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module Microlayer_m |
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Implicit none |
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contains |
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subroutine Microlayer(dter, dser, tkt, tks, hlb, tau, s_subskin, al, & |
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xlv, taur, rf, rain, qcol) |
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! H. Bellenger 2016 |
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use const, only: beta, cpw, grav, rhow |
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use fv_m, only: fv |
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real, intent(out):: dter(:) |
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! Temperature variation in the diffusive microlayer, that is |
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! ocean-air interface temperature minus subskin temperature. In K. |
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real, intent(out):: dser(:) |
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! Salinity variation in the diffusive microlayer, that is ocean-air |
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! interface salinity minus subskin salinity. In ppt. |
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real, intent(inout):: tkt(:) |
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! thickness of cool skin (microlayer), in m |
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real, intent(inout):: tks(:) |
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! thickness of mass diffusion layer (microlayer), in m |
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real, intent(in):: hlb(:) |
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! latent heat flux at the surface, positive upward (W m-2) |
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real, intent(in):: tau(:) ! wind stress, turbulent part only, in Pa |
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real, intent(in):: s_subskin(:) ! subskin salinity, in ppt |
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real, intent(in):: al(:) ! water thermal expansion coefficient (in K-1) |
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real, intent(in):: xlv(:) ! latent heat of evaporation (J/kg) |
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real, intent(in):: taur(:) ! momentum flux due to rainfall, in Pa |
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real, intent(in):: rf(:) |
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! sensible heat flux at the surface due to rainfall, in W m-2 |
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real, intent(in):: rain(:) ! rain mass flux, in kg m-2 s-1 |
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real, intent(in):: qcol(:) |
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! net flux at the surface, without sensible heat flux due to rain, in W m-2 |
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! Local: |
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real, dimension(size(qcol)):: usrk, usrct, usrcs, alq |
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real xlamx(size(qcol)) ! Saunders coefficient |
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real, parameter:: visw = 1e-6 |
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real, parameter:: tcw = 0.6 ! thermal conductivity of water |
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real, parameter:: mu = 0.0129e-7 ! in m2 / s |
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! molecular salinity diffusivity, Kraus and Businger, page 47 |
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real, parameter:: kappa = 1.49e-7 ! thermal diffusivity, in m2 / s |
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real, parameter:: afk = 4e-4 |
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real, parameter:: bfk = 1.3 |
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! a and b coefficient for the power function fitting the TKE flux |
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! carried by rain: Fk = a * R**b, derived form the exact solution |
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! of Soloviev and Lukas 2006 (Schlussel et al 1997, Craeye and |
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! Schlussel 1998) |
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!-------------------------------------------------------------------------- |
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alq = al * (qcol + rf * (1 - fV(tkt, rain))) - beta * s_subskin * cpw & |
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* (hlb / xlv - rain * (1 - fV(tks, rain))) |
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usrk = (afk / rhow)**(1. / 3.) * (rain * 3600.)**(bfk / 3.) |
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! Equivalent friction velocity due to the TKE input by the penetrating |
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! raindrops Fk |
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! Friction velocities in the air: |
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usrct = sqrt((tau + (1. - fV(tkt, rain)) * taur) / rhow & |
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+ (fV(0., rain) - fV(tkt, rain)) * usrk**2) |
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usrcs = sqrt((tau + (1. - fV(tks, rain)) * taur) / rhow & |
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+ (fV(0., rain) - fV(tks, rain)) * usrk**2) |
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where (alq > 0.) |
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! Fairall 1996 982, equation (14): |
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xlamx = 6. * (1. + (16. * grav * cpw * rhow * visw**3 * alq & |
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/ (tcw**2 * usrct**4 ))**0.75)**(- 1. / 3.) |
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! Fairall 1996 982, equation (12): |
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tkt = xlamx * visw / usrct |
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tks = xlamx * mu * (kappa / mu)**(2. / 3.) & |
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* visw * cpw * rhow / ( tcw * usrcs) |
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! From Saunders 1967 (4) |
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elsewhere |
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xlamx = 6. ! prevent excessive warm skins |
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tkt = min(.01, xlamx * visw / usrct) ! Limit tkt |
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tks = min(.001, xlamx * mu * (kappa / mu)**(2. / 3.) * visw * cpw & |
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* rhow / (tcw * usrcs)) |
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end where |
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! Fairall 1996 982, equation (13): |
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dter = - (qcol + rf * (1 - fV(tkt, rain))) * tkt / tcw |
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dser = s_subskin * (hlb / xlv - rain * (1 - fV(tks, rain))) * tks & |
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/ (rhow * mu) ! eq. fresh skin |
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end subroutine Microlayer |
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end module Microlayer_m |
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