on long-term variation of wind statistics long-term variation of wave statistics ” : estimationbased Addendum to “ Sea spray aerosol fl ux estimation basedon ScienceDirect

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Addendum to “Sea spray aerosol flux estimation based on long-term variation of wave statistics ”: estimation based on long-term variation of wind statistics ^§

Dag Myrhaug * , Hong Wang, Lars Erik Holmedal

DepartmentofMarineTechnology,NorwegianUniversityofScienceandTechnology(NTNU),Trondheim,Norway

Received1July2015;accepted27November2015 Availableonline23December2015

1. Introduction

Myrhaug et al. (2015) (hereafter referred to as MWH15) providedestimatesofthemeanseasprayaerosolfluxbased onlong-termvariationofwavestatisticsusingthewhitecap method applying thelimitingsteepnessandthreshold ver- ticalaccelerationcriteria.Herethelong-termwavestatistics representedopenoceandeepwaterwavesintheNorthern NorthSeaandtheNorthAtlantic.Thisnoteissupplementary to MWH15 with the purpose of demonstratinghow similar resultsforthemeanseasprayaerosolfluxcanbeobtainedby usingestimatesofthewhitecapcoveragebasedonlong-term variationofwindstatistics.Moreover,thewhitecapmethod used inMWH15hasbeenreplaced bytheCallaghan(2013) improvedseasprayaerosolproductionfluxmodel.

Thewhitecapcoverage,whichisdefinedasthearea of whitecaps per unit sea surface, has often been used to Oceanologia(2016)58,150—153

KEYWORDS

Seasprayaerosolflux;

Whitecapcoverage;

Meanwindspeed;

Windstatistics

Summary Thisnoteprovidesestimatesofthemeanwhitecapcoverageandthemeanseaspray aerosolfluxbasedonlong-termwindstatisticsfromtheNorthernNorthSea.Heretheimproved seasprayaerosolproductionfluxmodelbyCallaghan(2013)isused.Theresultsarecompared withthoseinMyrhaugetal.(2015)basedonlong-termwavestatisticsfromtheNorthernNorth SeaandtheNorthAtlantic.

#2016InstituteofOceanologyofthePolishAcademyofSciences.Production andhostingby Elsevier Sp. z o.o. This is an open access article under the CC BY-NC-ND license (http://

creativecommons.org/licenses/by-nc-nd/4.0/).

DOI of original article: http://dx.doi.org/10.1016/j.

oceano.2015.04.001.

PeerreviewundertheresponsibilityofInstituteofOceanologyofthe PolishAcademyofSciences.

§This work was carried out as a part ofthe project “Air-Sea Interaction and Transport Mechanisms in the Ocean” funded by theNorwegianResearchCouncil(221988).Thissupportisgratefully acknowledged.

* Correspondingauthorat:DepartmentofMarineTechnology,Nor- wegianUniversityofScienceandTechnology(NTNU),OttoNielsens vei10,NO-7491Trondheim,Norway.Tel.:+4773595527;fax:+4773 595528.

E-mailaddresses:dag.myrhaug@ntnu.no(D.Myrhaug), hong.wang@ntnu.no(H.Wang),

lars.erik.holmedal@ntnu.no(L.E.Holmedal).

Availableonlineatwww.sciencedirect.com

ScienceDirect

j o ur nal h o m ep a ge: w ww.e ls e vi e r.c o m /l o c at e/ o c ea no

http://dx.doi.org/10.1016/j.oceano.2015.11.003

0078-3234/#2016InstituteofOceanologyofthePolishAcademyofSciences.ProductionandhostingbyElsevierSp.zo.o.Thisisanopen accessarticleundertheCCBY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.0/).

quantifytheoccurrenceofbreakingwindwavesatsea.There aremanyparameterizationsofwhitecapcoverageavailable intheliterature;comprehensivereviewsaregiveninAngu- elovaandWebster(2006),Massel(2007)anddeLeeuwetal.

(2011).ParameterizationsarebasedonU10andu*.HereU10

[ms
¹]isthemeanwindspeedatthe10melevation,andu*

[ms
¹]isthefrictionvelocityequaltothesquarerootofthe vertical flux of horizontal momentum at the sea surface.

However, when plottingthe whitecapcoverage versus U10

andversusu*itisoftenfoundthatthedatascatterislarger whenplottedversusu*thanwhenplottedversusU10(seee.g.

Sugiharaetal.,2007).Thisisattributedtothelargeruncer- taintiesinestimatingu*thanmeasuringU10.Thereforethe parameterizations in the present study are based on U10.Otherimportantfactorsaffectingthewhitecapcoverage arethestratificationofthenear-surfaceairboundarylayer and the state of development of surfacewaves, see e.g.

Sugihara et al. (2007) and Myrhaug and Holmedal (2008).Reviews ofwhitecapcoverageatseaandhowit is linked to marine aerosol production are given by Massel (2007),deLeeuwetal.(2011)andCallaghan(2013).

2. Whitecap coverage and sea spray aerosol flux estimation based on long-term variation of wind statistics

2.1. Whitecapcoverageestimation

Thefollowingwhitecapcoverage(Wc)parameterizationswill beconsideredheretodemonstratetheuseofwavestatistics.

The Monahan and O'Muircheartaigh (1980) (hereafter referred to as MO80) parameterization is widely used and recognized(deLeeuwetal.,2011),givenasfraction,

Wc¼3:8410
⁶U^3:41₁₀ : (1)

The Callaghanetal. (2008)(hereafterreferredto as C08) parameterizationisbasedondatacollectedintheNorthEast Atlanticinsideageographicalareadefinedby9.58W,138W, 55.58Nand57.58N,giveninpercent,

Wc¼0:00318ðU10
3:70Þ³; 3:70ms
¹<U10<10:18ms
¹ Wc¼0:000482ðU10þ1:98Þ³;10:18ms
¹<U10<23:09ms
¹:

(2) It should be noted that the wave statistics in BGGS07 (Bitner-GregersenandGuedesSoares,2007)DataSets1to 5usedinMWH15isfromthesameoceanarea,i.e.fromthe NorthAtlantic.

According to Eqs. (1) and (2) the whitecap coverage isgivenfor aknown valueof U10.Thelong-term variation of the whitecap coveragecan be obtainedfrom available wind statistics, i.e. from long-term distributions of U10. Differentparametricmodelsforthecumulativedistribution function(cdf)or the probabilitydensity function(pdf) of U10are givenintheliterature.Arecentreview isgivenin Bitner-Gregersen (2015), where the joint statistics of U10

withsignificantwaveheightHsandspectralpeakperiodTp

arepresented.Inthepresentarticlethelong-termstatistics of Wc are exemplified by using the cdf of U10 given by Johannessenetal.(2001),wherewindmeasurementscover- ingthe years1973—1999 fromthe NorthernNorth Seaare

used as a database. This database consists of composite measurementsfromtheBrent,Troll,StatfjordandGullfaks fieldsaswellastheweathershipStevenson.Modeldatafrom the Norwegian hindcast archive (WINCH, gridpoint 1415) havebeen filledin forperiodswheremeasureddata were missing.Thusa25-yearlongcontinuoustimeserieshasbeen used(seeJohannessenetal.(2001)formoredetails),upon whichthecdfofthe1-hvaluesofU10isdescribedbythetwo- parameterWeibullmodel

PðU10Þ¼1
exp
U10

a

_b

" #

; U100; (3)

withtheWeibullparameters

a¼8:426; b¼1:708: (4)

It should be noted that the wave statistics in MGAU05 (Moanetal.,2005)usedinMWH15isfromthesameocean areaasthewindstatistics,i.e.fromtheNorthernNorthSea.

Ifx=U10 is defined for x1xx2, then x follows the truncatedWeibullcdfgivenby

PðxÞ¼ exph
^x_a¹_bi

exph
^x_a_bi exph
^x_a¹_bi

exph
^x_a²_bi ; x1xx2: (5) Nowthelong-termstatisticsofWccanbederivedbyusing thiscdf of x=U10.A statisticalquantity ofinterest isthe expected(mean)valueofWcgivenas

E½WcðxÞ¼ Z ₁

0

WcðxÞpðxÞdx; (6)

wherep(x)istheprobabilitydensityfunction(pdf)ofx=U10

givenbyp(x)=dP(x)/dxwhereP(x)isgiveninEq.(5).Then theintegralinEq.(6)canbecalculatedanalyticallybyusing theresultsin Abramowitz andStegun (1972, Chs. 6.5 and 26.4)

E½xⁿ¼ Z _x2

x₁

xⁿpðxÞdx

¼aⁿ

N G 1þn b; x1

a

 b



G 1þn b; x2

a

 b



; (7)

N¼exp
x1

a

 b



exp
x2

a

 b



; (8)

whereG(s,t)istheincompletegammafunction,andnisa realnumber(notnecessarilyaninteger).Itshouldbenoted that G(s, 0)=G(s) where G is the gamma function, and G(s, 1)=0.Here theresults are exemplified byusing the parameterizationsofWcinEqs.(1)and(2).Theresultsare

MO80: E½Wc¼1:10%; (9)

C08: E½Wc¼0:76%: (10)

TheestimateinEq.(9)isobtainedbyintegratingfromzeroto infinity,whiletheestimateinEq. (10)isobtainedbyinte- gratingfromx1=U10=3.70ms
¹toinfinity,i.e.givinga6%

largervaluethanbyintegratingtox2=U10=23.09ms
¹. The corresponding results obtainedin MWH15(see the resultsfortheMGAU05data(Northern NorthSea)andthe

Seasprayaerosolfluxestimation 151

BGGS07 Data Sets 1 to 5 (North Atlantic) in Table 5) are denotedasE[Fcov]byusingthelimitingsteepnesscriterion (Criterion1)andthethresholdverticalaccelerationcriterion (Criterion2).Itappearsthatsomeoftheexampleestimates based on the wind statistics agree well with some of the estimatesbasedonthewavestatistics,i.e.(1)theMO80wind statisticsestimateof1.1%agreeswellwiththemeanvalueof theestimatecorrespondingtoBGGS07DataSets1to5using Criterion2of1.2%;(2)theC08wind statisticsestimateof 0.76% agrees well with the estimate corresponding to MGAU05 using Criterion 1 of 0.77% (which is larger than theestimateusingCriterion2of0.58%).

2.2. Sea sprayaerosol fluxestimation

RatherthanpursuingthemethodusedinMWH15,arecent improved method given by Callaghan (2013) (hereafter referredto as C13)willbeused. Thus, followingC13, Eq.

(1)inMWH15should berewrittentoexplicitly includethe timescaleofthedecayingwhitecapareaas(i.e.usingthe notationinC13bytakinglogrlog10randrr80)

dFðrÞ

dðlogrÞ¼ dEðrÞ dðlogrÞWc

t : (11)

Herethetermonthelefthandsideoftheequationisthe numberofparticlesproducedperunitoceansurfaceareaand unittimeperradiussizebin.Thefirsttermontherighthand sideoftheequationisthenumberofparticlesproducedper whitecapareaperradiussizebin,Wcisthewhitecapperunit oceansurfacearea,andtisacharacteristicwhitecaptime scalewhichcannotbeincorporatedinthefirsttermonthe righthandsideoftheequationtoproduceanestimateofthe rate of particle production per whitecap area. Here the dropletradiusr is takento representr80, i.e.the droplet radiusinequilibriumwiththeatmosphereatagivenambient relativehumidity of80%. Moreover,followingC13 thefirst termontherighthandsideofEq.(11)isgivenby

dEðrÞ

dðlogrÞ¼29419rð1þ0:057r^3:45Þ

exp 3:68exp½
5:33ð0:433
logrÞ²

4:7lnr½1þQr
^0:017r
1:44

( )

; (12)

withtheunitm
²,whereQisanadjustableparameterwith 30asatypicallyassignedvalue.Thewhitecapcoveragein%is giveninEq.(2)(seeC13formoredetails).

Nowitfollowsthat dFðrÞ

dr ¼ r
¹ ln10

dFðrÞ

dðlogrÞ; (13)

withtheunitm
²s
¹mm,andconsequentlythetotalfluxfor particleswithradiiintheintervalr1tor2is

FðrÞ¼ Z _r2

r1

r
¹ ln10

dFðrÞ

dðlogrÞdr; (14)

with the unitm
²s
¹. The volume flux with unitms
¹ is obtainedbymultiplyingEq.(14)bythefactor(4p/3)r³.

Thetotalexpectedvolumeaerosolfluxofr=r80,E[F(r)], cannowbeestimatedbasedonthelong-termwindstatistics usedinSection2.1.Theresultsareobtainedbymultiplying Eq. (14) with E[Wc]=0.76% from Eq. (10) anddividing by

t=5.3s(seeC13).Byintegratingr=r80overtherange0.8—

10mm(asinMWH15)theresultis

E½FðrÞ¼0:8310
¹²ms
¹: (15)

ThecorrespondingresultsobtainedinMWH15byusingCrite- ria 1 and 2 (see the results for E½f_vol^ðtotÞ corresponding to MGAU05 in Table 4) are 15.310
¹²ms
¹ and 11.510
¹²ms
¹, respectively. The mean values corre- sponding to BGGS07 Data Sets 1 to 5 are 34.210
¹² ms
¹and23.910
¹²ms
¹,respectively.Thus,itappears thatthepresentresultinEq.(15)issignificantlylowerthan thoseobtainedinMWH15.Thisismainlyduetotheinherent featuresoftheimprovedseasprayaerosolproductionflux modelbyC13.

3. Summary

Estimate of thelong-term seaspray aerosol fluxbased on long-term variation of wind statistics from the Northern North Seais providedby adoptingtheimproved Callaghan (2013)model.Overall,someoftheexampleestimatesofthe meanwhitecapcoveragebasedonthewindstatisticsagree withthoseobtainedinMyrhaugetal.(2015)basedonwave statistics.However,thetotalmeanvolumeaerosolfluxbased on the improved Callaghan (2013) give significantly lower valuethanthoseobtainedinMyrhaugetal.(2015),whichis mainlyduetotheinherentfeaturesofthefirstmodel.

Overall, this work provides a procedure which can be applied to calculate the whitecapcoverageand seaspray aerosolfluxbasedonlong-termstatisticalinformationofthe windclimate.

Acknowledgement

Ananonymousreviewerisacknowledgedforathoroughand constructivereviewofthefirstversionofthepaper.

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