# csdms-contrib/slepian_alpha

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 function [lonlon,latlat,intlon,intlat,orlon,orlat]=equistat(c11,cmn,lonnum,latnum) % [lonlon,latlat,intlon,intlat,orlon,orlat]=EQUISTAT(c11,cmn,lonnum,latnum) % % Expresses a geographical grid of regularly spaced latitudes and % longitudes in terms of the true distances along the surface of the % sphere. Suitable to interpolate a geographical grid to a locally % regular Cartesian flat grid. % % INPUT: % % C11 [lon lat] of the upper left corner of the map [degrees] % CMN [lon lat] of the lower right corner of the map [degrees] % lonnum Number of samples across (E-W) % latnum Number of samples down (N-S) % % OUTPUT: % % lonlon The Cartesion x-coordinates of the geographical [lon lat] grid % latlat The Cartesion y-coordinates of the geographical [lon lat] grid % intlon Regular Cartesian longitudes for interpolation using GRIDDATA % intlat Regular Cartesian latitudes for interpolation using GRIDDATA % All of the above are with respect to a top left corner [0,0] % orlon The longitudes of the original geographical grid % orlat The latitudes of the original geographical grid % The above two with respect to the actual top left corner % % EXAMPLE I: % % XIM=[115 155]; YIM=[-5 -50]; % [lonlon,latlat,intlon,intlat,orlon,orlat]=... % equistat([XIM(1) YIM(1)],[XIM(2) YIM(2)],20,20); % fridplot(lonlon,latlat); hold on % co=fridplot(intlon,intlat); set(co,'Color','b') ; hold off % % EXAMPLE II: % % XIM=[100 160]; YIM=[1 -50]; %% Get the data on a regular geographical grid (longitude and latitude) % z=flipud(etopo(fullfile(getenv('IFILES'),'TOPOGRAPHY','EARTH'),5,sort(YIM),XIM)); % subplot(121) % imagef([XIM(1) YIM(1)],[XIM(2) YIM(2)],z); axis image; %% Plot the continental outlines, in geographical coordinates, on top % [a,b,XY]=plotcont([XIM(1) YIM(1)],[XIM(2) YIM(2)]); axis tight % cb=cax2dem([-8000 1500]); delete(cb) %% Find interpolation points on a regular Cartesian grid (E-W and N-S) %% contained in the original grid % [lonlon,latlat,intlon,intlat]=... % equistat([XIM(1) YIM(1)],[XIM(2) YIM(2)],size(z,2),size(z,1)); %% Interpolate the geographical grid to this regular Cartesian grid % zi=griddata(lonlon,latlat,z,intlon,intlat); % subplot(122) % Plot the interpolated image on the regular Cartesian grid % imagef([0 0],[range(intlon(:)) -range(intlat(:))],zi); axis image %% Project the continental outlines according to the same scheme % [flon,tlat]=project(XY(:,1),XY(:,2),[XIM(1) YIM(1)],[XIM(2) YIM(2)]); % cb=cax2dem([-8000 1500]); delete(cb) % The next line needs to be fixed !!!! %% hold on ; d=plot(flon...,tlat...,'k'); hold off % % See also UNPROJECT, PROJECT, POLARGRID, ELL2CAR, MASTERSET % % Last modified by fjsimons-at-alum.mit.edu, 09/24/2008 XIM=[c11(1) cmn(1)]; YIM=[c11(2) cmn(2)]; longrid=linspace(XIM(1),XIM(2),lonnum); latgrid=linspace(YIM(1),YIM(2),latnum); [orlon,orlat]=meshgrid(longrid,latgrid); lonlon=(orlon-c11(1)).*cos(orlat*pi/180); latlat=(orlat-c11(2)); % Origin in middle of data set shift=repmat((lonlon(1,lonnum)-lonlon(:,lonnum))/2,1,lonnum); lonlon=lonlon+shift; latlat=latlat; intval=max(lonlon(:,lonnum)-lonlon(:,lonnum-1)); minval=max(lonlon(:,1)); maxval=min(lonlon(:,lonnum)); intlon=repmat(minval:intval:maxval,latnum,1); intlat=repmat(latlat(:,1),1,size(intlon,2));