/
wrf_2nd_order_term_v2.m
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wrf_2nd_order_term_v2.m
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close all
clear all
clc
dt=1 %hr
%dx=3.4 %kms
%dy=3.4 %kms
%nums = linspace(3,4,101);
dx = 3.483;
dy=dx
%{
dt=3600 %s
dx=12*1000 %m
dy=12*1000 %m
%}
ncfile='hosiendata_wind_velocity.nc';
ncid=netcdf.open(ncfile,'NC_NOWRITE');
time_U = netcdf.getVar(ncid,0);
u = netcdf.getVar(ncid,3); %m/s
u = permute(u,[2,1,3]);
u(u==999)=nan;
u=3.6*u; %km/hr
v = netcdf.getVar(ncid,4); %m/s
v = permute(v,[2,1,3]);
v(v==999)=nan;
v=3.6*v; %km/hr
[ydim,xdim,tdim]=size(u);
%
[dudx,dudy,dudt] = gradient(u,dx,dy,dt);
[dvdx,dvdy,dvdt] = gradient(v,dx,dy,dt);
Du = dudt+u.*dudx+v.*dudy;
Dv = dvdt+u.*dvdx+v.*dvdy;
[dDudx,dDudy,dDudt] = gradient(Du,dx,dy,dt);
[dDvdx,dDvdy,dDvdt] = gradient(Dv,dx,dy,dt);
for t =25:length(time_U)
t
for i =1:ydim
for j = 1:xdim
if ~isnan(Du(i,j,t))&&~isnan(Dv(i,j,t))
Grad_v = [dudx(i,j,t), dudy(i,j,t);dvdx(i,j,t), dvdy(i,j,t)];
Grad_D = [dDudx(i,j,t), dDudy(i,j,t); dDvdx(i,j,t), dDvdy(i,j,t)];
S = 0.5*(Grad_v + Grad_v');
B = 0.5*(Grad_D + Grad_D')+(Grad_v'*Grad_v);
[V,D] = eig(S);
if ~issorted(diag(D))
[D,I] = sort(diag(D));
V = V(:, I);
end
s1_numerical(i,j,t) = D(1,1);
X1 = V(:,1);
cor_numerical(i,j,t) = -s1_numerical(i,j,t).^2+0.5*(X1'*B*X1);
else
s1_numerical(i,j,t) =nan;
cor_numerical(i,j,t)=nan;
end
end
end
end
ncfile='ftle_80m_small.nc';
ncid=netcdf.open(ncfile,'NC_NOWRITE');
%{
%Grab NC data
[ndims,nvars,ngatts,unlimdimid] = netcdf.inq(ncid);
%
%Loop through NC data infomation
for i = 1:nvars
i-1
[varname,xtype,dimids,natts] = netcdf.inqVar(ncid,i-1)
end
%}
time_ftle = netcdf.getVar(ncid,0); %days
%time_ftle=24*time_ftle(1:6:end); %hrs
time_ftle=24*time_ftle; %hrs
lon = netcdf.getVar(ncid,1,'double');
lat = netcdf.getVar(ncid,2,'double');
ftle = netcdf.getVar(ncid,4); %days^{-1}
%ftle=permute(squeeze(ftle(1,:,:,1:6:end)),[2,1,3]);
ftle=permute(squeeze(ftle(1,:,:,:)),[2,1,3]);
ftle(ftle==999999)=nan;
%ftle=1/(24*3.4)*ftle; %hrs^{-1}
ftle=1/(24)*ftle; %hrs^{-1}
[ydim,xdim,tdim]=size(ftle)
%
%ftle(s1_numerical==nan)=nan;
%ftle(cor_numerical==nan)=nan;
%}
%
%{
figure
surface(x,y,-s1_numerical(:,:,3)+1*cor_numerical(:,:,3),'edgecolor','none')
title('numerical')
colorbar()
%}
%}
s1 = s1_numerical(:,:,end);
c1 = cor_numerical(:,:,end);
ftle(:,:,end)=-s1;
time = 22-time_ftle;
n = length(time);
for i =1:n
T=time(i);
ftle_t = squeeze(ftle(:,:,end+1-i));
sig_true = reshape(ftle_t,[],1);
sig_approx = reshape(-s1-T*c1,[],1);
ind = ~isnan(sig_true) & ~isnan(sig_approx) ;
sig_true = sig_true(ind);
sig_approx = sig_approx(ind);
rmse_corrected(i) = sqrt(mean((sig_approx-sig_true).^2));
sa_bar = mean(sig_approx);
st_bar = mean(sig_true);
n=length(sig_true);
numerator = sum(sig_approx.*sig_true)-(n*sa_bar*st_bar);
den1 = sqrt(sum(sig_approx.^2)-n*sa_bar.^2);
den2 = sqrt(sum(sig_true.^2)-n*st_bar.^2);
denominator = den1*den2;
cor_corrected(i) = numerator./denominator;
sig_approx = reshape(-s1,[],1);
sig_approx = sig_approx(ind);
rmse_uncorrected(i) = sqrt(mean((sig_approx-sig_true).^2));
sa_bar = mean(sig_approx);
st_bar = mean(sig_true);
numerator = sum(sig_approx.*sig_true)-(n*sa_bar*st_bar);
den1 = sqrt(sum(sig_approx.^2)-n*sa_bar.^2);
den2 = sqrt(sum(sig_true.^2)-n*st_bar.^2);
denominator = den1*den2;
cor_uncorrected(i) = numerator./denominator;
%cor(i) = corr(sig_approx,sig_true);
end
%time=time(2:27)
close all
%{
start = 1;
stop = 14;
%time = time*60;
time=time(start:stop);
rmse_corrected=rmse_corrected(start:stop);
rmse_uncorrected=rmse_uncorrected(start:stop);
cor_corrected=cor_corrected(start:stop);
cor_uncorrected=cor_uncorrected(start:stop);
%}
size(time);
size(rmse_corrected);
%subplot(121)
%
t_want=linspace(0,0.7,101);
int = 1
rmse_corrected = interp1(-time(1:int:end),rmse_corrected(1:int:end),t_want,'spline')
rmse_uncorrected = interp1(-time(1:int:end),rmse_uncorrected(1:int:end),t_want,'spline')
time = t_want;
%yy = interp1(-time,rmse_corrected,t_want,'spline')
font = 'cmr'
width = 5+3/8
ratio =1.61803398875;
fig=figure('units','inch','position',[0,0,width,width/ratio],'DefaultTextFontName', font, 'DefaultAxesFontName', font);
subplot(121)
hold on
plot(t_want,rmse_corrected,'m-')
plot(t_want,rmse_uncorrected,'b-')
legend('-s1-T*corr','-s1','Location','northwest')
ylabel('RMSE hr^{-1}')
xlabel('|T| hr')
xlim([0,0.7])
%
%save wrf_plot_data rmse_corrected rmse_uncorrected time
ncfile='ftle_80m.nc';
ncid=netcdf.open(ncfile,'NC_NOWRITE');
time_ftle = netcdf.getVar(ncid,0); %days
%time_ftle=24*time_ftle(1:6:end); %hrs
time_ftle=24*time_ftle; %hrs
lon = netcdf.getVar(ncid,1,'double');
lat = netcdf.getVar(ncid,2,'double');
ftle = netcdf.getVar(ncid,4); %days^{-1}
%ftle=permute(squeeze(ftle(1,:,:,1:6:end)),[2,1,3]);
ftle=permute(squeeze(ftle(1,:,:,:)),[2,1,3]);
ftle(ftle==999999)=nan;
%ftle=1/(24*3.4)*ftle; %hrs^{-1}
ftle=1/(24)*ftle; %hrs^{-1}
[ydim,xdim,tdim]=size(ftle)
%
%ftle(s1_numerical==nan)=nan;
%ftle(cor_numerical==nan)=nan;
%}
%
%{
figure
surface(x,y,-s1_numerical(:,:,3)+1*cor_numerical(:,:,3),'edgecolor','none')
title('numerical')
colorbar()
%}
%}
s1 = s1_numerical(:,:,end);
c1 = cor_numerical(:,:,end);
ftle(:,:,end)=-s1;
time = 22-time_ftle;
n = length(time);
for i =1:n
T=time(i);
ftle_t = squeeze(ftle(:,:,end+1-i));
sig_true = reshape(ftle_t,[],1);
sig_approx = reshape(-s1-T*c1,[],1);
ind = ~isnan(sig_true) & ~isnan(sig_approx) ;
sig_true = sig_true(ind);
sig_approx = sig_approx(ind);
rmse_corrected(i) = sqrt(mean((sig_approx-sig_true).^2));
sa_bar = mean(sig_approx);
st_bar = mean(sig_true);
n=length(sig_true);
numerator = sum(sig_approx.*sig_true)-(n*sa_bar*st_bar);
den1 = sqrt(sum(sig_approx.^2)-n*sa_bar.^2);
den2 = sqrt(sum(sig_true.^2)-n*st_bar.^2);
denominator = den1*den2;
cor_corrected(i) = numerator./denominator;
sig_approx = reshape(-s1,[],1);
sig_approx = sig_approx(ind);
rmse_uncorrected(i) = sqrt(mean((sig_approx-sig_true).^2));
sa_bar = mean(sig_approx);
st_bar = mean(sig_true);
numerator = sum(sig_approx.*sig_true)-(n*sa_bar*st_bar);
den1 = sqrt(sum(sig_approx.^2)-n*sa_bar.^2);
den2 = sqrt(sum(sig_true.^2)-n*st_bar.^2);
denominator = den1*den2;
cor_uncorrected(i) = numerator./denominator;
%cor(i) = corr(sig_approx,sig_true);
end
subplot(122)
hold on
plot(-time,rmse_corrected,'m-')
plot(-time,rmse_uncorrected,'b-')
legend('-s1-T*corr','-s1','Location','northwest')
ylabel('RMSE hr^{-1}')
xlabel('|T| hr')
xlim([0,0.7])