Heat and momentum fluxes according to Fairall et al. (Source File: fairall.F90)

INTERFACE:

    subroutine fairall(sst,airt,u10,v10,precip,evap,taux,tauy,qe,qh)

DESCRIPTION:

The surface momentum flux vector, $(\tau_x^s,\tau_y^s)$, in [Nm$^{-2}$], the latent heat flux, $Q_e$, and the sensible heat flux, $Q_h$, both in [Wm$^{-2}$] are calculated here according to the Fairall et al. (1996b) bulk formulae, which are build on the Liu-Katsaros-Businger (Liu et al. (1979)) method. Cool skin and warm layer effects are considered according to the suggestions of Fairall et al. (1996a).

The air temperature airt and the sea surface temperature sst may be given in Kelvin or Celcius: if they are $>$ 100 - Kelvin is assumed.

This piece of code has been adapted from the COARE code originally written by David Rutgers and Frank Bradley - see http://www.coaps.fsu.edu/COARE/flux_algor/flux.html.

USES:

    use airsea_variables, only: kelvin,const06,rgas,rho_0,g,rho_0,kappa
    use airsea_variables, only: qs,qa,rhoa
    use airsea_variables, only: cpa,cpw
    use airsea, only: rain_impact,calc_evaporation
    IMPLICIT NONE

INPUT PARAMETERS:

    REALTYPE, intent(in)                :: sst,airt,u10,v10,precip

INPUT/OUTPUT PARAMETERS:

    REALTYPE, intent(inout)             :: evap

OUTPUT PARAMETERS:

    REALTYPE, intent(out)               :: taux,tauy,qe,qh

REVISION HISTORY:

    Original author(s): Adolf Stips
    $Log: fairall.F90,v $
    Revision 1.8  2009-01-07 07:25:38  kb
    fixed various compilation warnings found by gfortran
    Revision 1.7  2008-07-07 09:05:08  lars
    corrected typo in documentation
    Revision 1.6  2008-04-08 16:09:00  kb
    assure valid qh and qe under all circumstance - Bruggeman, Stips
    Revision 1.5  2008-01-02 15:30:44  kb
    added link to Fairall page
    Revision 1.4  2007-12-21 12:38:03  kb
    added precip/evap to kondo + cleaned
    Revision 1.3  2007-12-19 10:41:20  kb
    fixed m/s --> kg/m2/s conversion bug - Stips
    Revision 1.2  2007-10-02 10:14:08  kbk
    fixed rhoa calculation - rgas in airsea_variables module
    Revision 1.1  2007-09-25 10:06:10  kbk
    modularized the airsea module - added Fairall method

DEFINED PARAMETERS:

    Fairall LKB roughness Reynolds number to Von Karman
    REALTYPE,parameter        :: fdg = 1.0          ! non-dimensional
 
    Beta parameter evaluated from Fairall low windspeed turbulence data.
    REALTYPE,parameter        :: beta = 1.2         ! non-dimensional
 
    Zabl      Height (m) of atmospheric boundary layer.
    REALTYPE,parameter        :: Zabl = 600.0       ! in [m]
 
    REALTYPE, parameter       :: r3 = 1.0/3.0
    Liu et al. (1979) look-up table coefficients to compute roughness
    Reynolds number for temperature (rt) and moisture (rq) as a
    function of wind Reynolds number (rr):
         rt = Liu_a(:,1) * Rr   ** Liu_b(:,1)    temperature
         rq = Liu_a(:,2) * Rr   ** Liu_b(:,2)    moisture
    REALTYPE,parameter, dimension(8,2) :: Liu_a = reshape ( &
                  (/ 0.177,  1.376,    1.026,      1.625,   &
                     4.661, 34.904, 1667.190, 588000.0,     &
                     0.292,  1.808,    1.393,      1.956,   &
                     4.994, 30.709, 1448.680, 298000.0 /),  &
                  (/ 8, 2 /) )
 
    REALTYPE,parameter, dimension(8,2) :: Liu_b = reshape ( &
                  (/  0.0,    0.929, -0.599, -1.018,        &
                     -1.475, -2.067, -2.907, -3.935,        &
                      0.0,    0.826, -0.528, -0.870,        &
                     -1.297, -1.845, -2.682, -3.616 /),     &
                  (/ 8, 2 /) )
 
    REALTYPE,parameter, dimension(9) :: Liu_Rr =            &
                  (/    0.0,  0.11,   0.825,   3.0,         &
                       10.0, 30.0,  100.0,   300.0,         &
                     1000.0 /)
    Height (m) of surface air temperature measurement.
    REALTYPE, parameter       ::  zt= 2.0
    Height (m) of surface air humidity measurement
    REALTYPE, parameter       ::  zq= 2.0
    Height (m) of surface winds measurement
    REALTYPE, parameter       ::  zw= 10.0
    integer,  parameter       :: itermax = 20
 #ifdef GUSTINESS
    REALTYPE, parameter       :: wgust=0.2
 #else
    REALTYPE, parameter       :: wgust=0.0
 #endif
 
    REALTYPE,external         :: psi

LOCAL VARIABLES:

    REALTYPE                  :: tmp,cff,wgus
    REALTYPE                  :: L
    REALTYPE                  :: Cd
    REALTYPE                  :: ta,ta_k,tw,tw_k
    integer                   :: ier,iter,k
    REALTYPE                  :: vis_air
    REALTYPE                  :: tpsi,qpsi,wpsi,ZWoL,oL,ZToL,ZQoL,ZoW,ZoT, ZoQ
    REALTYPE                  :: Wstar,Tstar, Qstar, delQ, delT, rr,rt,rq
    REALTYPE                  :: TVstar,Bf, upvel,delw,Wspeed, w
    REALTYPE                  :: ri,cd_rain
    REALTYPE                  :: x1,x2,x3
    REALTYPE                  :: x
    REALTYPE                  :: rainfall
    REALTYPE, parameter       :: eps=1.0e-12