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gilles.boulet_ird.fr
committed
function [tsurf,ts,tv,t0,rns,rnv,g,hs,hv,les,lev]=SPARSE(input1,input2,typerun,typeohm,albe,emis,ta,rh,rg,ua,glai,lai,zf,za,rvvmin,xg,sigmoy)
% function that computes actual or bounding transpiration and soil evaporation with
% the SPARSE framework, i.e. Shuttleworht-Wallace dual source model with
% full linearization around air temperature
%License:
%This is free software under the GNU General Public License v3.0.
%See https://www.gnu.org/licenses/gpl-3.0.en.html for details or the LICENSE.txt file
% inputs
if typerun==1 % retrieval:
% imposed observed radiative temperature and view zenith angle
vza=input2;
betas=1;
betav=1;
else % precribed:
% imposed relative stress "beta" for the soil "s" and the vegetation "v"
betas=input1;
betav=input2;
vza=0;
end
% n: row number
% m: line number
n=size(glai,1);
m=size(glai,2);
gilles.boulet_ird.fr
committed
% emis = surface emissivity [-]
% ta = air temperature [K]
% rh = air relative humidity [%]
% rg = incoming solar radiation [W/m2]
% ua = wind speed [m/s]
% glai = green Leaf Are Index [m2/m2]
% lai = total Leaf Are Index [m2/m2]
% zf = vegetation height [m]
% za = wind speed meas. height [m]
% albe = OBSERVED albedo [-]
% rvvmin = mimimum stomatal resistance [s/m]
% xg = soil to soil net radiation ratio
% sigmoy = Beer Lambert law attenuation coefficient
% vza = view zenith angle [rad]
gilles.boulet_ird.fr
committed
% RETRIEVAL MODE: input1 = OBSERVED RADIATIVE surface temperature [C] % A
% PRECISER
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% PRESCRIBED mode: betas: relative stress factor for the soil [-]
% PRESCRIBED mode: betav: relative stress factor for the vegetation [-]
% outputs
% trad = radiative surface temperature (should be equal to tsobs in retrieval mode)
% ts = soil temperature in precribed conditions [K then C]
% tv = vegetation temperature [K then C]
% t0 = aerodynamic temperature [K then C]
% rns = soil net radiation [W/m2]
% rnv = vegetation net radiation [W/m2]
% g = soil heat flux [W/m2]
% hs = soil sensible heat flux [W/m2]
% hv = vegetation sensible heat flux [W/m2]
% les = soil evaporation [W/m2]
% lev = transpiration [W/m2]
% constants
rcp=1170; % product of air density and mass heat constant of the air
gamma=0.66; % psychrometric constant
sigma=5.66e-8; % Setfan Boltzmann constant
alfo=5e-3; % ?
xn=2.5;
zoms=5e-3; % bare soil roughness length
wl=0.05; % mean leaf width [m]
albv=0.2; % vegetation albedo
emisv=0.98; % vegetation emissivity
emiss=0.96; % soil emissivity
% initialisation
X0=5*ones(n,m); % aerodynamic temperature initialization
error=10; % criteria for convergence of aerodynamic temperature (stability loop)
k=0; % index for stability loop (stop 100)
lesmin=0;
% computes partial pressure from rh
ea=0.01*rh*6.1878.*exp(17.269*(ta-273)./(ta-35.86));
% fraction cover
fracover=(1-exp(-sigmoy*lai./cos(vza))); % fraction cover
gfracover=1-exp(-sigmoy*glai./cos(vza)); % green fraction cover
fracoverl=(1-exp(-0.9*lai)); % fraction cover longwave
% patch model: green LAI transformed into a clump green LAI:
if typeohm>1
glai=glai./gfracover;
end
% roughness length zom and displacement height d (several formulations)
d = 0.65*zf;
zom = max(0.13*zf,zoms);
%d= zf*(1-2*(1-exp(-lai/2))/lai); % shaw and pereira ?
%zom= zf*exp(-lai/2)*(1-exp(-lai/2));
% soil-air aerodynamic conductance
xkzf=0.4*0.4*ua.*(zf-d)./log((za-d)./zom);
ras=zf.*exp(xn).*(exp((-xn*zoms)./zf)-exp((-xn*(d+zom))./zf))./(xn*xkzf);
% leaf-air aerodynamic conductance
uzf=ua.*log((zf-d)./zom)./log((za-d)./zom);
%rav=xn*sqrt(wl/uzf)/(4*alfo*lai*(1-exp(-xn/2)));
rav=xn*sqrt(wl./uzf)./(4*alfo*glai*(1-exp(-xn/2)));
% emissivity of the air in clear sky conditions
emisa = 1.24*(ea./(ta)).^(1/7);
% Radiation components (longwave and total net radiation)
ratm=emisa.*sigma*ta.^4;
if typeohm==1 % layer approach
[albs,ans,bns,cns,anv,bnv,cnv,cnas,cnav]=calcrn_vect(rg,ratm,emiss,emisv,albe,albv,fracover,fracoverl);
arns=(ans.*sigma*4*ta.^3)*(1-xg);
aras=ans.*sigma*4*ta.^3;
brns=(bns.*sigma*4*ta.^3)*(1-xg);
bras=bns.*sigma*4*ta.^3;
arnv=anv.*sigma*4*ta.^3;
arav=arnv;
brnv=bnv.*sigma*4*ta.^3;
brav=brnv;
crns=((ans+bns).*sigma*ta.^4+cns)*(1-xg);
crnv=(anv+bnv).*sigma*ta.^4+cnv;
cras=(ans+bns).*sigma*ta.^4+cnas;
crav=(anv+bnv).*sigma*ta.^4+cnav;
else % patch approach
albs=(albe-fracover*albv)./(1-fracover);
arns=-(1-fracover).*emiss*(sigma*4*ta.^3)*(1-xg);
brns=zeros(n,m);
bras=zeros(n,m);
arnv=zeros(n,m);
arav=zeros(n,m);
brnv=-fracover.*emisv*sigma*4*ta.^3;
crns=(1-fracover).*((1-albs).*rg+emiss*(ratm-sigma*ta.^4))*(1-xg);
crnv=fracover.*((1-albv)*rg+emisv*(ratm-sigma*ta.^4));
aras=-(1-fracover).*emiss*sigma*4*ta.^3;
brav=brnv;
cras=(1-fracover).*emiss*(ratm-sigma*ta.^4);
crav=fracover.*emisv*(ratm-sigma*ta.^4);
end
% various terms appearing in the linearization
da=6.1878*exp(17.269*(ta-273)./(ta-35.86))-ea; % vapour pressure deficit VPD
delta=((da+ea).*4097.9337).*(ta-35.86).^-2; % slope of the saturation curve
rcpg=rcp/gamma;
rcpgd=rcpg*delta;
% leaf-air stomatal conductance
f=(0.0055*max(rg,10)*2)./glai;
frg=(1+f)./(f+rvvmin/5000); % stress factor / solar radiation
fea=1+0.04*da; % stress factor / VPD
% aerodynamic resistance in neutral conditions
alg = log((za-d)./zom);
ra0 = alg.*alg/(.4*.4*ua);
X0old=X0;
while error>1e-2 && k<100
k=k+1;
% air-air aerodynamic conductance
% Richardson number:
ri = 5*(za-d).*9.81.*X0./(ua.*ua.*ta);
if rg<100
ri=0;
end
p(X0>0) = 0.75; % unstable conditions
p(X0<0) = 2; % stable conditions
ra = ra0./(1+ri).^p;
ga=1./ra;
% layer approach
if typeohm==1
% aggregated conductances for the layer network
gav=1./rav;
gvv=betav./(rvvmin*fea*frg./glai+rav);
gas=1./ras;
gss=betas./ras;
g3a=ga+gas+gav;
g3=ga+gss+gvv;
else
% and for the patch network
ga2s=(1-fracover)./(ras+ra);
ga2v=fracover./(rav+ra);
g3s=betas.*(1-fracover)./(ras+ra);
g3v=betav.*fracover./(rav+rvvmin*fea*frg./glai+ra);
end
% RETRIEVAL MODE
if typerun==1
% MODE 1: potential rate transpiration
% var 1: LEs, var 2: Xs=Ts-Ta, var 3: Xv=Tv-Ta
if typeohm==1 % layer
A1_1=ones(n,m);
A1_2=-rcp*gas.*gas./g3a-arns+rcp*gas;
A1_3=-rcp*gas.*gav./g3a-brns;
B1=crns;
A2_1=-gvv./(gvv+ga);
A2_2=-rcp*gav.*gas./g3a-arnv;
A2_3=-rcpgd.*gvv.*gvv./(gvv+ga)-rcp*gav.*gav./g3a+rcpgd.*gvv+rcp.*gav-brnv;
B2=crnv-rcpg.*gvv.*ga.*da./(gvv+ga);
else % patch
A1_1=ones(n,m);
A1_2=-arns+rcp*ga2s;
A1_3=zeros(n,m);
B1=crns;
A2_1=zeros(n,m);
A2_2=zeros(n,m);
A2_3=rcpgd.*g3v+rcp*ga2v-brnv;
B2=crnv-rcpg.*g3v.*da;
end
% same equation for both approaches for the link between radiative and
% source surface temperatures
A3_1=zeros(n,m);
A3_2=-aras-arav;
A3_3=-bras-brav;
gilles.boulet_ird.fr
committed
% 3 cases according to the type of data:
%
Mrad=(1-emis).*ratm+sigma*ones(n,m).*emis.*(input1+273.15).^4;
B3=Mrad+cras+crav-ratm*ones(n,m);
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det=A1_1.*A2_2.*A3_3 - A1_1.*A2_3.*A3_2 - A1_2.*A2_1.*A3_3 + A1_2.*A2_3.*A3_1 + A1_3.*A2_1.*A3_2 - A1_3.*A2_2.*A3_1;
IA1_1=(A2_2.*A3_3 - A2_3.*A3_2)./det;
IA1_2=-(A1_2.*A3_3 - A1_3.*A3_2)./det;
IA1_3=(A1_2.*A2_3 - A1_3.*A2_2)./det;
IA2_1=-(A2_1.*A3_3 - A2_3.*A3_1)./det;
IA2_2=(A1_1.*A3_3 - A1_3.*A3_1)./det;
IA2_3=-(A1_1.*A2_3 - A1_3.*A2_1)./det;
IA3_1=(A2_1.*A3_2 - A2_2.*A3_1)./det;
IA3_2=-(A1_1.*A3_2 - A1_2.*A3_1)./det;
IA3_3=(A1_1.*A2_2 - A1_2.*A2_1)./det;
X1=IA1_1.*B1+IA1_2.*B2+IA1_3.*B3;
X2=IA2_1.*B1+IA2_2.*B2+IA2_3.*B3;
X3=IA3_1.*B1+IA3_2.*B2+IA3_3.*B3;
% outputs
les=X1;
if typeohm==1 % layer
X0=(gas.*X2+gav.*X3)./g3a;
d0=(rcpg.*ga.*da-X1-rcpgd.*gvv.*X3)./(rcpg.*(gvv+ga));
lev=rcpg.*gvv.*(d0+delta.*X3);
else % patch
X0=(ga2s.*X2+ga2v.*X3)./ga;
d0=da-X1./(ga.*rcpg)-g3v.*(da+delta.*X3)./ga;
lev=rcpg.*g3v.*(da+delta.*X3);
end
% MODE 2: case LES<lesmin: var 1 lev; var 2 Xs=ts-ta; var 3 Xv=tv-ta
if typeohm==1 % layer
A1_1(les<lesmin)=0;
A1_2(les<lesmin)=-rcp*gas(les<lesmin).*gas(les<lesmin)./g3a(les<lesmin)-arns(les<lesmin)+rcp*gas(les<lesmin);
A1_3(les<lesmin)=-rcp*gas(les<lesmin).*gav(les<lesmin)./g3a(les<lesmin)-brns(les<lesmin);
B1(les<lesmin)=crns(les<lesmin)-lesmin;
A2_1(les<lesmin)=1;
A2_2(les<lesmin)=-rcp*gav(les<lesmin).*gas(les<lesmin)./g3a(les<lesmin)-arnv(les<lesmin);
A2_3(les<lesmin)=-rcp*gav(les<lesmin).*gav(les<lesmin)./g3a(les<lesmin)+rcp*gav(les<lesmin)-brnv(les<lesmin);
B2(les<lesmin)=crnv(les<lesmin);
else % patch
A1_1(les<lesmin)=0;
A1_2(les<lesmin)=rcp*ga2s(les<lesmin)-arns(les<lesmin);
A1_3(les<lesmin)=0;
B1(les<lesmin)=crns(les<lesmin)-lesmin;
A2_1(les<lesmin)=1;
A2_2(les<lesmin)=0;
A2_3(les<lesmin)=rcp*ga2v(les<lesmin)-brnv(les<lesmin);
B2(les<lesmin)=crnv(les<lesmin);
end
% same equation for both approaches for the link between radiative and
% source surface temperatures
A3_1(les<lesmin)=0;
A3_2(les<lesmin)=-aras(les<lesmin)-arav(les<lesmin);
A3_3(les<lesmin)=-bras(les<lesmin)-brav(les<lesmin);
gilles.boulet_ird.fr
committed
B3(les<lesmin)=Mrad(les<lesmin)+cras(les<lesmin)+crav(les<lesmin)-ratm;
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det(les<lesmin)=A1_1(les<lesmin).*A2_2(les<lesmin).*A3_3(les<lesmin)...
- A1_1(les<lesmin).*A2_3(les<lesmin).*A3_2(les<lesmin) - A1_2(les<lesmin).*A2_1(les<lesmin).*A3_3(les<lesmin) + A1_2(les<lesmin).*A2_3(les<lesmin)...
.*A3_1(les<lesmin) + A1_3(les<lesmin).*A2_1(les<lesmin).*A3_2(les<lesmin) - A1_3(les<lesmin).*A2_2(les<lesmin).*A3_1(les<lesmin);
IA1_1(les<lesmin)=(A2_2(les<lesmin).*A3_3(les<lesmin) - A2_3(les<lesmin).*A3_2(les<lesmin))./det(les<lesmin);
IA1_2(les<lesmin)=-(A1_2(les<lesmin).*A3_3(les<lesmin) - A1_3(les<lesmin).*A3_2(les<lesmin))./det(les<lesmin);
IA1_3(les<lesmin)=(A1_2(les<lesmin).*A2_3(les<lesmin) - A1_3(les<lesmin).*A2_2(les<lesmin))./det(les<lesmin);
IA2_1(les<lesmin)=-(A2_1(les<lesmin).*A3_3(les<lesmin) - A2_3(les<lesmin).*A3_1(les<lesmin))./det(les<lesmin);
IA2_2(les<lesmin)=(A1_1(les<lesmin).*A3_3(les<lesmin) - A1_3(les<lesmin).*A3_1(les<lesmin))./det(les<lesmin);
IA2_3(les<lesmin)=-(A1_1(les<lesmin).*A2_3(les<lesmin) - A1_3(les<lesmin).*A2_1(les<lesmin))./det(les<lesmin);
IA3_1(les<lesmin)=(A2_1(les<lesmin).*A3_2(les<lesmin) - A2_2(les<lesmin).*A3_1(les<lesmin))./det(les<lesmin);
IA3_2(les<lesmin)=-(A1_1(les<lesmin).*A3_2(les<lesmin) - A1_2(les<lesmin).*A3_1(les<lesmin))./det(les<lesmin);
IA3_3(les<lesmin)=(A1_1(les<lesmin).*A2_2(les<lesmin) - A1_2(les<lesmin).*A2_1(les<lesmin))./det(les<lesmin);
X1(les<lesmin)=IA1_1(les<lesmin).*B1(les<lesmin)+IA1_2(les<lesmin).*B2(les<lesmin)+IA1_3(les<lesmin).*B3(les<lesmin);
X2(les<lesmin)=IA2_1(les<lesmin).*B1(les<lesmin)+IA2_2(les<lesmin).*B2(les<lesmin)+IA2_3(les<lesmin).*B3(les<lesmin);
X3(les<lesmin)=IA3_1(les<lesmin).*B1(les<lesmin)+IA3_2(les<lesmin).*B2(les<lesmin)+IA3_3(les<lesmin).*B3(les<lesmin);
lev(les<lesmin)=real(X1(les<lesmin));
les(les<lesmin)=lesmin;
% outputs
d0(les<lesmin)=da-(lesmin+X1(les<lesmin))./(rcpg.*ga(les<lesmin));
if typeohm==1 % layer
X0(les<lesmin)=(gas(les<lesmin).*X2(les<lesmin)+gav(les<lesmin).*X3(les<lesmin))./g3a(les<lesmin);
else % patch
X0(les<lesmin)=(ga2s(les<lesmin).*X2(les<lesmin)+ga2v(les<lesmin).*X3(les<lesmin))./ga(les<lesmin);
end
% end MODE 2
% MODE 3: LEv<0
if typeohm==1 % layer
A1_1(lev<0)=-arns(lev<0)+rcp*gas(lev<0)-rcp*gas(lev<0).*gas(lev<0)./g3a(lev<0);
A1_2(lev<0)=-brns(lev<0)-rcp*gas(lev<0).*gav(lev<0)./g3a(lev<0);
B1(lev<0)=crns(lev<0)-lesmin(lev<0);
A2_1(lev<0)=-arnv(lev<0)-rcp*gav(lev<0).*gas(lev<0)./g3a(lev<0);
A2_2(lev<0)=-brnv(lev<0)+rcp*gav(lev<0)-rcp*gav(lev<0).*gav(lev<0)./g3a(lev<0);
B2(lev<0)=crnv(lev<0);
det(lev<0)=A1_1(lev<0).*A2_2(lev<0)-A1_2(lev<0).*A2_1(lev<0);
X2(lev<0)=(1./det(lev<0)).*(A2_2(lev<0).*B1(lev<0)-A1_2(lev<0).*B2(lev<0));
X3(lev<0)=(1./det(lev<0)).*(-A2_1(lev<0).*B1(lev<0)+A1_1(lev<0).*B2(lev<0));
X0(lev<0)=(gas(lev<0)./g3a(lev<0)).*X2(lev<0)+(gav(lev<0)./g3a(lev<0)).*X3(lev<0);
d0(lev<0)=(ga(lev<0).*da-gss(lev<0).*delta.*X2(lev<0)-gvv(lev<0).*delta.*X3(lev<0))./g3(lev<0);
else % patch
X2(lev<0)=(crns(lev<0)-lesmin)./(-arns(lev<0)+rcp*ga2s(lev<0));
X3(lev<0)=crnv(lev<0)./(-brnv(lev<0)+rcp*ga2v(lev<0));
X0(lev<0)=ga2s(lev<0).*X2(lev<0)./ga(lev<0)+ga2v(lev<0).*X3(lev<0)./ga(lev<0);
d0(lev<0)=da-lesmin./(ga(lev<0).*rcpg);
end
les(lev<0)=lesmin;
lev(lev<0)=0;
else
% PRESCRIBED MODE
if typeohm==1 % layer
A1_1=-arns+rcp.*gas+rcpgd.*gss-rcp.*gas.*gas./g3a;
A1_1=A1_1-rcpgd.*gss.*gss./g3;
A1_2=-brns-rcp.*gas.*gav./g3a;
A1_2=A1_2-rcpgd.*gss.*gvv./g3;
B1=crns-rcpg.*gss.*ga.*da./g3;
A2_1=-arnv-rcp.*gav.*gas./g3a;
A2_1=A2_1-rcpgd.*gvv.*gas./g3;
A2_2=-brnv+rcp.*gav+rcpgd.*gvv-rcp.*gav.*gav./g3a;
A2_2=A2_2-rcpgd.*gvv.*gvv./g3;
B2=crnv-rcpg.*gvv.*ga.*da./g3;
det=A1_1.*A2_2-A1_2.*A2_1;
X2=(1./det).*(A2_2.*B1-A1_2.*B2);
X3=(1./det).*(-A2_1.*B1+A1_1.*B2);
X0=(gas./g3a).*X2+(gav./g3a).*X3;
d0=(ga.*da-gss.*delta.*X2-gvv.*delta.*X3)./g3;
les=real(rcpg.*gss.*(d0+delta.*X2));
lev=real(rcpg.*gvv.*(d0+delta.*X3));
else % patch
A1_1=-arns+rcp*ga2s+rcpgd.*g3s;
A1_2=zeros(n,m);
B1=crns-rcpg.*g3s.*da;
A2_1=zeros(n,m);
A2_2=-brnv+rcp*ga2v+rcpgd.*g3v;
B2=crnv-rcpg.*g3v.*da;
det=A1_1.*A2_2-A1_2.*A2_1;
X2=(1./det).*(A2_2.*B1-A1_2.*B2);
X3=(1./det).*(-A2_1.*B1+A1_1.*B2);
X0=(ga2s.*X2+ga2v.*X3)./ga;
%d0=da-(g3s.*(da+delta*X2)+g3v.*(da+delta*X3))./ga;
les=real(rcpg.*g3s.*(da+delta.*X2));
lev=real(rcpg.*g3v.*(da+delta.*X3));
end
end
% outputs whose formulation is the same for prescribed and retrieval modes
if typeohm==1
hs=real(rcp*gas.*(X2-X0));
hv=real(rcp*gav.*(X3-X0));
else
hs=real(rcp*ga2s.*X2);
hv=real(rcp*ga2v.*X3);
end
if k==100
'STOP k=100';
end
error=max(max(abs(X0-X0old)));
X0old=X0;
if rg<20
error=1e-3;
end
end % end stability loop
gilles.boulet_ird.fr
committed
tsurf=((emis.*ratm.*ones(n,m)-cras-crav-X2.*(aras+arav)-X3.*(bras+brav))/(sigma.*emis)).^0.25-273.15;