-b shows the longitudinal temporal and transverse spatial structural functions calculated from the vertical profiles of the wind velocity vector measured with the minisodar on May 25 2006 from 16 till 1610 LT Two elevated layers of enhanced turbulence at altitudes of 160-170 m and 140 m are clearly pronounced The horizontal homogeneity of the wind velocity field can be seen from figure 3a Figure 4 shows the vertical profiles of the structural characteristic CV

2(z) of the wind velocity field retrieved from the calculated values of Drr(z Δt) and Dtt(z Δr) shown in figure 3 The model profile of the structural characteristic is also shown in figure 4 It can be seen that the model profile describes well the altitude behavior of the structural characteristics retrieved from the sodar data From figure 4 it can be seen that the CV

2 values retrieved from the longitudinal velocity structural functions are smaller than those calculated from the transverse structure function 4 CONCLUSIONS In conclusion it should be noted that the suggested algorithm of sodar data processing can be used to visualize large-scale inhomogeneities of the wind velocity field in the atmospheric boundary layer thereby providing information about spatial structure and intermittence of atmospheric turbulence in

14th International Symposium for the Advancement of Boundary Layer Remote Sensing IOP PublishingIOP Conf Series Earth and Environmental Science 1 (2008) 012007 doi1010881755-130711012007

4

real time It also allows the structural functions to be calculated for long separations between the observation points An analysis of the structural functions demonstrates a highly inhomogeneous

20 40 60 80 100 120

50

100

150

200

m2s2

Drr(Δt)

Δt s

Z m

102030405060708090100110120130135

5 10 15 20

50

100

150

200

m2s2

Dtt(Δz)

ΔZ mZ

m

004

008

012

016

020

024

028

032

036

040

a b Figure 3 Longitudinal temporal Drr(z Δt) (a) and transverse spatial Dtt(z Δr) (b) velocity structural functions reconstructed from minisodar measurements on May 25 2006 from 16 till 1610 LT

0

50

100

150

001 01

Cv2model

Cv2rr

Cv2tt

Cv2 [m43s2]

H

[m]

Figure 4 Vertical profiles of the structural characteristics of the wind velocity field retrieved from the velocity structural functions Drr(z Δt) and Dtt(z Δr) shown in figures 3a and 3b spatial field structure At night in the presence of a wind shear a decrease in the longitudinal structural functions was observed under the wind shear region together with its significant increase above the shear region Under conditions of daytime convection the structural functions first increased with the separation of the observation points and then were saturated ACKNOWLEDGMENTS The author would like to acknowledge Professor N P Krasnenko and Ph D Ken Underwood for kindly providing sodar data REFERENCES [1] Rytov S M Kravtsov Yu A and Tatarskii V A 1978 Introduction to Statistical Radiophysics

Part 2 (Moscow Nauka)

14th International Symposium for the Advancement of Boundary Layer Remote Sensing IOP PublishingIOP Conf Series Earth and Environmental Science 1 (2008) 012007 doi1010881755-130711012007

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[2] Gladkikh V A Krasnenko N P and Fedorov V A 1997 Extended Abstracts of the COST-76 Profiler Workshop (Engelberg Switzerland) p 174-177

[3] httpminisodarorg [4] Tatarskii V I 1961 Wave Propagation in a Turbulent Medium (New York Dover) [5] Petenko I V Kallistratova M A and Bedulin A N 1996 Proc 8th Int Symp Acoustic Remote

Sensing and Associated Techniques of the Atmosphere and Oceans (Moscow Russia) p 355-360

[6] Bogushevich A Ya and Shamanaeva L G 1999 Atmos Oceanic Opt 12 54-57

14th International Symposium for the Advancement of Boundary Layer Remote Sensing IOP PublishingIOP Conf Series Earth and Environmental Science 1 (2008) 012007 doi1010881755-130711012007

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The most typical behavior of the spatial longitudinal and transverse structural functions in the morning is illustrated by Figs 1d and e Here the structural functions are shown for separation distances up to 3000 m The longitudinal structure function first increases with the separation distance Δr and then saturates the greater the sensing altitude z the smaller Δr at which Drr saturates This can be explained by larger values of the average wind velocity at these altitudes [6]

The transverse structure function monotonically increases with Δr It also increases with the sensing altitude As expected it is much smaller in comparison with Drr Below the wind shear region Drr and Dtt are strongly suppressed for all Δr Above the wind shear layer the structural functions noticeably increase The similarity and synchronism in variations of Drr and Dtt can also bee seen

Figures 2a and 2b illustrate the temporal and spatial longitudinal structural functions Drr(z Δt) and Drr(z Δr) reconstructed from sodar measurements on October 5 1996 at night hours from 01 till 0110 Tomsk local time It can be seen that the velocity structural functions are spatially inhomogeneous not only in the vertical but also in the horizontal plane with intermittence regions in which they differ significantly

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a b Figure 2 Longitudinal temporal Drr(z Δt) (a) and spatial Drr(z Δr) (b) velocity structural functions reconstructed from measurements with the Zvuk-2 sodar on October 5 1996 from 01 till 0110 Tomsk local time Figure 3a-b shows the longitudinal temporal and transverse spatial structural functions calculated from the vertical profiles of the wind velocity vector measured with the minisodar on May 25 2006 from 16 till 1610 LT Two elevated layers of enhanced turbulence at altitudes of 160-170 m and 140 m are clearly pronounced The horizontal homogeneity of the wind velocity field can be seen from figure 3a Figure 4 shows the vertical profiles of the structural characteristic CV

2(z) of the wind velocity field retrieved from the calculated values of Drr(z Δt) and Dtt(z Δr) shown in figure 3 The model profile of the structural characteristic is also shown in figure 4 It can be seen that the model profile describes well the altitude behavior of the structural characteristics retrieved from the sodar data From figure 4 it can be seen that the CV

2 values retrieved from the longitudinal velocity structural functions are smaller than those calculated from the transverse structure function 4 CONCLUSIONS In conclusion it should be noted that the suggested algorithm of sodar data processing can be used to visualize large-scale inhomogeneities of the wind velocity field in the atmospheric boundary layer thereby providing information about spatial structure and intermittence of atmospheric turbulence in

14th International Symposium for the Advancement of Boundary Layer Remote Sensing IOP PublishingIOP Conf Series Earth and Environmental Science 1 (2008) 012007 doi1010881755-130711012007

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real time It also allows the structural functions to be calculated for long separations between the observation points An analysis of the structural functions demonstrates a highly inhomogeneous

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a b Figure 3 Longitudinal temporal Drr(z Δt) (a) and transverse spatial Dtt(z Δr) (b) velocity structural functions reconstructed from minisodar measurements on May 25 2006 from 16 till 1610 LT

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Figure 4 Vertical profiles of the structural characteristics of the wind velocity field retrieved from the velocity structural functions Drr(z Δt) and Dtt(z Δr) shown in figures 3a and 3b spatial field structure At night in the presence of a wind shear a decrease in the longitudinal structural functions was observed under the wind shear region together with its significant increase above the shear region Under conditions of daytime convection the structural functions first increased with the separation of the observation points and then were saturated ACKNOWLEDGMENTS The author would like to acknowledge Professor N P Krasnenko and Ph D Ken Underwood for kindly providing sodar data REFERENCES [1] Rytov S M Kravtsov Yu A and Tatarskii V A 1978 Introduction to Statistical Radiophysics

Part 2 (Moscow Nauka)

14th International Symposium for the Advancement of Boundary Layer Remote Sensing IOP PublishingIOP Conf Series Earth and Environmental Science 1 (2008) 012007 doi1010881755-130711012007

5

[2] Gladkikh V A Krasnenko N P and Fedorov V A 1997 Extended Abstracts of the COST-76 Profiler Workshop (Engelberg Switzerland) p 174-177

[3] httpminisodarorg [4] Tatarskii V I 1961 Wave Propagation in a Turbulent Medium (New York Dover) [5] Petenko I V Kallistratova M A and Bedulin A N 1996 Proc 8th Int Symp Acoustic Remote

Sensing and Associated Techniques of the Atmosphere and Oceans (Moscow Russia) p 355-360

[6] Bogushevich A Ya and Shamanaeva L G 1999 Atmos Oceanic Opt 12 54-57

14th International Symposium for the Advancement of Boundary Layer Remote Sensing IOP PublishingIOP Conf Series Earth and Environmental Science 1 (2008) 012007 doi1010881755-130711012007

6

real time It also allows the structural functions to be calculated for long separations between the observation points An analysis of the structural functions demonstrates a highly inhomogeneous

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Δt s

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a b Figure 3 Longitudinal temporal Drr(z Δt) (a) and transverse spatial Dtt(z Δr) (b) velocity structural functions reconstructed from minisodar measurements on May 25 2006 from 16 till 1610 LT

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Figure 4 Vertical profiles of the structural characteristics of the wind velocity field retrieved from the velocity structural functions Drr(z Δt) and Dtt(z Δr) shown in figures 3a and 3b spatial field structure At night in the presence of a wind shear a decrease in the longitudinal structural functions was observed under the wind shear region together with its significant increase above the shear region Under conditions of daytime convection the structural functions first increased with the separation of the observation points and then were saturated ACKNOWLEDGMENTS The author would like to acknowledge Professor N P Krasnenko and Ph D Ken Underwood for kindly providing sodar data REFERENCES [1] Rytov S M Kravtsov Yu A and Tatarskii V A 1978 Introduction to Statistical Radiophysics

Part 2 (Moscow Nauka)

14th International Symposium for the Advancement of Boundary Layer Remote Sensing IOP PublishingIOP Conf Series Earth and Environmental Science 1 (2008) 012007 doi1010881755-130711012007

5

[2] Gladkikh V A Krasnenko N P and Fedorov V A 1997 Extended Abstracts of the COST-76 Profiler Workshop (Engelberg Switzerland) p 174-177

[3] httpminisodarorg [4] Tatarskii V I 1961 Wave Propagation in a Turbulent Medium (New York Dover) [5] Petenko I V Kallistratova M A and Bedulin A N 1996 Proc 8th Int Symp Acoustic Remote

Sensing and Associated Techniques of the Atmosphere and Oceans (Moscow Russia) p 355-360

[6] Bogushevich A Ya and Shamanaeva L G 1999 Atmos Oceanic Opt 12 54-57

14th International Symposium for the Advancement of Boundary Layer Remote Sensing IOP PublishingIOP Conf Series Earth and Environmental Science 1 (2008) 012007 doi1010881755-130711012007

6

[2] Gladkikh V A Krasnenko N P and Fedorov V A 1997 Extended Abstracts of the COST-76 Profiler Workshop (Engelberg Switzerland) p 174-177

[3] httpminisodarorg [4] Tatarskii V I 1961 Wave Propagation in a Turbulent Medium (New York Dover) [5] Petenko I V Kallistratova M A and Bedulin A N 1996 Proc 8th Int Symp Acoustic Remote

Sensing and Associated Techniques of the Atmosphere and Oceans (Moscow Russia) p 355-360

[6] Bogushevich A Ya and Shamanaeva L G 1999 Atmos Oceanic Opt 12 54-57

14th International Symposium for the Advancement of Boundary Layer Remote Sensing IOP PublishingIOP Conf Series Earth and Environmental Science 1 (2008) 012007 doi1010881755-130711012007

6