#include "cppdefs.h" MODULE bulk_flux_mod #ifdef BULK_FLUXES ! !svn $Id$ !================================================== Hernan G. Arango === ! Copyright (c) 2002-2009 The ROMS/TOMS Group ! ! Licensed under a MIT/X style license ! ! See License_ROMS.txt ! !======================================================================= ! ! ! This routine computes the bulk parameterization of surface wind ! ! stress and surface net heat fluxes. ! ! ! ! References: ! ! ! ! Fairall, C.W., E.F. Bradley, D.P. Rogers, J.B. Edson and G.S. ! ! Young, 1996: Bulk parameterization of air-sea fluxes for ! ! tropical ocean-global atmosphere Coupled-Ocean Atmosphere ! ! Response Experiment, JGR, 101, 3747-3764. ! ! ! ! Fairall, C.W., E.F. Bradley, J.S. Godfrey, G.A. Wick, J.B. ! ! Edson, and G.S. Young, 1996: Cool-skin and warm-layer ! ! effects on sea surface temperature, JGR, 101, 1295-1308. ! ! ! ! Liu, W.T., K.B. Katsaros, and J.A. Businger, 1979: Bulk ! ! parameterization of the air-sea exchange of heat and ! ! water vapor including the molecular constraints at ! ! the interface, J. Atmos. Sci, 36, 1722-1735. ! ! ! ! Adapted from COARE code written originally by David Rutgers and ! ! Frank Bradley. ! ! ! ! EMINUSP option for equivalent salt fluxes added by Paul Goodman ! ! (10/2004). ! ! ! ! Modified by Kate Hedstrom for COARE version 3.0 (03/2005). ! ! Modified by Jim Edson to correct specific hunidities. ! ! ! ! Reference: ! ! ! ! Fairall et al., 2003: J. Climate, 16, 571-591. ! ! ! ! Taylor, P. K., and M. A. Yelland, 2001: The dependence of sea ! ! surface roughness on the height and steepness of the waves. ! ! J. Phys. Oceanogr., 31, 572-590. ! ! ! ! Oost, W. A., G. J. Komen, C. M. J. Jacobs, and C. van Oort, 2002:! ! New evidence for a relation between wind stress and wave age ! ! from measurements during ASGAMAGE. Bound.-Layer Meteor., 103, ! ! 409-438. ! ! ! !======================================================================= ! implicit none PRIVATE PUBLIC :: bulk_flux, bulk_psiu, bulk_psit CONTAINS ! !*********************************************************************** SUBROUTINE bulk_flux (ng, tile) !*********************************************************************** ! USE mod_param USE mod_forces USE mod_grid USE mod_mixing USE mod_ocean USE mod_stepping ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile ! ! Local variable declarations. ! # include "tile.h" ! # ifdef PROFILE CALL wclock_on (ng, iNLM, 17) # endif CALL bulk_flux_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & nrhs(ng), & # ifdef MASKING & GRID(ng) % rmask, & & GRID(ng) % umask, & & GRID(ng) % vmask, & # endif & MIXING(ng) % alpha, & & MIXING(ng) % beta, & & OCEAN(ng) % rho, & & OCEAN(ng) % t, & & FORCES(ng) % Hair, & & FORCES(ng) % Pair, & & FORCES(ng) % Tair, & & FORCES(ng) % Uwind, & & FORCES(ng) % Vwind, & # ifdef CLOUDS & FORCES(ng) % cloud, & # endif # ifdef COARE_TAYLOR_YELLAND & FORCES(ng) % Hwave, & # endif # if defined COARE_TAYLOR_YELLAND || defined COARE_OOST & FORCES(ng) % Pwave_top, & # endif # if !defined DEEPWATER_WAVES && \ (defined COARE_TAYLOR_YELLAND || defined COARE_OOST) & FORCES(ng) % Lwave, & # endif & FORCES(ng) % rain, & & FORCES(ng) % lhflx, & & FORCES(ng) % lrflx, & & FORCES(ng) % shflx, & & FORCES(ng) % srflx, & & FORCES(ng) % stflx, & # ifdef EMINUSP & FORCES(ng) % EminusP, & & FORCES(ng) % evap, & # endif & FORCES(ng) % sustr, & & FORCES(ng) % svstr) # ifdef PROFILE CALL wclock_off (ng, iNLM, 17) # endif RETURN END SUBROUTINE bulk_flux ! !*********************************************************************** SUBROUTINE bulk_flux_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & nrhs, & # ifdef MASKING & rmask, umask, vmask, & # endif & alpha, beta, rho, t, & & Hair, Pair, Tair, Uwind, Vwind, & # ifdef CLOUDS & cloud, & # endif # ifdef COARE_TAYLOR_YELLAND & Hwave, & # endif # if defined COARE_TAYLOR_YELLAND || defined COARE_OOST & Pwave_top, & # endif # if !defined DEEPWATER_WAVES && \ (defined COARE_TAYLOR_YELLAND || defined COARE_OOST) & Lwave, & # endif & rain, lhflx, lrflx, shflx, & & srflx, stflx, & # ifdef EMINUSP & EminusP, evap, & # endif & sustr, svstr) !*********************************************************************** ! USE mod_param USE mod_scalars ! # if defined EW_PERIODIC || defined NS_PERIODIC USE exchange_2d_mod # endif # ifdef DISTRIBUTE USE mp_exchange_mod, ONLY : mp_exchange2d # endif ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile integer, intent(in) :: LBi, UBi, LBj, UBj integer, intent(in) :: IminS, ImaxS, JminS, JmaxS integer, intent(in) :: nrhs ! # ifdef ASSUMED_SHAPE # ifdef MASKING real(r8), intent(in) :: rmask(LBi:,LBj:) real(r8), intent(in) :: umask(LBi:,LBj:) real(r8), intent(in) :: vmask(LBi:,LBj:) # endif real(r8), intent(in) :: alpha(LBi:,LBj:) real(r8), intent(in) :: beta(LBi:,LBj:) real(r8), intent(in) :: rho(LBi:,LBj:,:) real(r8), intent(in) :: t(LBi:,LBj:,:,:,:) real(r8), intent(in) :: Hair(LBi:,LBj:) real(r8), intent(in) :: Pair(LBi:,LBj:) real(r8), intent(in) :: Tair(LBi:,LBj:) real(r8), intent(in) :: Uwind(LBi:,LBj:) real(r8), intent(in) :: Vwind(LBi:,LBj:) # ifdef CLOUDS real(r8), intent(in) :: cloud(LBi:,LBj:) # endif # ifdef COARE_TAYLOR_YELLAND real(r8), intent(in) :: Hwave(LBi:,LBj:) # endif # if defined COARE_TAYLOR_YELLAND || defined COARE_OOST real(r8), intent(in) :: Pwave_top(LBi:,LBj:) # endif # if !defined DEEPWATER_WAVES && \ (defined COARE_TAYLOR_YELLAND || defined COARE_OOST) real(r8), intent(in) :: Lwave(LBi:,LBj:) # endif real(r8), intent(in) :: rain(LBi:,LBj:) real(r8), intent(inout) :: lhflx(LBi:,LBj:) real(r8), intent(inout) :: lrflx(LBi:,LBj:) real(r8), intent(inout) :: shflx(LBi:,LBj:) real(r8), intent(inout) :: srflx(LBi:,LBj:) real(r8), intent(inout) :: stflx(LBi:,LBj:,:) # ifdef EMINUSP real(r8), intent(out) :: EminusP(LBi:,LBj:) real(r8), intent(out) :: evap(LBi:,LBj:) # endif real(r8), intent(out) :: sustr(LBi:,LBj:) real(r8), intent(out) :: svstr(LBi:,LBj:) # else # ifdef MASKING real(r8), intent(in) :: rmask(LBi:UBi,LBj:UBj) real(r8), intent(in) :: umask(LBi:UBi,LBj:UBj) real(r8), intent(in) :: vmask(LBi:UBi,LBj:UBj) # endif real(r8), intent(in) :: alpha(LBi:UBi,LBj:UBj) real(r8), intent(in) :: beta(LBi:UBi,LBj:UBj) real(r8), intent(in) :: rho(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: t(LBi:UBi,LBj:UBj,N(ng),3,NT(ng)) real(r8), intent(in) :: Hair(LBi:UBi,LBj:UBj) real(r8), intent(in) :: Pair(LBi:UBi,LBj:UBj) real(r8), intent(in) :: Tair(LBi:UBi,LBj:UBj) real(r8), intent(in) :: Uwind(LBi:UBi,LBj:UBj) real(r8), intent(in) :: Vwind(LBi:UBi,LBj:UBj) # ifdef CLOUDS real(r8), intent(in) :: cloud(LBi:UBi,LBj:UBj) # endif # ifdef COARE_TAYLOR_YELLAND real(r8), intent(in) :: Hwave(LBi:UBi,LBj:UBj) # endif # if defined COARE_TAYLOR_YELLAND || defined COARE_OOST real(r8), intent(in) :: Pwave_top(LBi:UBi,LBj:UBj) # endif # if !defined DEEPWATER_WAVES && \ (defined COARE_TAYLOR_YELLAND || defined COARE_OOST) real(r8), intent(in) :: Lwave(LBi:UBi,LBj:UBj) # endif real(r8), intent(in) :: rain(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: lhflx(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: lrflx(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: shflx(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: srflx(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: stflx(LBi:UBi,LBj:UBj,NT(ng)) # ifdef EMINUSP real(r8), intent(out) :: EminusP(LBi:UBi,LBj:UBj) real(r8), intent(out) :: evap(LBi:UBi,LBj:UBj) # endif real(r8), intent(out) :: sustr(LBi:UBi,LBj:UBj) real(r8), intent(out) :: svstr(LBi:UBi,LBj:UBj) # endif ! ! Local variable declarations. ! # ifdef DISTRIBUTE # ifdef EW_PERIODIC logical :: EWperiodic=.TRUE. # else logical :: EWperiodic=.FALSE. # endif # ifdef NS_PERIODIC logical :: NSperiodic=.TRUE. # else logical :: NSperiodic=.FALSE. # endif # endif integer :: Iter, i, j, k integer, parameter :: IterMax = 3 real(r8), parameter :: eps = 1.0E-20_r8 real(r8), parameter :: r3 = 1.0_r8/3.0_r8 real(r8) :: Bf, Cd, Hl, Hlw, Hscale, Hs, Hsr, IER real(r8) :: PairM, RH, Taur real(r8) :: Wspeed, ZQoL, ZToL real(r8) :: cff, cff1, cff2, diffh, diffw, oL, upvel real(r8) :: twopi_inv, wet_bulb # ifdef LONGWAVE real(r8) :: e_sat, vap_p # endif # ifdef COOL_SKIN real(r8) :: Clam, Fc, Hcool, Hsb, Hlb, Qbouy, Qcool, lambd # endif real(r8), dimension(IminS:ImaxS) :: CC real(r8), dimension(IminS:ImaxS) :: Cd10 real(r8), dimension(IminS:ImaxS) :: Ch10 real(r8), dimension(IminS:ImaxS) :: Ct10 real(r8), dimension(IminS:ImaxS) :: charn real(r8), dimension(IminS:ImaxS) :: Ct real(r8), dimension(IminS:ImaxS) :: Cwave real(r8), dimension(IminS:ImaxS) :: Cwet real(r8), dimension(IminS:ImaxS) :: delQ real(r8), dimension(IminS:ImaxS) :: delQc real(r8), dimension(IminS:ImaxS) :: delT real(r8), dimension(IminS:ImaxS) :: delTc real(r8), dimension(IminS:ImaxS) :: delW real(r8), dimension(IminS:ImaxS) :: L real(r8), dimension(IminS:ImaxS) :: L10 real(r8), dimension(IminS:ImaxS) :: Q real(r8), dimension(IminS:ImaxS) :: Qair real(r8), dimension(IminS:ImaxS) :: Qpsi real(r8), dimension(IminS:ImaxS) :: Qsea real(r8), dimension(IminS:ImaxS) :: Qstar real(r8), dimension(IminS:ImaxS) :: rhoAir real(r8), dimension(IminS:ImaxS) :: rhoSea real(r8), dimension(IminS:ImaxS) :: Ri real(r8), dimension(IminS:ImaxS) :: Ribcu real(r8), dimension(IminS:ImaxS) :: Rr real(r8), dimension(IminS:ImaxS) :: Scff real(r8), dimension(IminS:ImaxS) :: TairC real(r8), dimension(IminS:ImaxS) :: TairK real(r8), dimension(IminS:ImaxS) :: Tcff real(r8), dimension(IminS:ImaxS) :: Tpsi real(r8), dimension(IminS:ImaxS) :: TseaC real(r8), dimension(IminS:ImaxS) :: TseaK real(r8), dimension(IminS:ImaxS) :: Tstar real(r8), dimension(IminS:ImaxS) :: u10 real(r8), dimension(IminS:ImaxS) :: VisAir real(r8), dimension(IminS:ImaxS) :: WaveLength real(r8), dimension(IminS:ImaxS) :: Wgus real(r8), dimension(IminS:ImaxS) :: Wmag real(r8), dimension(IminS:ImaxS) :: Wpsi real(r8), dimension(IminS:ImaxS) :: Wstar real(r8), dimension(IminS:ImaxS) :: Zetu real(r8), dimension(IminS:ImaxS) :: Zo10 real(r8), dimension(IminS:ImaxS) :: ZoT10 real(r8), dimension(IminS:ImaxS) :: ZoL real(r8), dimension(IminS:ImaxS) :: ZoQ real(r8), dimension(IminS:ImaxS) :: ZoT real(r8), dimension(IminS:ImaxS) :: ZoW real(r8), dimension(IminS:ImaxS) :: ZWoL real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Hlv real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: LHeat real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: LRad real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: SHeat real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: SRad real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Taux real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Tauy # include "set_bounds.h" ! !======================================================================= ! Atmosphere-Ocean bulk fluxes parameterization. !======================================================================= ! Hscale=rho0*Cp twopi_inv=0.5_r8/pi DO j=Jstr-1,JendR DO i=Istr-1,IendR ! ! Input bulk parameterization fields. ! Wmag(i)=SQRT(Uwind(i,j)*Uwind(i,j)+Vwind(i,j)*Vwind(i,j)) PairM=Pair(i,j) TairC(i)=Tair(i,j) TairK(i)=TairC(i)+273.16_r8 TseaC(i)=t(i,j,N(ng),nrhs,itemp) TseaK(i)=TseaC(i)+273.16_r8 rhoSea(i)=rho(i,j,N(ng))+1000.0_r8 RH=Hair(i,j) SRad(i,j)=srflx(i,j)*Hscale Tcff(i)=alpha(i,j) Scff(i)=beta(i,j) ! ! Initialize. ! delTc(i)=0.0_r8 delQc(i)=0.0_r8 LHeat(i,j)=lhflx(i,j)*Hscale SHeat(i,j)=shflx(i,j)*Hscale Taur=0.0_r8 Taux(i,j)=0.0_r8 Tauy(i,j)=0.0_r8 ! !----------------------------------------------------------------------- ! Compute net longwave radiation (W/m2), LRad. !----------------------------------------------------------------------- # if defined LONGWAVE ! ! Use Berliand (1952) formula to calculate net longwave radiation. ! The equation for saturation vapor pressure is from Gill (Atmosphere- ! Ocean Dynamics, pp 606). Here the coefficient in the cloud term ! is assumed constant, but it is a function of latitude varying from ! 1.0 at poles to 0.5 at the equator). ! cff=(0.7859_r8+0.03477_r8*TairC(i))/ & & (1.0_r8+0.00412_r8*TairC(i)) e_sat=10.0_r8**cff ! saturation vapor pressure (hPa or mbar) vap_p=e_sat*RH ! water vapor pressure (hPa or mbar) cff2=TairK(i)*TairK(i)*TairK(i) cff1=cff2*TairK(i) LRad(i,j)=-emmiss*StefBo* & & (cff1*(0.39_r8-0.05_r8*SQRT(vap_p))* & & (1.0_r8-0.6823_r8*cloud(i,j)*cloud(i,j))+ & & cff2*4.0_r8*(TseaK(i)-TairK(i))) # elif defined LONGWAVE_OUT ! ! Treat input longwave data as downwelling radiation only and add ! outgoing IR from model sea surface temperature. ! LRad(i,j)=lrflx(i,j)*Hscale- & & emmiss*StefBo*TseaK(i)*TseaK(i)*TseaK(i)*TseaK(i) # else LRad(i,j)=lrflx(i,j)*Hscale # endif # ifdef MASKING LRad(i,j)=LRad(i,j)*rmask(i,j) # endif ! !----------------------------------------------------------------------- ! Compute specific humidities (kg/kg). ! ! note that Qair(i) is the saturation specific humidity at Tair ! Q(i) is the actual specific humidity ! Qsea(i) is the saturation specific humidity at Tsea ! ! Saturation vapor pressure in mb is first computed and then ! converted to specific humidity in kg/kg ! ! The saturation vapor pressure is computed from Teten formula ! using the approach of Buck (1981): ! ! Esat(mb) = (1.0007_r8+3.46E-6_r8*PairM(mb))*6.1121_r8* ! EXP(17.502_r8*TairC(C)/(240.97_r8+TairC(C))) ! ! The ambient vapor is found from the definition of the ! Relative humidity: ! ! RH = W/Ws*100 ~ E/Esat*100 E = RH/100*Esat if RH is in % ! E = RH*Esat if RH fractional ! ! The specific humidity is then found using the relationship: ! ! Q = 0.622 E/(P + (0.622-1)e) ! ! Q(kg/kg) = 0.62197_r8*(E(mb)/(PairM(mb)-0.378_r8*E(mb))) ! !----------------------------------------------------------------------- ! ! Compute air saturation vapor pressure (mb), using Teten formula. ! cff=(1.0007_r8+3.46E-6_r8*PairM)*6.1121_r8* & & EXP(17.502_r8*TairC(i)/(240.97_r8+TairC(i))) ! ! Compute specific humidity at Saturation, Qair (kg/kg). ! Qair(i)=0.62197_r8*(cff/(PairM-0.378_r8*cff)) ! ! Compute specific humidity, Q (kg/kg). ! IF (RH.lt.2.0_r8) THEN !RH fraction cff=cff*RH !Vapor pres (mb) Q(i)=0.62197_r8*(cff/(PairM-0.378_r8*cff)) !Spec hum (kg/kg) ELSE !RH input was actually specific humidity in g/kg Q(i)=RH/1000.0_r8 !Spec Hum (kg/kg) END IF ! ! Compute water saturation vapor pressure (mb), using Teten formula. ! cff=(1.0007_r8+3.46E-6_r8*PairM)*6.1121_r8* & & EXP(17.502_r8*TseaC(i)/(240.97_r8+TseaC(i))) ! ! Vapor Pressure reduced for salinity (Kraus & Businger, 1994, pp 42). ! cff=cff*0.98_r8 ! ! Compute Qsea (kg/kg) from vapor pressure. ! Qsea(i)=0.62197_r8*(cff/(PairM-0.378_r8*cff)) ! !----------------------------------------------------------------------- ! Compute Monin-Obukhov similarity parameters for wind (Wstar), ! heat (Tstar), and moisture (Qstar), Liu et al. (1979). !----------------------------------------------------------------------- ! ! Moist air density (kg/m3). ! rhoAir(i)=PairM*100.0_r8/(blk_Rgas*TairK(i)* & & (1.0_r8+0.61_r8*Q(i))) ! ! Kinematic viscosity of dry air (m2/s), Andreas (1989). ! VisAir(i)=1.326E-5_r8* & & (1.0_r8+TairC(i)*(6.542E-3_r8+TairC(i)* & & (8.301E-6_r8-4.84E-9_r8*TairC(i)))) ! ! Compute latent heat of vaporization (J/kg) at sea surface, Hlv. ! Hlv(i,j)=(2.501_r8-0.00237_r8*TseaC(i))*1.0E+6_r8 ! ! Assume that wind is measured relative to sea surface and include ! gustiness. ! Wgus(i)=0.5_r8 delW(i)=SQRT(Wmag(i)*Wmag(i)+Wgus(i)*Wgus(i)) delQ(i)=Qsea(i)-Q(i) delT(i)=TseaC(i)-TairC(i) ! ! Neutral coefficients. ! ZoW(i)=0.0001_r8 u10(i)=delW(i)*LOG(10.0_r8/ZoW(i))/LOG(blk_ZW(ng)/ZoW(i)) Wstar(i)=0.035_r8*u10(i) Zo10(i)=0.011_r8*Wstar(i)*Wstar(i)/g+ & & 0.11_r8*VisAir(i)/Wstar(i) Cd10(i)=(vonKar/LOG(10.0_r8/Zo10(i)))**2 Ch10(i)=0.00115_r8 Ct10(i)=Ch10(i)/sqrt(Cd10(i)) ZoT10(i)=10.0_r8/EXP(vonKar/Ct10(i)) Cd=(vonKar/LOG(blk_ZW(ng)/Zo10(i)))**2 ! ! Compute Richardson number. ! Ct(i)=vonKar/LOG(blk_ZT(ng)/ZoT10(i)) ! T transfer coefficient CC(i)=vonKar*Ct(i)/Cd delTc(i)=0.0_r8 # ifdef COOL_SKIN delTc(i)=blk_dter # endif Ribcu(i)=-blk_ZW(ng)/(blk_Zabl*0.004_r8*blk_beta**3) Ri(i)=-g*blk_ZW(ng)*((delT(i)-delTc(i))+ & & 0.61_r8*TairK(i)*delQ(i))/ & & (TairK(i)*delW(i)*delW(i)) IF (Ri(i).lt.0.0_r8) THEN Zetu(i)=CC(i)*Ri(i)/(1.0_r8+Ri(i)/Ribcu(i)) ! Unstable ELSE Zetu(i)=CC(i)*Ri(i)/(1.0_r8+3.0_r8*Ri(i)/CC(i)) ! Stable END IF L10(i)=blk_ZW(ng)/Zetu(i) ! ! First guesses for Monon-Obukhov similarity scales. ! Wstar(i)=delW(i)*vonKar/(LOG(blk_ZW(ng)/Zo10(i))- & & bulk_psiu(blk_ZW(ng)/L10(i),pi)) Tstar(i)=-(delT(i)-delTc(i))*vonKar/ & & (LOG(blk_ZT(ng)/ZoT10(i))- & & bulk_psit(blk_ZT(ng)/L10(i),pi)) Qstar(i)=-(delQ(i)-delQc(i))*vonKar/ & & (LOG(blk_ZQ(ng)/ZoT10(i))- & & bulk_psit(blk_ZQ(ng)/L10(i),pi)) ! ! Modify Charnock for high wind speeds. The 0.125 factor below is for ! 1.0/(18.0-10.0). ! IF (delW(i).gt.18.0_r8) THEN charn(i)=0.018_r8 ELSE IF ((10.0_r8.lt.delW(i)).and.(delW(i).le.18.0_r8)) THEN charn(i)=0.011_r8+ & & 0.125_r8*(0.018_r8-0.011_r8)*(delW(i)-10._r8) ELSE charn(i)=0.011_r8 END IF # if defined COARE_OOST || defined COARE_TAYLOR_YELLAND # if defined DEEPWATER_WAVES Cwave(i)=g*MAX(Pwave_top(i,j),eps)*twopi_inv WaveLength(i)=Cwave(i)*MAX(Pwave_top(i,j),eps) # else Cwave(i)=Lwave(i,j)/MAX(Pwave_top(i,j),eps) WaveLength(i)=Lwave(i,j) # endif # endif END DO ! ! Iterate until convergence. It usually converges within 3 iterations. # if defined COARE_OOST || defined COARE_TAYLOR_YELLAND ! Use wave info if we have it, two different options. # endif ! DO Iter=1,IterMax DO i=Istr-1,IendR # ifdef COARE_OOST ZoW(i)=(25.0_r8/pi)*WaveLength(i)* & & (Wstar(i)/Cwave(i))**4.5_r8+ & & 0.11_r8*VisAir(i)/(Wstar(i)+eps) # elif defined COARE_TAYLOR_YELLAND ZoW(i)=1200.0_r8*Hwave(i,j)* & & (Hwave(i,j)/WaveLength(i))**4.5_r8+ & & 0.11_r8*VisAir(i)/(Wstar(i)+eps) # else ZoW(i)=charn(i)*Wstar(i)*Wstar(i)/g+ & & 0.11_r8*VisAir(i)/(Wstar(i)+eps) # endif Rr(i)=ZoW(i)*Wstar(i)/VisAir(i) ! ! Compute Monin-Obukhov stability parameter, Z/L. ! ZoQ(i)=MIN(1.15e-4_r8,5.5e-5_r8/Rr(i)**0.6_r8) ZoT(i)=ZoQ(i) ZoL(i)=vonKar*g*blk_ZW(ng)* & & (Tstar(i)*(1.0_r8+0.61_r8*Q(i))+ & & 0.61_r8*TairK(i)*Qstar(i))/ & & (TairK(i)*Wstar(i)*Wstar(i)* & & (1.0_r8+0.61_r8*Q(i))+eps) L(i)=blk_ZW(ng)/(ZoL(i)+eps) ! ! Evaluate stability functions at Z/L. ! Wpsi(i)=bulk_psiu(ZoL(i),pi) Tpsi(i)=bulk_psit(blk_ZT(ng)/L(i),pi) Qpsi(i)=bulk_psit(blk_ZQ(ng)/L(i),pi) # ifdef COOL_SKIN Cwet(i)=0.622_r8*Hlv(i,j)*Qsea(i)/ & & (blk_Rgas*TseaK(i)*TseaK(i)) delQc(i)=Cwet(i)*delTc(i) # endif ! ! Compute wind scaling parameters, Wstar. ! Wstar(i)=MAX(eps,delW(i)*vonKar/ & & (LOG(blk_ZW(ng)/ZoW(i))-Wpsi(i))) Tstar(i)=-(delT(i)-delTc(i))*vonKar/ & & (LOG(blk_ZT(ng)/ZoT(i))-Tpsi(i)) Qstar(i)=-(delQ(i)-delQc(i))*vonKar/ & & (LOG(blk_ZQ(ng)/ZoQ(i))-Qpsi(i)) ! ! Compute gustiness in wind speed. ! Bf=-g/TairK(i)* & & Wstar(i)*(Tstar(i)+0.61_r8*TairK(i)*Qstar(i)) IF (Bf.gt.0.0_r8) THEN Wgus(i)=blk_beta*(Bf*blk_Zabl)**r3 ELSE Wgus(i)=0.2_r8 END IF delW(i)=SQRT(Wmag(i)*Wmag(i)+Wgus(i)*Wgus(i)) # ifdef COOL_SKIN ! !----------------------------------------------------------------------- ! Cool Skin correction. !----------------------------------------------------------------------- ! ! Cool skin correction constants. Clam: part of Saunders constant ! lambda; Cwet: slope of saturation vapor. ! Clam=16.0_r8*g*blk_Cpw*(rhoSea(i)*blk_visw)**3.0_r8/ & & (blk_tcw*blk_tcw*rhoAir(i)*rhoAir(i)) ! ! Set initial guesses for cool-skin layer thickness (Hcool). ! Hcool=0.001_r8 ! ! Backgound sensible and latent heat. ! Hsb=-rhoAir(i)*blk_Cpa*Wstar(i)*Tstar(i) Hlb=-rhoAir(i)*Hlv(i,j)*Wstar(i)*Qstar(i) ! ! Mean absoption in cool-skin layer. ! Fc=0.065_r8+11.0_r8*Hcool- & & (1.0_r8-EXP(-Hcool*1250.0_r8))*6.6E-5_r8/Hcool ! ! Total cooling at the interface. ! Qcool=LRad(i,j)+Hsb+Hlb-SRad(i,j)*Fc Qbouy=Tcff(i)*Qcool+Scff(i)*Hlb*blk_Cpw/Hlv(i,j) ! ! Compute temperature and moisture change. ! IF ((Qcool.gt.0.0_r8).and.(Qbouy.gt.0.0_r8)) THEN lambd=6.0_r8/ & & (1.0_r8+ & & (Clam*Qbouy/(Wstar(i)+eps)**4.0_r8)**0.75_r8)**r3 Hcool=lambd*blk_visw/(SQRT(rhoAir(i)/rhoSea(i))* & & Wstar(i)+eps) delTc(i)=Qcool*Hcool/blk_tcw ELSE delTc(i)=0.0_r8 END IF delQc(i)=Cwet(i)*delTc(i) # endif END DO END DO ! !----------------------------------------------------------------------- ! Compute Atmosphere/Ocean fluxes. !----------------------------------------------------------------------- ! DO i=Istr-1,IendR ! ! Compute transfer coefficients for momentum (Cd). ! Wspeed=SQRT(Wmag(i)*Wmag(i)+Wgus(i)*Wgus(i)) Cd=Wstar(i)*Wstar(i)/(Wspeed*Wspeed+eps) ! ! Compute turbulent sensible heat flux (W/m2), Hs. ! Hs=-blk_Cpa*rhoAir(i)*Wstar(i)*Tstar(i) ! ! Compute sensible heat flux (W/m2) due to rainfall (kg/m2/s), Hsr. ! diffw=2.11E-5_r8*(TairK(i)/273.16_r8)**1.94_r8 diffh=0.02411_r8*(1.0_r8+TairC(i)* & & (3.309E-3_r8-1.44E-6_r8*TairC(i)))/ & & (rhoAir(i)*blk_Cpa) cff=Qair(i)*Hlv(i,j)/(blk_Rgas*TairK(i)*TairK(i)) wet_bulb=1.0_r8/(1.0_r8+0.622_r8*(cff*Hlv(i,j)*diffw)/ & & (blk_Cpa*diffh)) Hsr=rain(i,j)*wet_bulb*blk_Cpw* & & ((TseaC(i)-TairC(i))+(Qsea(i)-Q(i))*Hlv(i,j)/blk_Cpa) SHeat(i,j)=(Hs+Hsr) # ifdef MASKING SHeat(i,j)=SHeat(i,j)*rmask(i,j) # endif ! ! Compute turbulent latent heat flux (W/m2), Hl. ! Hl=-Hlv(i,j)*rhoAir(i)*Wstar(i)*Qstar(i) ! ! Compute Webb correction (Webb effect) to latent heat flux, Hlw. ! upvel=-1.61_r8*Wstar(i)*Qstar(i)- & & (1.0_r8+1.61_r8*Q(i))*Wstar(i)*Tstar(i)/TairK(i) Hlw=rhoAir(i)*Hlv(i,j)*upvel*Q(i) LHeat(i,j)=(Hl+Hlw) # ifdef MASKING LHeat(i,j)=LHeat(i,j)*rmask(i,j) # endif ! ! Compute momentum flux (N/m2) due to rainfall (kg/m2/s). ! Taur=0.85_r8*rain(i,j)*Wmag(i) ! ! Compute wind stress components (N/m2), Tau. ! cff=rhoAir(i)*Cd*Wspeed Taux(i,j)=(cff*Uwind(i,j)+Taur*SIGN(1.0_r8,Uwind(i,j))) # ifdef MASKING Taux(i,j)=Taux(i,j)*rmask(i,j) # endif Tauy(i,j)=(cff*Vwind(i,j)+Taur*SIGN(1.0_r8,Vwind(i,j))) # ifdef MASKING Tauy(i,j)=Tauy(i,j)*rmask(i,j) # endif END DO END DO ! !======================================================================= ! Compute surface net heat flux and surface wind stress. !======================================================================= ! ! Compute kinematic, surface, net heat flux (degC m/s). Notice that ! the signs of latent and sensible fluxes are reversed because fluxes ! calculated from the bulk formulations above are positive out of the ! ocean. ! ! For EMINUSP option, EVAP = LHeat (W/m2) / Hlv (J/kg) = kg/m2/s ! PREC = rain = kg/m2/s ! ! To convert these rates to m/s divide by freshwater density, rhow. ! ! Note that when the air is undersaturated in water vapor (Q < Qsea) ! the model will evaporate and LHeat > 0: ! ! LHeat positive out of the ocean ! evap positive out of the ocean ! ! Note that if evaporating, the salt flux is positive ! and if raining, the salt flux is negative ! ! Note that fresh water flux is positive out of the ocean and the ! salt flux (stflx(isalt)) is positive into the ocean. It is converted ! to (psu m/s) for stflx(isalt) in "set_vbc.F". The E-P value is ! saved in variable EminusP for I/O purposes. ! Hscale=1.0_r8/(rho0*Cp) cff=1.0_r8/rhow DO j=JstrR,JendR DO i=IstrR,IendR lrflx(i,j)=LRad(i,j)*Hscale lhflx(i,j)=-LHeat(i,j)*Hscale shflx(i,j)=-SHeat(i,j)*Hscale stflx(i,j,itemp)=(srflx(i,j)+lrflx(i,j)+ & & lhflx(i,j)+shflx(i,j)) # ifdef EMINUSP evap(i,j)=LHeat(i,j)/Hlv(i,j) stflx(i,j,isalt)=cff*(evap(i,j)-rain(i,j)) # endif # ifdef MASKING stflx(i,j,itemp)=stflx(i,j,itemp)*rmask(i,j) # ifdef EMINUSP evap(i,j)=evap(i,j)*rmask(i,j) stflx(i,j,isalt)=stflx(i,j,isalt)*rmask(i,j) # endif # endif # ifdef EMINUSP EminusP(i,j)=stflx(i,j,isalt) # endif END DO END DO ! ! Compute kinematic, surface wind stress (m2/s2). ! cff=0.5_r8/rho0 DO j=JstrR,JendR DO i=Istr,IendR sustr(i,j)=cff*(Taux(i-1,j)+Taux(i,j)) # ifdef MASKING sustr(i,j)=sustr(i,j)*umask(i,j) # endif END DO END DO DO j=Jstr,JendR DO i=IstrR,IendR svstr(i,j)=cff*(Tauy(i,j-1)+Tauy(i,j)) # ifdef MASKING svstr(i,j)=svstr(i,j)*vmask(i,j) # endif END DO END DO # if defined EW_PERIODIC || defined NS_PERIODIC || defined DISTRIBUTE ! !----------------------------------------------------------------------- ! Exchange boundary data. !----------------------------------------------------------------------- ! # if defined EW_PERIODIC || defined NS_PERIODIC CALL exchange_r2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & lrflx) CALL exchange_r2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & lhflx) CALL exchange_r2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & shflx) CALL exchange_r2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & stflx(:,:,itemp)) # ifdef EMINUSP CALL exchange_r2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & evap) CALL exchange_r2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & EminusP) CALL exchange_r2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & stflx(:,:,isalt)) # endif CALL exchange_u2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & sustr) CALL exchange_v2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & svstr) # endif # ifdef DISTRIBUTE CALL mp_exchange2d (ng, tile, iNLM, 4, & & LBi, UBi, LBj, UBj, & & NghostPoints, EWperiodic, NSperiodic, & & lrflx, lhflx, shflx, & & stflx(:,:,itemp)) # ifdef EMINUSP CALL mp_exchange2d (ng, tile, iNLM, 3, & & LBi, UBi, LBj, UBj, & & NghostPoints, EWperiodic, NSperiodic, & & evap, EminusP, & & stflx(:,:,isalt)) # endif CALL mp_exchange2d (ng, tile, iNLM, 2, & & LBi, UBi, LBj, UBj, & & NghostPoints, EWperiodic, NSperiodic, & & sustr, svstr) # endif # endif RETURN END SUBROUTINE bulk_flux_tile FUNCTION bulk_psiu (ZoL, pi) ! !======================================================================= ! ! ! This function evaluates the stability function for wind speed ! ! by matching Kansas and free convection forms. The convective ! ! form follows Fairall et al. (1996) with profile constants from ! ! Grachev et al. (2000) BLM. The stable form is from Beljaars ! ! and Holtslag (1991). ! ! ! !======================================================================= ! USE mod_kinds ! ! Function result ! real(r8) :: bulk_psiu ! ! Imported variable declarations. ! real(r8), intent(in) :: ZoL, pi ! ! Local variable declarations. ! real(r8), parameter :: r3 = 1.0_r8/3.0_r8 real(r8) :: Fw, cff, psic, psik, x, y ! !----------------------------------------------------------------------- ! Compute stability function, PSI. !----------------------------------------------------------------------- ! ! Unstable conditions. ! IF (ZoL.lt.0.0_r8) THEN x=(1.0_r8-15.0_r8*ZoL)**0.25_r8 psik=2.0_r8*LOG(0.5_r8*(1.0_r8+x))+ & & LOG(0.5_r8*(1.0_r8+x*x))- & & 2.0_r8*ATAN(x)+0.5_r8*pi ! ! For very unstable conditions, use free-convection (Fairall). ! cff=SQRT(3.0_r8) y=(1.0_r8-10.15_r8*ZoL)**r3 psic=1.5_r8*LOG(r3*(1.0_r8+y+y*y))- & & cff*ATAN((1.0_r8+2.0_r8*y)/cff)+pi/cff ! ! Match Kansas and free-convection forms with weighting Fw. ! cff=ZoL*ZoL Fw=cff/(1.0_r8+cff) bulk_psiu=(1.0_r8-Fw)*psik+Fw*psic ! ! Stable conditions. ! ELSE cff=MIN(50.0_r8,0.35_r8*ZoL) bulk_psiu=-((1.0_r8+ZoL)+0.6667_r8*(ZoL-14.28_r8)/ & & EXP(cff)+8.525_r8) END IF RETURN END FUNCTION bulk_psiu FUNCTION bulk_psit (ZoL, pi) ! !======================================================================= ! ! ! This function evaluates the stability function for moisture and ! ! heat by matching Kansas and free convection forms. The convective ! ! form follows Fairall et al. (1996) with profile constants from ! ! Grachev et al. (2000) BLM. The stable form is from Beljaars and ! ! and Holtslag (1991). ! ! !======================================================================= ! ! ! USE mod_kinds ! ! Function result ! real(r8) :: bulk_psit ! ! Imported variable declarations. ! real(r8), intent(in) :: ZoL, pi ! ! Local variable declarations. ! real(r8), parameter :: r3 = 1.0_r8/3.0_r8 real(r8) :: Fw, cff, psic, psik, x, y ! !----------------------------------------------------------------------- ! Compute stability function, PSI. !----------------------------------------------------------------------- ! ! Unstable conditions. ! IF (ZoL.lt.0.0_r8) THEN x=(1.0_r8-15.0_r8*ZoL)**0.5_r8 psik=2.0_r8*LOG(0.5_r8*(1.0_r8+x)) ! ! For very unstable conditions, use free-convection (Fairall). ! cff=SQRT(3.0_r8) y=(1.0_r8-34.15_r8*ZoL)**r3 psic=1.5_r8*LOG(r3*(1.0_r8+y+y*y))- & & cff*ATAN((1.0_r8+2.0_r8*y)/cff)+pi/cff ! ! Match Kansas and free-convection forms with weighting Fw. ! cff=ZoL*ZoL Fw=cff/(1.0_r8+cff) bulk_psit=(1.0_r8-Fw)*psik+Fw*psic ! ! Stable conditions. ! ELSE cff=MIN(50.0_r8,0.35_r8*ZoL) bulk_psit=-((1.0_r8+2.0_r8*ZoL)**1.5_r8+ & & 0.6667_r8*(ZoL-14.28_r8)/EXP(cff)+8.525_r8) END IF RETURN END FUNCTION bulk_psit #endif END MODULE bulk_flux_mod