Scalar turbulent behavior in the roughness sublayer of an Amazonian forest

18 Pages·2016·1.55 MB·English

Atmos.Chem.Phys.,16,11349–11366,2016
www.atmos-chem-phys.net/16/11349/2016/
doi:10.5194/acp-16-11349-2016
©Author(s)2016.CCAttribution3.0License.
Scalar turbulent behavior in the roughness sublayer of an
Amazonian forest
EinaraZahn1,NelsonL.Dias2,AlessandroAraújo3,LeonardoD.A.Sá4,MatthiasSörgel5,IvonneTrebs6,
StefanWolff5,andAntônioManzi7
1GraduatePrograminEnvironmentalEngineering(PPGEA),FederalUniversityofParaná,Curitiba,PR,81531-980,Brazil
2DepartmentofEnvironmentalEngineering,FederalUniversityofParaná,Curitiba,PR,81531-980,Brazil
3EmpresaBrasileiradePesquisaAgropecuária(EMBRAPA),Trav.Dr.EnéasPinheiro,Belém,PA,66095-100,Brazil
4CentroRegionaldaAmazônia,InstitutoNacionaldePesquisasEspaciais(INPE),Av.Perimetral2651,Belém,PA,
66077-830,Brazil
5BiogeochemistryDepartment,MaxPlanckInstituteforChemistry,P.O.Box3060,55020Mainz,Germany
6LuxembourgInstituteofScienceandTechnology,EnvironmentalResearchandInnovation(ERIN)Department,
4422Belvaux,Luxembourg
7CentrodePrevisãodeTempoeEstudosClimáticos(CPTEC),InstitutoNacionaldePesquisasEspaciais(INPE),
RodoviaDutraKm39,CachoeiraPaulista,SP,12630-000,Brazil
Correspondenceto:NelsonL.Dias([email protected])
Received:22December2015–PublishedinAtmos.Chem.Phys.Discuss.:18January2016
Revised:16July2016–Accepted:6August2016–Published:13September2016
Abstract. An important current problem in micrometeorol- ment in the range 0◦<|Z|<20◦, and its values fall within
ogy is the characterization of turbulence in the roughness the range reported in the literature for the unstable surface
sublayer(RSL),wheremostofthemeasurementsabovetall layer.Ingeneral,ourresultsindicatethepossibilityofbetter
forests are made. There, scalar turbulent fluctuations dis- stability-derivedfluxestimatesforlowzenithangleranges.
play significant departures from the predictions of Monin–
Obukhov similarity theory (MOST). In this work, we ana-
lyze turbulence data of virtual temperature, carbon dioxide,
andwatervaporintheRSLaboveanAmazonianforest(with 1 Introduction
acanopyheightof40m),measuredat39.4and81.6mabove
thegroundunderunstableconditions.Wefoundthatdimen- In the atmospheric surface layer above the roughness sub-
sionless statistics related to the rate of dissipation of turbu- layer (RSL) height z∗ (approximately 3 times the height
lence kinetic energy (TKE) and the scalar variance display of the roughness obstacles, h – Cellier and Brunet, 1992),
significantdeparturesfromMOSTasexpected,whereasthe flux estimates based on mean concentration measurements
verticalvelocityvariancefollowsMOSTmuchmoreclosely. aremadewiththehelpofMonin–Obukhovsimilaritytheory
Muchbetteragreementbetweenthedimensionlessstatistics (MOST)andthecorrespondingsimilarityfunctions.Itisnow
with the Obukhov similarity variable, however, was found wellknown,however,thatMOST-basedsimilarityfunctions
for the subset of measurements made at a low zenith angle often fail, to various degrees, in the roughness sublayer. In
Z, in the range 0◦<|Z|<20◦. We conjecture that this im- thisregion,beyondtheclassicalgoverningvariablesfoundin
provement is due to the relationship between sunlight inci- MOST,thereareseveralmoreinterveningvariables,suchas
dence and the “activation–deactivation” of scalar sinks and tree spacing and vegetation density, among others (Garratt,
sourcesverticallydistributedintheforest.Finally,weevalu- 1980; Foken et al., 2012; Arnqvist and Bergström, 2015).
atedtherelaxationcoefficientofrelaxededdyaccumulation: Thisistheregionwheremostmeanconcentrationmeasure-
itisalsoaffectedbyzenithangle,withconsiderableimprove- ments above forests are made, and this is the case with the
82mtowerdataanalyzedinthiswork.
PublishedbyCopernicusPublicationsonbehalfoftheEuropeanGeosciencesUnion.
11350 E.Zahnetal.:ScalarturbulentbehaviorintheroughnesssublayerofanAmazonianforest
In principle, the availability of mean concentration data etal.(1999)displayamuchlargerscatterthanwhatisusu-
would make flux-gradient methods a natural choice to esti- ally found above the roughness sublayer. Such roughness
mate scalar fluxes above the forest. Unfortunately, the diffi- sublayer“dissimilarity”isnotrestrictedtoflux-gradientrela-
culty of applying MOST in the RSL adds considerable un- tionships:thedimensionlessstandarddeviationofascalara,
certaintytothisapproach. σa/a∗, has been found to be equally affected (Padro, 1993;
Maybe one of the earliest reports of the failure of Katul and Hsieh, 1999; von Randow et al., 2006; Williams
flux-gradient methods when measurements are performed etal.,2007;Diasetal.,2009).
too close to the roughness elements was made by Thom Inthispaper,weanalyzeroughnesssublayerdatacollected
etal.(1975),whocomparedflux-gradientandenergy-budget as part of the ATTO project (Amazon Tall Tower Observa-
Bowen ratio methods over a pine forest and found that the tory),aGerman–Brazilianprojectundertakenunderthelead-
dimensionlessgradients(cid:56)M and(cid:56)H ofMOSTareunderes- ershipoftheMaxPlanckInstitute(Germany),InstitutoNa-
timatedundersuchconditions.Thiswasgenerallyconfirmed cionaldePesquisasdaAmazônia(INPA),andUniversidade
byGarratt(1978),whoestimatedz∗=4.5hforthemomen- Estadual do Amazonas (UEA) (Brazil). A 325m tall tower
tumfluxandz∗=3hforthesensibleheatflux. hasbeenerectedasaforestsite150kmNEofManausandis
In the roughness sublayer, scalar and velocity gradients currentlyundergoinginstrumentation.Preliminarymeasure-
are weaker than above, leading to higher values of the cor- mentshavebeenmadeatan82mtalltowerbuiltatthesite,
respondingturbulentdiffusivities(CellierandBrunet,1992). and some analyses from the measured micrometeorological
Underneutralconditions,themomentumturbulentdiffusiv- dataaredescribedhere.
ityincreasesbyafactor1.1–1.5andthesensibleheatturbu- ThemainpurposeofATTOistobetterunderstandtherole
lentdiffusivityby2–3.TheturbulentPrandtlnumbercorre- of the Amazonian biome in the context of global climatic
spondinglydecreasesfromtocloseto1toapproximately0.5 changes.Specifically,theprojectaimsatabetterunderstand-
atthecanopytop(Finnigan,2000). ing and modeling of gaseous exchanges between the forest
CellierandBrunet(1992)proposeadimensionlessfactor andtheatmosphere(Andreaeetal.,2015).Formanyscalars
γ to account for the increase in turbulent diffusivity. Fol- ofinterest,suchasvolatileorganiccompounds(VOCs),the
lowing this suggestion, Schween et al. (1997), using data high-frequencymeasurementsneededintheeddycovariance
measured over a 12m tall oak and pine tree forest, found method are still difficult to make (particularly in long-term
γθ =2.2.Theypointedoutthatthedifferentbehaviorinthe campaigns),leavingtheirfluxestimatestomethodsbasedon
RSLmaybeduetofluxoriginatingbelowthezero-planedis- themeasurementoftheirmeanconcentrationsandgradients.
placementheight,sincein-canopyairmayhavesignificantly Given the importance of correctly estimating trace gas
different characteristics from above-canopy air. As we will fluxes over the Amazon forest, the lack of a theory for the
see,zenithangleanalysesinthepresentworkgivesupportto roughnesssublayerisclearlya majorobstacleintheunder-
thisconsideration. standingofsurface–atmosphereinteractionswithfar-ranging
Garratt (1980) proposed that for heights z<z∗, the ver- implicationsfortheregionalandglobalhydrology,ecology,
tical gradients depend on an additional length scale zs, due andclimate.
to the turbulent wake generated by the trees. The author in- Moreover, given the always present need to take into
vestigateddatafromasurfacecoveredbyscatteredtreesand account site-specific features in any micrometeorological
shrubs in Australia, referred to as subtropical scrub or sa- study, we here attempt to provide a general analysis of
vannah, of an average height of 8m and occupying about roughness-sublayer-relatedquestionsattheATTOsiteprior
25%ofthetotalsurfacearea.Heanalyzeddataintherange to the construction of the main tower. We expect that once
5<d/z <85(d isthezero-planedisplacementheightand measurements at the main tower become available, a better
0
z isthesurfaceroughness),suggestinganadditionaldepen- understanding of the questions preliminarily assessed here
0
dence of the dimensionless gradients on the variable z/z∗. willbepossible.
Considering the canopy physical characteristics, he found The variables analyzed in this study were chosen on the
thatarelevantlengthscaleisthetreespacingδandproposed basis of data availability (the preliminary campaigns had to
z∗=3δ. Regarding Garratt’s wake production assumption, berestrictedtofewervariablesthanthosethatwillbeavail-
ithasbeenarguedthatthiseffectdiesoutrapidlyabovethe able once ATTO is fully implemented) as well as their use-
canopyandthatitisnotthemaincauseforthelackofMOST fulnesstoassesstwomainquestions:(i)howdoestheAma-
complianceintheroughnesssublayer(Mölderetal.,1999). zonian RSL change the canonical (i.e., measured above the
Other attempts to organize roughness sublayer data in- RSLandreportedas“classical”)MOSTsimilarityfunctions,
cludetheuseofz/z∗ byCellier(1986)andtheMölderetal. and(ii)howusefulorpromisingwouldflux-gradientandre-
(1999) proposal of a function (z/z∗)n multiplying the di- latedmethodsappliedwithintheAmazonianRSLbeforthe
mensionlessgradients:Mölderetal.(1999)foundn=1for estimate of the fluxes of VOCs and other chemicals whose
scalarsandn=0.6formomentum;theyclaimthattheuseof high-frequencymeasurementmaybedifficulttoperformon
this factor produces acceptable results. Still, even with this along-termbasis?
correction, the resulting dimensionless functions in Mölder
Atmos.Chem.Phys.,16,11349–11366,2016 www.atmos-chem-phys.net/16/11349/2016/
E.Zahnetal.:ScalarturbulentbehaviorintheroughnesssublayerofanAmazonianforest 11351
In this work, the sections are organized as follows. In sultsfortemperaturewerecalculatedwiththesecorrectedθ
Sect. 2 we describe the experimental site in an Amazonian values.
forestanddatameasurement;wealsoshowthestepsofdata In the same vein, the instantaneous fluctuations of q and
qualitycontrol.Theoreticalconceptsusedtodevelopthisre- cwereusedtocalculatethefluxesandstatisticsofH Oand
2
searcharereviewedinSect.3,wherewedescribethedissi- CO , without the need of further density corrections (Webb
2
pationrate,verticalvelocityskewness,spectralanalysis,and et al., 1980). This is sometimes called the “direct method”
relaxed eddy accumulation inlight of MOST. An important (Miller et al., 2010; Prytherch, 2011) and produces results
question of whether the RSL departures from MOST affect comparable to the Webb–Pearman–Leuning (WPL) correc-
the inertial subrange behavior of the scalars is raised here, tionofWebbetal.(1980).
and a MOST function for the inertial subrange is proposed Recently, it has been found that the CSAT3 and Gill R3
to address it. In Sect. 4 we discuss these results. Variance sonic anemometers may require flow distortion corrections.
methodresultsintheroughnesssublayerandthezenithangle For the CSAT3, these corrections may change w(cid:48) estimates
influenceonseveralturbulencestatisticsareshowninSect.5, by approximately 8% (Frank et al., 2013) and σw by ap-
followedbyananalysisofscalarsimilarityindicesandtheir proximately 5–6% (Frank et al., 2013; Horst et al., 2015).
implicationsforfluxestimationinSect.6.Finally,inSect.7 In our case, we tested the flow distortion corrections with
wemakeourfinalconsiderations. theCSAT3atthe39.4mheight,butourresultschangedvery
little:forexample,thecorrectedw(cid:48) changedbyslightlyless
than4%.Inthiswork,therefore,thedataareprocessedwith-
2 Datameasurementandqualitycontrol outtheaforementionedflowdistortioncorrections.
2.1 Experimentalsite 2.2 Qualitycontrol
The study area is located at Reserva de Desenvolvimento The10Hzdatawereanalyzedin30mindatablocks(“runs”).
Sustentável Uatumã (RDSU) (Uatumã sustainable develop- Incomplete runs were excluded, and spikes were removed
ment reservation), in the counties of São Sebastião do Ua- following Vickers and Mahrt (1997). For the next phase of
tumã and Itapiranga, in the northeast of Amazonas State, quality control, fluctuations were extracted around a run-
Brazil.Thesiteis150kmnortheastofthestatecapitalMan- ningmean.Afterthat,eachrunwassubdividedinto15two-
◦ (cid:48) ◦ (cid:48) ◦ (cid:48)
aus, between the coordinates 59 10–58 4 W and 2 27– minute sub-runs, and a local (i.e., 2min) standard deviation
◦ (cid:48)
2 4 S. wascalculated.Wheneverthisvaluewaslessthanathresh-
Intheforest,between200and250treespeciesperhectare old(pre-stipulatedbasedonthesensoraccuracy),thewhole
canbefound,withameanheightof40mandwithsomein- 30minrunwasexcluded.
dividualsreaching50m.Thesiteitselfislocatedonaplateau As a result, 21.5% of the 81.6m level and 50.2% of the
(terrafirme),withanaltitudeof130m. 39.4m level runs were left. However, after this test, some
The micrometeorological data were measured at an 82m stronglynonstationarytimeseriesremained,mainlyinscalar
towerwitharectangularcrosssectionof2.5×1m2atthesite data,evenwhenlineardetrendingwasapplied.Forthisrea-
◦ (cid:48) (cid:48)(cid:48) ◦ (cid:48) (cid:48)(cid:48)
at2 840 S,59 010 W.Micrometeorologicalinstrumenta- son, these remaining data were further checked with two
tion was installed at the 23, 39.4, and 81.6m levels (above tests (both after the removal of the linear trend). The first
ground). wasthereversearrangementtest(BendatandPiersol,1986,
In this work, we analyze pilot data from the 39.4 and p. 97; Dias et al., 2004), performed on N =50 averages of
81.6m heights, measured during April 2012. The data an- the 30min run and a significance level α=0.05. The sec-
alyzed are the three wind components u, v, and w mea- ond test was defined by us based on a visual scrutiny of
sured by two sonic anemometers (CSAT3, Campbell Scien- the data. It consisted of calculating the difference between
tificInc.at39.4m;R3,GillInstrumentsLtd.,at81.6m),the the maximum and minimum values of the running mean
sonic temperature (which we assume to be the same as the withineach30minrun.Therunwasdiscardedwheneverthis
virtual temperature θ ), and the mass concentrations (mass difference exceeded (cid:49)θ =1.7◦C, (cid:49)c=0.11gkg−1, and
v v
of the species/total mass) of CO , c and H O, q, calcu- (cid:49)q=3gkg−1.Thesefurther testsreduceddataavailability
2 2
lated from the corresponding mass densities (mass of the to16.8%atthe81.6mleveland41.5%atthe39.4mlevel.
species/volume) measured by two infra-red gas analyzers Fortheseruns,a2-Dcoordinaterotationwasappliedforthe
(IRGAs;LI-7500A,LI-CORInc.). finalanalyses.
Both the CSAT3 and the Gill sonic anemometers report As a percentage of the unstable runs only (which are the
sonic virtual temperatures. The instantaneous values of θ ones actually analyzed in this work), the figures are 9.4%
v
from the sonic anemometers and of water vapor density ρ (81.6mlevel)and24.1%(39.4mlevel).Althoughtypicalof
v
andCO densityρ fromtheLI7500wereusedtoderivein- micrometeorological studies, this somewhat low number of
2 c
stantaneousvaluesofthermodynamictemperatureθ,ofspe- usablerunsisboundtolimit,forexample,thepercentageof
cifichumidityq,andCO massconcentrationc.Allourre- reliable fluxes that can be retrieved in long-term studies. It
2
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11352 E.Zahnetal.:ScalarturbulentbehaviorintheroughnesssublayerofanAmazonianforest
isalsolikelythatalargernumberofrunsfailqualitycontrol tiveintheinertialsublayer(RaupachandThom,1981;Fitz-
checksintheRSLincomparisonwithstandardapplications jarrald et al., 1990; von Randow et al., 2006). Some stud-
ofMOSTinthesurfacelayer.Inthiswork,weneededtocon- ies suggest that Sku tends to be positive in the roughness
centrate on the analysis of good-quality data at the expense sublayer and positive or near zero in the inertial sublayer
oftimecoverage.Paralleleffortswillberequiredtoincrease (Kaimal and Finnigan, 1994; Kruijt et al., 2000), but there
dataavailabilityandrepresentativeness. are also indications that it changes sign below or above the
canopyheightdependingonvegetationdensity(Poggietal.,
2004). At some level above the canopy, Skw changes sign,
3 Theoreticalbackground
anditseemsreasonabletoregardthisleveltobeameasureof
theroughnesssublayerheight.AccordingtoFitzjarraldetal.
Inthissection,webrieflyreviewsomeresults,whichareused
inthenextsectiontoanalyzethedata. (1990), the negative Skw values above canopies are largely
due to the fact that there is something below the “surface”
3.1 Dissipationrateofturbulencekineticenergy incanopylayers,andtherecanbedownwardturbulenttrans-
portofverticalvelocityvarianceassociatedwiththedropin
Thedimensionlessdissipationrateofturbulencekineticen- the TKE as one goes into the canopy. Kaimal and Finnigan
ergy(TKE)isgivenasfollows(KaimalandFinnigan,1994): (1994)attributetheconsiderablescatterinpublishedresults
primarily to morphological differences between canopies,
κ(z−d)(cid:15)
φ(cid:15) = , (1) butatanyratethiscombinationofstronglypositiveuskew-
u3
∗ ness and strongly negative w skewness indicates that the
where u∗ is the friction velocity, κ is the von Kármán con- turbulence is dominated by downward-moving gusts in the
stant, and (cid:15) is the rate of dissipation of TKE. In MOST, roughnesssublayer.
a function still widely used to predict φ(cid:15) is the following
(Kaimaletal.,1972): 3.3 Scalardissipationfromspectraandinertial
subrangebehavior
φ(cid:15) =(1+0.5|ζ|2/3)3/2, −2≤ζ ≤0, (2)
where ζ is the Monin–Obukhov stability parameter. As we Consider the temperature spectrum in the inertial subrange,
shallsee,intheroughnesssublayerthedissipationratedevi- intheform
ates from the prediction by Eq. (2). In this work, we assess
this departure from MOST by extending an index proposed k5/3Eθθ(k)=αθθ(cid:15)−1/3N, (6)
byMammarellaetal.(2008):
χ = u3∗/(cid:15) −1= L(cid:15) −1. (3) whereαθθ =0.8andN istherateofthedissipationofsemi-
κ(z−d)/φ κ(z−d) temperaturevariance(KaimalandFinnigan,1994,p.37).
(cid:15)
Alsoondimensionalgrounds,andwhenMOSTisvalid,a
InEq.(3),L(cid:15) isthelengthscalecalculatedfromthefriction
similarityfunctionexiststhatdescribesthetemperaturespec-
velocity and the rate of dissipation of TKE and adjusted to
trumintheinertialsubrange,viz.,
theeffectofbuoyancy:itcanberegardedasanintegralscale
of the flow. It can readily be verified that L(cid:15)/(κ(z−d))=
1⇒χ =0 indicates that the dissipation data follow MOST gθ(ζ)= αθθ(cid:15)−1/3N(z−d)2/3. (7)
perfectly. Originally, Mammarella et al. (2008) proposed χ θ∗2
to be used only under near-neutral conditions. As our data
comprisetoofewnear-neutralruns,itwasnecessarytotake
intoaccountstabilitybyincludingφ(cid:15) inthedenominatorof Again,weseektodeterminetowhatdegreegθ calculated
withroughnesssublayerdataobeysMOSTscaling.Theuse-
Eq.(3).
fulness of this indicator lies in its limited frequency range:
3.2 Verticalvelocityskewness both(cid:15)andN areinertial-subrangevariablesinthesensethat
theyareobtainedfromastraightforwardanalysisoftheiner-
Inthesurfacelayer,theskewnessesofuandware tialsubrangeofthevelocityandtemperaturespectra.There-
w(cid:48)3 fore,gθ issensitiveonlytothehighestrangeoffrequencies
Skw= , (4) (roughly>0.02Hz).Ifthedissimilaritydisplayedby“bulk”
σw3 dimensionless statistics such as σθ/θ∗ is due to the larger
u(cid:48)3 scalesonly,thengθ andsimilarvariablesshouldobeyMOST
Sku= . (5) muchmorecloselythantheformer.Ifontheotherhandthe
σ3
u dissimilarityisspreadoutthroughallfrequencyranges,then
In convective or near-neutral conditions, Skw is typically gθ shoulddisplaythesamesortofnonconformancetoMOST
observedtobenegativeintheroughnesssublayerandposi- astheotherbulkstatistics.
Atmos.Chem.Phys.,16,11349–11366,2016 www.atmos-chem-phys.net/16/11349/2016/
E.Zahnetal.:ScalarturbulentbehaviorintheroughnesssublayerofanAmazonianforest 11353
0.30 0.30
%) 0.25 (a)39.4m %) 0.25 (b)81.6m
( (
ncy 0.20 ncy 0.20
freque 0.15 freque 0.15
ve 0.10 ve 0.10
Relati 0.05 Relati 0.05
0.00 0.00
-5 0 5 10 15 20 25 -5 0 5 10 15 20 25
χ χ
Figure1.Histogramsofχ (seeEq.3)at(a)39.4and(b)81.6cm.
3.4 Therelaxededdyaccumulationmethodandrelated monoterpenes and isoprene being the most abundant fol-
analyses lowedbyalcohols,carbonyls,acids,aldehydes,ketones,and
esters. If applicable, the REA method will be an invaluable
The original eddy accumulation method was proposed by tool.
Desjardins(1972)withtheobjectiveofestimatingtheturbu- However,strictlyspeaking,tobevalidthemethodrequires
lentfluxofchemicalsnoteasilymeasuredatahighfrequency that the same value of b apply to all scalars. A sufficient
(seeRenetal.,2011).Inthemethod,conditionalsamplingis condition for this to happen, and the simplest although by
performedonthegas,whichisdirectedtoeitheroftworeser- no means a necessary condition, is the validity of the well-
voirsaccordingtothesignandintensityoftheverticalwind knownhypothesisofperfectsimilaritybetweenscalars(Hill,
velocity, w, by means of fast opening and closing valves. 1989;DiasandBrutsaert,1996),whichoftenfailsunderun-
Evident advantages are the fact that the method dispenses stable conditions due to phenomena originating above the
with high-frequency concentration measurements and that surface layer and to the transport of scalar variance from
onlyone-levelmeasurementsareneeded(Tsaietal.,2012). above(Cancellietal.,2012,2014).Furthermore,thephysics
Still, the method is not without difficulties, and to circum- oftheroughnesssublayerpropermaycomplicatethispicture
ventthemBusingerandOncley(1990)proposedthesimpler evenmore.
relaxed eddy accumulation (REA) method, which uses the Therefore, before applying the REA method to measure-
mean concentrations in each of two conditionally sampled mentsmadeclosetothecanopyoveraforest,itisimportant
reservoirs(c+andc−)tocalculatethefluxas toassessboththevalidityofscalarsimilarityandtheequal-
ity of the b’s for all scalars. A review of several REA stud-
w(cid:48)c(cid:48)=bcσw(c+−c−), (8) iesbyTsaietal.(2012)showedthatb canvarybyasmuch
as between 0.2 and 0.9, revealing the importance of its cor-
whereσwisthestandarddeviationoftheverticalvelocityand rect estimation. In Table 1 we give some values outside of
bc istherelaxationcoefficient,whichisempiricallyverified theroughnesssublayerfoundintheliterature,andinTable2
tobeadimensionlessconstant(itcouldbeaMOSTsimilarity values found by Gao (1995) for the roughness sublayer for
function) of the order of 0.6 (Businger and Oncley, 1990; differentvaluesoftheleaf-areaindex.
Katuletal.,1996).
Although initially developed and tested for the measure-
ment of CO , water vapor, and sensible heat fluxes (Pattey 4 Results
2
etal.,1993;BashandMiller,2007),theREAmethodisof-
4.1 Dissipationrates
tenextendedforthemeasurementofothergaseousorscalar
fluxes,usuallywithdirectsensibleorlatentheatfluxesused
TheratesofdissipationofTKEforeachrunwerecalculated
asproxiestoestimateb.Forexample,Zhuetal.(2000)used
from the longitudinal spectra on the basis of Kolmogorov’s
it to calculate ammonia fluxes and Mochizuki et al. (2014)
localisotropytheory(Kolmogorov,1941).Foreachrun,the
for isoprene and monoterpene fluxes; Matsuda et al. (2015)
inertialsubrangewasidentifiedandalinearregressionwith
used it to estimate sulfate and PM2.5 fluxes; Bowling et al. animposed−5/3slopewascalculatedtodetermine(cid:15).With
(1998) used it to calculate isoprene fluxes, Bash and Miller
(cid:15),wecalculatedφ(cid:15) inEq.(1)andtheindexχ inEq.(3).
(2007) and Sommar et al. (2013) for mercury fluxes, and
TheresultscanbeseeninFig.1wherethehistogramsof
Moraveketal.(2014)forperoxyacetylnitratefluxes.
χ at two levels are shown. As mentioned before, in the re-
IntheATTOproject,wewillfocusonthefluxesofseveral
gionofvalidityofMOST,wewouldexpecttheχ’stocluster
chemicals whose high-frequency measurement is still too
around0.
laborious, too expensive, or downright impossible. Among
these compounds are the VOCs released by the forests, the
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11354 E.Zahnetal.:ScalarturbulentbehaviorintheroughnesssublayerofanAmazonianforest
Table1.REAcoefficientsmeasuredabovetheroughnesssublayer,wherez isthemeasurementheight(inmeters)andnumbersbetween
bracketsaretheheightofthecanopies.
BusingerandOncley(1990) Katuletal.(1996) Bakeretal.(1992)
z(m) 4 5 –
Cover Crops Corn(2.4m) Soybeanfield
Grass(0.10m)
bθ 0.6 0.58±0.11 –
bq 0.6 0.58±0.15 0.56
bc – 0.56±0.06 0.56
bO3 – 0.56±0.06 –
39.4m
+1.0 +1.0
(a) (b)
+0.5 +0.5
ku +0.0 kw +0.0
S S
0.5 0.5
− −
1.0 1.0
− −
0.001 0.01 0.1 1 10 100 1000 0.001 0.01 0.1 1 10 100 1000
ζ ζ
− −
81.6m
+1.0 +1.0
(c) (d)
+0.5 +0.5
ku +0.0 kw +0.0
S S
0.5 0.5
− −
1.0 1.0
− −
0.001 0.01 0.1 1 10 100 1000 0.001 0.01 0.1 1 10 100 1000
ζ ζ
− −
Figure2.Horizontal(Sku)andvertical(Skw)velocityskewness:(a)Sku at39.4m;(b)Skw at39.4m;(c)Sku at81.6m;and(d)Skw at
81.6m.
Wefindthat,closetothecanopytop,at39.4m,theintegral to−0.8.Itisnoteworthythatatthe39.4mlevel,inspiteof
scaleL(cid:15) oftenfarexceedsκ(z−d):thismeansthatthelatter theprevalenceofnegativevaluesofSkw,positivevaluestyp-
is not a good estimate of the integral scale, as often found ically associated with the surface layer can also be found.
in the roughness sublayer. These results are in agreement This suggests that the roughness sublayer height is actually
withthefindingsbyRaoetal.(1973)andMammarellaetal. varying from run to run or that the physical picture is more
(2008). At 81.6m the spread of χ around zero is somewhat complicated, with the possibility of positive skewnesses in-
(but not very much) smaller, suggesting that, as expected, side the roughness layer. The skewness Sku of the longitu-
wearereachingtheupperlimitoftheroughnesssublayerat dinal velocity shows the opposite behavior, with a predom-
theseheights,againinagreementwithwhatisusuallyfound inance of positive values at the 39.4m level and a trend to-
intheliterature. wardsnegativevalueshigherup.Thisconfirms,atleastpar-
tially,thefindingsofPoggietal.(2004).Clearly,thesubject
4.2 Velocityskewness needsfurtherresearch.
InFig.2,weshowthehorizontalandverticalvelocityskew- 4.3 Inertialsubrangesimilarity
nessforthelevels39.4and81.6m,asafunctionofthestabil-
ityparameterζ.Theresultsconfirmthosefoundabovewith Similarly to the analysis of the longitudinal velocity spec-
the dissipation rate in Sect. 4.1: roughness sublayer charac- tra, we identified for each run the inertial subrange of the
teristics are still evident at the upper level, being obviously temperature spectrum and fitted a linear regression with a
morepronouncedatthelowerlevel,whereSkwreachesclose −5/3slope,inordertoextracttherateofdissipationofsemi-
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E.Zahnetal.:ScalarturbulentbehaviorintheroughnesssublayerofanAmazonianforest 11355
Table2.REAcoefficientsmeasuredwithintheroughnesssublayer(Gao,1995).
z(m) 43.1 34.2 18 14.4 10.5 5.9
bθ 0.58±0.04 0.55±0.04 0.51±0.03 – 0.61±0.06 0.62±0.09
bq – 0.55±0.02 0.51±0.05 0.61±0.05 – –
100 100
(a) (b)
10 10
) )
(ζ 1 (ζ 1
gθ gθ
0.1 0.1
0.01 0.01
0.0010.01 0.1 1 10 100 1000 0.0010.01 0.1 1 10 100 1000
ζ ζ
− −
Figure3.Inertialsubrangesimilarityfortemperaturespectra:(a)39.4mand(b)81.6m.
varianceoftemperature,N.Fromthelatterand(cid:15),thevalue Therandomizedφfunctions(notshown)tendedtofollow
ofgθ inEq.(7)wascalculated.Itisplottedagainstζ forthe a−1/3powerlawinthewholerangeofobservedζ’s,even
two levels in Fig. 3a and b. There is a clear pattern of de- atnear-neutralconditions,wheretheoriginaldatafollowthe
creasinggθ withζ,butthereisstillalargescattertypicalof predictedsimilarityfunctions.Ourresultsarequitesimilarto
roughnesssublayerresults. thoseofCavaetal.(2008).
This analysis suggests that inertial-subrange scales, ap- Wealsocalculatedthescalarfluxesforfairlytohighlyun-
proximately in the range 0.02–0.8Hz, are also influenced stableconditions(−ζ >0.2)usingtheflux-variancemethod
byroughnesssublayereffects:inotherwords,restrictingthe and compared them with the measured fluxes. We obtained
analysis to a range of smaller scales does not appreciably highcorrelations(infact,higherthanthosereportedbyCava
improve the predictions of MOST. Similar plots and results et al., 2008). As these authors comment, these fluxes are
were also obtained for the other scalars (water vapor and calculated without knowledge of u∗, and the success of the
CO )butarenotshownhere. methodunderthesemoreunstableconditionsgivesindepen-
2
dentconfirmationthatspuriouscorrelationisnotcontaminat-
ingouranalyses.
5 Variancemethodresults
Figures4and5showφw,φc,φq,andφθ forbothmeasure-
5.1 Generalbehaviorintheroughnesssublayer mentlevels.OnlynegativeCO2 fluxes(c∗<0)andpositive
latentandsensibleheatfluxes(q∗>0,θ∗>0)wereconsid-
ered for unstable conditions ζ <0. In the figures, we plot
The “variance method”, pioneered by Tillman (1972), is
widely used in micrometeorology for several purposes, in- empiricalφa(ζ)functionsfromexperimentaldataforwhich
goodMOSTagreementwasobserved(Katuletal.,1995).
cluding quality control procedures (Foken and Wichura,
Oncemore,thelargescattertypicalofroughnesssublayer
1996; Thomas and Foken, 2002; Lee et al., 2004) and flux
estimation (Hong et al., 2008). Here, we consider similar- data is found: note that the scatter is much larger in φθ, φc,
ityfunctionsofthetypeφa =σa/|a∗|,whereσa isthescalar and φq than in φw. Williams et al. (2007) suggest that this
lack of MOST compliance may be associated with hetero-
standarddeviationanda∗thescalar’sturbulentscale,defined
geneityofsourcesandsinksinsidethecanopy,contributing
by
to the larger standard deviation (relative to the scalar turbu-
w(cid:48)a(cid:48)=u∗a∗, (9) lentscale).
This tendency of φa data in the roughness sublayer to lie
aswellasφw=σw/u∗. above the corresponding MOST functions is generally ob-
Intheparticularcaseofφwinstableconditions,ithasbeen served in field experiments (Cava et al., 2008; Dias et al.,
argued that its observed behavior for large ζ may be an ar- 2009),butadefinitiveexplanationforitisstilllacking.
tifact of the self-correlation effects raised by Hicks (1981) The φw data, on the other hand, show the opposite trend
(see Pahlow et al., 2001). Even though we are dealing with (they fall below the corresponding MOST function for the
unstableconditions,weappliedtherandomizationprocedure surface sublayer), with much less scatter than in the scalar
recommendedbyAndreasandHicks(2002)totestforpos- case.
sibleself-correlationeffects.
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11356 E.Zahnetal.:ScalarturbulentbehaviorintheroughnesssublayerofanAmazonianforest
100 100
(a) (b)
10 10
u∗ θ|∗
σ/w 1 σ/θ|1
0.1 0.1
0.0010.01 0.1 1 10 100 1000 0.0010.01 0.1 1 10 100 1000
ζ ζ
− −
100 100
(c) (d)
10 10
c|∗ q|∗
/| /|
σc 1 σq 1
0.1 0.1
0.0010.01 0.1 1 10 100 1000 0.0010.01 0.1 1 10 100 1000
ζ ζ
− −
Figure4.Dimensionlessstandarddeviationforverticalvelocity(a),temperature(b),CO2(c),andwatervapor(d):39.4m.
100 100
(a) (b)
10 10
u∗ θ|∗
σ/w 1 σ/θ|1
0.1 0.1
0.0010.01 0.1 1 10 100 1000 0.0010.01 0.1 1 10 100 1000
ζ ζ
− −
100 100
(c) (d)
10 10
c|∗ q|∗
/| /|
σc 1 σq 1
0.1 0.1
0.0010.01 0.1 1 10 100 1000 0.0010.01 0.1 1 10 100 1000
ζ ζ
− −
Figure5.Dimensionlessstandarddeviationforverticalvelocity(a),temperature(b),CO2(c),andwatervapor(d):81.6m.
NotethatthisRSL“excessvariance”(incomparisonwith how deep light penetrates into the canopy. Therefore, the
MOSTpredictions)doesnotimpactthefluxes(Katuletal., zenith angle is an obvious candidate as a possible effect on
1995);itdoeshowevermakehypotheticalfluxestimateswith scalar transfer between the canopy and the atmosphere. In
the flux-variance method much more uncertain in the RSL the following, we redo the φa analysis for three different
(Diasetal.,2009).Inthenextsection,weshowthatthiscan classesofzenithangle(whichwerefoundbytrialanderror
bereducedsignificantlybytakingintoaccountthezenithan- toproducebestresultsforthecentralclass):0◦<|Z|≤20◦,
gle. 20◦<|Z|≤60◦,and60◦<|Z|≤90◦.
In Fig. 6 (for the 39.4m level), there is considerable im-
5.2 Zenithangleinfluence provementinthesimilarityrelationshipsforallscalarswhen
the sun is high in the 0◦<|Z|≤20◦ class of central zenith
It is known that the zenith angle (Z) can influence transfer
angles. Results are better for temperature than for CO and
2
characteristics between a vegetated surface and the atmo-
H O,butthismayberelatedtointrinsicdifficultiesofmea-
2
sphere, e.g., the scalar roughness length (Sugita and Brut-
suring the latter: dust and vapor condensation on the IRGA
saert,1996).Iwataetal.(2010)notethat,abovetallvegeta-
mirrorsurfacesandtheeffectsofsensorseparationarepossi-
tion,theverticaldistributionofsourcesandsinksofscalars
can vary both seasonally and during the day, depending on
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E.Zahnetal.:ScalarturbulentbehaviorintheroughnesssublayerofanAmazonianforest 11357
0 < Z 20 20 < Z 60 60 < Z 90
◦ ◦ ◦ ◦ ◦ ◦
| |≤ | |≤ | |≤
100 100 100
10 10 10
u∗ u∗ u∗
/ / /
w w w
σ 1 σ 1 σ 1
0.1 0.1 0.1
0.0010.01 0.1 1 10 100 1000 0.0010.01 0.1 1 10 100 1000 0.0010.01 0.1 1 10 100 1000
ζ ζ ζ
− − −
100 100 100
10 10 10
θ|∗ θ|∗ θ|∗
/| /| /|
σθ 1 σθ 1 σθ 1
0.1 0.1 0.1
0.0010.01 0.1 1 10 100 1000 0.0010.01 0.1 1 10 100 1000 0.0010.01 0.1 1 10 100 1000
ζ ζ ζ
− − −
100 100 100
10 10 10
c|∗ c|∗ c|∗
/| /| /|
σc 1 σc 1 σc 1
0.1 0.1 0.1
0.0010.01 0.1 1 10 100 1000 0.0010.01 0.1 1 10 100 1000 0.0010.01 0.1 1 10 100 1000
ζ ζ ζ
− − −
100 100 100
10 10 10
q|∗ q|∗ q|∗
/| /| /|
σq 1 σq 1 σq 1
0.1 0.1 0.1
0.0010.01 0.1 1 10 100 1000 0.0010.01 0.1 1 10 100 1000 0.0010.01 0.1 1 10 100 1000
ζ ζ ζ
− − −
Figure 6. Dimensionless standard deviation with solar angle: 39.4m. First row shows the velocity similarity function, the second shows
temperaturefunction,andthethirdandfourthshowCO2andwatervapor,respectively.
blecauses(Tsaietal.,2012).Similarresultswerefoundfor possible.Oneisverticalheterogeneityofsourcesandsinks,
the81.6mlevel. such as highlighted by Tsai et al. (2012): obviously, these
Theseresultsareencouraging:atleastinthehoursaround sourcesandsinksmaybemoreheterogeneousinthevertical
noon, similarity relationships as good as those observed in under lower sunlight penetration. Horizontal heterogeneity,
the surface layer over low vegetation can be obtained. This ontheotherhand,mayalsobeplayingarole:thevegetation
opens up the possibility of retrieving fluxes, by means of a heightisnotuniform,andapatchworkofshadedregionsis
hostofstandardMOSTmethodsforthesehoursoftheday. clearlyvisible,fromthetower,athighervaluesofthezenith
The results also require explanation. It is not immediately angle. This may be enough to “activate–deactivate” sources
clear why these low zenith angles produce best results, but of heat, CO , and H O at the nominal source level z−d,
2 2
at least two (entirely phenomenological) explanations seem producingwhatiseffectivelyanonhomogeneoushorizontal
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11358 E.Zahnetal.:ScalarturbulentbehaviorintheroughnesssublayerofanAmazonianforest
2 2 2
(a) (b) (c)
1 1 1
eθc 0 eθq 0 eqc 0
rt rt rt
-1 -1 -1
-2 -2 -2
0.01 0.1 1 10 100 0.01 0.1 1 10 100 0.01 0.1 1 10 100
ζ ζ ζ
− − −
1 1 1
(d) (e) (f)
0.8 0.8 0.8
eθc0.6 eθq0.6 eqc0.6
st 0.4 st 0.4 st 0.4
0.2 0.2 0.2
0 0 0
0.01 0.1 1 10 100 0.01 0.1 1 10 100 0.01 0.1 1 10 100
ζ ζ ζ
− − −
Figure7.Scalarfluxsimilarityindicesrte(above)andste(below)for0◦<|Z|≤20◦:θ−c(a,d);θ−q(b,e);andq−c(c,f).Forrte,some
datapointswereoffthescale.
2 2 2
(a) (b) (c)
1 1 1
eθc 0 eθq 0 eqc 0
rt rt rt
-1 -1 -1
-2 -2 -2
0.01 0.1 1 10 100 0.01 0.1 1 10 100 0.01 0.1 1 10 100
ζ ζ ζ
− − −
1 1 1
(d) (e) (f)
0.8 0.8 0.8
eθc0.6 eθq0.6 eqc0.6
st 0.4 st 0.4 st 0.4
0.2 0.2 0.2
0 0 0
0.01 0.1 1 10 100 0.01 0.1 1 10 100 0.01 0.1 1 10 100
ζ ζ ζ
− − −
Figure8.Scalarfluxsimilarityindicesrte(above)andste(below)for20◦<|Z|≤60◦:θ–c(a,d);θ–q (b,e);andq–c(c,f).Forrte,some
datapointswereoffthescale.
surfacewithlocaladvectioneffects,whichmaybeveryhard theremaybeaconnectionbetweentheresultsofDettoetal.
toidentifywithstandardtechniques. (2010) and ours. Unfortunately, concurrent good mean pro-
Stillwithrespecttoourresultsforthezenithangle,itisim- fileandturbulencedatawerenotavailableinourdataset,pre-
portant to mention that similar effects were found by Detto cludingfurtheranalyses.
et al. (2010) with regard to the storage term z∂s, where s
∂t
isthescalar’sconcentration.Theyfoundthatforsmallstor-
age,oftheorderof0.5%ofthescalarflux,thescatterinthe
φθ,q,c,m (wheremisformethane)wasconsiderablysmaller
thanunderotherconditions.Moreover,largerstorageswere
observed around sunset and sunrise (note that this will cor-
respondtolarger(absolute-value)zenithangles).Therefore,
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