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cool_skin.m
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cool_skin.m
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function [delta,Dter,Dqer] = cool_skin(sal,Tw,rhoa,cpa,Pa, ...
U_star,T_star,Q_star, ...
dlw,dsw,nsw,delta,g,Rgas, ...
CtoK,Qsat_coeff)
% COOL_SKIN: compute the cool-skin parameters.
% COOL_SKIN computes the cool-skin parameters. This code follows
% the fortran program bulk_v25b.f. For more details, see the cool-skin
% and warm layer paper by Fairall et al (1996), JGR, 101, 1295-1308.
% All input variables should be vectors (either row or column), except
% Rgas, CtoK, Qsat_coeff, and g, which can be scalars. Uses some
% functions from CSIRO SEAWATER TOOLBOX.
%
% INPUT: sal - salinity [psu (PSS-78)]
% Tw - water surface temperature [C]
% rhoa - air density [kg/m^3]
% cpa - specific heat capacity of air [J/kg/C]
% Pa - air pressure [mb]
% U_star - friction velocity including gustiness [m/s]
% T_star - temperature scale [C]
% Q_star - humidity scale [kg/kg]
% dlw - downwelling (INTO water) longwave radiation [W/m^2]
% dsw - measured insolation [W/m^2]
% nsw - net shortwave radiation INTO water [W/m^2]
% delta - cool-skin layer thickness [m]
% g - gravitational constant [m/s^2]
% Rgas - gas constant for dry air [J/kg/K]
% CtoK - conversion factor for deg C to K
% Qsat_coeff - saturation specific humidity coefficient
%
% OUTPUT: delta - cool-skin layer thickness [m]
% Dter - cool-skin temperature difference [C]; positive if
% surface is cooler than bulk (presently no warm skin
% permitted by model)
% Dqer - cool-skin specific humidity difference [kg/kg]
%
% USAGE: [delta,Dter,Dqer] = cool_skin(sal,Tw,rhoa,cpa,Pa, ...
% U_star,T_star,Q_star, ...
% dlw,dsw,nsw,delta,g,Rgas, ...
% CtoK,Qsat_coeff)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4/9/99: version 1.2 (contributed by AA)
% 8/5/99: version 2.0
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -> column vectors
sal = sal(:); Tw = Tw(:); rhoa = rhoa(:); cpa = cpa(:); Pa = Pa(:);
U_star = U_star(:); T_star = T_star(:); Q_star = Q_star(:);
dlw = dlw(:); nsw = nsw(:); delta = delta(:); Rgas = Rgas(:);
CtoK = CtoK(:); Qsat_coeff = Qsat_coeff(:); g = g(:);
size_data = size(Tw);
alpha = sw_alpha(sal,Tw,0); % thermal expansion coeff [1/C]
beta_sal = sw_beta(sal,Tw,0); % saline contraction coeff [1/psu]
cpw = sw_cp(sal,Tw,0); % specific heat capacity [J/kg/C]
rhow = sw_dens0(sal,Tw); % density at atmospheric press [kg/m^3]
viscw = sw_visc(sal,Tw,0); % kinematic viscosity of sea-water [m^2/s]
tcondw = sw_tcond(sal,Tw,0); % thermal conductivity of sea-water [W/m/K]
% the following are values used for COARE
% alpha = 2.1e-5*(Tw+3.2).^0.79;% as used for COARE data
% beta_sal = 0.026./sal; % as used for COARE data
% cpw = 4000*ones(size(Tw)); % as used for COARE data
% rhow = 1022*ones(size(Tw)); % as used for COARE data
% viscw = 1e-6*ones(size(Tw)); % as used for COARE data
% tcondw = 0.6*ones(size(Tw)); % as used for COARE data
% latent heat of water
Le = (2.501-0.00237*Tw)*10^6;
% saturation specific humidity;
Qs = Qsat_coeff.*qsat(Tw,Pa);
% a big constant
bigc = (16.*g.*cpw.*(rhow.*viscw).^3)./(tcondw.^2.*rhoa.^2);
% constant for correction of dq; slope of sat. vap.
wetc = 0.622.*Le.*Qs./(Rgas.*(Tw+CtoK).^2);
% compute fluxes out of the ocean (i.e., up = positive)
hsb = - rhoa.*cpa.*U_star.*T_star;
hlb = - rhoa.*Le.*U_star.*Q_star;
% net longwave (positive up)
nlw = - lwhf(Tw,dlw,dsw);
% total heat flux out of the water surface
qout = nlw + hsb + hlb;
% compute deltaSc = fc*Sns, see sec. 2.4 (p. 1297-1298) in cool-skin paper
% 3 choices; comment out those that are not used!
deltaSc = zeros(size_data);
ipos_nsw = find(nsw > 0);
deltaSc(ipos_nsw) = f_c(delta(ipos_nsw),1).*nsw(ipos_nsw); % Paulson and Simpson (1981)
% deltaSc(ipos_nsw) = f_c(delta(ipos_nsw),2).*nsw(ipos_nsw); % COARE approx. to Paulson
% deltaSc(ipos_nsw) = f_c(delta(ipos_nsw),3).*nsw(ipos_nsw); % Hasse (1971)
qcol = qout - deltaSc;
% initialize
alphaQb = zeros(size_data);
lamda = zeros(size_data);
Dter = zeros(size_data);
ipos_qcol = find(qcol > 0);
% eqn. 17 in cool-skin paper
alphaQb(ipos_qcol) = alpha(ipos_qcol).*qcol(ipos_qcol) + ...
sal(ipos_qcol).*beta_sal(ipos_qcol) ...
.*hlb(ipos_qcol).*cpw(ipos_qcol)./Le(ipos_qcol);
% eqn. 14 in cool-skin paper
lamda(ipos_qcol) = 6./(1+(bigc(ipos_qcol).*alphaQb(ipos_qcol) ...
./U_star(ipos_qcol).^4).^0.75).^(1/3);
% eqn. 12 in cool-skin paper
delta(ipos_qcol) = lamda(ipos_qcol).*viscw(ipos_qcol) ...
./(sqrt(rhoa(ipos_qcol)./rhow(ipos_qcol)) ...
.*U_star(ipos_qcol));
% eqn. 13 in cool-skin paper
Dter(ipos_qcol) = qcol(ipos_qcol).*delta(ipos_qcol)./tcondw(ipos_qcol);
Dqer = wetc.*Dter;
function fc = f_c(delta,option)
% F_C: computes the absorption coefficient fc.
% fc=F_C(delta,option) computes the absorption coefficient fc.
%
% INPUT: delta - thickness of cool-skin layer [m]
% option - 1 use Paulson and Simpson (1981) data for seawater;
% See also p. 1298 of Fairall et al (1996) JGR, 101,
% cool-skin and warm-layer paper.
%
% 2 use approximation to Paulson as given in
% p. 1298 of Fairall et al (1996) JGR, 101, cool-skin
% and warm-layer paper.
%
% 3 use fc = const. = 0.19, as suggested by Hasse (1971).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 8/5/99: version 1.2 (contributed by AA)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if option == 1
% Use Paulson and Simpson data
% Wavelength bands for the coefficients [um]
% 1) 0.2-0.6
% 2) 0.6-0.9
% 3) 0.9-1.2
% 4) 1.2-1.5
% 5) 1.5-1.8
% 6) 1.8-2.1
% 7) 2.1-2.4
% 8) 2.4-2.7
% 9) 2.7-3.0
% F_i is the amplitude
F_i = [0.237 0.360 0.179 0.087 0.080 0.0246 0.025 0.007 0.0004];
F_i1 = repmat(F_i,length(delta),1);
% Gam_i is the absorption length [m]
Gam_i = [34.8 2.27 3.15e-2 5.48e-3 8.32e-4 1.26e-4 3.13e-4 7.82e-5 1.44e-5];
Gam_i1 = repmat(Gam_i,length(delta),1);
delta1 = repmat(delta,1,length(Gam_i));
% fc is the absorption in the cool-skin layer of thickness delta
fc = sum(F_i1.*(1-(Gam_i1./delta1).*(1-exp(-delta1./Gam_i1))), 2);
elseif option == 2
% use COARE approximation to Paulson and Simpson data
fc = 0.137+11.*delta-(6.6e-5./delta).*(1-exp(-delta/8e-4));
elseif option == 3
% use Hasse simple approximation
fc = 0.19;
end