EstimationofTurb_省略_rnTibetanPlateau_王少影

ADVANCES IN ATMOSPHERIC SCIENCES,VOL.30,NO.2,2013,411–424

Estimation of Turbulent Fluxes Using the Flux-Variance Method over an Alpine Meadow Surface in the Eastern Tibetan Plateau

WANG Shaoying1(王少影),ZHANG Yu?1(张宇),L¨U Shihua1(吕世华),

LIU Heping2(刘和平),and SHANG Lunyu1(尚伦宇)

1Key Laboratory of Land Surface and Climate Change in Cold and Arid Regions,Cold and Arid Regions, Environmental and Engineering Research Institute,Chinese Academy of Sciences,Lanzhou730000 2Laboratory for Atmospheric Research,Department of Civil and Environmental Engineering,

Washington State University,Pullman,WA

(Received12March2012;revised11June2012)

ABSTRACT

The?ux-variance similarity relation and the vertical transfer of scalars exhibit dissimilarity over di?erent types of surfaces,resulting in di?erent parameterization approaches of relative transport e?ciency among scalars to estimate turbulent?uxes using the?ux-variance method.We investigated these issues using eddy-covariance measurements over an open,homogeneous and?at grassland in the eastern Tibetan Plateau in summer under intermediate hydrological conditions during rainy season.In unstable conditions,the tem-perature,water vapor,and CO2followed the?ux-variance similarity relation,but did not show in precisely the same way due to di?erent roles(active or passive)of these scalars.Similarity constants of temperature, water vapor and CO2were found to be1.12,1.19and1.17,respectively.Heat transportation was more e?-cient than water vapor and CO2.Based on the estimated sensible heat?ux,?ve parameterization methods of relative transport e?ciency of heat to water vapor and CO2were examined to estimate latent heat and CO2?uxes.The strategy of local determination of?ux-variance similarity relation is recommended for the estimation of latent heat and CO2?uxes.This approach is better for representing the averaged relative transport e?ciency,and technically easier to apply,compared to other more complex ones.

Key words:?ux-variance method,relative transfer e?ciency,eddy-covariance method,homogeneous land surface,turbulent?ux

Citation:Wang,S.Y.,Y.Zhang,S.H.L¨u,H.P.Liu,and L.Y.Shang,2013:Estimation of turbulent ?uxes using the?ux-variance method over an alpine meadow surface in the eastern Tibetan Plateau.Adv.

Atmos.Sci.,30(2),411–424,doi:10.1007/s00376-012-2056-1.

1.Introduction

The?ux-variance(FV)method,which is based on Monin–Obukhov similarity theory(MOST)and was ?rst introduced by Tillman(1972),has received long-term attention and wide application in surface mi-crometeorology(e.g.Wesely,1988;Lloyd et al.,1991; De Bruin et al.,1993;Katul et al.,1995;Castellvi and Mart′?nez-Cob,2005;Gao et al.,2006;Hsieh et al.,2008;Guo et al.,2009).In previous studies,the FV similarity relation has been widely used to inves-tigate the similarities in sources/sinks of scalars at the land surface(e.g.Hill,1989;Padro,1993;Katul et al.,1995),or to quantify similarities in turbulent transport e?ciencies of various scalars(e.g.McBean and Miyake,1972;De Bruin et al.,1993;Katul and Hsieh,1997;Asanuma and Brutsaert,1999;Lamaud and Irvine,2006;Detto et al.,2008).More recently, FV similarity relation has been proposed as a tool for the quality assessment of eddy-covariance(EC)?ux measurements(e.g.Foken and Wichura,1996;Foken et al.,2004),as well as a viable tool for gap-?lling long-term?ux data when high frequency wind veloc-ity measurements of the EC system are not available

?Corresponding author:ZHANG Yu,yuzhang@08c5de35650e52ea551898b5

?China National Committee for International Association of Meteorology and Atmospheric Sciences(IAMAS),Institute of Atmospheric Physics(IAP)and Science Press and Springer-Verlag Berlin Heidelberg2013

412FLUX-VARIANCE METHOD FOR FLUX ESTIMATIONS IN THE EASTERN TIBETAN PLATEAU VOL.30 (e.g.Choi et al.,2004;Guo et al.,2009).

Over the past two decades,comparisons between

FV-and EC-based estimations of latent heat?uxes

(LE)over a wide range of climates,land surface types

and atmospheric stability conditions have produced

mixed results(e.g.Weaver,1990;De Bruin et al.,

1993;Andreas et al.,1998;Asanuma and Brutsaert,

1999;Castellvi and Mart′?nez-Cob,2005;Hsieh et al.,

2008;Guo et al.,2009).For the estimation of LE

using the FV method,Hill(1989)proposed that the

correlation coe?cients of vertical velocity(w)with

temperature(T)and water vapor(q)must be equal,

i.e.R wT=R wq.In practice,there are numer-

ous case studies in the literatures where the method

worked quite well,albeit the inequality between the

two scalars’correlation with the turbulent vertical ve-

locity(e.g.Katul et al.,1995;Castellvi and Mart′?nez-

Cob,2005;Lamaud and Irvine,2006;Guo et al.,2009).

This dissimilarity among the scalars is generally at-

tributed to the following reasons(e.g.Cava et al.,

2008;Katul et al.,2008):(1)the active or passive

roles of scalars in the turbulent kinetic energy budget

equation;(2)advection of heat or water vapor(both

vertically and longitudinally);(3)non-stationarity in

the outer-layer?ow that can in?uence the atmospheric

surface layer;(4)source heterogeneity at the ground

surface;and(5)local entrainment processes from the

top of the atmospheric boundary layer.

Such a variety of factors has led many authors to

propose di?erent parameterization approaches of the

relative e?ciency of sensible heat?ux to latent heat

?ux(λT q=R wT/R wq)to improve estimations of LE

using the FV method.Hill(1989)pointed out that

surface layer similarity theory assumes a perfect scalar

correlation and adopted unity as the relative trans-

port e?ciency(λT q),but this approach is generally

unfeasible,owing to heterogeneity in sources/sinks of

scalars at the biosphere–atmosphere interface.Katul

et al.(1995)demonstrated thatλT q is equivalent to the

temperature–humidity correlation coe?cient(R T q),

but results showed that reproduced LE was systemati-

cally overestimated compared to direct measurements

in dry surface conditions.Bink and Meesters(1997)

argued thatλT q could be expressed with either R T q

when water vapor is transported more e?ciently than

sensible heat,i.e.λT q<1,which corresponds to wet

conditions,or R?1

T q when heat transport is more ef-

?cient than water vapor,i.e.λT q>1,which corre-sponds to dry conditions.They proved their conclu-sions using data from a dry area in the south of France. Lamaud and Irvine(2006)investigated the relation-ship betweenλT q and R T q using data measured at a pine forest site,and parameterized theλT q as a func-tion of R T q and the Bowen ratio B O in intermediate hydrological conditions.

Recently,some scientists have been interested in exploring FV similarity relationships for CO2,in ad-dition to T and q(e.g.Ohtaki,1985;Cava et al., 2008;Detto et al.,2008;Hsieh et al.,2008;Guo et al., 2009).Ohtaki(1985)pointed out that the stability dependence of normalized standard deviation of CO2 is very similar to those of T and q over two wheat ?elds in Japan.However,in other studies,the ecosys-tem respiration was an additional source,which in-troduced signi?cant dissimilarity in CO2sources and sinks when compared to water vapor(e.g.Cava et al.,2008).Furthermore,surface physiology changes with season,which can cause an impermanent pro-duction of inhomogeneity in the scalar sources/sinks ?eld,and result in dissimilarity,especially for CO2 (e.g.Williams et al.,2007).Hsieh et al.(2008)demon-strated that CO2did not satisfy the MOST,and the estimations of CO2?ux(F c)using the FV method were found to switch from poor to fair among the three sites(grassland,rice paddy?eld and forest).They at-tributed this to the complexity of CO2sources/sinks on the surface and their seasonal variation.However, Guo et al.(2009)found that CO2follows the FV rela-tion over a farmland,and relative transport e?ciency (λT c=R wT/R w c)can be described as a function of the correlation coe?cient(R T q)by introducing a new non-dimensional variable(α).

Although the MOST is based on the assumption of steadiness and horizontal homogeneity,it is practically only a conceptual framework in the realm of surface-layer meteorology(Andreas et al.,1998).Even when the terrain is uniform,some factors such as the ac-tive roles of temperature,modulations from the outer layer,and cloud e?ects on radiation can in?uence the FV relationships and the expressions of relative trans-port e?ciency between di?erent scalars,and result in some uncertainties in calculations of turbulent?ux (e.g.Katul et al.,1995;Roth and Oke,1995;Bink and Meesters,1997;Katul and Hsieh,1997;Katul and Hsieh,1999;Lamaud and Irvine,2006;Katul et al.,2008;Guo et al.,2009).The EC system can be used continuously for long-term measurements of en-ergy and mass exchanges in land surface processes. However,data coverage is severely in?uenced by envi-ronmental and anthropogenic factors,especially in the Tibetan Plateau,such as instrument problems,power supply,extreme weather and instrument maintenance. As a feasible tool,the FV method can be used for gap-?lling long-term?ux data when high frequency wind velocity measurements are not available under the extreme environmental conditions on the Tibetan Plateau.However,there is no agreement yet in the literature about parameterization approaches of rela-

NO.2WANG ET AL413

tive transport e?ciency.It is the importance of inves-tigating the FV relationship to the determination of turbulent?uxes that motivated this study over a ho-mogeneous short grass surface in the eastern Tibetan Plateau.The objectives of the work reported in this paper were to examine turbulent transportation char-acteristics over an alpine meadow surface in the east-ern Tibetan Plateau in terms of the FV relationship, and to examine di?erent parameterization approaches of relative transport e?ciency for estimating LE and

F c.

2.Materials

2.1Site

Measurements were carried out at a grassland site (33?53 N,102?08 E,3423m a.s.l.)in a typical alpine meadow,in the eastern part of the Tibetan Plateau, Gansu,China.This site is a long-term?ux monitor-ing station in the Yellow River source region.The meadow is dominated by Cyperaceae and Gramineae, with an average height of about0.2m.The soil is silt clay loam,which is composed of29.8%sand,66.7%silt and3.5%clay in the top40cm based on the classi?ca-tion of the United States Department of Agriculture. The annual mean air temperature is1.2?C,and mean air temperatures in January and July are?10?C and 11.7?C,respectively.The annual mean precipitation is620mm,which has mainly fallen in the short,cool summers over the last35years(Niu et al.,2009).The terrain is?at,homogeneous,and about3km from the nearest herder’s community.A picture of the?eld site is shown in Fig.1.2.2Micrometeorological measurements

A3-D sonic anemometer(CSAT3,Campbell Sci-enti?c Inc.,Logan,UT,USA)was used to measure high frequency wind velocity components(i.e.u,v and w)and sonic temperature(T).An open-path in-frared gas analyzer(LI-7500,LI-COR,Lincoln,NE, USA)was used to measure high frequency signals of water vapor density(q)and CO2concentration.The lateral separation between the two sensors was?xed at about15cm.As recommended in the LI-COR LI-7500manual,this instrument was tipped about15?from the vertical to facilitate drainage of condensa-tion and rain from the optical windows.A periodic(1 yr)calibration of the gas analyzer was performed by technicians.Those sensors were installed at a height of3.15m above the ground.Sampling rate was ad-justed to10Hz.Other slow response measurements set at the site included wind speed and direction,air temperature and humidity,radiation components,soil water content,soil temperature and soil heat?ux.All these slow response signals were sampled every30s. Data were recorded by a data logger CR3000(Camp-bell Scienti?c Inc.,Logan,UT,USA).

2.3Data selection and preliminary data-

processing

With the aforementioned measurements,data from 18fair weather days were selected during the summer from1July to30September2010.Half-hourly mean values of the turbulence statistics were calculated on the basis of the two-rotation method(McMillen,1988) to nullify the average cross-stream and vertical wind components.The planar?t method(Wilczak et al., 2001)was also used for tilt correction,but no

obvi-

414FLUX-VARIANCE METHOD FOR FLUX ESTIMATIONS IN THE EASTERN TIBETAN PLATEAU VOL.30 ous di?erence was found.Sonic temperature was con-

verted into actual temperature according to Schotanus

et al.(1983).The e?ects introduced by path length

averaging of the sonic anemometer and the gas ana-

lyzer,and for the spatial separation of sensors,were

corrected following Moore(1986).The in?uences of

air density variation induced by air temperature and

water vapor concentration?uctuations were corrected

following Webb et al.(1980).The non-stationarity test

was performed according to Foken et al.(2004)to min-

imize the e?ect of diurnal trends or weather patterns

on?ux computations.Data were collected under un-

stable and stationarity conditions during the daytime

(i.e.between1000and1600LST)were used for an-

alyzing the FV relationship and estimating turbulent

?ux.

3.Theory

3.1FV similarity relation

On the basis of the MOST,any normalized turbu-

lence statistic depends on the non-dimensional atmo-

spheric stability,

ζ=z?d

L

,(1)

where z=3.15m is the measurement height above the ground,d=0.13m is the zero-plane displacement (≈0.65h;h=0.2m is the canopy height)(Camp-bell and Norman,1998),and L is the Obukhov length given by

L=?

u3?T

kgw T

,(2)

where w T is the covariance between vertical veloc-ity and air temperature,T is mean air temperature, k=0.4is von Karman’s constant,g(9.81m s?2)is gravitational acceleration,and u?(m s?1)is friction velocity given by

u?=(u w 2+v w 2)1/4,(3) where u ,v ,and w are turbulent?uctuations in lon-gitudinal,latitudinal and vertical velocity(m s?1), respectively.The normalized standard deviation of scalar,s[s represents a scalar;namely,T for tempera-ture(?C),q for water vapor density(g m?3)and c for CO2concentration(mg m?3)],normalized standard deviationσs/s?,can be described as(e.g.Tillman, 1972;Businger,1973):

σs

|s?|

=Ψs(ζ),(4)

where s?=w s /u?is a scale parameter.The expres-sion ofΨs(ζ)must satisfy two limits:(1)in neutral conditions,?ζ→0andΨs(ζ)converge to a constant;

(2)in free convective conditions,?ζ→∞,andΨs(ζ) should become independent of u?(e.g.De Bruin,1982; De Bruin et al.,1993;De Bruin,1994;Albertson et al., 1995;Katul et al.,1995;Wesson et al.,2001;Cava et al.,2008).Based on those two limits,the form ofΨs(ζ) can be reduced to:

Ψs(ζ)=C s1(C s2?ζ)?1/3,(5) where C s1and C s2are empirical constants.In neutral conditions(?ζ=0),Ψs(ζ)approaches constant value C s1C?1/3

s2

.For free convection conditions,Eq.(5)is given by

Ψs(ζ)=C s3(?ζ)?1/3,(6) where C s3is a similarity constant of scalar s.

3.2Flux estimations using the FV method

Based on the de?nitions of Obukhov length(L)and temperature scale(T?),sensible heat?ux(H)leads to (e.g.Padro,1993;Katul et al.,1995;Choi et al.,2004; Hsieh et al.,2008)

H=ρc p w T =ρc p

σT

C T3

3/2

kg(z?d)

T

1/2

,(7)

whereρis the air density(kg m?3),c p is the speci?c heat capacity of dry air at constant pressure(=1005 J kg?1K?1).Furthermore,based on the estimated H using the FV method,LE and F c can be estimated from Eq.(7)by

w s =

R wsσs

R wTσT

×w T ,(8)

where R ws=w s /σwσs are the correlation coe?cients between w and s .McBean and Miyake(1972)de?ned the ratio R wT/R ws as the relative transport e?ciency of heat to scalar transport(denoted byλT s).Thus, Eq.(8)can be expressed as the following:

w s =λ?1

T s

×

σs

σT

×w T .(9)

Hence,to estimate LE and F c using Eq.(9),the relative e?cienciesλT q andλT c need to be deter-mined a priori.There have been?ve strategies pro-posed to representλT q andλT c in previous studies, as summarized by Guo et al.(2009;see their Ta-ble1).The strategies are,respectively:(1)for per-fect scalar similarity conditions,i.e.R wT=R wq and R wT=?R w c(Hill,1989);(2)for conditions where sensible heat is transported more e?ciently than wa-ter vapor and CO2,i.e.λT q<1andλT c<1,λT q=R T q andλT c=R T c(e.g.Katul et al.,1995);(3)for conditions where sensible heat is transported less ef-?ciently than water vapor and CO2,i.e.λT q>1and

NO.2WANG ET AL

415

Table 1.Flux-variance similarity constants for temperature (C T 3),humidity (C q 3),and CO 2(C c3)from the literature.Author(s)

C T 3C q 3C c3Ecosystem This work

1.12 1.19

1.17

grassland Tillman (1972)

0.95grassland Weaver (Weaver,1990) 1.00grassland Lloyd (1991)

grassland Katul et al.(1995)0.95 1.30grassland Choi et al.(2004)

1.1 1.10grassland Detto and Katul (2007)0.990.99grassland Hsieh et al.(2008) 1.10 1.100.95grassland H¨o gstr¨o m and Smedman-H¨o gstr¨o m (1974)0.92 1.04farmland Ohtaki (1985)0.95 1.10 1.10

farmland Lloyd (1991)

0.95farmland Gao et al.(2006) 1.09 1.49farmland Hsieh et al.(2008) 1.00 1.00 1.00farmland Guo et al.(2009) 1.160.92 1.10

farmland Padro (1993)

0.950.95forest Hsieh et al.(1996)

1.36forest Lamaud and Irvine (2006)0.95 1.30forest Cava et al.(2008) 1.09 1.61 1.32forest Hsieh et al.(2008)

1.25

1.50

1.70

forest

λT c >1,λT q =R ?1T q and λT c =R ?1

T c (e.g.Bink and Meesters,1997);(4)based on the FV similarity rela-tion λT q =C q 3/C T 3and λT c =?C c3/C T 3(e.g.Hsieh et al.,2008);(5)Lamaud and Irvine (2006)proposed

that λT q =R K

T q for all kinds hydrological conditions,where K =1for B O 0.1,K =?1?2log(B O )for 0.1

4.Results and Discussion

4.1

Analysis of FV similarity relation 4.1.1

Normalized standard deviation of scalars

The normalized standard deviations of tempera-ture (σT /T ?),water vapor density (σq /q ?)and CO 2concentration (σc /c ?)are plotted against the stability parameter ζin Fig.2.The ?1/3power law was evident for three scalars in unstable conditions.The similar-ity constants C T 3,C q 3and C c3were determined to be 1.12,1.19and 1.17,respectively.Lloyd et al.(1991)and Hsieh et al.(1996)found that the FV relation was the same for the surfaces considered.However,in pre-vious studies,as summarized in Table 1,even for the same ecosystem,di?erent authors have reported di?er-ent values of C T 3,C q 3or C c3,with larger di?erences

416FLUX-VARIANCE METHOD FOR FLUX ESTIMATIONS IN THE EASTERN TIBETAN PLATEAU VOL.30 Table2.Coe?cients of regression analyses between measured and estimated sensible heat(H),water vapor(LE),and CO2(F c)?uxes.

Flux Slope(A)Intercept(B)R2SEE

H0.9211.640.9210.22(W m?2)

LE(λT q=1)0.9631.520.8828.05(W m?2)

LE(λT q=R T q)0.9868.560.4978.62(W m?2)

LE(λT q=R?1

T q

)0.8812.510.8825.33(W m?2)

LE(λT q=C q3/C T3)0.9029.210.8826.27(W m?2)

LE(λT q=R K T q)0.9233.370.7939.88(W m?2)

F c(λT c=1)0.98?0.060.800.11(mg m?2s?1) F c(λT c=R T c)0.99?0.160.620.16(mg m?2s?1)

F c(λT c=R?1

T c )0.88?0.030.820.08(mg m?2s?1)

F c(λT c=?C c3/C T3)0.95?0.050.850.09(mg m?2s?1) F c[λT c=?(?R T c)M]0.88?0.130.810.12(mg m?2s?1)

usually among C T3,C q3and C c3for forest ecosystems,

while smaller di?erences for grassland/farmland.The

values of C T3,C q3and C c3at our site were within

these ranges,and the values of C q3and C c3were both

slightly higher than the value of C T3.This feature is

in agreement with results of several other studies con-

ducted over various surfaces(Table2),which points

to the fact that standard deviations of T,q and CO2

do not behave precisely in the same way(08c5de35650e52ea551898b5maud

and Irvine,2006),and suggests dissimilarity among T,

q and CO2(e.g.Gao et al.,2006).A possible cause

for the imperfect similarity is associated with di?erent

levels of scalar passivity(e.g.Guo et al.,2009).

4.1.2Correlation coe?cient between vertical velocity

and scalars

The correlation coe?cient between vertical veloc-

ity and scalars can be regarded as a measure of overall

e?ciency,which changes between0(no correlation)to

±1(optimal e?cient transfer)(Roth and Oke,1995).

In Fig.3,they are plotted against the stability param-

eterζ.The mean values(and standard deviations)of

R wT,R wq and R w c were0.52(0.05),0.49(0.05)and

?0.50(0.06),respectively.In Fig.3a,R wT is depen-

dent uponζ,increasing from about0.35atζ=?0.1

to about0.57atζ=?1,and R wT tends to approach

a constant with higher instabilities.This feature has

been noted by some other authors(e.g.De Bruin et

al.,1993;Roth and Oke,1995;Lamaud and Irvine,

2006;Moriwaki and Kanda,2006).The reason for

this increased heat transport withζover?at surfaces

is attributed to relatively lowσw/u?compared to the

data presented by Panofsky et al.(1977)(e.g.Roth

and Oke,1995;Moriwaki and Kanda,2006).The de-

pendencies of R wq and R w c(Figs.3b,c)upon?ζare

similar to that of R wT,but with smaller magnitudes.

NO.2WANG ET AL417

Figures4a,b and c show plots of the relative trans-

fer e?ciency of heat to water vapor(λT q),heat to CO2

(λT c),and water vapor to CO2(λq c),respectively.In

unstable conditions,heat transportation was more e?-

cient than water vapor and CO2,which is in agreement

with results from several other studies(e.g.Katul et

al.,1995;Roth and Oke,1995;Katul and Hsieh,1999;

Lamaud and Irvine,2006;Moriwaki and Kanda,2006;

Cava et al.,2008).Deviation from unity of relative

transfer e?ciency was in contrast to the MOST pre-

diction of unity indicating that scalars should be trans-

ported by the same mechanism in a homogeneous sur-

face layer(Roth and Oke,1995).Hill(1989)suggested

that the reason for relative transfer e?ciency deviated

from unity results from di?erent active or passive roles

of scalars.Katul et al.(1995)pointed out that statis-

tics for T and q could be di?erent,because T is an

active scalar but q is generally not.Furthermore,CO2

might be regarded as a passive scalar(e.g.Moriwaki

and Kanda,2006).Also,some authors have suggested

that relative transfer e?ciency deviating from unity

results from the heterogeneity of the surface structure

(e.g.Roth and Oke,1995),cloud e?ects on radia-

tion(e.g.Roth and Oke,1995),modulations from

the outer layer(e.g.McNaughton and Laubach,1998;

Moriwaki and Kanda,2006;Asanuma et al.,2007),

hydrologic conditions of the site(08c5de35650e52ea551898b5maud and

Irvine,2006;Guo et al.,2009),and the complexity of

CO2sources/sinks on the surface(e.g.Williams et al.,

2007;Hsieh et al.,2008).

At our site,however,the land surface is homoge-

neous short grassland,and data used for analysis were

from fair weather days and satis?ed the stationarity

test.So,heterogeneity of the surface structure can be

418FLUX-VARIANCE METHOD FOR FLUX ESTIMATIONS IN THE EASTERN TIBETAN PLATEAU VOL.30disregarded as a potential factor.Plus,cloud e?ects

on radiation and modulations from the outer layer can

also be minimized by data selection to a certain degree.

Lamaud and Irvine (2006)described wet and dry con-

ditions as B O 0.1and B O 1,and found that a quick

rise of λT q with B O when the latter was lower than

0.5.However,at our site,λT q and λT c were indepen-

dent of B O and α,as illustrated in Fig.5.Although,

following the data selection criteria,the complexity

of CO 2sources/sinks on the surface cannot be disre-

garded,because the photosynthesis and respiration of

an ecosystem are in?uenced by multiple environmen-

tal factors,such as air temperature,soil water con-

tent,vapor pressure de?cit,and precipitation (e.g.Xu

and Baldocchi,2004;Zhao et al.,2006,2010).Thus,

through the above analysis,di?erent roles (active or

passive)of these scalars and the complexity of CO 2

sources/sinks on the surface may be the main reason

for the deviation from unity of the relative transfer

e?ciency.

4.2Estimation of turbulent ?uxes using the

FV method

4.2.1Sensible heat ?ux

Using Eq.(7)and measured standard deviations

of temperature,sensible heat ?ux can be calculated

by the FV method.Figure 6shows the comparison

of sensible heat ?ux between FV estimations (H FV )

and EC measurements (H EC ).A regression model

(H EC =A ×H FV +B )was used to evaluate the FV

method estimated sensible heat ?ux.The coe?cient of

determination (R 2)and standard errors of

estimation (SEE)were 0.92and 10.22W m ?2,respectively.In the past,SEE for sensible heat ?ux estimation has ranged from 8.9W m ?2to 49.4W m ?2(e.g.Katul et al.,1995;Sugita and Kawakubo,2003;Hsieh et al.,2008).It is clear that,from Eq.(9),the accuracy of LE and F c estimations depends upon H FV .Thus,reasonable agreement between H FV and H EC implies that tem-perature is suitable to be used as a reference scalar for LE and F c estimation.4.2.2Latent heat ?ux The suitable expression of λT q is important to la-tent heat ?ux estimation,as described in Section 3.2.Figure 7plots the comparisons of latent heat ?ux between EC measurements (LE EC )and FV estima-tions (LE FV )using the ?ve representations of λT q as described in section 3.2.Figure 8a shows the rela-tionships between λT q and R T q .Coe?cients of re-gression analyses are shown in Table 2.Obviously,the FV method systematically overestimated the la-tent heat ?ux by about 6%(Fig.7a)with the strat-egy proposed by Hill (1989);R 2and SEE were 0.88and 28.05W m ?2,respectively.The primary reason is attributed to simpli?cation of λT q =1,which means that water vapor and heat are transported by the same mechanism in a homogeneous surface layer (e.g.Roth and Oke,1995).In contrast,at the present site,heat transportation was more e?cient than water vapor (Fig.8a),and the averaged λT q was 1.06.As implied in Fig.8a,the R T q is not a proper ex-pression for λT q ;the strategy λT q =R T q might only be valid when λT q <1,such as in Guo et al.(2009).

However,at our site,only very few of measured λT q

satis?ed this limit;the averaged R T q was 0.87,quite

di?erent from the averaged λT q ,which resulted in

the FV method systematically overestimating the EC-

measured LE by about 23%with the strategy proposed

by Katul et al.(1995)(Fig.7b);R 2and SEE were 0.49

and 78.62W m ?2,respectively.

Although most values of λT q were higher than

unity and the strategy proposed by Bink and Meesters

(1997)can potentially be applied to our site,they

were systematically less than R ?1T q (Fig.8a),and the

averaged value of R ?1T q was 1.18.Bink and Meesters

(1997)demonstrated that λT q is expressed by R ?1

T q

when relative transfer e?ciency of heat to water va-por is about twice the average,but this ratio is higher

than the value of averaged λT q in this study.Thus,

the FV method systematically underestimated the EC-

measured LE by about 8%with this strategy (Fig.7c);

R 2and SEE were 0.88and 25.33W m ?2,respectively.

Reasonable agreement between measured and pre-

dicted LE are shown in Fig.7d;R 2and SEE were

0.88and 26.27W m ?2,respectively.The ratio

NO.2WANG ET AL419

420FLUX-VARIANCE METHOD FOR FLUX ESTIMATIONS IN THE EASTERN TIBETAN PLATEAU VOL.30

Figure9plots the comparisons of CO2?ux between

EC measurements(F cEC)and FV calculations(F cFV)

using the?ve representations ofλT c as described in

Section3.2.Figure8c shows the relationships between

λT c and R T c.Coe?cients of regression analyses are

shown in Table2.As shown in Fig.9a,there was a

systematic overestimation of carbon uptake by strat-

egyλT c=?1,while R2and SEE were0.8and0.11

mg m?2s?1,respectively.The main reason is that

the heat is transported more e?ciently than CO2at

our site;the averagedλT c=?1.04.Also,neither

λT c=R T c norλT c=R?1

T c estimated CO2?ux feasi-

bly,overestimating(17%)and underestimating(10%) carbon uptake,owing to improper representations of

λT c(Fig.8c).The averaged R T c and R?1

T c were?0.9

and?1.11,respectively.Obviously,the strategy based on the FV similarity relation provided a reasonable agreement between measured and predicted CO2?ux (Fig.9d).The R2and SEE were0.85and0.09mg

NO.2WANG ET AL421

422FLUX-VARIANCE METHOD FOR FLUX ESTIMATIONS IN THE EASTERN TIBETAN PLATEAU VOL.30

m?2s?1,respectively.The ratio?C c3/C T3=?1.04 was equivalent to the averagedλT c.

As shown in Fig.9e,the CO2?ux estimated with the strategy proposed by Guo et al.(2008)was in agreement with measured results.However,as shown in Fig.8d,the relationship between power M andαcould not be reproduced by our data.The averaged λT c of Guo et al.(2009)was?0.92at the farmland station,whereas in our study it was?1.04.Moreover, R T c values for our site were also higher than values found by Guo et al.(2009).These di?erences might imply di?erent transfer mechanisms for these variables between the two sites.As Guo et al.(2009)pointed out,the M?αrelationship is likely to vary from site to site,and has to be further examined.Thus,based on our study,the strategyλT q=?C c3/C T3is recom-mended for CO2?ux estimation.

5.Conclusions

From measurements performed over a homoge-neous short grass surface in the eastern Tibetan Plateau,we examined the FV relationship of temper-ature,water vapor density and CO2concentration. Based on these relationships,?ve representations of relative transport e?ciency were applied to calculate latent heat and CO2?uxes using the FV method.Our results suggested the following:

In unstable conditions,the normalized standard deviation of temperature,water vapor density,and CO2concentration followed the FV similarity rela-tion,but did not behave in exactly the same way due to di?erent roles(active or passive)of these scalars in the production/destruction of turbulent kinetic en-ergy.Similarity constants for temperature(C T3),wa-ter vapor(C q3)and CO2(C c3)were found to be1.12, 1.19and1.17,respectively.Heat was transported more e?ciently than water vapor and CO2.

On the basis of the similarity constant C T3deter-mined locally,sensible heat?ux estimated by the FV method was in agreement with results measured by the EC system.

On the basis of estimated sensible heat?ux,?ve strategies were applied to calculate latent heat and CO2?uxes.The strategy of local determination of the FV similarity relation had the practical applicability for the estimation of latent heat and CO2?08c5de35650e52ea551898b5-pared to other more complex ones,this approach was better at representing the averaged relative transport e?ciency,and technically easier to apply.The rela-tionships of K?B O and M?αhave to be examined before using the FV method for estimating latent heat and CO2?uxes.

A?nal important point to make is that the data used in this paper were from summers under inter-mediate hydrological conditions,during rainy season. The results may not represent other drier seasons.

Acknowledgements.This work was supported by funding from the Chinese National Key Programme for Developing Basic Sciences(Grant No.2011CB952002), the National Natural Science Foundation of China(Grant No.40975008),the Key Program of the Chinese Academy of Sciences(Grant No.KZCX2-YW-328),the Na-tional Natural Science Foundation of China(Grant Nos. 40905032,41130961),and the Foundation for Excellent Young Scholars of CAREERI.We are grateful to PENG Xiaohui,CHEN Tianning,AO Yinhuan,LI Suosuo,CHEN Shiqiang,and many other people,who contributed to the ?eld work.

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