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insert_breaks_humidity.m
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insert_breaks_humidity.m
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function [dataDet, breaksDet, dataSto, breaksSto, perturbations2DDet, perturbations2DSto] = insert_breaks_humidity(data, date, stationNo, taperBreakFreqBegin)
% Insert uncorrelated break points in the benchmark dataset.
% The breaks are inserted such, that the end values are unchanged.
% Furthermore, no breaks are inserted if there are no measurements before
% or after this break, as these would be undetectable.
%
% data: A matrix with multiple stations of an additative variable, e.g. temperature
% noBreaks: The average number of breaks per measurement station.
breakSizeMeanDet = 0.7;
breakSizeMeanSto = 0.35;
breakSizeDeformation = 1.5;
seasonalBreakSizeDet = 0.7;
seasonalBreakSizeSto = 0.35;
trendBias = 0.02; % Bias of the perturbaition in % per year, leading to a trend bias in the inhomogeneous data
noValues = size(data, 1);
noStations = size(data, 2);
% Compute postions of the breaks
[breaks, noRandomBreaksNetwork] = compute_positions_breaks_network(data, date, noValues, stationNo, taperBreakFreqBegin);
% Implement the breaks
humidity = 1:100;
dataDet = data;
if ( noRandomBreaksNetwork > 0 )
for iStation = 1:noStations
stationBreaks = breaks([breaks.iStation]==iStation);
noStationBreaks = numel(stationBreaks);
if ( noStationBreaks > 0 )
[dummy, index] = sort([stationBreaks.iPos], 'ascend');
for iBreak = 1:noStationBreaks
if ( iBreak == 1 )
sectionIndices = 1:stationBreaks(index(iBreak)).iPos;
else
sectionIndices = stationBreaks(index(iBreak-1)).iPos+1:stationBreaks(index(iBreak)).iPos;
end
seasonalBreakPerturb = compute_seasonal_deviations(seasonalBreakSizeDet);
breakBias = trendBias * ( stationBreaks(index(iBreak)).time.year - date.year(end) );
deterministicPerturb = compute_deterministic_perturbations(breakSizeMeanDet, breakSizeDeformation, breakBias);
perturbations2DDet = taper_perturbations_near_saturation(seasonalBreakPerturb, deterministicPerturb); % Taper near 100% and 0% humidity to prevent unphysical values
figure(11)
imagesc(perturbations2DDet)
colorbar
xlabel(humidity)
ylabel(month)
excess = 0;
deficit = 0;
for iVal = sectionIndices
if ( isfinite( dataDet(iVal, iStation) ) )
perturbation = interp1(humidity, perturbations2DDet(date.julianDay(iVal), :), data(iVal, iStation));
perturbation = perturbation+excess+deficit;
newVal = dataDet(iVal, iStation) + perturbation;
if ( newVal >= 0 && newVal <= 100 )
dataDet(iVal, iStation) = newVal;
end
if ( newVal > 100 )
excess = newVal - 100;
deficit = 0;
dataDet(iVal, iStation) = 100;
end
if ( newVal < 0 )
deficit = newVal;
excess = 0;
dataDet(iVal, iStation) = 0;
end
end % if finite value
end
end % for all breaks in station
end % if there are breaks
end % for all stations
else
breaks(1).stationNo = NaN;
breaks(1).iStation = NaN;
breaks(1).time.year = NaN;
breaks(1).time.month = NaN;
breaks(1).time.day = NaN;
breaks(1).time.julianDay = NaN;
breaks(1).time.decYear = NaN;
breaks(1).iPos = NaN;
breaks(1).type = NaN;
end
% Generate the stochastic inhomogeneities
dataSto = dataDet; % The stochastic inhomogeneities consists of the deterministic inhomogeneities plus noisy inhomogeneities.
if ( noRandomBreaksNetwork > 0 )
for iStation = 1:noStations
stationBreaks = breaks([breaks.iStation]==iStation);
noStationBreaks = numel(stationBreaks);
if ( noStationBreaks > 0 )
[dummy, index] = sort([stationBreaks.iPos], 'ascend');
for iBreak = 1:noStationBreaks
if ( iBreak == 1 )
sectionIndices = 1:stationBreaks(index(iBreak)).iPos;
else
sectionIndices = stationBreaks(index(iBreak-1)).iPos+1:stationBreaks(index(iBreak)).iPos;
end
seasonalBreakPerturb = compute_seasonal_deviations(seasonalBreakSizeSto);
seasonalBreakPerturb = seasonalBreakPerturb - min(seasonalBreakPerturb);
breakBias = -1 * trendBias * ( stationBreaks(index(iBreak)).time.year - date.year(end) );
stochasticPerturb = compute_stochastic_perturbations(breakSizeMeanSto, breakBias);
perturbations2DSto = taper_perturbations_near_saturation(seasonalBreakPerturb, stochasticPerturb);
excess = 0;
deficit = 0;
for iVal = sectionIndices
if ( isfinite( dataSto(iVal, iStation) ) )
perturbationSize = interp1(humidity, perturbations2DSto(date.julianDay(iVal), :), data(iVal, iStation), 'linear', 'extrap');
perturbation = randn(1)*perturbationSize+excess+deficit;
newVal = dataSto(iVal, iStation) + perturbation;
if ( newVal >= 0 && newVal <= 100 )
dataSto(iVal, iStation) = dataSto(iVal, iStation) + perturbation;
end
if ( newVal > 100 )
excess = newVal - 100;
deficit = 0;
dataSto(iVal, iStation) = 100;
end
if ( newVal < 0 )
deficit = newVal;
excess = 0;
dataSto(iVal, iStation) = 0;
end
end % if finite value
end % for all values in this homogeneous subperiod
end % for all breaks in station
end % if there are breaks
end % for all stations
else
breaks(1).stationNo = NaN;
breaks(1).iStation = NaN;
breaks(1).time.year = NaN;
breaks(1).time.month = NaN;
breaks(1).time.day = NaN;
breaks(1).time.julianDay = NaN;
breaks(1).time.decYear = NaN;
breaks(1).iPos = NaN;
breaks(1).type = NaN;
end
breaksDet = breaks;
breaksSto = breaks;
% figure(20)
% diff = data-dataDeterm;
% imagesc(diff')
% axis xy
% colorbar
%
% figure(21)
% mplot(diff)
a=0;