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FUNCTION qlw_net_sclr( pdwlw, pts, l_ice )
!!---------------------------------------------------------------------------------
!! *** FUNCTION qlw_net_sclr ***
!!
!! ** Purpose : Estimate of the net longwave flux at the surface
!!----------------------------------------------------------------------------------
REAL(wp) :: qlw_net_sclr
REAL(wp), INTENT(in) :: pdwlw !: downwelling longwave (aka infrared, aka thermal) radiation [W/m^2]
REAL(wp), INTENT(in) :: pts !: surface temperature [K]
LOGICAL, INTENT(in), OPTIONAL :: l_ice !: we are above ice
REAL(wp) :: zemiss, zt2
LOGICAL :: lice
!!----------------------------------------------------------------------------------
lice = .FALSE.
IF( PRESENT(l_ice) ) lice = l_ice
IF( lice ) THEN
zemiss = emiss_i
ELSE
zemiss = emiss_w
END IF
zt2 = pts*pts
qlw_net_sclr = zemiss*( pdwlw - stefan*zt2*zt2) ! zemiss used both as the IR albedo and IR emissivity...
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REAL(wp), DIMENSION(jpi,jpj) :: qlw_net_vctr
REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pdwlw !: downwelling longwave (aka infrared, aka thermal) radiation [W/m^2]
REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pts !: surface temperature [K]
LOGICAL, INTENT(in), OPTIONAL :: l_ice !: we are above ice
LOGICAL :: lice
INTEGER :: ji, jj
!!----------------------------------------------------------------------------------
lice = .FALSE.
IF( PRESENT(l_ice) ) lice = l_ice
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
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qlw_net_vctr(ji,jj) = qlw_net_sclr( pdwlw(ji,jj) , pts(ji,jj), l_ice=lice )
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REAL(wp), DIMENSION(jpi,jpj) :: z0_from_Cd !: roughness length [m]
REAL(wp) , INTENT(in) :: pzu !: reference height zu [m]
REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pCd !: (neutral or non-neutral) drag coefficient []
REAL(wp), DIMENSION(jpi,jpj), INTENT(in), OPTIONAL :: ppsi !: "Psi_m(pzu/L)" stability correction profile for momentum []
!!
!! If pCd is the NEUTRAL-STABILITY drag coefficient then ppsi must be 0 or not given
!! If pCd is the drag coefficient (in stable or unstable conditions) then pssi must be provided
!!----------------------------------------------------------------------------------
IF( PRESENT(ppsi) ) THEN
!! Cd provided is the actual Cd (not the neutral-stability CdN) :
z0_from_Cd = pzu * EXP( - ( vkarmn/SQRT(pCd(:,:)) + ppsi(:,:) ) ) !LB: ok, double-checked!
ELSE
!! Cd provided is the neutral-stability Cd, aka CdN :
z0_from_Cd = pzu * EXP( - vkarmn/SQRT(pCd(:,:)) ) !LB: ok, double-checked!
END IF
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REAL(wp), DIMENSION(jpi,jpj) :: Cd_from_z0 !: (neutral or non-neutral) drag coefficient []
REAL(wp) , INTENT(in) :: pzu !: reference height zu [m]
REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pz0 !: roughness length [m]
REAL(wp), DIMENSION(jpi,jpj), INTENT(in), OPTIONAL :: ppsi !: "Psi_m(pzu/L)" stability correction profile for momentum []
!!
!! If we want to return the NEUTRAL-STABILITY drag coefficient then ppsi must be 0 or not given
!! If we want to return the stability-corrected Cd (i.e. in stable or unstable conditions) then pssi must be provided
!!----------------------------------------------------------------------------------
IF( PRESENT(ppsi) ) THEN
!! The Cd we return is the actual Cd (not the neutral-stability CdN) :
Cd_from_z0 = 1._wp / ( LOG( pzu / pz0(:,:) ) - ppsi(:,:) )
ELSE
!! The Cd we return is the neutral-stability Cd, aka CdN :
Cd_from_z0 = 1._wp / LOG( pzu / pz0(:,:) )
END IF
Cd_from_z0 = vkarmn2 * Cd_from_z0 * Cd_from_z0
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END FUNCTION Cd_from_z0
FUNCTION f_m_louis_sclr( pzu, pRib, pCdn, pz0 )
!!----------------------------------------------------------------------------------
!! Stability correction function for MOMENTUM
!! Louis (1979)
!!----------------------------------------------------------------------------------
REAL(wp) :: f_m_louis_sclr ! term "f_m" in Eq.(6) when option "Louis" rather than "Psi(zeta) is chosen, Lupkes & Gryanik (2015),
REAL(wp), INTENT(in) :: pzu ! reference height (height for pwnd) [m]
REAL(wp), INTENT(in) :: pRib ! Bulk Richardson number
REAL(wp), INTENT(in) :: pCdn ! neutral drag coefficient
REAL(wp), INTENT(in) :: pz0 ! roughness length [m]
!!----------------------------------------------------------------------------------
REAL(wp) :: ztu, zts, zstab
!!----------------------------------------------------------------------------------
zstab = 0.5 + SIGN(0.5_wp, pRib) ; ! Unstable (Ri<0) => zstab = 0 | Stable (Ri>0) => zstab = 1
!
ztu = pRib / ( 1._wp + 3._wp * rc2_louis * pCdn * SQRT( ABS( -pRib * ( pzu / pz0 + 1._wp) ) ) ) ! ABS is just here for when it's stable conditions and ztu is not used anyways
zts = pRib / SQRT( ABS( 1._wp + pRib ) ) ! ABS is just here for when it's UNstable conditions and zts is not used anyways
!
f_m_louis_sclr = (1._wp - zstab) * ( 1._wp - ram_louis * ztu ) & ! Unstable Eq.(A6)
& + zstab * 1._wp / ( 1._wp + ram_louis * zts ) ! Stable Eq.(A7)
!
END FUNCTION f_m_louis_sclr
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REAL(wp), DIMENSION(jpi,jpj) :: f_m_louis_vctr
REAL(wp), INTENT(in) :: pzu
REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pRib
REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pCdn
REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pz0
INTEGER :: ji, jj
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f_m_louis_vctr(ji,jj) = f_m_louis_sclr( pzu, pRib(ji,jj), pCdn(ji,jj), pz0(ji,jj) )
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END FUNCTION f_m_louis_vctr
FUNCTION f_h_louis_sclr( pzu, pRib, pChn, pz0 )
!!----------------------------------------------------------------------------------
!! Stability correction function for HEAT
!! Louis (1979)
!!----------------------------------------------------------------------------------
REAL(wp) :: f_h_louis_sclr ! term "f_h" in Eq.(6) when option "Louis" rather than "Psi(zeta) is chosen, Lupkes & Gryanik (2015),
REAL(wp), INTENT(in) :: pzu ! reference height (height for pwnd) [m]
REAL(wp), INTENT(in) :: pRib ! Bulk Richardson number
REAL(wp), INTENT(in) :: pChn ! neutral heat transfer coefficient
REAL(wp), INTENT(in) :: pz0 ! roughness length [m]
!!----------------------------------------------------------------------------------
REAL(wp) :: ztu, zts, zstab
!!----------------------------------------------------------------------------------
zstab = 0.5 + SIGN(0.5_wp, pRib) ; ! Unstable (Ri<0) => zstab = 0 | Stable (Ri>0) => zstab = 1
!
ztu = pRib / ( 1._wp + 3._wp * rc2_louis * pChn * SQRT( ABS(-pRib * ( pzu / pz0 + 1._wp) ) ) )
zts = pRib / SQRT( ABS( 1._wp + pRib ) )
!
f_h_louis_sclr = (1._wp - zstab) * ( 1._wp - rah_louis * ztu ) & ! Unstable Eq.(A6)
& + zstab * 1._wp / ( 1._wp + rah_louis * zts ) ! Stable Eq.(A7) !#LB: in paper it's "ram_louis" and not "rah_louis" typo or what????
!
END FUNCTION f_h_louis_sclr
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REAL(wp), DIMENSION(jpi,jpj) :: f_h_louis_vctr
REAL(wp), INTENT(in) :: pzu
REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pRib
REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pChn
REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pz0
INTEGER :: ji, jj
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f_h_louis_vctr(ji,jj) = f_h_louis_sclr( pzu, pRib(ji,jj), pChn(ji,jj), pz0(ji,jj) )
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FUNCTION UN10_from_ustar( pzu, pUzu, pus, ppsi )
!!----------------------------------------------------------------------------------
!! Provides the neutral-stability wind speed at 10 m
!!----------------------------------------------------------------------------------
REAL(wp), DIMENSION(jpi,jpj) :: UN10_from_ustar !: neutral stability wind speed at 10m [m/s]
REAL(wp), INTENT(in) :: pzu !: measurement heigh of wind speed [m]
REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pUzu !: bulk wind speed at height pzu m [m/s]
REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pus !: friction velocity [m/s]
REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ppsi !: "Psi_m(pzu/L)" stability correction profile for momentum []
!!----------------------------------------------------------------------------------
UN10_from_ustar(:,:) = pUzu(:,:) - pus(:,:)/vkarmn * ( LOG(pzu/10._wp) - ppsi(:,:) )
!!
END FUNCTION UN10_from_ustar
FUNCTION UN10_from_CD( pzu, pUb, pCd, ppsi )
!!----------------------------------------------------------------------------------
!! Provides the neutral-stability wind speed at 10 m
!!----------------------------------------------------------------------------------
REAL(wp), DIMENSION(jpi,jpj) :: UN10_from_CD !: [m/s]
REAL(wp), INTENT(in) :: pzu !: measurement heigh of bulk wind speed
REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pUb !: bulk wind speed at height pzu m [m/s]
REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pCd !: drag coefficient
REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ppsi !: "Psi_m(pzu/L)" stability correction profile for momentum []
!!----------------------------------------------------------------------------------
!! Reminder: UN10 = u*/vkarmn * log(10/z0)
!! and: u* = sqrt(Cd) * Ub
!! u*/vkarmn * log( 10 / z0 )
UN10_from_CD(:,:) = SQRT(pCd(:,:))*pUb/vkarmn * LOG( 10._wp / z0_from_Cd( pzu, pCd(:,:), ppsi=ppsi(:,:) ) )
!!
END FUNCTION UN10_from_CD
FUNCTION z0tq_LKB( iflag, pRer, pz0 )
!!---------------------------------------------------------------------------------
!! *** FUNCTION z0tq_LKB ***
!!
!! ** Purpose : returns the "temperature/humidity roughness lengths"
!! * iflag==1 => temperature => returns: z_{0t}
!! * iflag==2 => humidity => returns: z_{0q}
!! from roughness reynold number "pRer" (i.e. [z_0 u*]/Nu_{air})
!! between 0 and 1000. Out of range "pRer" indicated by prt=-999.
!! and roughness length (for momentum)
!!
!! Based on Liu et al. (1979) JAS 36 1722-1723s
!!
!! Note: this is what is used into COARE 2.5 to estimate z_{0t} and z_{0q}
!!
!! ** Author: L. Brodeau, April 2020 / AeroBulk (https://github.com/brodeau/aerobulk/)
!!----------------------------------------------------------------------------------
REAL(wp), DIMENSION(jpi,jpj) :: z0tq_LKB
INTEGER, INTENT(in) :: iflag !: 1 => dealing with temperature; 2 => dealing with humidity
REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pRer !: roughness Reynolds number [z_0 u*]/Nu_{air}
REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pz0 !: roughness length (for momentum) [m]
!-------------------------------------------------------------------
! Scalar Re_r relation from Liu et al.
REAL(wp), DIMENSION(8,2), PARAMETER :: &
& XA = RESHAPE( (/ 0.177, 1.376, 1.026, 1.625, 4.661, 34.904, 1667.19, 5.88e5, &
& 0.292, 1.808, 1.393, 1.956, 4.994, 30.709, 1448.68, 2.98e5 /), (/8,2/) )
!!
REAL(wp), DIMENSION(8,2), PARAMETER :: &
& XB = RESHAPE( (/ 0., 0.929, -0.599, -1.018, -1.475, -2.067, -2.907, -3.935, &
& 0., 0.826, -0.528, -0.870, -1.297, -1.845, -2.682, -3.616 /), (/8,2/) )
!!
REAL(wp), DIMENSION(0:8), PARAMETER :: &
& XRAN = (/ 0., 0.11, 0.825, 3.0, 10.0, 30.0, 100., 300., 1000. /)
!-------------------------------------------------------------------
!
!-------------------------------------------------------------------
! Scalar Re_r relation from Moana Wave data.
!
! real*8 A(9,2),B(9,2),RAN(9),pRer,prt
! integer iflag
! DATA A/0.177,2.7e3,1.03,1.026,1.625,4.661,34.904,1667.19,5.88E5,
! & 0.292,3.7e3,1.4,1.393,1.956,4.994,30.709,1448.68,2.98E5/
! DATA B/0.,4.28,0,-0.599,-1.018,-1.475,-2.067,-2.907,-3.935,
! & 0.,4.28,0,-0.528,-0.870,-1.297,-1.845,-2.682,-3.616/
! DATA RAN/0.11,.16,1.00,3.0,10.0,30.0,100.,300.,1000./
!-------------------------------------------------------------------
LOGICAL :: lfound=.FALSE.
REAL(wp) :: zrr
INTEGER :: ji, jj, jm
z0tq_LKB(:,:) = -999._wp
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
zrr = pRer(ji,jj)
lfound = .FALSE.
IF( (zrr > 0.).AND.(zrr < 1000.) ) THEN
jm = 0
DO WHILE ( .NOT. lfound )
jm = jm + 1
lfound = ( (zrr > XRAN(jm-1)) .AND. (zrr <= XRAN(jm)) )
END DO
z0tq_LKB(ji,jj) = XA(jm,iflag)*zrr**XB(jm,iflag) * pz0(ji,jj)/zrr
END IF
END_2D
z0tq_LKB(:,:) = MIN( MAX(ABS(z0tq_LKB(:,:)), 1.E-9) , 0.05_wp )
END FUNCTION z0tq_LKB
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