Computtion nd Modeling of the Air-e et nd Momentum Fluxes By Dr. Nsser. Zker ICTP June 00
1 Introduction The ocen receives energy through the ir-se interfce by exchnge of momentum nd het. The turbulent momentum flux is the source of the wind driven circultion of the ocen, smller scle circultion, mixed lter development nd wve genertion. The trnsfer of het cross the ir-se interfce determines the distribution of temperture in the ocen nd without such trnsfer there world be no vritions in the ocen temperture (except from compression) nd tht prt of the ocen circultion drives by temperture density vritions would be bsent. The turbulent fluxes of het, globlly verged, re the lrgest contributions to the het loss of the ocen. Ocen-tmosphere fluxes estblish the link between ocen-surfce temperture chnges nd tmospheric circultion vribility. On the other hnd, they provide the mechnism of by which ocen vribility is forced by the tmosphere. Thus ccurte knowledge of the flux vribility is extremely importnt for understnding climtologicl nd ocenic vritions in the coupled ocen-tmosphere system (Pickrd nd Emery, 1990) There re mny requirements for surfce flux vlues, for exmple, opertionl modelling, nowcsting nd forecsting; climte chnge studies; tmospheric nd ocenic synoptic scle studies; shelf nd costl se studies; ocenic, climte nd erth observing systems; wve forecsting; mrine engineering, etc (Tylor et l., 000). Momentum is trnsferred from the tmosphere to the ocen in the turbulent sher flow t the tmospheric boundry lyer ner the se surfce. The momentum flux is expressed s wind stress _ cting on the se surfce. Turbulent trnsfer of het nd moisture between the tmosphere nd the ocen is due to the temperture nd humidity grdients ner the se surfce. The net het exchnge t the surfce cn be divided into four most effective terms: + + + (1) s b Where is the net incoming short-wve rdition, s b is the net long-wve rdition, nd re the turbulent fluxes of sensible nd ltent het, respectively.
Incoming solr rdition The min source of het flux through the se surfce is incoming solr rdition received either directly or by reflection nd scttering from the clouds nd the tmosphere. The rte t which short-wve solr energy enters the se,,, depends upon number of fctors including: the length of the dy, bsorption in the tmosphere, the sun ltitude, the cloud cover nd the reflection t the se surfce. ong-wve rdition b The bck rdition term b is the net mount of energy lost by the se s long-wve rdition. The vlue of this term is ctully the difference between the energy rdition outwrd from the se surfce in proportion to the fourth power of its bsolute temperture nd tht received by the se from the tmosphere which lso rdites t rte proportionl to the fourth power of its bsolute temperture. The outwrd rdition from the se is lwys greter thn the inwrd rdition from the tmosphere nd so presents loss of energy from the se. b lwys tent het flux The most significnt prt in terms of het trnsfer from the se to the tmosphere is The rte of het loss is the equl to the rte of vporiztion times ltent het of evportion. where cn be computed by ppliction of formul of the type K e is diffusion coefficient for wter vpor nd vpor concentrtion in the ir bove the se surfce. de / dz K d dz, e e / is the grdient of wter et conduction ensible het flux is due to the temperture grdient in the ir bove the se. The het my be lost or gined from the se surfce into the tmosphere. The rte of loss or gin of het is proportionl to the temperture grdient, het conductivity nd the specific het of ir t constnt pressure. In this cse convection will ply role in ssisting the het
loss from the ocen in times of wrmer ocen surfce temperture. The se on the whole is wrmer thn the ir djcent to it nd therefore, is het loss. Rditive fluxes -1 Direct mesurement of rditive fluxes Direct mesurement of the ir-se fluxes trditionlly is best provided by the pyrnometer for short wve rdition nd the pyrgeometer for long wve rdition. Both re similr in form nd fce prticulr problems in use t se including contmintion by slt, nd especilly motion of the ship or buoy t se. With the new knowledge nd technology, sophisticted rdition instruments for mesuring the rditive fluxes re rpidly developing. owever, the direct mesurement of the ir-se fluxes re too few to contribute directly to the clcultion of lrge scle flux fields nd they re used for developing, clibrting, nd verifying the prmeteriztion formul used to estimte the fluxes from the bsic vribles (Tylor et l., 000). - Prmeteriztion of rditive fluxes --1 Prmeteriztion of short wve rditive flux hort wve rdition flux on the se surfce in generl my be prmeterize s: T () f top where top is the short wve rdition t the top of the tmosphere, equl to r0 I 0 cos( z) r where I 0 is the solr constnt, r is the Erth-un distnce, r 0 is the men Erth-un distnce nd Z is the Zenit ngle of Erth. T f represents the frction of the solr rdition t the top of the tmosphere tht reches the open surfce. T f is prmeterized in terms of cloud cover nd thermodynmic prmeters of the tmosphere. It is preferble tht T f be divided into two terms. One represents the modifiction of short wve rdition under cler sky condition (stronomy, temperture, humidity nd erosols) nd the other the cloud modifiction of the cler sky rdition. In this cse, the generl formul for short wve rdition becomes 0T f ' where 0 is solr rdition 4
t the se surfce under cler sky nd is ssumed to be function of the stronomy nd of the trnsmission for the cler sky tmosphere. T ' f is the empiricl function of the frctionl cloud cover, ir temperture, nd solr ltitude. Reed (1977) formule for the dily men net shortwve flux using the clculted men vlues for the frctionl cloud cover n, nd the noon solr elevtion in degree, is presented s: 0 (1 Cnn +.0019 )(1 ) where C n 0.6 the cloud ttenution fctor, nd is the lbedo. 0 is the short wve insoltion t the surfce under cler skies. -- Prmeteriztion of long wve rditive flux The mount of long wve flux is dependent to the surfce wter temperture, tmosphere temperture, humidity nd cloud cover. For exmple (Clrk et l, 1974) W T 4 (09 0.05 e () )(1 T ) Where 0.98, is the tefn-boltzmn constnt, e is the wter vpor pressure, n the frctionl cloud cover, nd T nd T s re the ir nd se tempertures in K. The cloud cover coefficient vries with ltitude. 0.5 n ) + 4 T ( T -- Rditive Fluxes by Remote ensing The determintion of the short wve nd long wve fluxes from stellite dt involves mesuring the rditive fluxes t the top of the tmosphere nd ccounting for the effects of the tmosphere using rditive trnsfer model. The problem is llowing for the effects of clouds. It hs been proved esier to model the scttering nd bsorption of short wve rditions thn long wve rdition.the problem for long wve mesurement is tht the surfce budget is dependent on the height of the lowest cloud, quntity not esily determined by stellite. The different lgorithms differ in the cloud informtion used nd the sophistiction of the RTM. While vrious methods hve been proposed tht use the nrrow bnd (visible) stellite rdinces directly together with n RTM (Pinker nd szlo, 199) 5
Turbulent fluxes Exchnge between the tmosphere nd ocen re most esily mesured in the tmospheric surfce lyer where the fluctuting verticl velocity trnsports fluid properties up nd down (rge nd Pond, 198). Turbulent fluxes of momentum nd het cn be defined by norml Reynolds verges. (4) u' C p e t' q' is Wind stress ensible het flux tent het flux, u horizontl wind verticl wind, temperture, nd specific humidity het of ir e tent het of vporiztion ',, t', q' Air temperture re Turbulent fluctutions C pecific p Using Monin-Obukhov similrity theory Wind stress ensible et (5) tent et u' u C t' p e q' C t p e q u u where her velocity (6) u 1/ ( ) u' 1/ -1 Direct mesurement of turbulent fluxes The most direct flux mesurement is the Reynolds flux method or eddy correltion method. Integrtion of the u, w cospectrum Φ ( f ) over ll contributing frequencies f gives the covrince nd hence momentum flux. The limittion in the extend of the mesurement time nd lrge mount of dt required, nd the sensitivity of the method to u' 6
instrument orienttion, which is gret problem on ships nd buoys, re disdvntge of this method. Although the Reynolds flux method is not esily pplicble to remote open se opertion, it hs become the stndrd to which the other methods re compred (rge, nd Pond, 198). - Prmeteriztion of turbulent fluxes For mny resons the expressions of turbulent fluxes bsed on turbulent fluctution products re not very useful, nd bulk expressions relting the fluxes to more esy mesurble tmospheric vribles hve been developed (mith et l, 1996). In this method the turbulent fluxes re determined from formule using the bsic vribles such s wind speed, ir temperture, etc. The sme bulk formul re pplicble whether the bsic vribles hve been oriented by in situ mesurements or by remote sensing or hve been clculted by numericl tmosphere model. The prmeterized bulk formul for momentum nd het fluxes would be presented s follows: (7) CE u z ( qz q0 ) e Where C D (drg coefficient), C (tnton number), nd C E (Dlton Number) re trnsfer coefficients. The trnsfer coefficients hve been trditionlly obtined by mesuring the surfce fluxes, using one of severl techniques, together with mesurement of the men physicl vribles required. CD u C z C u p z ( t z t 0 ) For wind stress, the drg coefficient vlues used in mny pst studies were those obtined by rge nd Pond (1981, 198) or mith (1980, 1988). For 10m wind speeds u 10 less thn 10 m/s they found constnt vlue ( 10 1.1 ± 0.), nd for u 10 between 10 nd 5 m/s suggest CD 10 n liner increse given by ( 10 0.49 + 0.065 u 10 ) Other schemes suggest liner reltion CD 10 n over the entire rnge of vlidity; Grrtt (1977) gives ( 10 0.75 + 0.067 u 10 for wind from CD 10 n 4-1 m/s nd mith (1980) gives ( 10 CD 10 n 0.61 + 0.06 u 10 ) from 6- m/s (Figure 1). 7
Figure 1: Exmples for the Drg Coefficient, C 10 plotted s function of wind speed, D n U10n -4 Trnsfer Coefficient for ensible nd tent et Unlike the drg coefficient, trditionl estimtes of CE 10n nd C 10n over the ocen tend to support firly constnt vlue over wide rnge of wind speed. Friehe nd chmitt (1976) recommend constnt Dlton number (10 C E10n 1. ± 0.07) on the bsis of severl turbulence-bsed dtsets where the highest wind speed ws 4 m/s. After criticl ssessment of previous studies, mith (1989) lso suggested constnt consensus vlue (10 C E10n 1. ± 0.1) for winds between 4 nd 14 ms-1. DeCosmo et l.(1996) lso suggest ner constnt vlue with (10 CE10n, 1.1 ± 0.4 ) for winds up to 18 m/s. For the tnton number, Friehe nd chmitt (1976) obtined slightly different vlues for unstble nd stble conditions (10 C 10n 0.97 nd 0.86 respectively. mith (1988) suggested 10 1.0. CE 10 n 8
4 References Clrk, N.E., R. M.Eber, J.A.Renner nd J.F.T.ur, 1974: et exchnge between ocen nd tmosphere in the estern North Pcific for 196-71. NOAA Tech.Rep. NMF RF-68, U..Dept.Commerce, Wsh.,D.C. Friehe, C.A. nd K.B. chmitt, (1976): Prmeteriztion of ir-se interfce fluxes of sensible het nd moisture by the bulk erodynmic formuls. J. Phys. Ocenog., 6, 801-809. Pickrd, G.. nd Emery, W.J. (198) Descriptive physicl Ocenogrphy. Pergmon Press, Fifth Edition. Reed, R.K., 1977: On estimting insoltion over the ocen. J. Phys. Ocen., 7, 48-485. effects. J. Climte,, 104-15. mith,.d. Firll, C.W., Geernert, G.. nd sse,. (1996) Air-e Fluxes: 5 Yers of Progress. Boundry-yer Meteorl., 78, 47-90 mith,. D., 1989: Coefficients for se surfce wind stress, het flux, nd wind profiles s function of wind speed nd temperture. J. Geophys. Res., 9,15467-1547. mith,. D., 1980: Wind stress nd het flux over the ocen in gle force winds. J. Phys. Ocenog., 10, 709-76. Tylor, P.K.(Editor), (000), Intercomprison nd Vlidtion OF Ocen-Atmosphere energy flux field 9