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gen_Fig_8.m
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clear
clc
bK = [ 0, 0, 0 ]/255;
bL = [ 30, 144, 255 ]/255;
rD = [ 255, 51, 51 ]/255;
gR = [ 0, 153, 0 ]/255;
pR = [ 153, 51, 255 ]/255;
oR = [ 255, 153, 51 ]/255;
gY = [.8, .8, .8];
volume = '/Volumes/DRIVE/Work/rd_enkf/l96/';
filter = 'EnKF_all/';
diags = 'imperfect/';
diagpath = strcat(volume, filter, diags);
% diag files:
tFile = strcat(diagpath, '../true_state.nc');
pFile = strcat(diagpath, 'preassim_alp0.0_for1.0_T.nc');
% read state:
ncid = netcdf.open(pFile,'NC_NOWRITE');
[~, Ne] = netcdf.inqDim(ncid, 1);
[~, Nt] = netcdf.inqDim(ncid, 2);
[~, Nx] = netcdf.inqDim(ncid, 5);
xt = squeeze(ncread(tFile, 'state'));
time = ncread(tFile, 'time');
forc = 1:15; Nf = length(forc);
alp = 0:.1:0.8; Na = length(alp);
for jj = 1:Na
p1 = sprintf('%.1f', alp(jj));
for ii = 1:Nf
p2 = sprintf('%.1f', forc(ii));
pFile = strcat(diagpath, 'preassim_alp', p1, '_for', p2, '_T.nc');
aFile = strcat(diagpath, 'analysis_alp', p1, '_for', p2, '_T.nc');
xfm = ncread(pFile, 'state_mean');
xfs = ncread(pFile, 'state_sd');
xim = ncread(pFile, 'state_priorinf_mean');
xam = ncread(aFile, 'state_mean');
xas = ncread(aFile, 'state_sd');
% If the run failed
if size(xfm, 2) < size(xt, 2)
xfm = NaN * ones(size(xt));
xfs = xfm;
xim = xfm;
xam = xfm;
xas = xfm;
end
prior(jj, ii).rmse = sqrt(mean( (xfm - xt).^2 ));
prior(jj, ii).sprd = sqrt(mean( (xfs - 0 ).^2 ));
prior(jj, ii).bias = mean( (xfm - xt) );
prior_mRMS(jj, ii) = sum(prior(jj, ii).rmse) / Nt;
prior_mSTD(jj, ii) = sum(prior(jj, ii).sprd) / Nt;
prior_mBAS(jj, ii) = sum(prior(jj, ii).bias) / Nt;
prior(jj, ii).mINF = mean(xim, 2);
prior_mINF(jj, ii) = sum(prior(jj, ii).mINF) / Nx;
analy(jj, ii).rmse = sqrt(mean( (xam - xt).^2 ));
analy(jj, ii).sprd = sqrt(mean( (xas - 0 ).^2 ));
analy(jj, ii).bias = mean( (xam - xt) );
analy_mRMS(jj, ii) = sum(analy(jj, ii).rmse) / Nt;
analy_mSTD(jj, ii) = sum(analy(jj, ii).sprd) / Nt;
analy_mBAS(jj, ii) = sum(analy(jj, ii).bias) / Nt;
end
end
for jj = 1:Na
p1 = sprintf('%.1f', alp(jj));
for ii = 1:Nf
p2 = sprintf('%.1f', forc(ii));
pFile = strcat(diagpath, 'preassim_alp', p1, '_for', p2, '_inf_T.nc');
aFile = strcat(diagpath, 'analysis_alp', p1, '_for', p2, '_inf_T.nc');
xfm = ncread(pFile, 'state_mean');
xfs = ncread(pFile, 'state_sd');
xim = ncread(pFile, 'state_priorinf_mean');
xam = ncread(aFile, 'state_mean');
xas = ncread(aFile, 'state_sd');
% If the run failed
if size(xfm, 2) < size(xt, 2)
xfm = NaN * ones(size(xt));
xfs = xfm;
xim = xfm;
xam = xfm;
xas = xfm;
end
iprior(jj, ii).rmse = sqrt(mean( (xfm - xt).^2 ));
iprior(jj, ii).sprd = sqrt(mean( (xfs - 0 ).^2 ));
iprior(jj, ii).bias = mean( (xfm - xt) );
iprior_mRMS(jj, ii) = sum(iprior(jj, ii).rmse) / Nt;
iprior_mSTD(jj, ii) = sum(iprior(jj, ii).sprd) / Nt;
iprior_mBAS(jj, ii) = sum(iprior(jj, ii).bias) / Nt;
iprior(jj, ii).mINF = mean(xim, 2);
iprior_mINF(jj, ii) = sum(iprior(jj, ii).mINF) / Nx;
ianaly(jj, ii).rmse = sqrt(mean( (xam - xt).^2 ));
ianaly(jj, ii).sprd = sqrt(mean( (xas - 0 ).^2 ));
ianaly(jj, ii).bias = mean( (xam - xt) );
ianaly_mRMS(jj, ii) = sum(ianaly(jj, ii).rmse) / Nt;
ianaly_mSTD(jj, ii) = sum(ianaly(jj, ii).sprd) / Nt;
ianaly_mBAS(jj, ii) = sum(ianaly(jj, ii).bias) / Nt;
end
end
%%% for_every_obs: false
for jj = 1:Na
p1 = sprintf('%.1f', alp(jj));
for ii = 1:Nf
p2 = sprintf('%.1f', forc(ii));
pFile = strcat(diagpath, 'preassim_alp', p1, '_for', p2, '_F.nc');
aFile = strcat(diagpath, 'analysis_alp', p1, '_for', p2, '_F.nc');
xfm = ncread(pFile, 'state_mean');
xfs = ncread(pFile, 'state_sd');
xim = ncread(pFile, 'state_priorinf_mean');
xam = ncread(aFile, 'state_mean');
xas = ncread(aFile, 'state_sd');
% If the run failed
if size(xfm, 2) < size(xt, 2)
xfm = NaN * ones(size(xt));
xfs = xfm;
xim = xfm;
xam = xfm;
xas = xfm;
end
fprior(jj, ii).rmse = sqrt(mean( (xfm - xt).^2 ));
fprior(jj, ii).sprd = sqrt(mean( (xfs - 0 ).^2 ));
fprior(jj, ii).bias = mean( (xfm - xt) );
fprior_mRMS(jj, ii) = sum(fprior(jj, ii).rmse) / Nt;
fprior_mSTD(jj, ii) = sum(fprior(jj, ii).sprd) / Nt;
fprior_mBAS(jj, ii) = sum(fprior(jj, ii).bias) / Nt;
fprior(jj, ii).mINF = mean(xim, 2);
fprior_mINF(jj, ii) = sum(fprior(jj, ii).mINF) / Nx;
fanaly(jj, ii).rmse = sqrt(mean( (xam - xt).^2 ));
fanaly(jj, ii).sprd = sqrt(mean( (xas - 0 ).^2 ));
fanaly(jj, ii).bias = mean( (xam - xt) );
fanaly_mRMS(jj, ii) = sum(fanaly(jj, ii).rmse) / Nt;
fanaly_mSTD(jj, ii) = sum(fanaly(jj, ii).sprd) / Nt;
fanaly_mBAS(jj, ii) = sum(fanaly(jj, ii).bias) / Nt;
end
end
for jj = 1:Na
p1 = sprintf('%.1f', alp(jj));
for ii = 1:Nf
p2 = sprintf('%.1f', forc(ii));
pFile = strcat(diagpath, 'preassim_alp', p1, '_for', p2, '_inf_F.nc');
aFile = strcat(diagpath, 'analysis_alp', p1, '_for', p2, '_inf_F.nc');
xfm = ncread(pFile, 'state_mean');
xfs = ncread(pFile, 'state_sd');
xim = ncread(pFile, 'state_priorinf_mean');
xam = ncread(aFile, 'state_mean');
xas = ncread(aFile, 'state_sd');
% If the run failed
if size(xfm, 2) < size(xt, 2)
xfm = NaN * ones(size(xt));
xfs = xfm;
xim = xfm;
xam = xfm;
xas = xfm;
end
fiprior(jj, ii).rmse = sqrt(mean( (xfm - xt).^2 ));
fiprior(jj, ii).sprd = sqrt(mean( (xfs - 0 ).^2 ));
fiprior(jj, ii).bias = mean( (xfm - xt) );
fiprior_mRMS(jj, ii) = sum(fiprior(jj, ii).rmse) / Nt;
fiprior_mSTD(jj, ii) = sum(fiprior(jj, ii).sprd) / Nt;
fiprior_mBAS(jj, ii) = sum(fiprior(jj, ii).bias) / Nt;
fiprior(jj, ii).mINF = mean(xim, 2);
fiprior_mINF(jj, ii) = sum(fiprior(jj, ii).mINF) / Nx;
fianaly(jj, ii).rmse = sqrt(mean( (xam - xt).^2 ));
fianaly(jj, ii).sprd = sqrt(mean( (xas - 0 ).^2 ));
fianaly(jj, ii).bias = mean( (xam - xt) );
fianaly_mRMS(jj, ii) = sum(fianaly(jj, ii).rmse) / Nt;
fianaly_mSTD(jj, ii) = sum(fianaly(jj, ii).sprd) / Nt;
fianaly_mBAS(jj, ii) = sum(fianaly(jj, ii).bias) / Nt;
end
end
%%
figure('pos', [220, 500, 850, 560])
ai = 6; %50%
subplot(2,2,[1, 3])
plot(forc, prior_mRMS(1, :), '-o', 'Color', bL, 'LineWidth', 2, 'MarkerSize', 10, 'MarkerFaceColor', 'auto'); hold on; grid on
plot(forc, prior_mRMS(ai, :), '-o', 'Color', rD, 'LineWidth', 2, 'MarkerSize', 10, 'MarkerFaceColor', 'auto');
plot(forc, prior_mSTD(1, :), ':o', 'Color', bL, 'LineWidth', 2, 'MarkerSize', 10, 'MarkerFaceColor', 'auto')
plot(forc, prior_mSTD(ai, :), ':o', 'Color', rD, 'LineWidth', 2, 'MarkerSize', 10, 'MarkerFaceColor', 'auto')
yy = get(gca, 'YLim');
plot([8, 8], yy, '--', 'Color', gY, 'LineWidth', 1.5)
set(gca, 'FontSize', 16, 'XLim', [forc(1), forc(Nf)], 'XTick', 1:Nf, 'XTickLabel', forc, 'XGrid', 'off')
ylabel('Prior Diagnostics', 'FontSize', 18)
xlabel('Perturbed Forcing', 'FontSize', 18)
legend('EnKF RMSE', 'RD-EnKF RMSE', 'EnKF Spread', 'RD-EnKF Spread', 'Location', 'NorthWest', 'box', 'off')
title('No Inflation Case', 'FontSize', 22)
subplot(2,2,2)
plot(forc, iprior_mRMS(1, :), '-o', 'Color', bL, 'LineWidth', 2, 'MarkerSize', 10, 'MarkerFaceColor', 'auto'); hold on; grid on
plot(forc, iprior_mRMS(ai, :), '-o', 'Color', rD, 'LineWidth', 2, 'MarkerSize', 10, 'MarkerFaceColor', 'auto');
plot(forc, iprior_mSTD(1, :), ':o', 'Color', bL, 'LineWidth', 2, 'MarkerSize', 10, 'MarkerFaceColor', 'auto')
plot(forc, iprior_mSTD(ai, :), ':o', 'Color', rD, 'LineWidth', 2, 'MarkerSize', 10, 'MarkerFaceColor', 'auto')
set(gca, 'FontSize', 16, 'XLim', [forc(1), forc(Nf)], 'XTick', 1:Nf, 'XTickLabel', forc, 'YLim', [0, 2], 'XGrid', 'off')
ylabel('Prior Diagnostics', 'FontSize', 18)
yy = get(gca, 'YLim');
plot([8, 8], yy, '--', 'Color', gY, 'LineWidth', 1.5)
title('Adaptive Inflation Case', 'FontSize', 22)
subplot(2,2,4)
plot(forc, iprior_mINF(1, :), '-o', 'Color', bL, 'LineWidth', 2, 'MarkerSize', 10, 'MarkerFaceColor', 'auto'); hold on
plot(forc, iprior_mINF(ai, :), '-o', 'Color', rD, 'LineWidth', 2, 'MarkerSize', 10, 'MarkerFaceColor', 'auto'); grid on
yy = get(gca, 'YLim');
plot([8, 8], yy, '--', 'Color', gY, 'LineWidth', 1.5)
set(gca, 'FontSize', 16, 'XLim', [forc(1), forc(Nf)], 'XTick', 1:Nf, 'XTickLabel', forc, 'XGrid', 'off')
ylabel('Average Prior Inflation', 'FontSize', 18)
xlabel('Perturbed Forcing', 'FontSize', 18)