%WAVETEST Example Matlab script for WAVELET, using NINO3 SST dataset % % See "http://paos.colorado.edu/research/wavelets/" % Written January 1998 by C. Torrence % % Modified Oct 1999, changed Global Wavelet Spectrum (GWS) to be sideways, % changed all "log" to "log2", changed logarithmic axis on GWS to % a normal axis. load 'sst_nino3.dat' % input SST time series sst = sst_nino3; %------------------------------------------------------ Computation % normalize by standard deviation (not necessary, but makes it easier % to compare with plot on Interactive Wavelet page, at % "http://paos.colorado.edu/research/wavelets/plot/" variance = std(sst)^2; sst = (sst - mean(sst))/sqrt(variance) ; n = length(sst); dt = 0.25 ; time = [0:length(sst)-1]*dt + 1871.0 ; % construct time array xlim = [1870,2000]; % plotting range pad = 1; % pad the time series with zeroes (recommended) dj = 0.25; % this will do 4 sub-octaves per octave s0 = 2*dt; % this says start at a scale of 6 months j1 = 7/dj; % this says do 7 powers-of-two with dj sub-octaves each lag1 = 0.72; % lag-1 autocorrelation for red noise background mother = 'Morlet'; % Wavelet transform: [wave,period,scale,coi] = wavelet(sst,dt,pad,dj,s0,j1,mother); power = (abs(wave)).^2 ; % compute wavelet power spectrum % Significance levels: (variance=1 for the normalized SST) [signif,fft_theor] = wave_signif(1.0,dt,scale,0,lag1,-1,-1,mother); sig95 = (signif')*(ones(1,n)); % expand signif --> (J+1)x(N) array sig95 = power ./ sig95; % where ratio > 1, power is significant % Global wavelet spectrum & significance levels: global_ws = variance*(sum(power')/n); % time-average over all times dof = n - scale; % the -scale corrects for padding at edges global_signif = wave_signif(variance,dt,scale,1,lag1,-1,dof,mother); % Scale-average between El Nino periods of 2--8 years avg = find((scale >= 2) & (scale < 8)); Cdelta = 0.776; % this is for the MORLET wavelet scale_avg = (scale')*(ones(1,n)); % expand scale --> (J+1)x(N) array scale_avg = power ./ scale_avg; % [Eqn(24)] scale_avg = variance*dj*dt/Cdelta*sum(scale_avg(avg,:)); % [Eqn(24)] scaleavg_signif = wave_signif(variance,dt,scale,2,lag1,-1,[2,7.9],mother); whos %------------------------------------------------------ Plotting %--- Plot time series subplot('position',[0.1 0.75 0.65 0.2]) plot(time,sst) set(gca,'XLim',xlim(:)) xlabel('Time (year)') ylabel('NINO3 SST (degC)') title('a) NINO3 Sea Surface Temperature (seasonal)') hold off %--- Contour plot wavelet power spectrum subplot('position',[0.1 0.37 0.65 0.28]) levels = [0.0625,0.125,0.25,0.5,1,2,4,8,16] ; Yticks = 2.^(fix(log2(min(period))):fix(log2(max(period)))); contour(time,log2(period),log2(power),log2(levels)); %*** or use 'contourfill' %imagesc(time,log2(period),log2(power)); %*** uncomment for 'image' plot xlabel('Time (year)') ylabel('Period (years)') title('b) NINO3 SST Wavelet Power Spectrum') set(gca,'XLim',xlim(:)) set(gca,'YLim',log2([min(period),max(period)]), ... 'YDir','reverse', ... 'YTick',log2(Yticks(:)), ... 'YTickLabel',Yticks) % 95% significance contour, levels at -99 (fake) and 1 (95% signif) hold on contour(time,log2(period),sig95,[-99,1],'k'); hold on % cone-of-influence, anything "below" is dubious plot(time,log2(coi),'k') hold off %--- Plot global wavelet spectrum subplot('position',[0.77 0.37 0.2 0.28]) plot(global_ws,log2(period)) hold on plot(global_signif,log2(period),'--') hold off xlabel('Power (degC^2)') title('c) Global Wavelet Spectrum') set(gca,'YLim',log2([min(period),max(period)]), ... 'YDir','reverse', ... 'YTick',log2(Yticks(:)), ... 'YTickLabel','') set(gca,'XLim',[0,1.25*max(global_ws)]) %--- Plot 2--8 yr scale-average time series subplot('position',[0.1 0.07 0.65 0.2]) plot(time,scale_avg) set(gca,'XLim',xlim(:)) xlabel('Time (year)') ylabel('Avg variance (degC^2)') title('d) 2-8 yr Scale-average Time Series') hold on plot(xlim,scaleavg_signif+[0,0],'--') hold off % end of code