MATLAB & Practical Application on Climate Variability Studies EXERCISES

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1 B.Aires, 20-24/02/06 - Centro de Investigaciones del Mar y la Atmosfera & Department of Atmospheric and Oceanic Sciences (UBA) DAY3 Exercise n. 9 Aim: Compute Mean, Standard Deviation for U wind component field DO_mean_and_std.m & Zonal Mean DO_zonal_mean.m Data:..esercizi\day_3\ Data\ uwnd3.mon.mean.nc Solution: DO_mean_and_std.m % Performs means, std, % and zonal mean of U velocity. %%%%%%%%%%%%%%%%%% %% Load 3d U wind component for the period clear all; load coast lati=lat;clear lat;loni=long;clear long; filenamein = '../Data/uwnd3.mon.mean.nc'; % Input file name. nomevar='uwnd'; % Variable name. f = netcdf(filenamein,'r'); % f is the netcdf object. var1 = f{nomevar}; % var1 is the ncvar object. autoscale(var1,0); u=var1(505:624,:,:,:); ncload(filenamein,'level','lat','lon'); u=u.* ; %% Calculate MEAN and STD in time u_10y=squeeze(mean(u)); u_10y_std=squeeze(std(u)); %% Plot U MEAN and U STD at 1000 mb [x,y]=meshgrid(lon,lat); miniu=round(min(min((u_10y(1,:,:))))); maxiu=round(max(max((u_10y(1,:,:))))); figure project1; pcolorm(y,x,squeeze(u_10y(1,:,:))); caxis([miniu maxiu]); cmap=colormap(jet(maxiu-miniu)); cmap(find([miniu:maxiu]==0),:)=1; % set no-autoscaling in reading data. [Line12] % Load the u component % for the period % 120x17x73x144 % Load level, lat, lon % Scale factor & offset % N.B. comment this line if % you want autoscaling (and % set autoscale(var1,1) in % line12. % 17x73x144 % 17x73x144 % set N. of colors. % set to white the 1

2 shading interp colorbar('horiz'); [c,h]=contourm(y,x,squeeze(u_10y(1,:,:)),[miniu:2.5:maxiu],'b'); ht=clabel(c,h,'fontsize',8); set(ht,'color','k'); plotm(lati,loni,'color','k','linewidth',2.5); title('u1000 MEAN years [m/s]','fontweight','bold'); print -djpeg90./output/uwnd_1000mb_mean_ jpg % first value > 0 exercise 9. miniu_std=round(min(min((u_10y_std(1,:,:))))); maxiu_std=round(max(max((u_10y_std(1,:,:))))); figure project1; pcolorm(y,x,squeeze(u_10y_std(1,:,:))); caxis([miniu_std maxiu_std]); cmap=colormap(jet(2*(maxiu_std-miniu_std))); % set N. of colors. shading interp colorbar('horiz'); [c,h]=contourm(y,x,squeeze(u_10y_std(1,:,:)),[miniu_std:1:maxiu_std],'k'); ht=clabel(c,h,'fontsize',8); set(ht,'color','k'); plotm(lati,loni,'color','k','linewidth',2.5); title('u1000 STD years [m/s]','fontweight','bold'); print -djpeg90./output/uwnd_1000mb_std_ jpg 2

3 DO_zonal_mean.m exercise 9. % Performs means, std, % and zonal mean of U velocity. %%%%%%%%%%%%%%%%%% %% Load 3d U wind component for the period clear all; load coast lati=lat;clear lat;loni=long;clear long; filenamein = '../Data/uwnd3.mon.mean.nc'; % Input file name. nomevar='uwnd'; % Variable name. f = netcdf(filenamein,'r'); % f is the netcdf object. var1 = f{nomevar}; % var1 is the ncvar object. autoscale(var1,0); u=var1(505:624,:,:,:); ncload(filenamein,'level','lat','lon'); u=u.* ; % set no-autoscaling in reading data. [Line12] % Load the u component % for the period % 120x17x73x144 % Load level, lat, lon % Scale factor & offset % N.B. comment this line if % you want autoscaling (and % set autoscale(var1,1) in % line12. %% Calculate MEAN and STD in time u_10y=squeeze(mean(u)); % 17x73x144 %% Calculate zonal mean and interpolate in Z. u_10y_zm=squeeze(mean(u_10y,3)); % 17x73 u_10y_zm=u_10y_zm(1:10,:); % Select levels % from 1000 to x73 level2=flipud([200:20:1000]'); % set YI = 1000:20:200 u_10y_zm_i=interp2... % ZI = INTERP2(X,Y,Z,XI,YI) (lat, level(1:10), u_10y_zm, lat,level2'); %% Plot U ZONAL MEAN u_10y_zm_i_p=flipdim(u_10y_zm_i,2); lat_p=flipud(lat); figure pcolor(u_10y_zm_i_p); % flipdim because % lat is 90 : -90 % and we need -90 : 90 set(gca,'xtick',[1:6:73],'xticklabel',lat_p(1:6:)); set(gca,'ytick',[1:5:41],'yticklabel',level2(1:5:)); xlabel('latitude [deg N]');ylabel('Pressure [mb]'); title('u zonal mean Period ','fontweight','bold'); shading interp; hold on; miniu=round(min(u_10y_zm_i_p(:))); maxiu=round(max(u_10y_zm_i_p(:))); caxis([miniu maxiu]); cmap=colormap(jet(maxiu-miniu)); cmap(1:find([miniu:maxiu]==0)-1,:)=1; colorbar('horiz'); %%% Labels for contours <=0 -- %%% % set N. of colors. % set to white the % values < 0 3

4 [cs h]=contour(u_10y_zm_i_p,[miniu:2:0 0],'k--'); hcs=clabel(cs,h,'labelspacing',720,'fontsize',8); %%% Labels for contours >0 - %%% [cs1 h1]=contour(u_10y_zm_i_p,[0:2:maxiu],'k-'); hcs1=clabel(cs1,h1,'labelspacing',720,'fontsize',8); %%% Equatorial line. line([37 37],[0 41],'color','k','linewidth',1.5); print -djpeg90./output/uwnd_zonal_mean_ jpg exercise 9. 4

5 Exercise n. 10 Aim: Correlation maps nino3 Sea Level Pressure & Filtering. Data:...esercizi/day_1/ex2/output/ssta_nino3_30y.dat...esercizi/day_3/Data/slp.25x25.????.mat Solution: DO_ccmap.m % Performs correlation maps, applying a filter to a 30y mm time series. clear all; close all; %%%%%%%%%%%%%%%%%%%%%%%%%%% % Settings... filter = 'yes'; filter_type = 'HP' dataset = [ ' ' ]; dt = 12 resol = [145 73]; itt = 360; in1= [ '../../day_1/ex2/output/ssta_nino3_30y.dat' ]; in2 = [ '..\Data\slp.25x25.' ]; % 'yes','no' % 'HP', 'LP', 'BP' % N of data for each year. % Resolution % Time series length % Input ssta nino3 time series % Input 2D field switch filter case 'yes' out1 = [ './output/hcm_ninio3' filter_type '-SLP' ] % Output plot case 'no' out1 = [ './output/hcm_ninio3-raw-slp' ] % of settings % Grid 2.5 x 2.5 alatg = [ -90:2.5:90 ]; along = [ 0:2.5:360 ]; [axllon,axllat]=meshgrid(along,alatg); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Reading the time serie % and the bidimensional field fid=fopen(in1,'r','b'); % Read nino3 ssta 30y tserie=fread(fid,'float32'); % time series in binary format % stored at the of the Exe-2. field=[ ]; for it=1970:1:1999 % Read slp mm fields year=num2str(it); load( [ in2 year '.mat' ] ) % 12x73x145 slp=permute(slp,[ ]); % 73x145x12 slp=reshape(slp,resol(2)*resol(1),12); % 10585x12 field=[ field slp ]; % 10585x360 5

6 exercise 10. % Filtering... switch filter case 'yes' [tserie]=filtering(tserie,filter_type,dt); % Doing correlations... field=field'; nn=resol(1)*resol(2); for n=1:nn [CC(n,1), PVAL1(n,1)] = corr(field(:,n),tserie(:,1)); % CC --> 10585x1 CC1=reshape(CC,resol(2),resol(1)); % CC1 --> 173x145 maxcc1=max(max(cc1)) mincc1=min(min(cc1)) % Plotting % Pannels title... titstr=cell(size(1:2)); switch filter case 'yes' titstr{1} = [ 'HCM, Ninio3-SLP, ' filter_type ', ' dataset ]; titstr{2} = [ 'HCM, Ninio3-SLP (sign at 0.05), ' filter_type ', ' dataset ]; case 'no' titstr{1} = [ 'HCM, Ninio3-SLP-RAW, ' dataset ]; titstr{2} = [ 'HCM, Ninio3-SLP-RAW (sign at 0.05), ' dataset ]; % Plotting HCM... a4 mn=-0.7; % Set Color Axis mx=0.7; % and nco=14; % number of palette colors. % top pannel subplot(211); map_global title ( titstr{1} ); % Shading h=pcolorm(axllat,axllon,cc1(:,:)); caxis([mn mx]); colormap(jet(nco)); colorbar('horizon'); shading interp % zero hold on; [c3,h3]=contourm(axllat,axllon,cc1(:,:),[ 0 0 ],'k'); set(h3,'linestyle','-','linewidth',1.2,'visible','on') hold on; % load coast plotm(lat,long,'k') hold on; %%%%%%%% Significant correlations... % if PVAL <= 0.05 then CC is significant (differs from zero)... % then, introduce NaNs if CC is not significant: ind1 = find( PVAL1(:,1) > 0.05); 6

7 exercise 10. CC(ind1,1)=NaN; CC1m=reshape(CC,resol(2),resol(1)); maxcc1m=max(max(cc1m)) mincc1m=min(min(cc1m)) % Bottom pannel subplot(212) map_global title ( titstr{2} ); % Shading h=pcolorm(axllat,axllon,cc1m(:,:)); caxis([mn mx]); colormap(jet(nco)); colorbar('horizon'); load coast plotm(lat,long,'k') hold on; print('-djpeg100',[ out1 '.jpeg']); return % 10585x1 7

8 Exercise n. 11 Aim: Compute and plot ACW Hovmoeller. Data:...esercizi/day_3/Data/SST_ T42.grd Solution: DO_Hov_ACW.m % Perform ACW Hovmoeller % Use icontourf, ecolorbar & bluewhitered additional functions. %% Set values for reading grd file. [info ctl file needed]. clear in='../data/sst_ t42.grd'; % HadISST1.1 SST data % Period resol = [128 64]; % Resolution itt = 216; % Time series length type='direct'; % 'direct' or 'sequential' undef= ; lon=[0: :360]; % lon & lat.. from ctl lon=lon(1:-1); lat=[ ]; [X,Y]=meshgrid(lon,lat); %% Load HadISST1.1 SST grd data [fid,message]=fopen(in,'r','b'); [var]=read_grd(fid,type,resol(1),resol(2),itt); fclose(fid); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Weight by cos(lat) fcos=cos(y(:,:)*3.14/180); fcos=fcos'; fcos=reshape(fcos,resol(1)*resol(2),1); for it=1:itt var(:,it)=var(:,it).*fcos(:,1); %% undef -> nan var(var==undef)=nan; %% calculate anomaly sst=reshape(var,resol(1),resol(2),itt); % 128x64x216 sst=permute(sst,[2 1 3]); % 64x128x216 sst56s=squeeze(sst(12,:,:)); % lat(12)= ~= -56 % 128x216 sst56s_m=reshape(sst56s,resol(1),12,itt/12); % 128x12x18 sst56s_clima=nanmean(sst56s_m,3); % 128x12 8

9 % N.B. replace nanmean with % local function 'nanmeann' if % you are running on MATLAB 6 sst56s_clima_r=repmat(sst56s_clima,[1 1 18]); % 128x12x18 sst56s_anoma=sst56s_m-sst56s_clima_r; % 128x12x18 sst56s_anoma_r=reshape(sst56s_anoma,resol(1),12*itt/12); % 128x216 exercise 11. %% band pass filtering 3-7 months [b,a] = butter(1,[ 1/7 1/3 ],'stop'); y=filter(b,a,sst56s_anoma_r); %% Plot ACW Hovmoeller mini_c=-1; maxi_c=1; a4 icontourf(y',[mini_c:0.05:maxi_c],'none'); set(gca,'ytick',[1:12:216]); set(gca,'yticklabel',[1982:1:1999]); set(gca,'xtick',[1:16:128]); set(gca,'xticklabel',lon(1:16:)); ylabel('time [years]','fontweight','bold'); xlabel('longitude','fontweight','bold'); % y' to have lon in x % and time in y. colormap(bluewhitered); % Use bluewhitered colorbar, % see the bluewhitered.m fun. ecolorbar([mini_c:0.05:maxi_c]); % N.B. replace this line with the following, % using MATLAB 6. %colorbar; set(gca,'position',[ ]) title('interannual Anomalies along 56 Sud HadISST'...,'fontweight','bold'); print -djpeg90./output/acw_hovmoeller_ jpg 9

10 Exercise n. 12 Aim: 2D Field Interpolation on regular grids DO_interp2.m irregular grids DO_griddata.m Data:..esercizi/day_1/data/skt.mon.mean.nc Solutions: DO_interp2.m % Perform interpolation between different regular grids. clear filenamein = '../../day_1/data/skt.mon.mean.nc'; f = netcdf(filenamein,'nowrite'); var1= f{'skt'}; skt_grid1=var1(1,:,:); % Get the first time step % of the NCEP SKT series % 94x192. lat_grid1=f{'lat'}(:); % Get the lat [94] lon_grid1=f{'lon'}(:); % and lon [192] vectors %% Interp. SKT field on a T30 gaussian grid -> ZI = INTERP2(X,Y,Z,XI,YI) [lon_grid2,lat_grid2]=gridcoord('t30'); % Load lat,lon vectors - res. T30 skt_grid2 = interp2(lon_grid1',lat_grid1,... % 192,94 skt_grid1,... % 94x192 lon_grid2,lat_grid2'); % 96,48 %% Plotting [xlon_grid1,xlat_grid1]=meshgrid(lon_grid1,lat_grid1); [xlon_grid2,xlat_grid2]=meshgrid(lon_grid2,lat_grid2); load coast; mini=round(min(skt_grid1(:))); maxi=round(max(skt_grid1(:))); cmap=colormap(jet(round(maxi-mini))); figure subplot(211); project1; pcolorm(xlat_grid1,xlon_grid1,skt_grid1); plotm(lat,long,'k'); caxis([mini maxi]); title('skt jan 1948 on NCEP Data GRID 94x192','fontweight','bold'); subplot(212); project1; pcolorm(xlat_grid2,xlon_grid2,skt_grid2); plotm(lat,long,'k'); caxis([mini maxi]); title('skt jan 1948 on T30 Gaussian GRID 48x96','fontweight','bold'); subplot('position',[ ]);project1; pcolorm(xlat_grid1,xlon_grid1,skt_grid1); % set N. of colors. 10

11 caxis([mini maxi]); h=colorbar('horiz'); set(h,'position',[ ]); print -djpeg90./output/skt_interp2.jpg exercise 12. DO_griddata.m % Perform interpolation between different irregular grids. clear cd C:\ENRICO\tutorials\esercizi\day_3\ex12; filenamein = '../../day_1/data/skt.mon.mean.nc'; f = netcdf(filenamein,'nowrite'); var1= f{'skt'}; skt_grid1=var1(1,:,:); % Get the first time step % of the NCEP SKT series % 94x192. lat_grid1=f{'lat'}(:); % Get the lat [94] lon_grid1=f{'lon'}(:); % and lon [192] vectors %% Interp. SKT field on ORCA2 ARAKAWA-C grid -> %% ZI = [XI,YI,ZI]=GRIDDATA(X,Y,Z,XI,YI) % see in./grids_figure/ the two grids: gaussian and arakawa-c % grid_ncep_94x192.jpg & grid_orca2_149x182.jpg [lon_grid2,lat_grid2]=gridcoord('orca2','t'); % Load lat,lon ORCA matrices lon_grid2=lon_grid2+360; % Set >0 lon values nota360=find(lon_grid2 > 360); % lon_grid2(nota360)=lon_grid2(nota360)-360; % skt_grid2 = griddata(lon_grid1',lat_grid1,... % 192,94 skt_grid1,... % 94x192 lon_grid2,lat_grid2); % 149x182,149x182 %% Plotting [xlon_grid1,xlat_grid1]=meshgrid(lon_grid1,lat_grid1); load coast; mini=round(min(skt_grid1(:))); maxi=round(max(skt_grid1(:))); cmap=colormap(jet(round(maxi-mini))); % set N. of colors. figure subplot(211); project1; pcolorm(xlat_grid1,xlon_grid1,skt_grid1); plotm(lat,long,'k'); caxis([mini maxi]); title('skt jan 1948 on NCEP Data GRID 94x192','fontweight','bold'); subplot(212); project1; pcolorm(lat_grid2,lon_grid2,skt_grid2); plotm(lat,long,'k'); caxis([mini maxi]); title('skt jan 1948 on ARAKAWA-C GRID 149x182','fontweight','bold'); subplot('position',[ ]);project1; pcolorm(xlat_grid1,xlon_grid1,skt_grid1); 11

12 caxis([mini maxi]); h=colorbar('horiz'); set(h,'position',[ ]); print -djpeg90./output/skt_griddata.jpg exercise

13 Exercise n. 13 Aim: GLOBAL EOFs slp & Saving in grd format. Data:...esercizi/day_3/data/ z500.25ond.grd Solution: DO_EOF.m % Estimating, plotting and saving in grd format EOFs of a z500 dataset clear all; %%%%%%%%%%%%%%%%%%%%%%%%%%% %% Main Settings month = [ 'OND' ]; dataset = [ 'NCEP' ]; namevar = [ 'Z500' ]; in = [ '..\Data\z500.25ond.grd' ]; type='direct'; alatg = [ -90:2.5:90 ]; along = [ 0:2.5:360 ]; resol = [144 73]; itt = 25; linear_detr = 'yes'; factor = 100.; signo = -1.; nro = [ 8 ]; mode=1; % Input dataset 25 y OND % 'direct' or 'sequential' % Info about the grid % Resolution [longitude latitude] % Time series length [years] % Perform a linear detr? % 'yes' or 'no' % Factor to plotting issues... % If you want to change the sign (flip-flop) % Number of modes to save % Mode to plot % of settings %%%%%%%%%%%%%%%%%%%%%%%%%%% % Grid 2.5x2.5 [axllon,axllat]=meshgrid(along,alatg); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Read data [fid,message]=fopen(in,'r','b') [var]=read_grd(fid,type,resol(1),resol(2),itt); % 10512x25 fclose(fid); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Weight by cos(lat) lat=axllat(:,1:resol(1)); fcos=cos(lat(:,:)*3.14/180); %fcos 13 1 fcos=fcos'; fcos=reshape(fcos,resol(1)*resol(2),1); for it=1:itt 13

14 exercise 13. var(:,it)=var(:,it).*fcos(:,1); % %% Detr? switch linear_detr case 'yes' dt=['dt']; vart=var'; vart=detr(vart,'linear'); var=vart'; case 'no' dt=['nodt']; vart=var'; vart=detr(vart,'constant'); var=vart'; %% Compute EOF [u,lam,v,proj]=eof(var,nro); tit = [ dataset ', ' namevar ', ' month ]; stat1 = [ 'EOF' ]; stat2 = [ 'PC' ]; %% flip-flop u=u*signo; proj=proj*signo; %% Plot EOFs % Title including the variance titstr=cell(size(1:nro)); modeindex=[ 1:1:nro ] for i=1:nro ii=modeindex(i); titstr{i} = [ stat1 '-' num2str(ii) ' ' num2str(lam(ii)*100,'%-2.0f') '%']; %%%% %% multiply by factor u=u*factor; % 10512x8 %% closing the grid... 73x145xnro u=reshape(u,resol(1),resol(2),nro); % 144x73x8 ub=zeros([ resol(1)+1 resol(2) nro ]); % 145x73x8 ub(1:resol(1),:,:)=u(:,:,:); % 145x73x8 ub(145,:,:)=u(1,:,:); % 145x73x8 ub=permute(ub, [ ]); % 73x145x8 max(max(ub(:,:,mode))) min(min(ub(:,:,mode))) %% plotting the EOF map_global title ( tit ); h=pcolorm(axllat,axllon,ub(:,:,mode)); caxis([-3 3]); cmap=colormap(jet(24)); % set N. of colors. cmap([12 13],:)=1; colorbar('horizon'); shading interp; % Contours % hold on; % [c1,h1]=contourm(axllat,axllon,ub(:,:,mode),[-3:0.2:-0.2],'b'); % set(h1,'linestyle','--','linewidth',1.0,'visible','on') % hold on; 14

15 % [c2,h2]=contourm(axllat,axllon,ub(:,:,mode),[0.2:0.2:3],'r'); % set(h2,'linestyle','-','linewidth',1.0,'visible','on') hold on; [c3,h3]=contourm(axllat,axllon,ub(:,:,mode),[ 0 0 ],'k'); set(h3,'linestyle','-','linewidth',1.5,'visible','on') hold on; load coast plotm(lat,long,'k') %% EOFn and variance text('position',[1.1,1.8],'string',titstr(mode)) out1 = [ './output/' stat1 num2str(mode) '_' namevar '_' month ] % Save figure print('-djpeg100',[ out1 '.jpeg']); exercise 13. %% Plotting the PC pc_plot(tit,(proj(:,mode)/factor),mode); out2 = [ './output/' stat2 num2str(mode) namevar '_' month ] % Save figure print('-djpeg100',[ out2 '.jpeg']); %% Saving PC and VARIANCE in mat format % saving the PCs file1 = [ './output/' stat2 's_' namevar '_' month '.mat' ] pc=proj; eval ([ ' save ', file1, ' pc ' ]); % saving the variance filevar = [ './output/' stat1 '_varianza_' namevar '_' month '.mat' ] varianza = lam(:)*100 eval ([ ' save ', filevar, ' varianza ' ]); %% saving the EOFs in grd format %file11 = [ './' stat1 's_' namevar '_' month '.mat' ] %eof=ub; %eval ([ ' save ', file11, ' eof ' ]); eof2save=ones(1,73,145,8);eof2save(:)=nan; eof2save(1,:,:,:)=ub; % 1x73x145x8 eof2save=permute(eof2save,[ ]); % 8x1x73x145 we use the modes as time output = [./output/ stat1 's_' namevar '_' month] % for grd writing. m2grd(eof2save,'eof',[1],alatg',along,output,'float32') 15