!===============================================================================
! SVN $Id: shr_flux_mod.F90 19407 2009-11-13 19:36:31Z tcraig $
! SVN $URL: https://svn-ccsm-models.cgd.ucar.edu/csm_share/branch_tags/cesm1_0_rel_tags/cesm1_0_rel01_share3_100616/shr/shr_flux_mod.F90 $
!===============================================================================
!BOP ===========================================================================
!
! !MODULE: flux_mod -- CCSM shared flux calculations.
!
! !DESCRIPTION:
!
! CCSM shared flux calculations.
!
! !REVISION HISTORY:
! 2006-Nov-07 - B. Kauffman - first version, code taken/migrated from cpl6
!
! !INTERFACE: ------------------------------------------------------------------
module shr_flux_mod 2,5
! !USES:
use shr_kind_mod
! shared kinds
use shr_const_mod ! shared constants
use shr_sys_mod ! shared system routines
use shr_log_mod, only: s_loglev => shr_log_Level
use shr_log_mod, only: s_logunit => shr_log_Unit
implicit none
private ! default private
! !PUBLIC TYPES:
! none
! !PUBLIC MEMBER FUNCTIONS:
public :: shr_flux_atmOcn ! computes atm/ocn fluxes
public :: shr_flux_atmIce ! computes atm/ice fluxes
public :: shr_flux_MOstability ! boundary layer stability scales/functions
! !PUBLIC DATA MEMBERS:
integer(SHR_KIND_IN),parameter,public :: shr_flux_MOwScales = 1 ! w scales option
integer(SHR_KIND_IN),parameter,public :: shr_flux_MOfunctions = 2 ! functions option
real (SHR_KIND_R8),parameter,public :: shr_flux_MOgammaM = 3.59_SHR_KIND_R8
real (SHR_KIND_R8),parameter,public :: shr_flux_MOgammaS = 7.86_SHR_KIND_R8
!EOP
!--- rename kinds for local readability only ---
integer,parameter :: R8 = SHR_KIND_R8 ! 8 byte real
integer,parameter :: IN = SHR_KIND_IN ! native/default integer
integer,parameter :: debug = 0 ! internal debug level
!===============================================================================
contains
!===============================================================================
!===============================================================================
! !BOP =========================================================================
!
! !IROUTINE: shr_flux_atmOcn -- internal atm/ocn flux calculation
!
! !DESCRIPTION:
!
! Internal atm/ocn flux calculation
!
! !REVISION HISTORY:
! 2002-Jun-10 - B. Kauffman - code migrated from cpl5 to cpl6
! 2003-Apr-02 - B. Kauffman - taux & tauy now utilize ocn velocity
! 2003-Apr-02 - B. Kauffman - tref,qref,duu10n mods as per Bill Large
! 2006-Nov-07 - B. Kauffman - code migrated from cpl6 to share
!
! !INTERFACE: ------------------------------------------------------------------
SUBROUTINE shr_flux_atmOcn(nMax ,zbot ,ubot ,vbot ,thbot , & 1
& qbot ,rbot ,tbot ,us ,vs , &
& ts ,mask ,sen ,lat ,lwup , &
& evap ,taux ,tauy ,tref ,qref , &
& duu10n, ustar_sv ,re_sv ,ssq_sv )
! !USES:
implicit none
! !INPUT/OUTPUT PARAMETERS:
!--- input arguments --------------------------------
integer(IN),intent(in) :: nMax ! data vector length
integer(IN),intent(in) :: mask (nMax) ! ocn domain mask 0 <=> out of domain
real(R8) ,intent(in) :: zbot (nMax) ! atm level height (m)
real(R8) ,intent(in) :: ubot (nMax) ! atm u wind (m/s)
real(R8) ,intent(in) :: vbot (nMax) ! atm v wind (m/s)
real(R8) ,intent(in) :: thbot(nMax) ! atm potential T (K)
real(R8) ,intent(in) :: qbot (nMax) ! atm specific humidity (kg/kg)
real(R8) ,intent(in) :: rbot (nMax) ! atm air density (kg/m^3)
real(R8) ,intent(in) :: tbot (nMax) ! atm T (K)
real(R8) ,intent(in) :: us (nMax) ! ocn u-velocity (m/s)
real(R8) ,intent(in) :: vs (nMax) ! ocn v-velocity (m/s)
real(R8) ,intent(in) :: ts (nMax) ! ocn temperature (K)
!--- output arguments -------------------------------
real(R8),intent(out) :: sen (nMax) ! heat flux: sensible (W/m^2)
real(R8),intent(out) :: lat (nMax) ! heat flux: latent (W/m^2)
real(R8),intent(out) :: lwup (nMax) ! heat flux: lw upward (W/m^2)
real(R8),intent(out) :: evap (nMax) ! water flux: evap ((kg/s)/m^2)
real(R8),intent(out) :: taux (nMax) ! surface stress, zonal (N)
real(R8),intent(out) :: tauy (nMax) ! surface stress, maridional (N)
real(R8),intent(out) :: tref (nMax) ! diag: 2m ref height T (K)
real(R8),intent(out) :: qref (nMax) ! diag: 2m ref humidity (kg/kg)
real(R8),intent(out) :: duu10n(nMax) ! diag: 10m wind speed squared (m/s)^2
real(R8),intent(out),optional :: ustar_sv(nMax) ! diag: ustar
real(R8),intent(out),optional :: re_sv (nMax) ! diag: sqrt of exchange coefficient (water)
real(R8),intent(out),optional :: ssq_sv (nMax) ! diag: sea surface humidity (kg/kg)
! !EOP
!--- local constants --------------------------------
real(R8),parameter :: umin = 0.5_R8 ! minimum wind speed (m/s)
real(R8),parameter :: zref = 10.0_R8 ! reference height (m)
real(R8),parameter :: ztref = 2.0_R8 ! reference height for air T (m)
!--- local variables --------------------------------
integer(IN) :: n ! vector loop index
real(R8) :: vmag ! surface wind magnitude (m/s)
real(R8) :: thvbot ! virtual temperature (K)
real(R8) :: ssq ! sea surface humidity (kg/kg)
real(R8) :: delt ! potential T difference (K)
real(R8) :: delq ! humidity difference (kg/kg)
real(R8) :: stable ! stability factor
real(R8) :: rdn ! sqrt of neutral exchange coeff (momentum)
real(R8) :: rhn ! sqrt of neutral exchange coeff (heat)
real(R8) :: ren ! sqrt of neutral exchange coeff (water)
real(R8) :: rd ! sqrt of exchange coefficient (momentum)
real(R8) :: rh ! sqrt of exchange coefficient (heat)
real(R8) :: re ! sqrt of exchange coefficient (water)
real(R8) :: ustar ! ustar
real(R8) :: qstar ! qstar
real(R8) :: tstar ! tstar
real(R8) :: hol ! H (at zbot) over L
real(R8) :: xsq ! ?
real(R8) :: xqq ! ?
real(R8) :: psimh ! stability function at zbot (momentum)
real(R8) :: psixh ! stability function at zbot (heat and water)
real(R8) :: psix2 ! stability function at ztref reference height
real(R8) :: alz ! ln(zbot/zref)
real(R8) :: al2 ! ln(zref/ztref)
real(R8) :: u10n ! 10m neutral wind
real(R8) :: tau ! stress at zbot
real(R8) :: cp ! specific heat of moist air
real(R8) :: bn ! exchange coef funct for interpolation
real(R8) :: bh ! exchange coef funct for interpolation
real(R8) :: fac ! vertical interpolation factor
!--- local functions --------------------------------
real(R8) :: qsat ! function: the saturation humididty of air (kg/m^3)
real(R8) :: cdn ! function: neutral drag coeff at 10m
real(R8) :: psimhu ! function: unstable part of psimh
real(R8) :: psixhu ! function: unstable part of psimx
real(R8) :: Umps ! dummy arg ~ wind velocity (m/s)
real(R8) :: Tk ! dummy arg ~ temperature (K)
real(R8) :: xd ! dummy arg ~ ?
qsat(Tk) = 640380.0_R8 / exp(5107.4_R8/Tk)
cdn(Umps) = 0.0027_R8 / Umps + 0.000142_R8 + 0.0000764_R8 * Umps
psimhu(xd) = log((1.0_R8+xd*(2.0_R8+xd))*(1.0_R8+xd*xd)/8.0_R8) - 2.0_R8*atan(xd) + 1.571_R8
psixhu(xd) = 2.0_R8 * log((1.0_R8 + xd*xd)/2.0_R8)
!--- formats ----------------------------------------
character(*),parameter :: subName = '(shr_flux_atmOcn) '
character(*),parameter :: F00 = "('(shr_flux_atmOcn) ',4a)"
!-------------------------------------------------------------------------------
! PURPOSE:
! computes atm/ocn surface fluxes
!
! NOTES:
! o all fluxes are positive downward
! o net heat flux = net sw + lw up + lw down + sen + lat
! o here, tstar = <WT>/U*, and qstar = <WQ>/U*.
! o wind speeds should all be above a minimum speed (eg. 1.0 m/s)
!
! ASSUMPTIONS:
! o Neutral 10m drag coeff: cdn = .0027/U10 + .000142 + .0000764 U10
! o Neutral 10m stanton number: ctn = .0327 sqrt(cdn), unstable
! ctn = .0180 sqrt(cdn), stable
! o Neutral 10m dalton number: cen = .0346 sqrt(cdn)
! o The saturation humidity of air at T(K): qsat(T) (kg/m^3)
!-------------------------------------------------------------------------------
if (debug > 0 .and. s_loglev > 0) write(s_logunit,F00) "enter"
al2 = log(zref/ztref)
DO n=1,nMax
if (mask(n) /= 0) then
!--- compute some needed quantities ---
vmag = max(umin, sqrt( (ubot(n)-us(n))**2 + (vbot(n)-vs(n))**2) )
thvbot = thbot(n) * (1.0_R8 + shr_const_zvir * qbot(n)) ! virtual temp (K)
ssq = 0.98_R8 * qsat(ts(n)) / rbot(n) ! sea surf hum (kg/kg)
delt = thbot(n) - ts(n) ! pot temp diff (K)
delq = qbot(n) - ssq ! spec hum dif (kg/kg)
alz = log(zbot(n)/zref)
cp = shr_const_cpdair*(1.0_R8 + shr_const_cpvir*ssq)
!------------------------------------------------------------
! first estimate of Z/L and ustar, tstar and qstar
!------------------------------------------------------------
!--- neutral coefficients, z/L = 0.0 ---
stable = 0.5_R8 + sign(0.5_R8 , delt)
rdn = sqrt(cdn(vmag))
rhn = (1.0_R8-stable) * 0.0327_R8 + stable * 0.018_R8
ren = 0.0346_R8
!--- ustar, tstar, qstar ---
ustar = rdn * vmag
tstar = rhn * delt
qstar = ren * delq
!--- compute stability & evaluate all stability functions ---
hol = shr_const_karman*shr_const_g*zbot(n)* &
(tstar/thbot(n)+qstar/(1.0_R8/shr_const_zvir+qbot(n)))/ustar**2
hol = sign( min(abs(hol),10.0_R8), hol )
stable = 0.5_R8 + sign(0.5_R8 , hol)
xsq = max(sqrt(abs(1.0_R8 - 16.0_R8*hol)) , 1.0_R8)
xqq = sqrt(xsq)
psimh = -5.0_R8*hol*stable + (1.0_R8-stable)*psimhu(xqq)
psixh = -5.0_R8*hol*stable + (1.0_R8-stable)*psixhu(xqq)
!--- shift wind speed using old coefficient ---
rd = rdn / (1.0_R8 + rdn/shr_const_karman*(alz-psimh))
u10n = vmag * rd / rdn
!--- update transfer coeffs at 10m and neutral stability ---
rdn = sqrt(cdn(u10n))
ren = 0.0346_R8
rhn = (1.0_R8-stable)*0.0327_R8 + stable * 0.018_R8
!--- shift all coeffs to measurement height and stability ---
rd = rdn / (1.0_R8 + rdn/shr_const_karman*(alz-psimh))
rh = rhn / (1.0_R8 + rhn/shr_const_karman*(alz-psixh))
re = ren / (1.0_R8 + ren/shr_const_karman*(alz-psixh))
!--- update ustar, tstar, qstar using updated, shifted coeffs --
ustar = rd * vmag
tstar = rh * delt
qstar = re * delq
!------------------------------------------------------------
! iterate to converge on Z/L, ustar, tstar and qstar
!------------------------------------------------------------
!--- compute stability & evaluate all stability functions ---
hol = shr_const_karman*shr_const_g*zbot(n)* &
(tstar/thbot(n)+qstar/(1.0_R8/shr_const_zvir+qbot(n)))/ustar**2
hol = sign( min(abs(hol),10.0_R8), hol )
stable = 0.5_R8 + sign(0.5_R8 , hol)
xsq = max(sqrt(abs(1.0_R8 - 16.0_R8*hol)) , 1.0_R8)
xqq = sqrt(xsq)
psimh = -5.0_R8*hol*stable + (1.0_R8-stable)*psimhu(xqq)
psixh = -5.0_R8*hol*stable + (1.0_R8-stable)*psixhu(xqq)
!--- shift wind speed using old coeffs ---
rd = rdn / (1.0_R8 + rdn/shr_const_karman*(alz-psimh))
u10n = vmag * rd/rdn
!--- update transfer coeffs at 10m and neutral stability ---
rdn = sqrt(cdn(u10n))
ren = 0.0346_R8
rhn = (1.0_R8 - stable)*0.0327_R8 + stable * 0.018_R8
!--- shift all coeffs to measurement height and stability ---
rd = rdn / (1.0_R8 + rdn/shr_const_karman*(alz-psimh))
rh = rhn / (1.0_R8 + rhn/shr_const_karman*(alz-psixh))
re = ren / (1.0_R8 + ren/shr_const_karman*(alz-psixh))
!--- update ustar, tstar, qstar using updated, shifted coeffs ---
ustar = rd * vmag
tstar = rh * delt
qstar = re * delq
!------------------------------------------------------------
! compute the fluxes
!------------------------------------------------------------
tau = rbot(n) * ustar * ustar
!--- momentum flux ---
taux(n) = tau * (ubot(n)-us(n)) / vmag
tauy(n) = tau * (vbot(n)-vs(n)) / vmag
!--- heat flux ---
sen (n) = cp * tau * tstar / ustar
lat (n) = shr_const_latvap * tau * qstar / ustar
lwup(n) = -shr_const_stebol * ts(n)**4
!--- water flux ---
evap(n) = lat(n)/shr_const_latvap
!------------------------------------------------------------
! compute diagnositcs: 2m ref T & Q, 10m wind speed squared
!------------------------------------------------------------
hol = hol*ztref/zbot(n)
xsq = max( 1.0_R8, sqrt(abs(1.0_R8-16.0_R8*hol)) )
xqq = sqrt(xsq)
psix2 = -5.0_R8*hol*stable + (1.0_R8-stable)*psixhu(xqq)
fac = (rh/shr_const_karman) * (alz + al2 - psixh + psix2 )
tref(n) = thbot(n) - delt*fac
tref(n) = tref(n) - 0.01_R8*ztref ! pot temp to temp correction
fac = (re/shr_const_karman) * (alz + al2 - psixh + psix2 )
qref(n) = qbot(n) - delq*fac
duu10n(n) = u10n*u10n ! 10m wind speed squared
!------------------------------------------------------------
! optional diagnostics, needed for water tracer fluxes (dcn)
!------------------------------------------------------------
if (present(ustar_sv)) ustar_sv(n) = ustar
if (present(re_sv )) re_sv(n) = re
if (present(ssq_sv )) ssq_sv(n) = ssq
else
!------------------------------------------------------------
! no valid data here -- out of domain
!------------------------------------------------------------
sen (n) = shr_const_spval ! sensible heat flux (W/m^2)
lat (n) = shr_const_spval ! latent heat flux (W/m^2)
lwup (n) = shr_const_spval ! long-wave upward heat flux (W/m^2)
evap (n) = shr_const_spval ! evaporative water flux ((kg/s)/m^2)
taux (n) = shr_const_spval ! x surface stress (N)
tauy (n) = shr_const_spval ! y surface stress (N)
tref (n) = shr_const_spval ! 2m reference height temperature (K)
qref (n) = shr_const_spval ! 2m reference height humidity (kg/kg)
duu10n(n) = shr_const_spval ! 10m wind speed squared (m/s)^2
if (present(ustar_sv)) ustar_sv(n) = shr_const_spval
if (present(re_sv )) re_sv (n) = shr_const_spval
if (present(ssq_sv )) ssq_sv (n) = shr_const_spval
endif
ENDDO
END subroutine shr_flux_atmOcn
!BOP ===========================================================================
!
! !IROUTINE: shr_flux_atmIce -- computes atm/ice fluxes
!
! !DESCRIPTION:
! Computes atm/ice fluxes
!
! !REVISION HISTORY:
! 2006-Jun-12 - B. Kauffman, first version, adapted from dice6 code
!
! !INTERFACE: ------------------------------------------------------------------
subroutine shr_flux_atmIce(mask ,zbot ,ubot ,vbot ,thbot & 1
& ,qbot ,rbot ,tbot ,ts ,sen &
& ,lat ,lwup ,evap ,taux ,tauy &
& ,tref ,qref )
implicit none
! !INPUT/OUTPUT PARAMETERS:
!--- input arguments --------------------------------
integer(IN),intent(in) :: mask (:) ! 0 <=> cell NOT in model domain
real(R8) ,intent(in) :: zbot (:) ! atm level height (m)
real(R8) ,intent(in) :: ubot (:) ! atm u wind (m/s)
real(R8) ,intent(in) :: vbot (:) ! atm v wind (m/s)
real(R8) ,intent(in) :: thbot(:) ! atm potential T (K)
real(R8) ,intent(in) :: qbot (:) ! atm specific humidity (kg/kg)
real(R8) ,intent(in) :: rbot (:) ! atm air density (kg/m^3)
real(R8) ,intent(in) :: tbot (:) ! atm T (K)
real(R8) ,intent(in) :: ts (:) ! surface temperature
!--- output arguments -------------------------------
real(R8) ,intent(out) :: sen (:) ! sensible heat flux (W/m^2)
real(R8) ,intent(out) :: lat (:) ! latent heat flux (W/m^2)
real(R8) ,intent(out) :: lwup (:) ! long-wave upward heat flux (W/m^2)
real(R8) ,intent(out) :: evap (:) ! evaporative water flux ((kg/s)/m^2)
real(R8) ,intent(out) :: taux (:) ! x surface stress (N)
real(R8) ,intent(out) :: tauy (:) ! y surface stress (N)
real(R8) ,intent(out) :: tref (:) ! 2m reference height temperature
real(R8) ,intent(out) :: qref (:) ! 2m reference height humidity
!EOP
!--- local constants --------------------------------
real(R8),parameter :: umin = 1.0_R8 ! minimum wind speed (m/s)
real(R8),parameter :: zref = 10.0_R8 ! ref height ~ m
real(R8),parameter :: ztref = 2.0_R8 ! ref height for air T ~ m
real(R8),parameter :: spval = shr_const_spval ! special value
real(R8),parameter :: g = shr_const_g ! gravity
real(R8),parameter :: cpdair = shr_const_cpdair ! spec heat of dry air
real(R8),parameter :: cpvir = shr_const_cpvir ! cpwv/cpdair - 1.0
real(R8),parameter :: zvir = shr_const_zvir ! rh2o/rair - 1.0
real(R8),parameter :: latvap = shr_const_latvap ! latent heat of evap
real(R8),parameter :: latice = shr_const_latice ! latent heat of fusion
real(R8),parameter :: stebol = shr_const_stebol ! Stefan-Boltzmann
real(R8),parameter :: karman = shr_const_karman ! Von Karman constant
real(R8),parameter :: zzsice = 0.0005_R8 ! ice surface roughness
!--- local variables --------------------------------
integer(IN) :: lsize ! array dimensions
integer(IN) :: n ! array indicies
real(R8) :: vmag ! surface wind magnitude (m/s)
real(R8) :: thvbot ! virtual temperature (K)
real(R8) :: ssq ! sea surface humidity (kg/kg)
real(R8) :: dssqdt ! derivative of ssq wrt Ts (kg/kg/K)
real(R8) :: delt ! potential T difference (K)
real(R8) :: delq ! humidity difference (kg/kg)
real(R8) :: stable ! stability factor
real(R8) :: rdn ! sqrt of neutral exchange coefficient (momentum)
real(R8) :: rhn ! sqrt of neutral exchange coefficient (heat)
real(R8) :: ren ! sqrt of neutral exchange coefficient (water)
real(R8) :: rd ! sqrt of exchange coefficient (momentum)
real(R8) :: rh ! sqrt of exchange coefficient (heat)
real(R8) :: re ! sqrt of exchange coefficient (water)
real(R8) :: ustar ! ustar
real(R8) :: qstar ! qstar
real(R8) :: tstar ! tstar
real(R8) :: hol ! H (at zbot) over L
real(R8) :: xsq ! temporary variable
real(R8) :: xqq ! temporary variable
real(R8) :: psimh ! stability function at zbot (momentum)
real(R8) :: psixh ! stability function at zbot (heat and water)
real(R8) :: alz ! ln(zbot/z10)
real(R8) :: ltheat ! latent heat for surface
real(R8) :: tau ! stress at zbot
real(R8) :: cp ! specific heat of moist air
real(R8) :: bn ! exchange coef funct for interpolation
real(R8) :: bh ! exchange coef funct for interpolation
real(R8) :: fac ! interpolation factor
real(R8) :: ln0 ! log factor for interpolation
real(R8) :: ln3 ! log factor for interpolation
!--- local functions --------------------------------
real(R8) :: Tk ! temperature (K)
real(R8) :: qsat ! the saturation humididty of air (kg/m^3)
real(R8) :: dqsatdt ! derivivative of qsat wrt surface temperature
real(R8) :: xd ! dummy argument
real(R8) :: psimhu ! unstable part of psimh
real(R8) :: psixhu ! unstable part of psimx
qsat(Tk) = 627572.4_R8 / exp(5107.4_R8/Tk)
dqsatdt(Tk) = (5107.4_R8 / Tk**2) * 627572.4_R8 / exp(5107.4_R8/Tk)
psimhu(xd) = log((1.0_R8+xd*(2.0_R8+xd))*(1.0_R8+xd*xd)/8.0_R8) - 2.0_R8*atan(xd) + 1.571_R8
psixhu(xd) = 2.0_R8 * log((1.0_R8 + xd*xd)/2.0_R8)
!--- formats ----------------------------------------
character(*),parameter :: subName = "(shr_flux_atmIce) "
!-------------------------------------------------------------------------------
! PURPOSE:
! using atm & ice state variables, compute atm/ice fluxes
! and diagnostic 10m air temperature and humidity
!
! NOTE:
! o all fluxes are positive downward
! o net heat flux = net sw + lw up + lw down + sen + lat
! o here, tstar = <WT>/U*, and qstar = <WQ>/U*.
! o wind speeds should all be above a minimum speed (eg. 1.0 m/s)
!
! ASSUME:
! o The saturation humidity of air at T(K): qsat(T) (kg/m^3)
!-------------------------------------------------------------------------------
lsize = size(tbot)
do n = 1,lsize
if (mask(n) == 0) then
sen (n) = spval
lat (n) = spval
lwup (n) = spval
evap (n) = spval
taux (n) = spval
tauy (n) = spval
tref (n) = spval
qref (n) = spval
else
!--- define some needed variables ---
vmag = max(umin, sqrt(ubot(n)**2+vbot(n)**2))
thvbot = thbot(n)*(1.0_R8 + zvir * qbot(n)) ! virtual pot temp (K)
ssq = qsat (ts(n)) / rbot(n) ! sea surf hum (kg/kg)
dssqdt = dqsatdt(ts(n)) / rbot(n) ! deriv of ssq wrt Ts
delt = thbot(n) - ts(n) ! pot temp diff (K)
delq = qbot(n) - ssq ! spec hum dif (kg/kg)
alz = log(zbot(n)/zref)
cp = cpdair*(1.0_R8 + cpvir*ssq)
ltheat = latvap + latice
!----------------------------------------------------------
! first estimate of Z/L and ustar, tstar and qstar
!----------------------------------------------------------
!--- neutral coefficients, z/L = 0.0 ---
rdn = karman/log(zref/zzsice)
rhn = rdn
ren = rdn
!--- ustar,tstar,qstar ----
ustar = rdn * vmag
tstar = rhn * delt
qstar = ren * delq
!--- compute stability & evaluate all stability functions ---
hol = karman * g * zbot(n) &
& * (tstar/thvbot+qstar/(1.0_R8/zvir+qbot(n))) / ustar**2
hol = sign( min(abs(hol),10.0_R8), hol )
stable = 0.5_R8 + sign(0.5_R8 , hol)
xsq = max(sqrt(abs(1.0_R8 - 16.0_R8*hol)) , 1.0_R8)
xqq = sqrt(xsq)
psimh = -5.0_R8*hol*stable + (1.0_R8-stable)*psimhu(xqq)
psixh = -5.0_R8*hol*stable + (1.0_R8-stable)*psixhu(xqq)
!--- shift all coeffs to measurement height and stability ---
rd = rdn / (1.0_R8+rdn/karman*(alz-psimh))
rh = rhn / (1.0_R8+rhn/karman*(alz-psixh))
re = ren / (1.0_R8+ren/karman*(alz-psixh))
!--- update ustar, tstar, qstar w/ updated, shifted coeffs --
ustar = rd * vmag
tstar = rh * delt
qstar = re * delq
!----------------------------------------------------------
! iterate to converge on Z/L, ustar, tstar and qstar
!----------------------------------------------------------
!--- compute stability & evaluate all stability functions ---
hol = karman * g * zbot(n) &
& * (tstar/thvbot+qstar/(1.0_R8/zvir+qbot(n))) / ustar**2
hol = sign( min(abs(hol),10.0_R8), hol )
stable = 0.5_R8 + sign(0.5_R8 , hol)
xsq = max(sqrt(abs(1.0_R8 - 16.0_R8*hol)) , 1.0_R8)
xqq = sqrt(xsq)
psimh = -5.0_R8*hol*stable + (1.0_R8-stable)*psimhu(xqq)
psixh = -5.0_R8*hol*stable + (1.0_R8-stable)*psixhu(xqq)
!--- shift all coeffs to measurement height and stability ---
rd = rdn / (1.0_R8+rdn/karman*(alz-psimh))
rh = rhn / (1.0_R8+rhn/karman*(alz-psixh))
re = ren / (1.0_R8+ren/karman*(alz-psixh))
!--- update ustar, tstar, qstar w/ updated, shifted coeffs --
ustar = rd * vmag
tstar = rh * delt
qstar = re * delq
!----------------------------------------------------------
! compute the fluxes
!----------------------------------------------------------
tau = rbot(n) * ustar * ustar
!--- momentum flux ---
taux(n) = tau * ubot(n) / vmag
tauy(n) = tau * vbot(n) / vmag
!--- heat flux ---
sen (n) = cp * tau * tstar / ustar
lat (n) = ltheat * tau * qstar / ustar
lwup(n) = -stebol * ts(n)**4
!--- water flux ---
evap(n) = lat(n)/ltheat
!----------------------------------------------------------
! compute diagnostic: 2m reference height temperature
!----------------------------------------------------------
!--- Compute function of exchange coefficients. Assume that
!--- cn = rdn*rdn, cm=rd*rd and ch=rh*rd, and therefore
!--- 1/sqrt(cn(n))=1/rdn and sqrt(cm(n))/ch(n)=1/rh
bn = karman/rdn
bh = karman/rh
!--- Interpolation factor for stable and unstable cases
ln0 = log(1.0_R8 + (ztref/zbot(n))*(exp(bn) - 1.0_R8))
ln3 = log(1.0_R8 + (ztref/zbot(n))*(exp(bn - bh) - 1.0_R8))
fac = (ln0 - ztref/zbot(n)*(bn - bh))/bh * stable &
& + (ln0 - ln3)/bh * (1.0_R8-stable)
fac = min(max(fac,0.0_R8),1.0_R8)
!--- actual interpolation
tref(n) = ts(n) + (tbot(n) - ts(n))*fac
qref(n) = qbot(n) - delq*fac
endif
enddo
end subroutine shr_flux_atmIce
!===============================================================================
! !BOP =========================================================================
!
! !IROUTINE: shr_flux_MOstability -- Monin-Obukhov BL stability functions
!
! !DESCRIPTION:
!
! Monin-Obukhov boundary layer stability functions, two options:
! turbulent velocity scales or gradient and integral functions
! via option = shr_flux_MOwScales or shr_flux_MOfunctions
!
! !REVISION HISTORY:
! 2007-Sep-19 - B. Kauffman, Bill Large - first version
!
! !INTERFACE: ------------------------------------------------------------------
subroutine shr_flux_MOstability(option,arg1,arg2,arg3,arg4,arg5),4
! !USES:
implicit none
! !INPUT/OUTPUT PARAMETERS:
integer(IN),intent(in) :: option ! shr_flux_MOwScales or MOfunctions
real(R8) ,intent(in) :: arg1 ! scales: uStar (in) funct: zeta (in)
real(R8) ,intent(inout) :: arg2 ! scales: zkB (in) funct: phim (out)
real(R8) ,intent(out) :: arg3 ! scales: phim (out) funct: phis (out)
real(R8) ,intent(out) :: arg4 ! scales: phis (out) funct: psim (out)
real(R8) ,intent(out),optional :: arg5 ! scales: (unused) funct: psis (out)
! !EOP
!----- local variables -----
real(R8) :: zeta ! z/L
real(R8) :: uStar ! friction velocity
real(R8) :: zkB ! (height)*(von Karman)*(surface bouyancy flux)
real(R8) :: phim ! momentum gradient function or scale
real(R8) :: phis ! temperature gradient function or scale
real(R8) :: psim ! momentum integral function or scale
real(R8) :: psis ! temperature integral function or scale
real(R8) :: temp ! temporary-variable/partial calculation
!----- local variables, stable case -----
real(R8),parameter :: uStarMin = 0.001_R8 ! lower bound on uStar
real(R8),parameter :: a = 1.000_R8 ! constant from Holtslag & de Bruin, equation 12
real(R8),parameter :: b = 0.667_R8 ! constant from Holtslag & de Bruin, equation 12
real(R8),parameter :: c = 5.000_R8 ! constant from Holtslag & de Bruin, equation 12
real(R8),parameter :: d = 0.350_R8 ! constant from Holtslag & de Bruin, equation 12
!----- local variables, unstable case -----
real(R8),parameter :: a2 = 3.0_R8 ! constant from Wilson, equation 10
!----- formats -----
character(*),parameter :: subName = '(shr_flux_MOstability) '
character(*),parameter :: F00 = "('(shr_flux_MOstability) ',4a)"
character(*),parameter :: F01 = "('(shr_flux_MOstability) ',a,i5)"
!-------------------------------------------------------------------------------
! Notes::
! o this could be two routines, but are one to help keep them aligned
! o the stable calculation is taken from...
! A.A.M. HoltSlag and H.A.R. de Bruin, 1988:
! "Applied Modeling of the Nighttime Surface Energy Balance over Land",
! Journal of Applied Meteorology, Vol. 27, No. 6, June 1988, 659-704
! o the unstable calculation is taken from...
! D. Keith Wilson, 2001: "An Alternative Function for the Wind and
! Temperature Gradients in Unstable Surface Layers",
! Boundary-Layer Meteorology, 99 (2001), 151-158
!-------------------------------------------------------------------------------
!----- check for consistancy between option and arguments ------------------
if (debug > 1 .and. s_loglev > 0) then
if (debug > 2) write(s_logunit,F01) "enter, option = ",option
if ( option == shr_flux_MOwScales .and. present(arg5) ) then
write(s_logunit,F01) "ERROR: option1 must have four arguments"
call shr_sys_abort(subName//"option inconsistant with arguments")
else if ( option == shr_flux_MOfunctions .and. .not. present(arg5) ) then
write(s_logunit,F01) "ERROR: option2 must have five arguments"
call shr_sys_abort(subName//"option inconsistant with arguments")
else
write(s_logunit,F01) "invalid option = ",option
call shr_sys_abort(subName//"invalid option")
end if
end if
!------ velocity scales option ----------------------------------------------
if (option == shr_flux_MOwScales) then
!--- input ---
uStar = arg1
zkB = arg2
if (zkB >= 0.0_R8) then ! ----- stable -----
zeta = zkB/(max(uStar,uStarMin)**3)
temp = exp(-d*zeta)
phim = uStar/(1.0_R8 + zeta*(a + b*(1.0_R8 + c - d*zeta)*temp))
phis = phim
else ! ----- unstable -----
temp = (zkB*zkB)**(1.0_R8/a2) ! note: zkB < 0, zkB*zkB > 0
phim = sqrt(uStar**2 + shr_flux_MOgammaM*temp)
phis = sqrt(uStar**2 + shr_flux_MOgammaS*temp)
end if
!--- output ---
arg3 = phim
arg4 = phis
! arg5 = <unused>
!------ stability function option -------------------------------------------
else if (option == shr_flux_MOfunctions) then
!--- input ---
zeta = arg1
if (zeta >= 0.0_R8) then ! ----- stable -----
temp = exp(-d*zeta)
phim = 1.0_R8 + zeta*(a + b*(1.0_R8 + c - d*zeta)*temp)
phis = phim
psim = -a*zeta - b*(zeta - c/d)*temp - b*c/d
psis = psim
else ! ----- unstable ----
temp = (zeta*zeta)**(1.0_R8/a2) ! note: zeta < 0, zeta*zeta > 0
phim = 1.0_R8/sqrt(1.0_R8 + shr_flux_MOgammaM*temp)
phis = 1.0_R8/sqrt(1.0_R8 + shr_flux_MOgammaS*temp)
psim = a2*log(0.5_R8 + 0.5_R8/phim)
psis = a2*log(0.5_R8 + 0.5_R8/phis)
end if
!--- output ---
arg2 = phim
arg3 = phis
arg4 = psim
arg5 = psis
!----------------------------------------------------------------------------
else
write(s_logunit,F01) "invalid option = ",option
call shr_sys_abort(subName//"invalid option")
endif
end subroutine shr_flux_MOstability
!===============================================================================
!===============================================================================
end module shr_flux_mod