Meteorologische Zeitschrift Vol16 No 4 367-373 (August 2007) (published online 2007)ccopy by Gebruumlder Borntraeger 2007 Article

The vertical structure of turbulent momentum flux in thelower part of the atmospheric boundary layer

ROSTISLAV KOUZNETSOVlowast VALERII F KRAMAR and MARGARITA A K ALLISTRATOVA

Obukhov Institute of Atmospheric Physics Moscow Russia

(Manuscript received October 21 2006 in revised form April 4 2007 accepted April 4 2007)

AbstractThe acoustic sounder (sodar) can be used to measure the parameters of turbulence in the lower part of theatmospheric boundary layer We suggest a new method to estimate the vertical structure of the momentumflux up to the height of several hundred meters above the surface The method uses sodar-measured profilesof mean wind and of the variance of vertical wind componentσ2

w The field experiment have shown a goodagreement of sodar-derived momentum flux values with those measuredin situ We obtained the typicalprofiles of momentum flux with the method

ZusammenfassungDas akustische Fernmessgeraumlt Sodar kann benutzt werden umTurbulenzparameter im unteren Teil der atmo-sphaumlrischen Grenzschicht zu messen Wir schlagen eine neueMethode vor das Vertikalprofil des turbulentenImpulsflusses bis zu einer Houmlhe von einigen hundert Metern uumlber dem Boden abzuschaumltzen Die Methodebasiert auf den mit dem Sodar gemessenen Vertikalprofilen der mittleren Windgeschwindigkeit und der Vari-anz der vertikalen Windkomponenteσ2

w Feldexperimente haben eine gute Uumlbereinstimmung des mit demSodar bestimmten Impulsflusses mit in-situ-Messungen gezeigt Die Impulsflussprofile zeigen das erwarteteVerhalten

1 Introduction

The information on the vertical structure of turbulentmomentum flux is of importance for understanding thedynamics of air flows in the Atmospheric BoundaryLayer (ABL) It can be used to derive the turbulent trans-fer in the ABL Modern mesoscale models of the ABLrequire a lot of empirical information The lack of mea-sured data is compensated by usage of many parameteri-zations The accuracy of such modeling can be improvedsignificantly by using the measured profiles of wind andturbulence characteristics for a particular location andtime as the initial conditions instead of modelled onessince the model turbulence profiles do not describe realprofiles well under non-ideal conditions (FISCHERet al1998)

Momentum flux profiles together with wind speedprofiles can be used to estimate the eddy viscosity Thisparameter is essential for different models of the ABLboth in research and in operational applications

The traditionalin situ measurements of turbulenceparameters are not suitable for most of applicationsWindprofiler radars Doppler lidars and radio-acousticsounding systems (RASS) in principle can be used tomeasure momentum flux profiles in the ABL (see egCAMPISTRON et al 1991 EBERHARD 1992 PETERS

lowastCorresponding author Rostislav Kouznetsov Obukhov Institute ofAtmospheric Physics 3 Pyzhevskii 109017 Moscow Russia e-mail rouxifaranru

and KIRTZEL 1994 ENGELBART et al 2002) howeverno comprehensive evaluation of the accuracy of thesemeasurements is known to us The principle of remoteestimate of the momentum flux is based on the ability ofa sensor to measure the variance of radial Doppler ve-locity along the line connecting the sensor and the mea-suring volume

There are two basic techniques of such measure-ments One of them requires the four-beam or scanningmeasurements of radial velocity variances These datatogether with assumption of horizontal homogeneity offlow give straight-forward method to derive momentumflux These remote methods require relatively expensivestate-of-the-art equipment since the commercial sound-ing systems use three fixed beams in most cases

Another approach (EMEIS 2004 KOUZNETSOV

et al 2004) is based on vertical velocity variance (σ2w)

measurements and simple empirical relationships be-tween the Reynolds stress components Usually the mo-mentum flux is taken to be equal toσ2

w multiplied bysome factor In the simplest case of neutrally stratifiedsurface layer this factor is constant For the neutrallystratified boundary layer the factor is not constant but afunction of dimentionless height (see eg STULL 1991)In this paper we discuss the extension of this approach tothe case of thermally stratified boundary layer by takingthe coefficient to be a function of local stability parame-ter

DOI 1011270941-294820070205

0941-294820070205 $ 315

ccopy Gebruumlder Borntraeger Berlin Stuttgart 2007

368 R Kouznetsov et al Turbulent momentum flux Meteorol Z 16 2007

2 The method

In the lower part of the neutrally stratified boundarylayer a simple relationship between the momentum flux〈uw〉 and the variance of vertical wind componentσ2

wholds (KOUZNETSOVet al 2004)

〈uw〉 = minus077σ2w (21)

This relationship was derived from the data taken at al-titudes 50 to 100 meters agl The numerous data takenin the surface layer give slightly smaller value of the co-efficient 062 ndash 07 (see eg STULL 1991)

Using this relationship one can estimate the verti-cal structure of momentum flux in neutrally stratifiedABL by means of a sodar (or any other remote sensingtool) that is able to measureσ2

w accurately enough Toadopt this relationship to arbitrary stratification condi-tions KOUZNETSOVand BEYRICH (2004) suggested toreplace the coefficient in (21) by an empirical functionof some stratification parameter

The Monin-Obukhov (MO) stability parameterzLis used to describe the stratification of the atmosphericsurface layer in the similarity theory In many text books(eg TENNEKES 1982) it is introduced as a more conve-nient replacement of the flux Richardson number How-ever the derivation ofzL implies the presence of a log-arithmic wind profile which is not the case for the wholeABL

In the case of absence of directional wind shear theflux Richardson number is defined as (MONIN and YA-GLOM 1968)

Rf =gΘ

〈wθ〉〈uw〉 partVpart z

(22)

whereg ndash gravityΘ ndash potential temperaturepartVpart z ndashwind shear and〈wθ〉 is the temperature flux Rf is theratio of buoyancy and mechanical production of turbu-lent kinetic energy

The flux Richardson number can be used as a para-meter of universal functions in a similar way aszL isused in Monin-Obukhov theory We introduce the em-pirical function Fm f (Rf) such as

〈uw〉 = Fm f (Rf) middotσ2w (23)

If the function Fm f (Rf) is known wind profileV (z) σ2w

and temperature flux can be used to estimate the mo-mentum flux one can substitute Eq (22) into Eq (23)and solve this equation with respect to〈uw〉

Sodar is unable to measure the temperature flux how-ever the shape of the function Fm f (Rf) (Fig 1) is suchthat the estimate of momentum flux does not requireprecise data on temperature flux For this applicationthe temperature flux can be parameterized as a lin-ear function of altitude (CENEDESEet al 1998) It is

-1

-08

-06

-04

-02

0

-2 -1 0 1

ltuw

gtσ

w2

Rf

Zvenigorod 56mLINEX2000 50mLINEX2000 90m

Figure 1 The empirical function Fm f (Rf)

equal to the surface value at the ground and zero at thetop of the mixing layer The height of a mixing layercan be derived from sodar echo signal intensity plot(echogramme) (See eg SEIBERT et al 1998) The sur-face value of the heat flux should be obtained from sup-plementary measurements

In case the wind field has a directional shear andornon-monotonous velocity profile one should take thelongitudinal wind component at each height to be di-rected along the wind shear vector This forces the mo-mentum flux to be down-gradient in these cases Thisseems to be reasonable since the model uses only lo-cal parameters of the flow In a similar manner theeddy viscosity can be calculated for such cases usingK-approach

〈uw〉 = minusKmpartVpart z

(24)

The universal function Fm f (Rf) was estimated from adata of LINEX-2000 experiment by KOUZNETSOVandBEYRICH (2004) at altitudes 50 and 90 meters above flathomogeneous terrain In a similar manner it was calcu-lated from Zvenigorod-2005 data (see below) These es-timates are summarized in Fig 1 Each data point on theplot is the result of averaging of about 50 half-hour-longtime series It is seen that different estimates of Fm f (Rf)agree well In further calculations we use a piecewiselinear approximation of function Fm f (Rf) The nodes ofthis approximation are summarized in Table 1

The shape of the empirical function Fm f (Rf) indi-cates that the error in Rf estimate leads to much smallerrelative error in〈uw〉

3 Measuring site and equipment

The measurements were performed during July 2005 atZvenigorod Scientific Station (ZSS) of Obukhov Insti-tute of atmospheric physics ZSS is located in a ruralarea with slightly inhomogeneous terrain 45 km to the

Meteorol Z 16 2007 R Kouznetsov et al Turbulent momentum flux 369

Table 1 The approximation of empirical universal function Fm f (Rf)

Rf ndash54 ndash20 ndash15 ndash10 ndash05 ndash025 ndash01 00Fm f (Rf) ndash027 ndash047 ndash05 ndash055 ndash062 ndash07 ndash078 ndash08

Rf 00 01 03 05 07 10Fm f (Rf) ndash08 ndash07 ndash042 ndash038 ndash036 ndash034

west from Moscow The measurements were performedby a PC-based LATAN-3 sodar and two sonic anemome-ters USA-1

To estimate the accuracy of sodar-derived parameterswe compared them with data ofin situ measurementsfrom an acoustic anemometer USA-1 (METEK GmbHGermany see PETERSet al 1998) installed at the top of56-m meteorological tower Another sonic anemometerof the same type was operated at the top of 6-meter mastclose to the 56-m tower for surface measurements Thesonic anemometers were operated at the same samplingfrequency 15 Hz The instantaneous data were recordedand averaged afterwards In this study we use 30-minuteaveraged data

During the experiment we used the sodar with the 12meter dish antennae The zenith angle of the inclinedantennae was 30 The sodar was operated at 1700 Hzcarrier frequency with 100 ms pulse length (20 metersrange resolution) and height range 20ndash600 meters Thesounding cycle repeated every 15 seconds

The distance between the sodar and the 56-m towerwas about 50 meters The data obtained from the secondrange gate of the sodar (approximately 50ndash70m agl) arecompared to the data of sonic anemometer installed at56 m agl The data of sonic anemometer are consideredas reference

The sodar LATAN-3 was developed at Obukhov In-stitute of Atmospheric Physics (KOUZNETSOV 2006)The primary motivation for the development was a needfor a sounding system for turbulence measurements inthe atmospheric boundary layer (ABL)

The sodar contains a minimum of electronic mod-ules see Fig 2 The generation of sounding signal anddigitizing of echo-signal is implemented on a PC soundcard The main electronic modules are power ampli-fier (Amp1) switch (SW) and microphone amplifier(Amp2) The switch is controlled by the parallel port ofthe PC

The sodar is designed to be operated with a par-abolic dish antennae It had been successfully operatedwith antennae of LATAN-1 (IAPh Russia) and Echo1D(H Hertz Institute Germany) sodars as well as withLATAN-2 mini-sodar antennae without any modifica-tion in hardware

The sodar algorithms are designed to process eachparticular echo-signal separately The processing pro-gram extracts from each echo-signal three values foreach range gate signal intensity noise intensity and

radial velocity component Afterwards the mean windspeed components and their variances can be estimatedThe radial wind components for each range gate are es-timated from the power FFT-spectrum of correspondingpart of echo-signal The signal intensity is estimated astotal power in narrow band (plusmn15 Hz)1 around the spec-tral peak corresponding to Doppler signal frequencyThe noise estimate is derived from intensity in two 30Hz bands neighboring the signal band The signal peaksearch band is adapted sequentially from the first (bot-tom) range gate to the upper one This improves the per-formance of the sodar in noisy conditions

4 The experimental tests

In order to verify the validity of the method to real so-dar data we have to check that the sodar is able to pro-vide the reasonable accuracy ofσ2

w measurements andthat the momentum flux values calculated from thatσ2

wagree well with conventional measurements of momen-tum flux

41 Theσ2w measurements

The ability of a common 3-component sodar to measuremean profiles of wind speed and direction with accu-racy sufficient for many applications has been confirmedby many field tests (KAIMAL et al 1984 KALLISTRA -TOVA et al 1987) The accuracy of measurements ofwind speed fluctuations is much more poor (GAYNOR

et al 1990 KOUZNETSOVet al 2004) The direct mea-surement of Reynolds stress components by means ofconventional 3-beam sodar is hardly possible Such a at-tempt has been made by ITO et al (1996) with a 5-beamresearch sodar Below we show that the radial velocityvariances can be derived from sodar conventional con-figuration with reasonable accuracy

In Fig 3a the results of vertical wind component vari-anceσ2

w measured by sodar are compared withσ2w mea-

sured by sonic anemometer The points are from a one-month long series of 30-minute averaged data Note agood agreement between these data The regression co-efficient is high (094) though the difference betweenmeasuring volumes and frequency response of the sen-sors is significant Thus we can conclude that sodar-measuredσ2

w are reliable at least when the flow can beassumed to be more or less stationary

1For 1700 Hz Depends on the sounding frequency

370 R Kouznetsov et al Turbulent momentum flux Meteorol Z 16 2007

A1 A3 A2Line IN

LPT

Line OUT

Amp1

Amp2

Rcv

Send

SW

Figure 2 The LATAN-3 sodar hardware

0

02

04

06

08

1

12

0 02 04 06 08 1 12

Sod

ar

Sonic

a) σ2w m2s2

y = 097x+012m2s2

r = 094

-12

-1

-08

-06

-04

-02

0

-12 -1 -08 -06 -04 -02 0

Sod

ar

Sonic

b) ltuwgt m2s2 (Fmf=-077)

y = 083x-01m2s2

r = 080

-12

-1

-08

-06

-04

-02

0

-12 -1 -08 -06 -04 -02 0

Sod

ar

Sonic

c) ltuwgt m2s2

y = 085x-004m2s2

r = 090

Figure 3 Comparison of vertical velocity varianceσ2w (a) and momentum flux〈uw〉 (b c) measured by sonic anemometer and derived

from the sodar data

Some overestimate of sodar-measuredσ2w seems to

be a systematic error In all further calculations the cor-rection 008 m2s2 (the minimum of sodar-measuredσ2

w)is subtracted

We can expect a similar accuracy of estimates of ra-dial wind component variances measured by inclinedantennae since the same electronics and algorithms areused for them Thus they can be used for turbulent mea-surements as well In this study only the data on thevertical-component variance are used

42 Momentum flux measurements

We applied the method described in section 2 to the dataof sodar measurements In Figs 3b and c the values ofmomentum flux estimated from sodar measurements arecompared to those measured by sonic anemometer InFig 3b we used Fm f (Rf) =minus077 and in Fig 3c we ac-counted stratification according to the Eq (23) The sur-face heat flux necessary to apply the method was takenfrom the sonic anemometer installed at 6 meters agl andthe mixing height was derived from sodar echogrammesOne can see that accounting of stratification improvesthe agreement significantly compared to the use of con-stant Fm f (Rf) The accuracy of momentum flux derivedfrom sodar measurements using the Eq (23) is similarto that forσ2

w This means that the limiting factor for theaccuracy of momentum flux estimate is the accuracy ofσ2

w measured by the sodar

5 The profiles of turbulence parameters

To illustrate the application of the method we havechosen the data set for 10 July 2005 as a typical fairday for the time and site of the experiment The so-dar echogrammes and temperature and heat fluxHf =Cpρ 〈wθ〉 time series (from sonic anemometers) mea-sured in Zvenigorod are shown in Fig 5 One can distin-guish three typical states of the boundary layer for thisday

I Stably stratified boundary layer (0ndash6 h and 23ndash24 h) Negative heat flux suppresses the gen-eration of turbulence The air cools down withrate of aboutminus05Ch The black layer on theechogramme represents the layer of strong tem-perature inhomogeneities Its height correspondsto the mixed layer height

In corresponding wind profiles Fig 4b one cansee pronounced maxima in wind speed espe-cially at (0ndash6 h) This phenomenon called low-level jet is common for some areas and wellknown (BLACKADAR 1957) however till nowmany guidelines on atmospheric dispersion mod-eling usually exclude it from consideration (seeeg FISCHER et al 1998) Instead these guide-lines recommend to assume the wind speed con-stant above the maximum which is not correct formany cases As it is seen from the profiles at thefigure the wind speed above the maximum falls

Meteorol Z 16 2007 R Kouznetsov et al Turbulent momentum flux 371

Figure 4 The evolution of boundary layer structure ZSS 10 July 2005 a) sodarechogramme b) wind speed profiles c)σ2w profiles d)

time series of temperatureT and heat fluxHf

back to about half of its maximum value Thewind direction (not shown) changes almost lin-early with height from W to N so the absolutevalue of a wind shear monotonously decreaseswith height

II Convective boundary layer (7ndash20 h) appears soonafter sunrise and vanishes several hours beforesunset It forms from the bottom around 7ndash8 h andin a couple of hours reaches the top of observedlayer The temperature rise in the boundary layeris provided by high heat fluxes

III Neutrally stratified boundary layer forms duringshort transitional periods (630ndash730 LT) It ap-pears on echogramme as a light area The heat fluxduring this periods is around zero and the temper-ature almost does not change with time

The vertical profiles of wind speedσ2w 〈uw〉 and

eddy viscosity coefficientKm for these three statesof the ABL are shown in Fig 5 stably stratified at0200 LT transitional neutrally stratified at the bottomand 0700 LT and unstable convective boundary layer at1500 LT The circles denote the sonic anemometer data

We approximated the wind speed data by logarithmicprofiles with friction velocityulowast and roughness lengthz0as parameters to calculate the wind shear from themFor the upper part of jet profile we used a approxi-mation from SCHLICHTING and GERSTEIN (2000) andmatched it by value with the lower part of the profileFor approximation we used least-square procedure overlower 9ndash15 points of profile The wind shear for the sta-ble case was calculated from both horizontal wind com-ponents using a central difference method the absolutevalue of shear is used in further calculations For neu-tral and unstable cases the wind shear is small so weused analytical approximations mentioned above to cal-culate the wind shear For these cases we did not ac-counted the directional shear since it did not exceed 15

in the sounding range The heat fluxes that are neces-sary for calculation of Rf and〈uw〉 are not likely to varymuch with height for unstable and neutral case We takethem equal to their surface values for the whole profilein these cases In the stable case the heat flux estimatedfrom its surface value and mixing layer height agreeswell with the value (ndash24 Wm2 ) from sonic anemome-ter at 56 m Note that from this value and coolingrate (minus05Ch) the mixing height can be estimated as

372 R Kouznetsov et al Turbulent momentum flux Meteorol Z 16 2007

a) 0200 stable stratification

b) 0700 transitional

c) 1500 convection

Figure 5 Typical profiles of wind speedσ2w momentum flux and

eddy viscosity obtained from sodar measurements Dots in circles ndash

the data ofin situ measurements

200 meters that agrees well with echogramme pattern(Fig 4a)

The profiles of wind speedσ2w momentum flux and

eddy viscosity obtained from sodar measurements areshown in Fig 5 Dots in circles are the data ofin situmeasurements The bold lines are analytical approxima-tions of wind speed profiles the thin lines are spline ap-proximations of corresponding turbulence profiles Forthe stable case the absolute value of momentum fluxmis plotted instead of momentum flux itself

In the stable case (Fig 5a) the values ofσ2w decrease

slightly with height within the mixing layer due to de-crease of shear generation of turbulence The eddy vis-cosity within the mixing layer is of several m2s2

The reason of increase ofσ2w andKm above the mix-

ing layer is not completely clear It may be caused ei-ther by gravity waves that provide the mechanism toexchange momentum without mixing or by the degra-dation of σ2

w accuracy due to small reflectivity in thislayer

In case of neutrally stratified boundary layer (Fig 5b)and convective boundary layer (Fig 5c) the profilesagree well with simple models The wind speed can bewell described by logarithmic profile The eddy viscos-ity in case of unstable stratification increases by orderof magnitude compared to the case of stable or neutralstratification

In neutrally stratified boundary layer (Fig 5b) thebottom part of eddy viscosity profile increases linearlywith height This agrees with widely used approxima-tion for Km (HINTZE 1960 MONIN and YAGLOM1968)

6 Conclusion

The method for the remote estimation of the momentumflux in the ABL is described It can be used with anysounder (sodar lidar or radar) that is able to measureprofiles of wind speed andσ2

w accurately enough Theapplication of the method to the data of acoustic soundergives a good agreement within situ measurements Theaccount of different turbulence structure via local sta-bility parameter (Richardson flux number) gives a nat-ural way to apply the method to complex wind field Themethod gives reasonable profiles of momentum flux andeddy viscosity that agree well with well-known modelsin simplest cases

The method requires more comprehensive studies tobe useful for routine applications

Acknowledgements

This work was supported by the Russian Foundationfor Basic Research through grants 04-05-64167 06-05-08086 and 06-05-65270

References

BLACKADAR A K 1957 Boundary layer wind maxima andtheir significance for the growth of nocturnal inversions ndashBull Amer Meteor Soc38 283ndash290

CAMPISTRON B AW HUGGINS AB LONG 1991 Amethod of Retrieving Turbulence parameters from Volumeprocessing of Single-Doppler radar measurements ndash J At-mos Oceanic Technol8 491ndash505

368 R Kouznetsov et al Turbulent momentum flux Meteorol Z 16 2007

2 The method

In the lower part of the neutrally stratified boundarylayer a simple relationship between the momentum flux〈uw〉 and the variance of vertical wind componentσ2

wholds (KOUZNETSOVet al 2004)

〈uw〉 = minus077σ2w (21)

This relationship was derived from the data taken at al-titudes 50 to 100 meters agl The numerous data takenin the surface layer give slightly smaller value of the co-efficient 062 ndash 07 (see eg STULL 1991)

Using this relationship one can estimate the verti-cal structure of momentum flux in neutrally stratifiedABL by means of a sodar (or any other remote sensingtool) that is able to measureσ2

w accurately enough Toadopt this relationship to arbitrary stratification condi-tions KOUZNETSOVand BEYRICH (2004) suggested toreplace the coefficient in (21) by an empirical functionof some stratification parameter

The Monin-Obukhov (MO) stability parameterzLis used to describe the stratification of the atmosphericsurface layer in the similarity theory In many text books(eg TENNEKES 1982) it is introduced as a more conve-nient replacement of the flux Richardson number How-ever the derivation ofzL implies the presence of a log-arithmic wind profile which is not the case for the wholeABL

In the case of absence of directional wind shear theflux Richardson number is defined as (MONIN and YA-GLOM 1968)

Rf =gΘ

〈wθ〉〈uw〉 partVpart z

(22)

whereg ndash gravityΘ ndash potential temperaturepartVpart z ndashwind shear and〈wθ〉 is the temperature flux Rf is theratio of buoyancy and mechanical production of turbu-lent kinetic energy

The flux Richardson number can be used as a para-meter of universal functions in a similar way aszL isused in Monin-Obukhov theory We introduce the em-pirical function Fm f (Rf) such as

〈uw〉 = Fm f (Rf) middotσ2w (23)

If the function Fm f (Rf) is known wind profileV (z) σ2w

and temperature flux can be used to estimate the mo-mentum flux one can substitute Eq (22) into Eq (23)and solve this equation with respect to〈uw〉

Sodar is unable to measure the temperature flux how-ever the shape of the function Fm f (Rf) (Fig 1) is suchthat the estimate of momentum flux does not requireprecise data on temperature flux For this applicationthe temperature flux can be parameterized as a lin-ear function of altitude (CENEDESEet al 1998) It is

-1

-08

-06

-04

-02

0

-2 -1 0 1

ltuw

gtσ

w2

Rf

Zvenigorod 56mLINEX2000 50mLINEX2000 90m

Figure 1 The empirical function Fm f (Rf)

equal to the surface value at the ground and zero at thetop of the mixing layer The height of a mixing layercan be derived from sodar echo signal intensity plot(echogramme) (See eg SEIBERT et al 1998) The sur-face value of the heat flux should be obtained from sup-plementary measurements

In case the wind field has a directional shear andornon-monotonous velocity profile one should take thelongitudinal wind component at each height to be di-rected along the wind shear vector This forces the mo-mentum flux to be down-gradient in these cases Thisseems to be reasonable since the model uses only lo-cal parameters of the flow In a similar manner theeddy viscosity can be calculated for such cases usingK-approach

〈uw〉 = minusKmpartVpart z

(24)

The universal function Fm f (Rf) was estimated from adata of LINEX-2000 experiment by KOUZNETSOVandBEYRICH (2004) at altitudes 50 and 90 meters above flathomogeneous terrain In a similar manner it was calcu-lated from Zvenigorod-2005 data (see below) These es-timates are summarized in Fig 1 Each data point on theplot is the result of averaging of about 50 half-hour-longtime series It is seen that different estimates of Fm f (Rf)agree well In further calculations we use a piecewiselinear approximation of function Fm f (Rf) The nodes ofthis approximation are summarized in Table 1

The shape of the empirical function Fm f (Rf) indi-cates that the error in Rf estimate leads to much smallerrelative error in〈uw〉

3 Measuring site and equipment

The measurements were performed during July 2005 atZvenigorod Scientific Station (ZSS) of Obukhov Insti-tute of atmospheric physics ZSS is located in a ruralarea with slightly inhomogeneous terrain 45 km to the

Meteorol Z 16 2007 R Kouznetsov et al Turbulent momentum flux 369

Table 1 The approximation of empirical universal function Fm f (Rf)

Rf ndash54 ndash20 ndash15 ndash10 ndash05 ndash025 ndash01 00Fm f (Rf) ndash027 ndash047 ndash05 ndash055 ndash062 ndash07 ndash078 ndash08

Rf 00 01 03 05 07 10Fm f (Rf) ndash08 ndash07 ndash042 ndash038 ndash036 ndash034

west from Moscow The measurements were performedby a PC-based LATAN-3 sodar and two sonic anemome-ters USA-1

To estimate the accuracy of sodar-derived parameterswe compared them with data ofin situ measurementsfrom an acoustic anemometer USA-1 (METEK GmbHGermany see PETERSet al 1998) installed at the top of56-m meteorological tower Another sonic anemometerof the same type was operated at the top of 6-meter mastclose to the 56-m tower for surface measurements Thesonic anemometers were operated at the same samplingfrequency 15 Hz The instantaneous data were recordedand averaged afterwards In this study we use 30-minuteaveraged data

During the experiment we used the sodar with the 12meter dish antennae The zenith angle of the inclinedantennae was 30 The sodar was operated at 1700 Hzcarrier frequency with 100 ms pulse length (20 metersrange resolution) and height range 20ndash600 meters Thesounding cycle repeated every 15 seconds

The distance between the sodar and the 56-m towerwas about 50 meters The data obtained from the secondrange gate of the sodar (approximately 50ndash70m agl) arecompared to the data of sonic anemometer installed at56 m agl The data of sonic anemometer are consideredas reference

The sodar LATAN-3 was developed at Obukhov In-stitute of Atmospheric Physics (KOUZNETSOV 2006)The primary motivation for the development was a needfor a sounding system for turbulence measurements inthe atmospheric boundary layer (ABL)

The sodar contains a minimum of electronic mod-ules see Fig 2 The generation of sounding signal anddigitizing of echo-signal is implemented on a PC soundcard The main electronic modules are power ampli-fier (Amp1) switch (SW) and microphone amplifier(Amp2) The switch is controlled by the parallel port ofthe PC

The sodar is designed to be operated with a par-abolic dish antennae It had been successfully operatedwith antennae of LATAN-1 (IAPh Russia) and Echo1D(H Hertz Institute Germany) sodars as well as withLATAN-2 mini-sodar antennae without any modifica-tion in hardware

The sodar algorithms are designed to process eachparticular echo-signal separately The processing pro-gram extracts from each echo-signal three values foreach range gate signal intensity noise intensity and

radial velocity component Afterwards the mean windspeed components and their variances can be estimatedThe radial wind components for each range gate are es-timated from the power FFT-spectrum of correspondingpart of echo-signal The signal intensity is estimated astotal power in narrow band (plusmn15 Hz)1 around the spec-tral peak corresponding to Doppler signal frequencyThe noise estimate is derived from intensity in two 30Hz bands neighboring the signal band The signal peaksearch band is adapted sequentially from the first (bot-tom) range gate to the upper one This improves the per-formance of the sodar in noisy conditions

4 The experimental tests

In order to verify the validity of the method to real so-dar data we have to check that the sodar is able to pro-vide the reasonable accuracy ofσ2

w measurements andthat the momentum flux values calculated from thatσ2

wagree well with conventional measurements of momen-tum flux

41 Theσ2w measurements

The ability of a common 3-component sodar to measuremean profiles of wind speed and direction with accu-racy sufficient for many applications has been confirmedby many field tests (KAIMAL et al 1984 KALLISTRA -TOVA et al 1987) The accuracy of measurements ofwind speed fluctuations is much more poor (GAYNOR

et al 1990 KOUZNETSOVet al 2004) The direct mea-surement of Reynolds stress components by means ofconventional 3-beam sodar is hardly possible Such a at-tempt has been made by ITO et al (1996) with a 5-beamresearch sodar Below we show that the radial velocityvariances can be derived from sodar conventional con-figuration with reasonable accuracy

In Fig 3a the results of vertical wind component vari-anceσ2

w measured by sodar are compared withσ2w mea-

sured by sonic anemometer The points are from a one-month long series of 30-minute averaged data Note agood agreement between these data The regression co-efficient is high (094) though the difference betweenmeasuring volumes and frequency response of the sen-sors is significant Thus we can conclude that sodar-measuredσ2

w are reliable at least when the flow can beassumed to be more or less stationary

1For 1700 Hz Depends on the sounding frequency

370 R Kouznetsov et al Turbulent momentum flux Meteorol Z 16 2007

A1 A3 A2Line IN

LPT

Line OUT

Amp1

Amp2

Rcv

Send

SW

Figure 2 The LATAN-3 sodar hardware

0

02

04

06

08

1

12

0 02 04 06 08 1 12

Sod

ar

Sonic

a) σ2w m2s2

y = 097x+012m2s2

r = 094

-12

-1

-08

-06

-04

-02

0

-12 -1 -08 -06 -04 -02 0

Sod

ar

Sonic

b) ltuwgt m2s2 (Fmf=-077)

y = 083x-01m2s2

r = 080

-12

-1

-08

-06

-04

-02

0

-12 -1 -08 -06 -04 -02 0

Sod

ar

Sonic

c) ltuwgt m2s2

y = 085x-004m2s2

r = 090

Figure 3 Comparison of vertical velocity varianceσ2w (a) and momentum flux〈uw〉 (b c) measured by sonic anemometer and derived

from the sodar data

Some overestimate of sodar-measuredσ2w seems to

be a systematic error In all further calculations the cor-rection 008 m2s2 (the minimum of sodar-measuredσ2

w)is subtracted

We can expect a similar accuracy of estimates of ra-dial wind component variances measured by inclinedantennae since the same electronics and algorithms areused for them Thus they can be used for turbulent mea-surements as well In this study only the data on thevertical-component variance are used

42 Momentum flux measurements

We applied the method described in section 2 to the dataof sodar measurements In Figs 3b and c the values ofmomentum flux estimated from sodar measurements arecompared to those measured by sonic anemometer InFig 3b we used Fm f (Rf) =minus077 and in Fig 3c we ac-counted stratification according to the Eq (23) The sur-face heat flux necessary to apply the method was takenfrom the sonic anemometer installed at 6 meters agl andthe mixing height was derived from sodar echogrammesOne can see that accounting of stratification improvesthe agreement significantly compared to the use of con-stant Fm f (Rf) The accuracy of momentum flux derivedfrom sodar measurements using the Eq (23) is similarto that forσ2

w This means that the limiting factor for theaccuracy of momentum flux estimate is the accuracy ofσ2

w measured by the sodar

5 The profiles of turbulence parameters

To illustrate the application of the method we havechosen the data set for 10 July 2005 as a typical fairday for the time and site of the experiment The so-dar echogrammes and temperature and heat fluxHf =Cpρ 〈wθ〉 time series (from sonic anemometers) mea-sured in Zvenigorod are shown in Fig 5 One can distin-guish three typical states of the boundary layer for thisday

I Stably stratified boundary layer (0ndash6 h and 23ndash24 h) Negative heat flux suppresses the gen-eration of turbulence The air cools down withrate of aboutminus05Ch The black layer on theechogramme represents the layer of strong tem-perature inhomogeneities Its height correspondsto the mixed layer height

In corresponding wind profiles Fig 4b one cansee pronounced maxima in wind speed espe-cially at (0ndash6 h) This phenomenon called low-level jet is common for some areas and wellknown (BLACKADAR 1957) however till nowmany guidelines on atmospheric dispersion mod-eling usually exclude it from consideration (seeeg FISCHER et al 1998) Instead these guide-lines recommend to assume the wind speed con-stant above the maximum which is not correct formany cases As it is seen from the profiles at thefigure the wind speed above the maximum falls

Meteorol Z 16 2007 R Kouznetsov et al Turbulent momentum flux 371

Figure 4 The evolution of boundary layer structure ZSS 10 July 2005 a) sodarechogramme b) wind speed profiles c)σ2w profiles d)

time series of temperatureT and heat fluxHf

back to about half of its maximum value Thewind direction (not shown) changes almost lin-early with height from W to N so the absolutevalue of a wind shear monotonously decreaseswith height

II Convective boundary layer (7ndash20 h) appears soonafter sunrise and vanishes several hours beforesunset It forms from the bottom around 7ndash8 h andin a couple of hours reaches the top of observedlayer The temperature rise in the boundary layeris provided by high heat fluxes

III Neutrally stratified boundary layer forms duringshort transitional periods (630ndash730 LT) It ap-pears on echogramme as a light area The heat fluxduring this periods is around zero and the temper-ature almost does not change with time

The vertical profiles of wind speedσ2w 〈uw〉 and

eddy viscosity coefficientKm for these three statesof the ABL are shown in Fig 5 stably stratified at0200 LT transitional neutrally stratified at the bottomand 0700 LT and unstable convective boundary layer at1500 LT The circles denote the sonic anemometer data

We approximated the wind speed data by logarithmicprofiles with friction velocityulowast and roughness lengthz0as parameters to calculate the wind shear from themFor the upper part of jet profile we used a approxi-mation from SCHLICHTING and GERSTEIN (2000) andmatched it by value with the lower part of the profileFor approximation we used least-square procedure overlower 9ndash15 points of profile The wind shear for the sta-ble case was calculated from both horizontal wind com-ponents using a central difference method the absolutevalue of shear is used in further calculations For neu-tral and unstable cases the wind shear is small so weused analytical approximations mentioned above to cal-culate the wind shear For these cases we did not ac-counted the directional shear since it did not exceed 15

in the sounding range The heat fluxes that are neces-sary for calculation of Rf and〈uw〉 are not likely to varymuch with height for unstable and neutral case We takethem equal to their surface values for the whole profilein these cases In the stable case the heat flux estimatedfrom its surface value and mixing layer height agreeswell with the value (ndash24 Wm2 ) from sonic anemome-ter at 56 m Note that from this value and coolingrate (minus05Ch) the mixing height can be estimated as

372 R Kouznetsov et al Turbulent momentum flux Meteorol Z 16 2007

a) 0200 stable stratification

b) 0700 transitional

c) 1500 convection

Figure 5 Typical profiles of wind speedσ2w momentum flux and

eddy viscosity obtained from sodar measurements Dots in circles ndash

the data ofin situ measurements

200 meters that agrees well with echogramme pattern(Fig 4a)

The profiles of wind speedσ2w momentum flux and

eddy viscosity obtained from sodar measurements areshown in Fig 5 Dots in circles are the data ofin situmeasurements The bold lines are analytical approxima-tions of wind speed profiles the thin lines are spline ap-proximations of corresponding turbulence profiles Forthe stable case the absolute value of momentum fluxmis plotted instead of momentum flux itself

In the stable case (Fig 5a) the values ofσ2w decrease

slightly with height within the mixing layer due to de-crease of shear generation of turbulence The eddy vis-cosity within the mixing layer is of several m2s2

The reason of increase ofσ2w andKm above the mix-

ing layer is not completely clear It may be caused ei-ther by gravity waves that provide the mechanism toexchange momentum without mixing or by the degra-dation of σ2

w accuracy due to small reflectivity in thislayer

In case of neutrally stratified boundary layer (Fig 5b)and convective boundary layer (Fig 5c) the profilesagree well with simple models The wind speed can bewell described by logarithmic profile The eddy viscos-ity in case of unstable stratification increases by orderof magnitude compared to the case of stable or neutralstratification

In neutrally stratified boundary layer (Fig 5b) thebottom part of eddy viscosity profile increases linearlywith height This agrees with widely used approxima-tion for Km (HINTZE 1960 MONIN and YAGLOM1968)

6 Conclusion

The method for the remote estimation of the momentumflux in the ABL is described It can be used with anysounder (sodar lidar or radar) that is able to measureprofiles of wind speed andσ2

w accurately enough Theapplication of the method to the data of acoustic soundergives a good agreement within situ measurements Theaccount of different turbulence structure via local sta-bility parameter (Richardson flux number) gives a nat-ural way to apply the method to complex wind field Themethod gives reasonable profiles of momentum flux andeddy viscosity that agree well with well-known modelsin simplest cases

The method requires more comprehensive studies tobe useful for routine applications

Acknowledgements

This work was supported by the Russian Foundationfor Basic Research through grants 04-05-64167 06-05-08086 and 06-05-65270

References

BLACKADAR A K 1957 Boundary layer wind maxima andtheir significance for the growth of nocturnal inversions ndashBull Amer Meteor Soc38 283ndash290

CAMPISTRON B AW HUGGINS AB LONG 1991 Amethod of Retrieving Turbulence parameters from Volumeprocessing of Single-Doppler radar measurements ndash J At-mos Oceanic Technol8 491ndash505

Meteorol Z 16 2007 R Kouznetsov et al Turbulent momentum flux 369

Table 1 The approximation of empirical universal function Fm f (Rf)

Rf ndash54 ndash20 ndash15 ndash10 ndash05 ndash025 ndash01 00Fm f (Rf) ndash027 ndash047 ndash05 ndash055 ndash062 ndash07 ndash078 ndash08

Rf 00 01 03 05 07 10Fm f (Rf) ndash08 ndash07 ndash042 ndash038 ndash036 ndash034

west from Moscow The measurements were performedby a PC-based LATAN-3 sodar and two sonic anemome-ters USA-1

To estimate the accuracy of sodar-derived parameterswe compared them with data ofin situ measurementsfrom an acoustic anemometer USA-1 (METEK GmbHGermany see PETERSet al 1998) installed at the top of56-m meteorological tower Another sonic anemometerof the same type was operated at the top of 6-meter mastclose to the 56-m tower for surface measurements Thesonic anemometers were operated at the same samplingfrequency 15 Hz The instantaneous data were recordedand averaged afterwards In this study we use 30-minuteaveraged data

During the experiment we used the sodar with the 12meter dish antennae The zenith angle of the inclinedantennae was 30 The sodar was operated at 1700 Hzcarrier frequency with 100 ms pulse length (20 metersrange resolution) and height range 20ndash600 meters Thesounding cycle repeated every 15 seconds

The distance between the sodar and the 56-m towerwas about 50 meters The data obtained from the secondrange gate of the sodar (approximately 50ndash70m agl) arecompared to the data of sonic anemometer installed at56 m agl The data of sonic anemometer are consideredas reference

The sodar LATAN-3 was developed at Obukhov In-stitute of Atmospheric Physics (KOUZNETSOV 2006)The primary motivation for the development was a needfor a sounding system for turbulence measurements inthe atmospheric boundary layer (ABL)

The sodar contains a minimum of electronic mod-ules see Fig 2 The generation of sounding signal anddigitizing of echo-signal is implemented on a PC soundcard The main electronic modules are power ampli-fier (Amp1) switch (SW) and microphone amplifier(Amp2) The switch is controlled by the parallel port ofthe PC

The sodar is designed to be operated with a par-abolic dish antennae It had been successfully operatedwith antennae of LATAN-1 (IAPh Russia) and Echo1D(H Hertz Institute Germany) sodars as well as withLATAN-2 mini-sodar antennae without any modifica-tion in hardware

The sodar algorithms are designed to process eachparticular echo-signal separately The processing pro-gram extracts from each echo-signal three values foreach range gate signal intensity noise intensity and

radial velocity component Afterwards the mean windspeed components and their variances can be estimatedThe radial wind components for each range gate are es-timated from the power FFT-spectrum of correspondingpart of echo-signal The signal intensity is estimated astotal power in narrow band (plusmn15 Hz)1 around the spec-tral peak corresponding to Doppler signal frequencyThe noise estimate is derived from intensity in two 30Hz bands neighboring the signal band The signal peaksearch band is adapted sequentially from the first (bot-tom) range gate to the upper one This improves the per-formance of the sodar in noisy conditions

4 The experimental tests

In order to verify the validity of the method to real so-dar data we have to check that the sodar is able to pro-vide the reasonable accuracy ofσ2

w measurements andthat the momentum flux values calculated from thatσ2

wagree well with conventional measurements of momen-tum flux

41 Theσ2w measurements

The ability of a common 3-component sodar to measuremean profiles of wind speed and direction with accu-racy sufficient for many applications has been confirmedby many field tests (KAIMAL et al 1984 KALLISTRA -TOVA et al 1987) The accuracy of measurements ofwind speed fluctuations is much more poor (GAYNOR

et al 1990 KOUZNETSOVet al 2004) The direct mea-surement of Reynolds stress components by means ofconventional 3-beam sodar is hardly possible Such a at-tempt has been made by ITO et al (1996) with a 5-beamresearch sodar Below we show that the radial velocityvariances can be derived from sodar conventional con-figuration with reasonable accuracy

In Fig 3a the results of vertical wind component vari-anceσ2

w measured by sodar are compared withσ2w mea-

sured by sonic anemometer The points are from a one-month long series of 30-minute averaged data Note agood agreement between these data The regression co-efficient is high (094) though the difference betweenmeasuring volumes and frequency response of the sen-sors is significant Thus we can conclude that sodar-measuredσ2

w are reliable at least when the flow can beassumed to be more or less stationary

1For 1700 Hz Depends on the sounding frequency

370 R Kouznetsov et al Turbulent momentum flux Meteorol Z 16 2007

A1 A3 A2Line IN

LPT

Line OUT

Amp1

Amp2

Rcv

Send

SW

Figure 2 The LATAN-3 sodar hardware

0

02

04

06

08

1

12

0 02 04 06 08 1 12

Sod

ar

Sonic

a) σ2w m2s2

y = 097x+012m2s2

r = 094

-12

-1

-08

-06

-04

-02

0

-12 -1 -08 -06 -04 -02 0

Sod

ar

Sonic

b) ltuwgt m2s2 (Fmf=-077)

y = 083x-01m2s2

r = 080

-12

-1

-08

-06

-04

-02

0

-12 -1 -08 -06 -04 -02 0

Sod

ar

Sonic

c) ltuwgt m2s2

y = 085x-004m2s2

r = 090

Figure 3 Comparison of vertical velocity varianceσ2w (a) and momentum flux〈uw〉 (b c) measured by sonic anemometer and derived

from the sodar data

Some overestimate of sodar-measuredσ2w seems to

be a systematic error In all further calculations the cor-rection 008 m2s2 (the minimum of sodar-measuredσ2

w)is subtracted

We can expect a similar accuracy of estimates of ra-dial wind component variances measured by inclinedantennae since the same electronics and algorithms areused for them Thus they can be used for turbulent mea-surements as well In this study only the data on thevertical-component variance are used

42 Momentum flux measurements

We applied the method described in section 2 to the dataof sodar measurements In Figs 3b and c the values ofmomentum flux estimated from sodar measurements arecompared to those measured by sonic anemometer InFig 3b we used Fm f (Rf) =minus077 and in Fig 3c we ac-counted stratification according to the Eq (23) The sur-face heat flux necessary to apply the method was takenfrom the sonic anemometer installed at 6 meters agl andthe mixing height was derived from sodar echogrammesOne can see that accounting of stratification improvesthe agreement significantly compared to the use of con-stant Fm f (Rf) The accuracy of momentum flux derivedfrom sodar measurements using the Eq (23) is similarto that forσ2

w This means that the limiting factor for theaccuracy of momentum flux estimate is the accuracy ofσ2

w measured by the sodar

5 The profiles of turbulence parameters

To illustrate the application of the method we havechosen the data set for 10 July 2005 as a typical fairday for the time and site of the experiment The so-dar echogrammes and temperature and heat fluxHf =Cpρ 〈wθ〉 time series (from sonic anemometers) mea-sured in Zvenigorod are shown in Fig 5 One can distin-guish three typical states of the boundary layer for thisday

I Stably stratified boundary layer (0ndash6 h and 23ndash24 h) Negative heat flux suppresses the gen-eration of turbulence The air cools down withrate of aboutminus05Ch The black layer on theechogramme represents the layer of strong tem-perature inhomogeneities Its height correspondsto the mixed layer height

In corresponding wind profiles Fig 4b one cansee pronounced maxima in wind speed espe-cially at (0ndash6 h) This phenomenon called low-level jet is common for some areas and wellknown (BLACKADAR 1957) however till nowmany guidelines on atmospheric dispersion mod-eling usually exclude it from consideration (seeeg FISCHER et al 1998) Instead these guide-lines recommend to assume the wind speed con-stant above the maximum which is not correct formany cases As it is seen from the profiles at thefigure the wind speed above the maximum falls

Meteorol Z 16 2007 R Kouznetsov et al Turbulent momentum flux 371

Figure 4 The evolution of boundary layer structure ZSS 10 July 2005 a) sodarechogramme b) wind speed profiles c)σ2w profiles d)

time series of temperatureT and heat fluxHf

back to about half of its maximum value Thewind direction (not shown) changes almost lin-early with height from W to N so the absolutevalue of a wind shear monotonously decreaseswith height

II Convective boundary layer (7ndash20 h) appears soonafter sunrise and vanishes several hours beforesunset It forms from the bottom around 7ndash8 h andin a couple of hours reaches the top of observedlayer The temperature rise in the boundary layeris provided by high heat fluxes

III Neutrally stratified boundary layer forms duringshort transitional periods (630ndash730 LT) It ap-pears on echogramme as a light area The heat fluxduring this periods is around zero and the temper-ature almost does not change with time

The vertical profiles of wind speedσ2w 〈uw〉 and

eddy viscosity coefficientKm for these three statesof the ABL are shown in Fig 5 stably stratified at0200 LT transitional neutrally stratified at the bottomand 0700 LT and unstable convective boundary layer at1500 LT The circles denote the sonic anemometer data

We approximated the wind speed data by logarithmicprofiles with friction velocityulowast and roughness lengthz0as parameters to calculate the wind shear from themFor the upper part of jet profile we used a approxi-mation from SCHLICHTING and GERSTEIN (2000) andmatched it by value with the lower part of the profileFor approximation we used least-square procedure overlower 9ndash15 points of profile The wind shear for the sta-ble case was calculated from both horizontal wind com-ponents using a central difference method the absolutevalue of shear is used in further calculations For neu-tral and unstable cases the wind shear is small so weused analytical approximations mentioned above to cal-culate the wind shear For these cases we did not ac-counted the directional shear since it did not exceed 15

in the sounding range The heat fluxes that are neces-sary for calculation of Rf and〈uw〉 are not likely to varymuch with height for unstable and neutral case We takethem equal to their surface values for the whole profilein these cases In the stable case the heat flux estimatedfrom its surface value and mixing layer height agreeswell with the value (ndash24 Wm2 ) from sonic anemome-ter at 56 m Note that from this value and coolingrate (minus05Ch) the mixing height can be estimated as

372 R Kouznetsov et al Turbulent momentum flux Meteorol Z 16 2007

a) 0200 stable stratification

b) 0700 transitional

c) 1500 convection

Figure 5 Typical profiles of wind speedσ2w momentum flux and

eddy viscosity obtained from sodar measurements Dots in circles ndash

the data ofin situ measurements

200 meters that agrees well with echogramme pattern(Fig 4a)

The profiles of wind speedσ2w momentum flux and

eddy viscosity obtained from sodar measurements areshown in Fig 5 Dots in circles are the data ofin situmeasurements The bold lines are analytical approxima-tions of wind speed profiles the thin lines are spline ap-proximations of corresponding turbulence profiles Forthe stable case the absolute value of momentum fluxmis plotted instead of momentum flux itself

In the stable case (Fig 5a) the values ofσ2w decrease

slightly with height within the mixing layer due to de-crease of shear generation of turbulence The eddy vis-cosity within the mixing layer is of several m2s2

The reason of increase ofσ2w andKm above the mix-

ing layer is not completely clear It may be caused ei-ther by gravity waves that provide the mechanism toexchange momentum without mixing or by the degra-dation of σ2

w accuracy due to small reflectivity in thislayer

In case of neutrally stratified boundary layer (Fig 5b)and convective boundary layer (Fig 5c) the profilesagree well with simple models The wind speed can bewell described by logarithmic profile The eddy viscos-ity in case of unstable stratification increases by orderof magnitude compared to the case of stable or neutralstratification

In neutrally stratified boundary layer (Fig 5b) thebottom part of eddy viscosity profile increases linearlywith height This agrees with widely used approxima-tion for Km (HINTZE 1960 MONIN and YAGLOM1968)

6 Conclusion

The method for the remote estimation of the momentumflux in the ABL is described It can be used with anysounder (sodar lidar or radar) that is able to measureprofiles of wind speed andσ2

w accurately enough Theapplication of the method to the data of acoustic soundergives a good agreement within situ measurements Theaccount of different turbulence structure via local sta-bility parameter (Richardson flux number) gives a nat-ural way to apply the method to complex wind field Themethod gives reasonable profiles of momentum flux andeddy viscosity that agree well with well-known modelsin simplest cases

The method requires more comprehensive studies tobe useful for routine applications

Acknowledgements

This work was supported by the Russian Foundationfor Basic Research through grants 04-05-64167 06-05-08086 and 06-05-65270

References

BLACKADAR A K 1957 Boundary layer wind maxima andtheir significance for the growth of nocturnal inversions ndashBull Amer Meteor Soc38 283ndash290

CAMPISTRON B AW HUGGINS AB LONG 1991 Amethod of Retrieving Turbulence parameters from Volumeprocessing of Single-Doppler radar measurements ndash J At-mos Oceanic Technol8 491ndash505

370 R Kouznetsov et al Turbulent momentum flux Meteorol Z 16 2007

A1 A3 A2Line IN

LPT

Line OUT

Amp1

Amp2

Rcv

Send

SW

Figure 2 The LATAN-3 sodar hardware

0

02

04

06

08

1

12

0 02 04 06 08 1 12

Sod

ar

Sonic

a) σ2w m2s2

y = 097x+012m2s2

r = 094

-12

-1

-08

-06

-04

-02

0

-12 -1 -08 -06 -04 -02 0

Sod

ar

Sonic

b) ltuwgt m2s2 (Fmf=-077)

y = 083x-01m2s2

r = 080

-12

-1

-08

-06

-04

-02

0

-12 -1 -08 -06 -04 -02 0

Sod

ar

Sonic

c) ltuwgt m2s2

y = 085x-004m2s2

r = 090

Figure 3 Comparison of vertical velocity varianceσ2w (a) and momentum flux〈uw〉 (b c) measured by sonic anemometer and derived

from the sodar data

Some overestimate of sodar-measuredσ2w seems to

be a systematic error In all further calculations the cor-rection 008 m2s2 (the minimum of sodar-measuredσ2

w)is subtracted

We can expect a similar accuracy of estimates of ra-dial wind component variances measured by inclinedantennae since the same electronics and algorithms areused for them Thus they can be used for turbulent mea-surements as well In this study only the data on thevertical-component variance are used

42 Momentum flux measurements

We applied the method described in section 2 to the dataof sodar measurements In Figs 3b and c the values ofmomentum flux estimated from sodar measurements arecompared to those measured by sonic anemometer InFig 3b we used Fm f (Rf) =minus077 and in Fig 3c we ac-counted stratification according to the Eq (23) The sur-face heat flux necessary to apply the method was takenfrom the sonic anemometer installed at 6 meters agl andthe mixing height was derived from sodar echogrammesOne can see that accounting of stratification improvesthe agreement significantly compared to the use of con-stant Fm f (Rf) The accuracy of momentum flux derivedfrom sodar measurements using the Eq (23) is similarto that forσ2

w This means that the limiting factor for theaccuracy of momentum flux estimate is the accuracy ofσ2

w measured by the sodar

5 The profiles of turbulence parameters

To illustrate the application of the method we havechosen the data set for 10 July 2005 as a typical fairday for the time and site of the experiment The so-dar echogrammes and temperature and heat fluxHf =Cpρ 〈wθ〉 time series (from sonic anemometers) mea-sured in Zvenigorod are shown in Fig 5 One can distin-guish three typical states of the boundary layer for thisday

I Stably stratified boundary layer (0ndash6 h and 23ndash24 h) Negative heat flux suppresses the gen-eration of turbulence The air cools down withrate of aboutminus05Ch The black layer on theechogramme represents the layer of strong tem-perature inhomogeneities Its height correspondsto the mixed layer height

In corresponding wind profiles Fig 4b one cansee pronounced maxima in wind speed espe-cially at (0ndash6 h) This phenomenon called low-level jet is common for some areas and wellknown (BLACKADAR 1957) however till nowmany guidelines on atmospheric dispersion mod-eling usually exclude it from consideration (seeeg FISCHER et al 1998) Instead these guide-lines recommend to assume the wind speed con-stant above the maximum which is not correct formany cases As it is seen from the profiles at thefigure the wind speed above the maximum falls

Meteorol Z 16 2007 R Kouznetsov et al Turbulent momentum flux 371

Figure 4 The evolution of boundary layer structure ZSS 10 July 2005 a) sodarechogramme b) wind speed profiles c)σ2w profiles d)

time series of temperatureT and heat fluxHf

back to about half of its maximum value Thewind direction (not shown) changes almost lin-early with height from W to N so the absolutevalue of a wind shear monotonously decreaseswith height

II Convective boundary layer (7ndash20 h) appears soonafter sunrise and vanishes several hours beforesunset It forms from the bottom around 7ndash8 h andin a couple of hours reaches the top of observedlayer The temperature rise in the boundary layeris provided by high heat fluxes

III Neutrally stratified boundary layer forms duringshort transitional periods (630ndash730 LT) It ap-pears on echogramme as a light area The heat fluxduring this periods is around zero and the temper-ature almost does not change with time

The vertical profiles of wind speedσ2w 〈uw〉 and

eddy viscosity coefficientKm for these three statesof the ABL are shown in Fig 5 stably stratified at0200 LT transitional neutrally stratified at the bottomand 0700 LT and unstable convective boundary layer at1500 LT The circles denote the sonic anemometer data

We approximated the wind speed data by logarithmicprofiles with friction velocityulowast and roughness lengthz0as parameters to calculate the wind shear from themFor the upper part of jet profile we used a approxi-mation from SCHLICHTING and GERSTEIN (2000) andmatched it by value with the lower part of the profileFor approximation we used least-square procedure overlower 9ndash15 points of profile The wind shear for the sta-ble case was calculated from both horizontal wind com-ponents using a central difference method the absolutevalue of shear is used in further calculations For neu-tral and unstable cases the wind shear is small so weused analytical approximations mentioned above to cal-culate the wind shear For these cases we did not ac-counted the directional shear since it did not exceed 15

in the sounding range The heat fluxes that are neces-sary for calculation of Rf and〈uw〉 are not likely to varymuch with height for unstable and neutral case We takethem equal to their surface values for the whole profilein these cases In the stable case the heat flux estimatedfrom its surface value and mixing layer height agreeswell with the value (ndash24 Wm2 ) from sonic anemome-ter at 56 m Note that from this value and coolingrate (minus05Ch) the mixing height can be estimated as

372 R Kouznetsov et al Turbulent momentum flux Meteorol Z 16 2007

a) 0200 stable stratification

b) 0700 transitional

c) 1500 convection

Figure 5 Typical profiles of wind speedσ2w momentum flux and

eddy viscosity obtained from sodar measurements Dots in circles ndash

the data ofin situ measurements

200 meters that agrees well with echogramme pattern(Fig 4a)

The profiles of wind speedσ2w momentum flux and

eddy viscosity obtained from sodar measurements areshown in Fig 5 Dots in circles are the data ofin situmeasurements The bold lines are analytical approxima-tions of wind speed profiles the thin lines are spline ap-proximations of corresponding turbulence profiles Forthe stable case the absolute value of momentum fluxmis plotted instead of momentum flux itself

In the stable case (Fig 5a) the values ofσ2w decrease

slightly with height within the mixing layer due to de-crease of shear generation of turbulence The eddy vis-cosity within the mixing layer is of several m2s2

The reason of increase ofσ2w andKm above the mix-

ing layer is not completely clear It may be caused ei-ther by gravity waves that provide the mechanism toexchange momentum without mixing or by the degra-dation of σ2

w accuracy due to small reflectivity in thislayer

In case of neutrally stratified boundary layer (Fig 5b)and convective boundary layer (Fig 5c) the profilesagree well with simple models The wind speed can bewell described by logarithmic profile The eddy viscos-ity in case of unstable stratification increases by orderof magnitude compared to the case of stable or neutralstratification

In neutrally stratified boundary layer (Fig 5b) thebottom part of eddy viscosity profile increases linearlywith height This agrees with widely used approxima-tion for Km (HINTZE 1960 MONIN and YAGLOM1968)

6 Conclusion

The method for the remote estimation of the momentumflux in the ABL is described It can be used with anysounder (sodar lidar or radar) that is able to measureprofiles of wind speed andσ2

w accurately enough Theapplication of the method to the data of acoustic soundergives a good agreement within situ measurements Theaccount of different turbulence structure via local sta-bility parameter (Richardson flux number) gives a nat-ural way to apply the method to complex wind field Themethod gives reasonable profiles of momentum flux andeddy viscosity that agree well with well-known modelsin simplest cases

The method requires more comprehensive studies tobe useful for routine applications

Acknowledgements

This work was supported by the Russian Foundationfor Basic Research through grants 04-05-64167 06-05-08086 and 06-05-65270

References

BLACKADAR A K 1957 Boundary layer wind maxima andtheir significance for the growth of nocturnal inversions ndashBull Amer Meteor Soc38 283ndash290

CAMPISTRON B AW HUGGINS AB LONG 1991 Amethod of Retrieving Turbulence parameters from Volumeprocessing of Single-Doppler radar measurements ndash J At-mos Oceanic Technol8 491ndash505

Meteorol Z 16 2007 R Kouznetsov et al Turbulent momentum flux 371

Figure 4 The evolution of boundary layer structure ZSS 10 July 2005 a) sodarechogramme b) wind speed profiles c)σ2w profiles d)

time series of temperatureT and heat fluxHf

back to about half of its maximum value Thewind direction (not shown) changes almost lin-early with height from W to N so the absolutevalue of a wind shear monotonously decreaseswith height

II Convective boundary layer (7ndash20 h) appears soonafter sunrise and vanishes several hours beforesunset It forms from the bottom around 7ndash8 h andin a couple of hours reaches the top of observedlayer The temperature rise in the boundary layeris provided by high heat fluxes

III Neutrally stratified boundary layer forms duringshort transitional periods (630ndash730 LT) It ap-pears on echogramme as a light area The heat fluxduring this periods is around zero and the temper-ature almost does not change with time

The vertical profiles of wind speedσ2w 〈uw〉 and

eddy viscosity coefficientKm for these three statesof the ABL are shown in Fig 5 stably stratified at0200 LT transitional neutrally stratified at the bottomand 0700 LT and unstable convective boundary layer at1500 LT The circles denote the sonic anemometer data

We approximated the wind speed data by logarithmicprofiles with friction velocityulowast and roughness lengthz0as parameters to calculate the wind shear from themFor the upper part of jet profile we used a approxi-mation from SCHLICHTING and GERSTEIN (2000) andmatched it by value with the lower part of the profileFor approximation we used least-square procedure overlower 9ndash15 points of profile The wind shear for the sta-ble case was calculated from both horizontal wind com-ponents using a central difference method the absolutevalue of shear is used in further calculations For neu-tral and unstable cases the wind shear is small so weused analytical approximations mentioned above to cal-culate the wind shear For these cases we did not ac-counted the directional shear since it did not exceed 15

in the sounding range The heat fluxes that are neces-sary for calculation of Rf and〈uw〉 are not likely to varymuch with height for unstable and neutral case We takethem equal to their surface values for the whole profilein these cases In the stable case the heat flux estimatedfrom its surface value and mixing layer height agreeswell with the value (ndash24 Wm2 ) from sonic anemome-ter at 56 m Note that from this value and coolingrate (minus05Ch) the mixing height can be estimated as

372 R Kouznetsov et al Turbulent momentum flux Meteorol Z 16 2007

a) 0200 stable stratification

b) 0700 transitional

c) 1500 convection

Figure 5 Typical profiles of wind speedσ2w momentum flux and

eddy viscosity obtained from sodar measurements Dots in circles ndash

the data ofin situ measurements

200 meters that agrees well with echogramme pattern(Fig 4a)

The profiles of wind speedσ2w momentum flux and

eddy viscosity obtained from sodar measurements areshown in Fig 5 Dots in circles are the data ofin situmeasurements The bold lines are analytical approxima-tions of wind speed profiles the thin lines are spline ap-proximations of corresponding turbulence profiles Forthe stable case the absolute value of momentum fluxmis plotted instead of momentum flux itself

In the stable case (Fig 5a) the values ofσ2w decrease

slightly with height within the mixing layer due to de-crease of shear generation of turbulence The eddy vis-cosity within the mixing layer is of several m2s2

The reason of increase ofσ2w andKm above the mix-

ing layer is not completely clear It may be caused ei-ther by gravity waves that provide the mechanism toexchange momentum without mixing or by the degra-dation of σ2

w accuracy due to small reflectivity in thislayer

In case of neutrally stratified boundary layer (Fig 5b)and convective boundary layer (Fig 5c) the profilesagree well with simple models The wind speed can bewell described by logarithmic profile The eddy viscos-ity in case of unstable stratification increases by orderof magnitude compared to the case of stable or neutralstratification

In neutrally stratified boundary layer (Fig 5b) thebottom part of eddy viscosity profile increases linearlywith height This agrees with widely used approxima-tion for Km (HINTZE 1960 MONIN and YAGLOM1968)

6 Conclusion

The method for the remote estimation of the momentumflux in the ABL is described It can be used with anysounder (sodar lidar or radar) that is able to measureprofiles of wind speed andσ2

w accurately enough Theapplication of the method to the data of acoustic soundergives a good agreement within situ measurements Theaccount of different turbulence structure via local sta-bility parameter (Richardson flux number) gives a nat-ural way to apply the method to complex wind field Themethod gives reasonable profiles of momentum flux andeddy viscosity that agree well with well-known modelsin simplest cases

The method requires more comprehensive studies tobe useful for routine applications

Acknowledgements

This work was supported by the Russian Foundationfor Basic Research through grants 04-05-64167 06-05-08086 and 06-05-65270

References

BLACKADAR A K 1957 Boundary layer wind maxima andtheir significance for the growth of nocturnal inversions ndashBull Amer Meteor Soc38 283ndash290

CAMPISTRON B AW HUGGINS AB LONG 1991 Amethod of Retrieving Turbulence parameters from Volumeprocessing of Single-Doppler radar measurements ndash J At-mos Oceanic Technol8 491ndash505

372 R Kouznetsov et al Turbulent momentum flux Meteorol Z 16 2007

a) 0200 stable stratification

b) 0700 transitional

c) 1500 convection

Figure 5 Typical profiles of wind speedσ2w momentum flux and

eddy viscosity obtained from sodar measurements Dots in circles ndash

the data ofin situ measurements

200 meters that agrees well with echogramme pattern(Fig 4a)

The profiles of wind speedσ2w momentum flux and

eddy viscosity obtained from sodar measurements areshown in Fig 5 Dots in circles are the data ofin situmeasurements The bold lines are analytical approxima-tions of wind speed profiles the thin lines are spline ap-proximations of corresponding turbulence profiles Forthe stable case the absolute value of momentum fluxmis plotted instead of momentum flux itself

In the stable case (Fig 5a) the values ofσ2w decrease

slightly with height within the mixing layer due to de-crease of shear generation of turbulence The eddy vis-cosity within the mixing layer is of several m2s2

The reason of increase ofσ2w andKm above the mix-

ing layer is not completely clear It may be caused ei-ther by gravity waves that provide the mechanism toexchange momentum without mixing or by the degra-dation of σ2

w accuracy due to small reflectivity in thislayer

In case of neutrally stratified boundary layer (Fig 5b)and convective boundary layer (Fig 5c) the profilesagree well with simple models The wind speed can bewell described by logarithmic profile The eddy viscos-ity in case of unstable stratification increases by orderof magnitude compared to the case of stable or neutralstratification

In neutrally stratified boundary layer (Fig 5b) thebottom part of eddy viscosity profile increases linearlywith height This agrees with widely used approxima-tion for Km (HINTZE 1960 MONIN and YAGLOM1968)

6 Conclusion

The method for the remote estimation of the momentumflux in the ABL is described It can be used with anysounder (sodar lidar or radar) that is able to measureprofiles of wind speed andσ2

w accurately enough Theapplication of the method to the data of acoustic soundergives a good agreement within situ measurements Theaccount of different turbulence structure via local sta-bility parameter (Richardson flux number) gives a nat-ural way to apply the method to complex wind field Themethod gives reasonable profiles of momentum flux andeddy viscosity that agree well with well-known modelsin simplest cases

The method requires more comprehensive studies tobe useful for routine applications

Acknowledgements

This work was supported by the Russian Foundationfor Basic Research through grants 04-05-64167 06-05-08086 and 06-05-65270

References

BLACKADAR A K 1957 Boundary layer wind maxima andtheir significance for the growth of nocturnal inversions ndashBull Amer Meteor Soc38 283ndash290

CAMPISTRON B AW HUGGINS AB LONG 1991 Amethod of Retrieving Turbulence parameters from Volumeprocessing of Single-Doppler radar measurements ndash J At-mos Oceanic Technol8 491ndash505

Meteorol Z 16 2007 R Kouznetsov et al Turbulent momentum flux 373

CENEDESE A G COSEMANS H ERBRINK R STUBI1998 Vertical profiles of wind temperature and turbu-lence ndash In B E A Fischer JJ Erbrink S Finardi PJeannet S Joffre MG Morselli U Pechinger P Seib-ert DJ Thomson (Eds) COST Action 710 ndash Final re-port Harmonization of the pre-processing of meteorolog-ical data for atmospheric dispersion models Directorate-General Science Research and Development 431 pp

EBERHARD W L 1992 Estimations of atmospheric bound-ary layer fluxes and other turbulence parameters fromDoppler lidar data ndash J Geophys Res97 18409ndash18423

EMEIS S 2004 Parameterization of turbulent viscosity overorography ndash Meteorol Z13 33ndash38

ENGELBART D A M H STEINHAGEN MA K ALLIS -TRATOVA 2002 LINEX-2000 Assessment of differentmethods for determination of reference flux profiles ndash InProc 12th Int Symp Acoust Rem Sens Rome Italy339ndash342

FISCHER B E A JJ ERBRINK S FINARDI P JEAN-NET S JOFFRE MG MORSELLI U PECHINGER PSEIBERT DJ THOMSON (Eds) 1998 COST Action 710ndash Final report Harmonization of the pre-processing ofmeteorological data for atmospheric dispersion models ndashDirectorate-General Science Research and Development

GAYNOR J E CB BAKER JC KAIMAL 1990 The in-ternational sodar intercomparison experiment ndash In Proc5th Int Symp Acoust Rem Sens Tata McGraw-Hill NewDelhi India 67ndash74

HINTZE J O 1960 Turbulence ndash McGraw-Hill NYITO Y T HANAFUSA Y M ITSUTA 1996 Wind measure-

ments using five-beam phased array doppler sodar ndash InProc 8th Int Symp Acoust Rem Sens Moscow Russia31ndash36

KAIMAL J C JE GAYNOR PL FINKELSTEIN MEGRAVES TJ LOCKHART 1984 An evaluation of windmeasurements by four doppler sodars ndash Technical Re-port 5 NOAABAO Boulder Colorado USA

KALLISTRATOVA M A IV PETENKO EA SHURYGIN1987 Sodar study of wind field in the lower troposphere(in russian) Izvestiya Atmos Ocean Phys23 451ndash462

KOUZNETSOV R D 2006 The new PC-based so-dar LATAN-3 ndash In Proc 13th Int Symp AcoustRem Sens Garmisch-Partenkirchen Germany Wiss BerForschungszentrum Karlsruhe FZKA 7222 97ndash98

KOUZNETSOV R D F BEYRICH 2004 Richardson fluxnumber and estimation of momentum flux in the lowerABL ndash In Proc 12th Int Symp Acoust Rem Sens Cam-bridge UK 49ndash53

KOUZNETSOV R D VF KRAMAR F BEYRICH D EN-GELBART 2004 Sodar-based estimation of TKE and mo-mentum flux profiles in the atmospheric boundary layerTest of a parameterization model ndash Meteor Atmos Phys85 93ndash99

MONIN A S AM YAGLOM 1968 Statistical Fluid Me-chanics I ndash MIT Press Cambridge Mass

PETERS G H-J KIRTZEL 1994 Measurements of mo-mentum flux in the boundary layer by RASS ndash J AtmosOceanic Technol11 63ndash75

PETERS G B FISCHER H-J KIRTZEL 1998 One-year operational measurements with a sonic anemometer-thermometer and a Doppler sodar ndash J Atmos OceanicTechnol15 18ndash28

SCHLICHTING H K GERSTEIN 2000 Boundary LayerTheory ndash Springer Verlag New York 8 ed

SEIBERT P F BEYRICHS-E GRYNING S JOFFRE ARASMUSSEN R TERCIER 1998 Mixing height deter-mination for dispersion modellinga ndash In FISCHER BEA JJ ERBRINK S FINARDI P JEANNET S JOF-FRE MG MORSELLI U PECHINGER P SEIBERT DJTHOMSON (Eds) 1998 COST Action 710 ndash Final re-port Harmonization of the pre-processing of meteorologi-cal data for atmospheric dispersion models ndash Directorate-General Science Research and Development

STULL R B 1991 An introduction to Boundary Layer Me-teorology ndash Kluwer Acad Publish

TENNEKES H 1982 Similarity laws and spectral dynam-ics ndash In NIEUWSTADT F T M H VAN DOP (Eds)Atmospheric Turbulence and Air Pollution Modelling DReidel Publishing Company Boston 37ndash68