coare40vn.m

function A=coare40vn(u,zu,t,zt,rh,zq,P,ts,Rs,Rl,lat,zi,rain,cp,sigH)
% function [A,B]=coare40vn(uwind,vwind,zu,t,zt,qv,zq,P,ts,Rs,Rl,lat)
%
% Vectorized version of COARE 3 code (Fairall et al, 2003) with 
% modification based on the CLIMODE, MBL and CBLAST experiments 
% (Edson et al., JPO, 43, 2013). 
%
% ************************************************************************
% *************** IMPORTANT NOTICE ***************************************
% ************************************************************************
% The current version of the code includes the wind-speed, wave-age and
% sea-state dependent parameterizations of the Charnock variabile as
% described in Edson et al. (2013).  The parameterization is chosen by the 
% inputed values of
%    cp = phase speed of dominant waves (m/s)  
%  sigH = significant wave height (m)
%
% Specifically, if the user inputs:
%
% A=coare35vn(u,zu,t,zt,rh,zq,P,ts,Rs,Rl,lat,zi,rain,NaN,NaN)  :  the wind-speed dependent formulation is used
% A=coare35vn(u,zu,t,zt,rh,zq,P,ts,Rs,Rl,lat,zi,rain,cp,NaN)   :  the wave-age dependent formulation is used
% A=coare35vn(u,zu,t,zt,rh,zq,P,ts,Rs,Rl,lat,zi,rain,cp,sigH)  :  the sea-state dependent formulation is used
%
% The sea-state dependent formulation requires both cp and sigH.
%
%********************************************************************
% The cool skin option is retained but the warm layer code is removed.  
% An m-file that applies the warm layer correction and calls this version 
% of COARE 3 (coare35vnWarm) is available.
%
% An important component of this code is whether the inputed ts 
% represents the skin temperature of a near surface temperature.  
% How this variable is treated is determined by the jcool parameter:
% set jcool=1 if Ts is bulk ocean temperature (default),
%     jcool=0 if Ts is true ocean skin temperature. 
%********************************************************************

jcool=1;

% The code assumes u,t,rh,ts are vectors; 
% sensor heights zu,zt,zl, latitude lat, and PBL height zi are constants;
% air pressure P and radiation Rs,Rl may be vectors or constants. 
% Default values are assigned for P,Rs,Rl,lat,and zi if these data are not 
% available.  Input NaNs to indicate no data. Defaults should be set to 
% representative regional values if possible.
%
% Inputs:  
%
%     u = relative wind speed (m/s) at heigth zu 
%    zu = height of wind speed measurement (m)
%     t = bulk air temperature (degC) at height zt
%    zt = height of temperature measurement (m)
%    rh = relative humidity (%) at height zq  (0-100)
%    zq = height of relative humidity measurement (m)
%     P = surface air pressure (mb) (default = 1015)
%    ts = water temperature (degC) see jcool below
%    Rs = downward shortwave radiation (W/m^2) (default = 150) 
%    Rl = downward longwave radiation (W/m^2) (default = 370)
%   lat = latitude (default = +45 N)
%    zi = PBL height (m) (default = 600m)
%  rain = rain rate (mm/hr) - not required for turbulent flux estimates,
%         set to NaN if unavailable.
%    cp = phase speed of dominant waves (m/s)  
%  sigH = significant wave height (m)
%
% The user controls the output.  This is currently set as:
% 
%A=[usr tau hsb hlb hbb hsbb wbar  tsr qsr zot zoq Cd Ch Ce  L zet dter dqer tkt Urf Trf Qrf RHrf UrfN Rnl Le rhoa UN U10 U10N Cdn_10 Chn_10 Cen_10 RF Qs Evap T10 Q10 RH10];
%   1   2   3   4   5   6    7      8   9  10  11  12 13 14 15 16   17   18   19  20  21  22  23   24   25 26  27  28  29  30    31     32     33   34 35  36  37  38   39
%  where
%
%   usr = friction velocity that includes gustiness (m/s)
%   tau = wind stress (N/m^2)
%   hsb = sensible heat flux into ocean (W/m^2)
%   hlb = latent heat flux into ocean (W/m^2)
%   hbb = buoyany flux into ocean (W/m^2)
%   hsbb = "sonic" buoyancy flux measured directly by sonic anemometer 
%   wbar = the vertical velocity required to "Webb Correct" direct
%          covariance fluxes
%   tsr = temperature scaling parameter (K)
%   qsr = specific humidity scaling parameter (g/Kg)
%   zot = thermal roughness length (m)
%   zoq = moisture roughness length (m)
%   Cd = wind stress transfer (drag) coefficient at height zu   
%   Ch = sensible heat transfer coefficient (Stanton number) at height zu   
%   Ce = latent heat transfer coefficient (Dalton number) at height zu
%    L = Obukhov length scale (m) 
%  zet = Monin-Obukhov stability parameter zu/L 
% dter = cool-skin temperature depression (degC)
% dqer = cool-skin humidity depression (degC)
%  tkt = cool-skin thickness (m)
%  Urf = wind speed at reference height (user can select height below)
%  Trf = temperature at reference height
%  Qrf = specific humidity at reference height
% RHrf = relative humidity at reference height
% UrfN = neutral value of wind speed at reference height
%  Rnl = Upwelling IR radiation computed by COARE
%   Le = latent heat of vaporization
% rhoa = density of air
%   UN = neutral value of wind speed at zu
%  U10 = wind speed adjusted to 10 m
% UN10 = neutral value of wind speed at 10m
%Cdn_10 = neutral value of drag coefficient at 10m    
%Chn_10 = neutral value of Stanton number at 10m    
%Cen_10 = neutral value of Dalton number at 10m
%    RF = sensible heat flux due to rain (W/m^2)
%    Qs = surface value of specific humidity (g/kg) without cool skin
%         correction
%  Evap = evaporation rate from surface in mm/hr
%   T10 = temperarure at 10 m 
%   Q10 = specific humidity at 10 m
%  RH10 = relative humidity at 10 m
%

% Notes: 1) u is the relative wind speed, i.e., the magnitude of the
%           difference between the wind (at zu) and ocean surface current 
%           vectors.
%        2) Set jcool=0 in code if ts is true surface skin temperature,
%           otherwise ts is assumed the bulk temperature and jcool=1.
%        3) Set P=NaN to assign default value if no air pressure data 
%           available. 
%        4) Set Rs=NaN, Rl=NaN if no radiation data available.  This assigns 
%           default values to Rs, Rl so that cool skin option can be applied. 
%        5) Set lat=NaN and/or zi=NaN to assign default values if latitude
%           and/or PBL height not given. 
%        6) The code to compute the heat flux caused by precipitation is 
%           included if rain data is available (default is no rain).
%        7) Code updates the cool-skin temperature depression dter and thickness
%           tkt during iteration loop for consistency.
%        8) Number of iterations set to nits = 6.

% Reference:
%
%  Fairall, C.W., E.F. Bradley, J.E. Hare, A.A. Grachev, and J.B. Edson (2003),
%  Bulk parameterization of air sea fluxes: updates and verification for the 
%  COARE algorithm, J. Climate, 16, 571-590.

% Code history:
% 
% 1. 12/14/05 - created based on scalar version coare26sn.m with input
%    on vectorization from C. Moffat.  
% 2. 12/21/05 - sign error in psiu_26 corrected, and code added to use variable
%    values from the first pass through the iteration loop for the stable case
%    with very thin M-O length relative to zu (zetu>50) (as is done in the 
%    scalar coare26sn and COARE3 codes).
% 3. 7/26/11 - S = dt was corrected to read S = ut.
% 4. 7/28/11 - modification to roughness length parameterizations based 
%    on the CLIMODE, MBL, Gasex and CBLAST experiments are incorporated
%
%-----------------------------------------------------------------------

% %--------Siqi
% u=sqrt(uwind.^2+vwind.^2);
% t=t-273.16;
% ts=ts-273.16;
% 
% rh=t;
% rh=6.112*exp(17.67*rh/(rh+243.5));
% rh=0.622*rh/(P-rh);
% rh=qv*100/rh;
% rh(rh>100.)=100.;
% %--------Siqi

% convert input to column vectors
u=u(:);t=t(:);rh=rh(:);P=P(:);ts=ts(:);
Rs=Rs(:);Rl=Rl(:);lat=lat(:);zi=zi(:);
zu=zu(:);zt=zt(:);zq=zq(:);
rain=rain(:);
rain=nan;
N=length(u);


% set local variables to default values if input is NaN
if isnan(P); P=1013*ones(N,1); end      % pressure
if isnan(Rs); Rs=150*ones(N,1); end     % incident shortwave radiation
if isnan(Rl); Rl=370*ones(N,1); end     % incident longwave radiation
if isnan(lat); lat=45; end              % latitude
if isnan(zi); zi=600; end               % PBL height



waveage=0;
seastate=0;
if ~isnan(cp(1))
    waveage=1;
    if ~isnan(sigH(1))
        seastate=1;
    else
        sigH=ones(N,1)*NaN;
    end
else
    cp=ones(N,1)*NaN;
    sigH=ones(N,1)*NaN;
end


%************************************************************************
% Check on which parameterization you are using.  You can remove the 
% pause once you are familiar with how the code selects the 
% appropriate parameterization based on the input variables.
%************************************************************************

if waveage && seastate
    disp('You are about to use the seastate dependent parameterization.')
%     display('Press any key to continue ...') % Siqi
%     pause
end
if waveage && ~seastate
    disp('You are about to use the waveage dependent parameterization.')
%     display('Press any key to continue ...') % Siqi
%     pause
end

% input variable u is assumed relative wind speed (magnitude of difference
% between wind and surface current vectors). to follow orginal Fairall code, set
% surface current speed us=0. if us data are available, construct u prior to
% using this code.
us = 0*u;

% convert rh to specific humidity
Qs = qsat26sea(ts,P)./1000;    % surface water specific humidity (g/kg)
Q  = qsat26air(t,P,rh);  % specific humidity of air (g/kg)
% [Q,Pv]  = qsat26air(t,P,rh);  % specific humidity of air (g/kg)   % Siqi
Q=Q./1000;

%***********  set constants **********************************************
% zref=10;      % Siqi
Beta = 1.2;
von  = 0.4;
fdg  = 1.00; % Turbulent Prandtl number
tdk  = 273.16;
grav = grv(lat);

%***********  air constants **********************************************
Rgas = 287.05;
Le   = (2.501-.00237*ts)*1e6;
cpa  = 1004.67;
% cpv  = cpa*(1+0.84*Q);   % Siqi
rhoa = P*100./(Rgas*(t+tdk).*(1+0.61*Q));
% rhodry = (P-Pv)*100./(Rgas*(t+tdk));  % Siqi
visa = 1.326e-5*(1+6.542e-3.*t+8.301e-6*t.^2-4.84e-9*t.^3);
% lapse=grav./cpa;      % Siqi

%***********  cool skin constants  ***************************************
Al   = 2.1e-5*(ts+3.2).^0.79;
be   = 0.026;
cpw  = 4000;
rhow = 1022;
visw = 1e-6;
tcw  = 0.6;
bigc = 16*grav*cpw*(rhow*visw)^3./(tcw.^2*rhoa.^2);
wetc = 0.622*Le.*Qs./(Rgas*(ts+tdk).^2);

%***********  net radiation fluxes ***************************************
Rns = 0.945.*Rs; % albedo correction
% IRup = eps*sigma*T^4 + (1-eps)*IR
% Rnl = IRup - IR
% Rnl = eps*sigma*T^4 - eps*IR  as below

Rnl = 0.97*(5.67e-8*(ts-0.3*jcool+tdk).^4-Rl); % initial value

% IRup = Rnl + IR

%****************  begin bulk loop ********************************************

%***********  first guess ************************************************
% rovcp=Rgas/cpa;    % Siqi
lapse=grav/cpa;

du = u-us;
dt = ts-t-lapse.*zt;
dq = Qs-Q;

ta = t+tdk;
tv = ta.*(1+0.61*Q);
ug = 0.5;
dter  = 0.3;
dqer = dter*wetc; 
ut    = sqrt(du.^2+ug.^2);
u10   = ut.*log(10/1e-4)./log(zu/1e-4);
usr   = 0.035*u10;
zo10  = 0.011*usr.^2./grav + 0.11*visa./usr;
Cd10  = (von./log(10./zo10)).^2;
Ch10  = 0.00115;
Ct10  = Ch10./sqrt(Cd10);
zot10 = 10./exp(von./Ct10);
Cd    = (von./log(zu./zo10)).^2;
Ct    = von./log(zt./zot10);
CC    = von*Ct./Cd;
Ribcu = -zu./zi./.004/Beta^3;
Ribu  = -grav.*zu./ta.*((dt-dter*jcool)+.61*ta.*dq)./ut.^2;
zetu = CC.*Ribu.*(1+27/9*Ribu./CC);
k50=find(zetu>50); % stable with very thin M-O length relative to zu
k=find(Ribu<0); 
if length(Ribcu)==1
    zetu(k)=CC(k).*Ribu(k)./(1+Ribu(k)./Ribcu); clear k;
else
    zetu(k)=CC(k).*Ribu(k)./(1+Ribu(k)./Ribcu(k)); clear k;
end
L10 = zu./zetu;
gf=ut./du;
usr = ut.*von./(log(zu./zo10)-psiu_26(zu./L10));
tsr = -(dt-dter*jcool).*von*fdg./(log(zt./zot10)-psit_26(zt./L10));
qsr = -(dq-dqer*jcool)*von*fdg./(log(zq./zot10)-psit_26(zq./L10));

tkt = 0.001*ones(N,1);

%**********************************************************
%  The Charnock variable for COARE 3.0
%**********************************************************
charn = 0.011*ones(N,1);
k=find(ut>10); 
charn(k)=0.011+(ut(k)-10)/(18-10)*(0.018-0.011); clear k;
k=find(ut>18); charn(k)=.018; clear k;

%**********************************************************
%  The following gives the new formulation for the
%  Charnock variable in COARE 3.5
%**********************************************************

charnC = 0.011*ones(N,1);
umax=19;
a1=0.0017;
a2=-0.0050;

charnC=a1*u10+a2;  %wind-speed dependent coefficients
k=find(u10>umax);
charnC(k)=a1*umax+a2;

A=0.114;  %wave-age dependent coefficients
B=0.622;
charnW=A.*(usr./cp).^B;

Ad=0.091;  %Sea-state/wave-age dependent coefficients
Bd=2.0;
zoS=sigH.*Ad.*(usr./cp).^Bd;
charnS=zoS.*grav./usr./usr;

nits=10; % number of iterations

%**************  bulk loop **************************************************

for i=1:9%nits
    
    zet=von.*grav.*zu./tv.*(tsr.*(1+0.61*Q) +.61*ta.*qsr)./(usr.^2);
%     zet=von.*grav.*zu./tv.*(tsr +.61*ta.*qsr)./(usr.^2);
    if waveage
        if seastate
            charn=charnS;
        else
            charn=charnW;
        end
    else
        charn=charnC;
    end
    L=zu./zet;
    zo=charn.*usr.^2./grav+0.11*visa./usr; % surface roughness
    rr=zo.*usr./visa;
    zoq=min(1.6e-4,6e-3./rr.^1.6);   % These thermal roughness lengths give Stanton   
    zot=zoq;                         % and Dalton numbers for COARE 4.0
    cdhf=von./(log(zu./zo)-psiu_26(zu./L));
    cqhf=von.*fdg./(log(zq./zoq)-psit_26(zq./L));
    cthf=von.*fdg./(log(zt./zot)-psit_26(zt./L));
    usr=ut.*cdhf;
    qsr=-(dq-dqer*jcool).*cqhf;
    tsr=-(dt-dter*jcool).*cthf;
    tvsr=tsr+0.61*ta.*qsr;
    tssr=tsr+0.51*ta.*qsr;
    Bf=-grav./tv.*usr.*tvsr;
    ug=0.2*ones(N,1);
    k=find(Bf>0); 
    if length(zi)==1
        ug(k)=max(0.2,Beta*(Bf(k).*zi).^.333); clear k;
    else
        ug(k)=max(0.2,Beta*(Bf(k).*zi(k)).^.333); clear k;
    end
    ut=sqrt(du.^2+ug.^2);
    gf=ut./du;
    hsb=-rhoa*cpa.*usr.*tsr;
    hlb=-rhoa.*Le.*usr.*qsr;
    qout=Rnl+hsb+hlb;
    dels=Rns.*(0.065+11*tkt-6.6e-5./tkt.*(1-exp(-tkt/8.0e-4)));
    qcol=qout-dels;
    alq=Al.*qcol+be*hlb*cpw./Le;
    xlamx=6.0*ones(N,1);
    tkt=min(0.01, xlamx.*visw./(sqrt(rhoa./rhow).*usr));
    k=find(alq>0); xlamx(k)=6./(1+(bigc(k).*alq(k)./usr(k).^4).^0.75).^0.333;
    tkt(k)=xlamx(k).*visw./(sqrt(rhoa(k)./rhow).*usr(k)); clear k;
    dter=qcol.*tkt./tcw;
    sst=ts-dter;  
    dqer=Qs-qsat26sea(sst,P)./1000; %wetc.*dter;
    Rnl=0.97*(5.67e-8*(ts-dter.*jcool+tdk).^4-Rl); % update dter
    if i==1 % save first iteration solution for case of zetu>50;
        usr50=usr(k50);tsr50=tsr(k50);qsr50=qsr(k50);L50=L(k50);
        zet50=zet(k50);dter50=dter(k50);dqer50=dqer(k50);tkt50=tkt(k50);
    end
    u10N = usr./von./gf.*log(10./zo);
    if waveage
        if seastate
            zoS=sigH.*Ad.*(usr./cp).^Bd-0.11*visa./usr;
            charnS=zoS.*grav./usr./usr;
        else
            charnW=A.*(usr./cp).^B;
        end
    else
        charnC=a1*u10N+a2;
        k=find(u10N>umax);
        charnC(k)=a1*umax+a2;
    end 
%     disp([i zet zo usr cdhf]) % Siqi
end

% insert first iteration solution for case with zetu>50
usr(k50)=usr50;tsr(k50)=tsr50;qsr(k50)=qsr50;L(k50)=L50;
zet(k50)=zet50;dter(k50)=dter50;dqer(k50)=dqer50;tkt(k50)=tkt50;

%****************  compute fluxes  ********************************************
tau=rhoa.*usr.*usr./gf;      % wind stress
hsb=-rhoa.*cpa.*usr.*tsr;     % sensible heat flux
hlb=-rhoa.*Le.*usr.*qsr;      % latent heat flux
hbb=-rhoa.*cpa.*usr.*tvsr;    % buoyancy flux
hsbb=-rhoa.*cpa.*usr.*tssr;   % sonic heat flux
wbar=1.61*hlb./Le./(1+1.61*Q)./rhoa+hsb./rhoa./cpa./ta; %Useful for Webb Correction
%hlwebb=rhoa.*wbar.*Q.*Le;
Evap=1000*hlb./Le./1000*3600;   %mm/hour

%*****  compute transfer coeffs relative to ut @ meas. ht  ********************
Cd=tau./rhoa./ut./max(.1,du);
Ch=-usr.*tsr./ut./(dt-dter*jcool);
Ce=-usr.*qsr./(dq-dqer*jcool)./ut;

%***  compute 10-m neutral coeff relative to ut (output if needed) ************
Cdn_10=1000*von.^2./log(10./zo).^2;
Chn_10=1000*von.^2.*fdg./log(10./zo)./log(10./zot);
Cen_10=1000*von.^2.*fdg./log(10./zo)./log(10./zoq);

%***  compute 10-m neutral coeff relative to ut (output if needed) ************
%  Find the stability functions
%*********************************
zrf_u=2;             %User defined reference heights to
zrf_t=2;             %compute values at zrf.
zrf_q=2;
psi=psiu_26(zu./L);
psi10=psiu_26(10./L);
psirf=psiu_26(zrf_u./L);
psiT=psit_26(zt./L);
psi10T=psit_26(10./L);
psirfT=psit_26(zrf_t./L);
psirfQ=psit_26(zrf_q./L);
gf=ut./du;

%*********************************************************
%  Determine the wind speeds relative to ocean surface
%  Note that usr is the friction velocity that includes 
%  gustiness usr = sqrt(Cd) S, which is equation (18) in
%  Fairall et al. (1996)
%*********************************************************
S = ut;
U = du;
S10 = S + usr./von.*(log(10./zu)-psi10+psi);
U10 = S10./gf;
% or U10 = U + usr./von./gf.*(log(10/zu)-psi10+psi);
Urf = U + usr./von./gf.*(log(zrf_u./zu)-psirf+psi);
UN = U + psi.*usr/von./gf;
U10N = U10 + psi10.*usr/von./gf;
UrfN = Urf + psirf.*usr/von./gf;

UN2 = usr/von./gf.*log(zu./zo);
U10N2 = usr./von./gf.*log(10./zo);
UrfN2  = usr./von./gf.*log(zrf_u./zo);

%******** rain heat flux (save to use if desired) *****************************
if isnan(rain(1))
    RF=zeros(size(usr));
else
    dwat=2.11e-5*((t+tdk)./tdk).^1.94; %! water vapour diffusivity
    dtmp=(1. + 3.309e-3*t - 1.44e-6.*t.*t).*0.02411./(rhoa.*cpa); %! heat diffusivity
    dqs_dt=Q.*Le./(Rgas.*(t+tdk).^2); %! Clausius-Clapeyron
    alfac= 1./(1+0.622*(dqs_dt.*Le.*dwat)./(cpa.*dtmp)); %! wet bulb factor
    RF= rain.*alfac.*cpw.*((ts-t-dter*jcool)+(Qs-Q-dqer*jcool).*Le./cpa)./3600;
end

lapse=grav/cpa;
SST=ts-dter*jcool;

T = t;
T10 = T + tsr./von.*(log(10./zt)-psi10T+psiT) + lapse.*(zt-10);
Trf = T + tsr./von.*(log(zrf_t./zt)-psirfT+psiT) + lapse.*(zt-zrf_t);
TN = T + psiT.*tsr/von;
T10N = T10 + psi10T.*tsr/von;
TrfN = Trf + psirfT.*tsr/von;

TN2 = SST + tsr/von.*log(zt./zot)-lapse.*zt;
T10N2 = SST + tsr/von.*log(10./zot)-lapse.*10;
TrfN2 = SST + tsr/von.*log(zrf_t./zot)-lapse.*zrf_t;

dqer=(Qs-qsat26sea(SST,P)./1000)*jcool; %wetc.*dter*jcool;
SSQ=Qs-dqer;
SSQ=SSQ*1000;
Q=Q*1000;
qsr=qsr*1000;
Q10 = Q + qsr./von.*(log(10./zq)-psi10T+psiT);
Qrf = Q + qsr./von.*(log(zrf_q./zq)-psirfQ+psiT);
QN = Q + psiT.*qsr/von./sqrt(gf);
Q10N = Q10 + psi10T.*qsr/von;
QrfN = Qrf + psirfQ.*qsr/von;

QN2 = SSQ + qsr/von.*log(zq./zoq);
Q10N2 = SSQ + qsr/von.*log(10./zoq);
QrfN2 = SSQ + qsr/von.*log(zrf_q./zoq);
RHrf=RHcalc(Trf,P,Qrf/1000);
RH10=RHcalc(T10,P,Q10/1000);

%****************  output  ****************************************************

% %--------Siqi
% t=t+273.16;
% ts=ts+273.16;
% 
% hsb=-hsb;
% hlb=-hlb;
% Rl=Rl-0.98*5.6697*((ts*0.01)^4);
% net=Rl+Rs+hsb+hlb;
% B=[net Rs Rl hlb hsb];
% %--------Siqi

A=[usr tau hsb hlb hbb hsbb wbar  tsr qsr zot zoq Cd Ch Ce  L zet dter dqer tkt Urf Trf Qrf RHrf UrfN Rnl Le rhoa UN U10 U10N Cdn_10 Chn_10 Cen_10 RF Qs Evap T10 Q10 RH10 gf];
%   1   2   3   4   5   6    7      8   9  10  11  12 13 14 15 16   17   18  19  20  21  22  23   24   25 26  27  28  29  30    31     32     33   34 35  36  37  38   39  40]
end
%------------------------------------------------------------------------------
function psi=psit_26(zet)
% computes temperature structure function
dzet=min(50,0.35*zet); % stable
psi=-((1+0.6667*zet).^1.5+0.6667*(zet-14.28).*exp(-dzet)+8.525);
k=find(zet<0); % unstable
x=(1-16*zet(k)).^0.5;
psik=2*log((1+x)./2);
x=(1-34.15*zet(k)).^0.3333;
psic=1.5*log((1+x+x.^2)./3)-sqrt(3)*atan((1+2*x)./sqrt(3))+4*atan(1)./sqrt(3);
f=zet(k).^2./(1+zet(k).^2);
psi(k)=(1-f).*psik+f.*psic;
end
%------------------------------------------------------------------------------
function psi=psiu_26(zet)
% computes velocity structure function
dzet=min(50,0.35*zet); % stable
a=0.7;
b=3/4;
c=5;
d=0.35;
psi=-(a*zet+b*(zet-c/d).*exp(-dzet)+b*c/d);
k=find(zet<0); % unstable
x=(1-16*zet(k)).^0.25;
psik=2*log((1+x)/2)+log((1+x.*x)/2)-2*atan(x)+2*atan(1);
x=(1-10.15*zet(k)).^0.3333;
psic=1.5*log((1+x+x.^2)/3)-sqrt(3)*atan((1+2*x)./sqrt(3))+4*atan(1)./sqrt(3);
f=zet(k).^2./(1+zet(k).^2);
psi(k)=(1-f).*psik+f.*psic;
end
%------------------------------------------------------------------------------
function psi=psiu_40(zet)
% computes velocity structure function
dzet=min(50,0.35*zet); % stable
a=1;
b=3/4;
c=5;
d=0.35;
psi=-(a*zet+b*(zet-c/d).*exp(-dzet)+b*c/d);
k=find(zet<0); % unstable
x=(1-18*zet(k)).^0.25;
psik=2*log((1+x)/2)+log((1+x.*x)/2)-2*atan(x)+2*atan(1);
x=(1-10*zet(k)).^0.3333;
psic=1.5*log((1+x+x.^2)/3)-sqrt(3)*atan((1+2*x)./sqrt(3))+4*atan(1)./sqrt(3);
f=zet(k).^2./(1+zet(k).^2);
psi(k)=(1-f).*psik+f.*psic;
end
%------------------------------------------------------------------------------
function exx=bucksat(T,P)
% computes saturation vapor pressure [mb]
% given T [degC] and P [mb]
exx=6.1121.*exp(17.502.*T./(T+240.97)).*(1.0007+3.46e-6.*P);
end
%------------------------------------------------------------------------------
function qs=qsat26sea(T,P)
% computes surface saturation specific humidity [g/kg]
% given T [degC] and P [mb]
ex=bucksat(T,P);
es=0.98*ex; % reduction at sea surface
qs=622*es./(P-0.378*es);
end
%------------------------------------------------------------------------------
function [q,em]=qsat26air(T,P,rh)
% computes saturation specific humidity [g/kg]
% given T [degC] and P [mb]
es=bucksat(T,P);
em=0.01*rh.*es;
q=622*em./(P-0.378*em);
end
%------------------------------------------------------------------------------
function g=grv(lat)
% computes g [m/sec^2] given lat in deg
gamma=9.7803267715;
c1=0.0052790414;
c2=0.0000232718;
c3=0.0000001262;
c4=0.0000000007;
phi=lat*pi/180;
x=sin(phi);
g=gamma*(1+c1*x.^2+c2*x.^4+c3*x.^6+c4*x.^8);
end

%------------------------------------------------------------------------------
function RHrf=RHcalc(T,P,Q)
% computes relative humidity given T,P, & Q

es=6.1121.*exp(17.502.*T./(T+240.97)).*(1.0007+3.46e-6.*P);
em=Q.*P./(0.378.*Q+0.622);
RHrf=100*em./es;
end