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gforget |
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function []=rads_noice_mad(choiceData,l0,L0,doTesting); |
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if isempty(who('doTesting')); doTesting=0; end; |
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%directories |
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dirData='/net/nares/raid11/ecco-shared/ecco-version-4/input/input_rads/'; |
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topexfile = 'RADS_TJ_v4'; |
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ersfile = 'RADS_ERS_ENV_v4'; |
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gfofile = 'RADS_GFO_v4'; |
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dirIce='/net/nares/raid11/ecco-shared/ecco-version-4/input/input_nsidc_all/'; |
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fileIce='nsidc79_daily'; |
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dirOutput='ecco_it0003/sea_level_analyses/results_outliers/'; |
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%dirOutput='ecco_it0003/sea_level_analyses/tmp/'; |
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%testing switches |
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if doTesting; l0=-170; L0=-80; choiceData='gfofile'; end; |
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%select region |
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gcmfaces_global; |
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XC=convert2gcmfaces(mygrid.XC.*mygrid.mskC(:,:,1)); XC=XC(:); |
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YC=convert2gcmfaces(mygrid.YC.*mygrid.mskC(:,:,1)); YC=YC(:); |
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ii=find(XC>=l0-10&XC<=l0+10&YC>=L0-10&YC<=L0+10); |
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ni=length(ii); |
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nt=6940;%corresponds to 1992-2010 |
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%load data |
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eval(['fileData=' choiceData ';']); |
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allData=zeros(ni,nt); |
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ndata=0; |
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for yy=1992:2010; |
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fprintf(['reading ' fileData '_' num2str(yy) '\n']); |
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tmp1=dir([dirData fileData '_' num2str(yy)]); tmp0=tmp1.bytes/90/1170/4; |
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tmp1=read2memory([dirData fileData '_' num2str(yy)],[90*1170 tmp0]); |
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allData(:,ndata+[1:tmp0])=tmp1(ii,:); |
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tmp1=read2memory([dirIce fileIce '_' num2str(yy)],[90*1170 tmp0]); |
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allIce(:,ndata+[1:tmp0])=tmp1(ii,:); |
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ndata=ndata+tmp0; |
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end; |
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allData(allData<-999)=NaN; allData=allData/100; |
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allIce(allIce<-999)=NaN; allIce=allIce; |
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if ndata~=nt; error('nt was mispecified'); end; |
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%if doTesting; eval(['save ' dirOutput 'rads_noice_mad.demo.mat allData allIce ndata;']); end; |
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%if doTesting; eval(['load ' dirOutput 'rads_noice_mad.demo.mat allData allIce ndata;']); end; |
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%only keep ice free data points |
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noiceData=allData; noiceData(allIce>0)=NaN; |
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iceRejectPerc=100*(1-nansum(~isnan(noiceData(:)))/nansum(~isnan(allData(:)))); |
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%the outliers filtering |
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medianData=nanmedian(noiceData,2)*ones(1,nt);%center of distribution |
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madData=1.4826*mad(noiceData,1,2);%width of the distribution |
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cutoff=4*madData*ones(1,nt);%a factor 4 corresponds to a typical cost of 16 |
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goodData=noiceData; goodData(abs(noiceData-medianData)>cutoff)=NaN; |
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madRejectPerc=100*(1-nansum(~isnan(goodData(:)))/nansum(~isnan(noiceData(:)))); |
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%output result |
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[iceRejectPerc madRejectPerc] |
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%note : original testing was done with gfofile, l0=-170; L0=-80; |
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% including ice points madRejectPerc is ~ 3.9% |
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% excluding ice points madRejectPerc drops to 0.33% |
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if ~doTesting; |
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eval(['save ' dirOutput fileData 'l0is' num2str(l0) 'L0is' num2str(L0) ... |
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' ii goodData madData medianData iceRejectPerc madRejectPerc ']); |
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end; |
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%------- testing case -----% |
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if doTesting; |
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%note : original testing was done with ersfile, l0=-170; L0=-80; |
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% the last point (see next line) happened to be work as an example |
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jj=find(~isnan(madData)); |
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%do example of mad detection of ice covered points as outliers at one grid point |
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kk=jj(end); xc_kk=XC(ii(kk)); yc_kk=YC(ii(kk)); |
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all_kk=allData(kk,:); |
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median_kk=nanmedian(all_kk);%center of distribution |
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mad_kk=1.4826*mad(all_kk,1,2);%width of distribution |
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cutoff_kk=4*mad_kk*ones(1,nt);%a factor 4 corresponds to a typical cost of 16 |
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good_kk=all_kk; good_kk(abs(good_kk-median_kk)>cutoff_kk)=NaN; |
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reject_kk=100*(1-nansum(~isnan(good_kk))/nansum(~isnan(all_kk))); |
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%compute the various statistics |
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msk=1+0*allIce; msk(isnan(allData))=NaN; |
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%in the testing case we dont filter out the ice points : msk(allIce>0)=NaN; |
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stdOut=nanstd(msk.*allData,0,2);%sample standard deviation |
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iqrOut=0.7413*iqr(msk.*allData,2);%intequartile range estimate of std |
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madOut=1.4826*mad(msk.*allData,1,2);%median absolute difference estimate of std |
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jj=find(~isnan(stdOut)); |
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%plot region |
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if L0>60; myproj=2; elseif L0<-60; myproj=3; else; myproj=1; end; |
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figureL; m_map_gcmfaces(mygrid.Depth,myproj,{'myCaxis',[0 6e3]}); |
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colormap('gray'); colorbar off; |
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m_map_gcmfaces({'plot',XC(ii),YC(ii),'m.'},myproj,{'doHold',1}); |
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m_map_gcmfaces({'plot',xc_kk,yc_kk,'k.','MarkerSize',24},myproj,{'doHold',1}); |
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saveas(gcf,[dirOutput 'outliers_0'],'fig'); |
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eval(['print -djpeg90 ' dirOutput 'outliers_0.jpg']); |
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eval(['print -depsc ' dirOutput 'outliers_0.eps']); |
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%plot sensitivity of std estimates to outliers |
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figureL; set(gca,'FontSize',16); |
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plot(stdOut(jj),'.-'); hold on; plot(madOut(jj),'r.-'); plot(iqrOut(jj),'g.-'); |
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legend('SSTD','MAD*1.4826','IQR*0.7413'); |
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xlabel('grid point index'); ylabel('estimated standard deviation'); |
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saveas(gcf,[dirOutput 'outliers_1'],'fig'); |
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eval(['print -djpeg90 ' dirOutput 'outliers_1.jpg']); |
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eval(['print -depsc ' dirOutput 'outliers_1.eps']); |
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%plot distributions for the overall region |
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figureL; |
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subplot(3,1,1); set(gca,'FontSize',16); |
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%all data points |
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tmp1=allData(jj,:); hist(tmp1(:),[-1.5:0.02:1.5]); |
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aa=axis; aa(1:2)=[-1 1]; axis(aa); title('all data points'); |
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%and the corresponding normal distribution |
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[xx,yy]=normal_distribution([-1.5:0.02:1.5],tmp1(:)); |
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hold on; plot(xx,yy,'m','LineWidth',0.5); |
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% |
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subplot(3,1,2); set(gca,'FontSize',16); |
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tmp1=noiceData(jj,:); hist(tmp1(:),[-1.5:0.02:1.5]); |
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aa=axis; aa(1:2)=[-1 1]; axis(aa); title('ice free data points'); |
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[xx,yy]=normal_distribution([-1.5:0.02:1.5],tmp1(:)); |
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hold on; plot(xx,yy,'m','LineWidth',0.5); |
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subplot(3,1,3); set(gca,'FontSize',16); |
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tmp1=allData(jj,:); tmp1(~isnan(noiceData(jj,:)))=NaN; hist(tmp1(:),[-1.5:0.02:1.5]); |
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aa=axis; aa(1:2)=[-1 1]; axis(aa); title('icy data points'); |
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[xx,yy]=normal_distribution([-1.5:0.02:1.5],tmp1(:)); |
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hold on; plot(xx,yy,'m','LineWidth',0.5); |
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saveas(gcf,[dirOutput 'outliers_2'],'fig'); |
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eval(['print -djpeg90 ' dirOutput 'outliers_2.jpg']); |
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eval(['print -depsc ' dirOutput 'outliers_2.eps']); |
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figureL; |
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subplot(2,1,1); set(gca,'FontSize',16); |
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hist(all_kk,[-1.5:0.02:1.5]); |
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aa=axis; aa(1:2)=[-1 1]; axis(aa); title('before MAD detection'); |
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%and the corresponding normal distribution |
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[xx,yy]=normal_distribution([-1.5:0.02:1.5],all_kk(:)); |
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hold on; plot(xx,yy,'m','LineWidth',2); |
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subplot(2,1,2); set(gca,'FontSize',16); |
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hist(good_kk,[-1.5:0.02:1.5]); |
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aa=axis; aa(1:2)=[-1 1]; axis(aa); title('after MAD detection'); |
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%and the corresponding normal distribution |
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[xx,yy]=normal_distribution([-1.5:0.02:1.5],all_kk(:)); |
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hold on; plot(xx,yy,'m','LineWidth',2); |
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saveas(gcf,[dirOutput 'outliers_3'],'fig'); |
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eval(['print -djpeg90 ' dirOutput 'outliers_3.jpg']); |
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eval(['print -depsc ' dirOutput 'outliers_3.eps']); |
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end; |
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function [xx,yy]=normal_distribution(xx,data); |
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dx=diff(xx); |
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dx=median(dx); |
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%dx=unique(dx); if length(dx)>1; error('plot_normal_distribution expect regular spacing\n'); end; |
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mm=nanmedian(data); |
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ss=1.4826*mad(data,1); |
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nn=sum(~isnan(data)); |
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%for testing : mm=0.2; ss=0.1; nn=100; |
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xx=xx+mm;%reset xx to center of distribution |
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yy=nn*dx/ss/sqrt(2*pi)*exp(-0.5*xx.*xx/ss/ss);%compute distribution |
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%for testing : sum(yy)/nn |
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