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function [val]=gcmfaces_interp_2d(fld,lon,lat,method); |
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%[val]=GCMFACES_INTERP_2D(fld,lon,lat,method); |
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% interpolates a gcmfaces field (fld) to a set of locations (lon, lat) |
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% using one of several methods: 'polygons' (default), 'natural', 'linear', |
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% 'nearest', or 'mix'. |
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% |
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% If instead fld is is an array (of the same size as lon and lat) |
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% then the field is interpolated to the gcmfaces grid (in mygrid). |
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% |
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% The 'polygons' method is a particular implementation of bilinear |
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% interpolation on the sphere. The other methods applies on DelaunayTri |
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% in longitude/latitude coordinates. In particular, the 'mix' option |
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% is `natural' extended with 'nearest' when the input field |
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% has been land-masked with NaNs. |
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% |
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%Example: |
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% lon=[-179.9:0.2:179.9]; lat=[-89.9:0.2:89.9]; |
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% [lat,lon] = meshgrid(lat,lon); |
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% fld=mygrid.Depth.*mygrid.mskC(:,:,1); |
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% [val]=gcmfaces_interp_2d(fld,lon,lat); |
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% figureL; pcolor(lon,lat,val); shading flat; |
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|
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% note: using gcmfaces_bindata to determine nearest neighbors on the sphere |
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% can be problematic. To illustrate the problem: uncomment the old |
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% method (using gcmfaces_bindata) in gcmfaces_loc_tile.m, set myenv.verbose |
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% to 2 and run the example as explained above. Points at the edge |
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% of tile 59 provide an example -- see display generated by |
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% gcmfaces_interp_coeffs.m |
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|
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gcmfaces_global; |
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|
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%backward compatibility checks: |
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if ~isfield(myenv,'useDelaunayTri'); |
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myenv.useDelaunayTri=~isempty(which('DelaunayTri')); |
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end; |
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|
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if isempty(whos('method')); method='polygons'; end; |
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|
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if ~ischar(method); |
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error('fourth argument to gcmfaces_interp_2d is now ''method'''); |
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end; |
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|
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if ~myenv.useDelaunayTri&~strcmp(method,'polygons');; |
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warning('DelaunayTri is missing -> reverting to old tsearch method'); |
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if ~isa(fld,'gcmfaces'); |
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error('old tsearch method only treats gcmfaces inputs (fld)'); |
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end; |
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end; |
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|
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if ~isa(fld,'gcmfaces')&strcmp(method,'polygons'); |
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error('polygons method only treats gcmfaces inputs (fld)'); |
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end; |
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|
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%%use TriScatteredInterp |
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if strcmp(method,'linear')|strcmp(method,'nearest')|strcmp(method,'natural')|strcmp(method,'mix'); |
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|
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if isa(fld,'gcmfaces'); |
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XC=convert2array(mygrid.XC); |
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YC=convert2array(mygrid.YC); |
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VEC=convert2array(fld); |
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else; |
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XC=lon; |
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YC=lat; |
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VEC=fld; |
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lon=convert2gcmfaces(mygrid.XC); |
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lat=convert2gcmfaces(mygrid.YC); |
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end; |
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|
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val=NaN*lon; |
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for ii=1:3; |
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if ii==1; |
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myXC=XC; myXC(myXC<0)=myXC(myXC<0)+360; |
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jj=find(lon>90); |
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elseif ii==2; |
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myXC=XC; |
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jj=find(lon>=-90&lon<=90); |
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else; |
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myXC=XC; myXC(myXC>0)=myXC(myXC>0)-360; |
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jj=find(lon<-90); |
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end; |
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kk=find(~isnan(myXC)); |
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TRI=DelaunayTri(myXC(kk),YC(kk)); |
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if strcmp(method,'mix'); |
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F = TriScatteredInterp(TRI, VEC(kk),'natural'); |
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tmp1=F(lon(jj),lat(jj)); |
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F = TriScatteredInterp(TRI, VEC(kk),'nearest'); |
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tmp2=F(lon(jj),lat(jj)); |
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tmp1(isnan(tmp1))=tmp2(isnan(tmp1)); |
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val(jj)=tmp1; |
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else; |
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F = TriScatteredInterp(TRI, VEC(kk),method); |
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val(jj)=F(lon(jj),lat(jj)); |
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end; |
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end; |
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|
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if ~isa(fld,'gcmfaces'); |
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val=convert2gcmfaces(val); |
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end; |
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|
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end; |
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|
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%%old linear interpolation method: |
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if strcmp(method,'tsearch'); |
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|
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% Generate triangulation |
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global mytri; |
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gcmfaces_bindata; |
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|
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%switch longitude range to -180+180 or 0-360 according to grid |
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if max(mygrid.XC)<0; |
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lon(find(lon>180))=lon(find(lon>180))-360; |
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end; |
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if max(mygrid.XC)>180; |
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lon(find(lon<0))=lon(find(lon<0))+360; |
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end; |
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|
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% Find the nearest triangle (t) |
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x=convert2array(mygrid.XC); x=x(mytri.kk); |
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y=convert2array(mygrid.YC); y=y(mytri.kk); |
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VEC=convert2array(fld); VEC=VEC(mytri.kk); |
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t = tsearch(x,y,mytri.TRI,lon',lat')';%the order of dims matters!! |
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|
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% Only keep the relevant triangles. |
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out = find(isnan(t)); |
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if ~isempty(out), t(out) = ones(size(out)); end |
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tri = mytri.TRI(t(:),:); |
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|
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% Compute Barycentric coordinates (w). P. 78 in Watson. |
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del = (x(tri(:,2))-x(tri(:,1))) .* (y(tri(:,3))-y(tri(:,1))) - ... |
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(x(tri(:,3))-x(tri(:,1))) .* (y(tri(:,2))-y(tri(:,1))); |
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w(:,3) = ((x(tri(:,1))-lon(:)).*(y(tri(:,2))-lat(:)) - ... |
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(x(tri(:,2))-lon(:)).*(y(tri(:,1))-lat(:))) ./ del; |
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w(:,2) = ((x(tri(:,3))-lon(:)).*(y(tri(:,1))-lat(:)) - ... |
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(x(tri(:,1))-lon(:)).*(y(tri(:,3))-lat(:))) ./ del; |
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w(:,1) = ((x(tri(:,2))-lon(:)).*(y(tri(:,3))-lat(:)) - ... |
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(x(tri(:,3))-lon(:)).*(y(tri(:,2))-lat(:))) ./ del; |
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|
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val = sum(VEC(tri) .* w,2); |
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val(out)=NaN; |
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val=reshape(val,size(lon)); |
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|
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end;%if strcmp(method,'tsearch'); |
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|
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|
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%%use gcmfaces_interp_coeffs (under development): |
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if strcmp(method,'polygons'); |
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siz=size(lon); |
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lon=lon(:); |
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lat=lat(:); |
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|
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ni=30; nj=30; |
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%ni=51; nj=51; |
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map_tile=gcmfaces_loc_tile(ni,nj); |
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|
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loc_tile=gcmfaces_loc_tile(ni,nj,lon,lat); |
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loc_tile=loc_tile.tileNo; |
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[loc_interp]=gcmfaces_interp_coeffs(lon,lat,ni,nj); |
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|
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fld=exch_T_N(fld); |
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[tmp1,tmp2,n3,n4]=size(fld{1}); |
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arr=NaN*zeros(length(lon),n3,n4); |
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|
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for ii_tile=1:max(map_tile); |
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ii=find(loc_tile==ii_tile&nansum(loc_interp.w,2)); |
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if ~isempty(ii); |
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%1) determine face of current tile |
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tmp1=1*(map_tile==ii_tile); |
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tmp11=sum(sum(tmp1,1),2); tmp12=[]; |
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for kk=1:tmp11.nFaces; tmp12=[tmp12,tmp11{kk}]; end; |
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ii_face=find(tmp12); |
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%... and its index range within face ... |
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tmp1=tmp1{ii_face}; |
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tmp11=sum(tmp1,2); |
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iiMin=min(find(tmp11)); iiMax=max(find(tmp11)); |
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tmp11=sum(tmp1,1); |
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jjMin=min(find(tmp11)); jjMax=max(find(tmp11)); |
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|
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%2) determine points and weights for next step |
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interp_i=1+loc_interp.i(ii,:); |
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interp_j=1+loc_interp.j(ii,:); |
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interp_k=(interp_j-1)*(ni+2)+interp_i;%index after reshape |
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interp_w=loc_interp.w(ii,:);%bininear weights |
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|
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%3) get the tile array |
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til=fld{ii_face}(iiMin:iiMax+2,jjMin:jjMax+2,:,:); |
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msk=1*(~isnan(til)); |
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til(isnan(til))=0; |
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|
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%4) interpolate each month to profile locations |
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tmp0=repmat(interp_w,[1 1 n3 n4]); |
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tmp1=reshape(til,[(ni+2)*(nj+2) n3 n4]); |
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tmp2=reshape(msk,[(ni+2)*(nj+2) n3 n4]); |
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tmp11=tmp1(interp_k(:),:); tmp11=reshape(tmp11,[size(interp_k) n3 n4]); |
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tmp22=tmp2(interp_k(:),:); tmp22=reshape(tmp22,[size(interp_k) n3 n4]); |
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tmp1=squeeze(sum(tmp0.*tmp11,2)); |
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tmp2=squeeze(sum(tmp0.*tmp22,2)); |
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arr(ii,:,:,:)=tmp1./tmp2; |
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|
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end;%if ~isempty(ii); |
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end;%for ii_tile=1:117; |
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|
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if sum(siz~=1)<=1; |
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val=reshape(arr,[prod(siz) n3 n4]); |
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else; |
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val=reshape(arr,[siz n3 n4]); |
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end; |
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% val=squeeze(reshape(arr,[siz n3 n4])); |
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% if size(val,1)~=size(lon,1); val=val'; end; |
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end; |
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