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gforget |
1.1 |
function [FLD]=diffsmooth2D(fld,mskOut); |
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%object: implementation (gforget@mit.edu) of a diffusive smoother (Weaver and Courtier 2001) |
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%input: fld field to be smoothed (masked with NaN) |
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% dxCsm,dyCsm scale in first/second direction |
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%output:FLD smoothed field |
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%asumption: dxCsm/dyCsm are assumed to be given at the positions of U/V points |
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global mygrid; |
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dxC=mygrid.DXC; dyC=mygrid.DYC; |
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dxG=mygrid.DXG; dyG=mygrid.DYG; |
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rA=mygrid.RAC; |
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dxCsm=dxC; dyCsm=dyC; |
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mskFreeze=fld; mskFreeze(find(~isnan(mskFreeze)))=0; mskFreeze(find(isnan(mskFreeze)))=1; |
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%check for domain edge points where no exchange is possible: |
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tmp1=mskOut; tmp1(:)=1; tmp2=exch_T_N(tmp1); |
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for iF=1:mskOut.nFaces; |
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tmp3=mskOut{iF}; tmp4=tmp2{iF}; |
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tmp4=tmp4(2:end-1,1:end-2)+tmp4(2:end-1,3:end)+tmp4(1:end-2,2:end-1)+tmp4(3:end,2:end-1); |
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if ~isempty(find(isnan(tmp4)&~isnan(tmp3))); fprintf('warning: mask was modified\n'); end; |
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tmp3(isnan(tmp4))=NaN; mskOut{iF}=tmp3; |
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end; |
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%put 0 first guess if needed and switch land mask: |
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fld(find(isnan(fld)))=0; fld=fld.*mskOut; |
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%scale the diffusive operator: |
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tmp0=dxCsm./dxC; tmp0(isnan(mskOut))=NaN; tmp00=nanmax(tmp0); |
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tmp0=dyCsm./dyC; tmp0(isnan(mskOut))=NaN; tmp00=max([tmp00 nanmax(tmp0)]); |
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smooth2D_nbt=tmp00; |
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smooth2D_nbt=ceil(1.1*2*smooth2D_nbt^2); |
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smooth2D_dt=1; |
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smooth2D_T=smooth2D_nbt*smooth2D_dt; |
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smooth2D_Kux=dxCsm.*dxCsm/smooth2D_T/2; |
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smooth2D_Kvy=dyCsm.*dyCsm/smooth2D_T/2; |
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%form matrix problem: |
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tmp1=convert2array(mskOut); |
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kk=find(~isnan(tmp1)); |
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KK=tmp1; KK(kk)=kk; KK=convert2array(KK,fld); |
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nn=length(kk); |
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NN=tmp1; NN(kk)=[1:nn]; %NN=convert2array(NN,fld); |
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dFLDdt_op=sparse([],[],[],nn,nn,nn*5); |
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for iF=1:fld.nFaces; for ii=1:3; for jj=1:3; |
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FLDones=fld; FLDones(find(~isnan(fld)))=0; |
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FLDones{iF}(ii:3:end,jj:3:end)=1; |
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FLDones(find(isnan(fld)))=NaN; |
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FLDkkFROMtmp=fld; FLDkkFROMtmp(find(~isnan(fld)))=0; |
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FLDkkFROMtmp{iF}(ii:3:end,jj:3:end)=KK{iF}(ii:3:end,jj:3:end); |
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FLDkkFROMtmp(find(isnan(fld)))=0; |
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FLDkkFROM=exch_T_N(FLDkkFROMtmp); |
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for iF2=1:fld.nFaces; |
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tmp1=FLDkkFROM{iF2}; tmp2=zeros(size(tmp1)-2); |
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for ii2=1:3; for jj2=1:3; tmp2=tmp2+tmp1(ii2:end-3+ii2,jj2:end-3+jj2); end; end; |
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FLDkkFROM{iF2}=tmp2; |
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end; |
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%clear FLDkkFROMtmp; |
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[dTdxAtU,dTdyAtV]=calc_T_grad(FLDones,0); |
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tmpU=dTdxAtU.*smooth2D_Kux; |
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tmpV=dTdyAtV.*smooth2D_Kvy; |
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[fldDIV]=calc_UV_div(tmpU,tmpV); |
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dFLDdt=smooth2D_dt*fldDIV./rA; |
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dFLDdt=dFLDdt.*mskFreeze; |
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dFLDdt=convert2array(dFLDdt); FLDkkFROM=convert2array(FLDkkFROM); FLDkkTO=convert2array(KK); |
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tmp1=find(dFLDdt~=0&~isnan(dFLDdt)); |
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dFLDdt=dFLDdt(tmp1); FLDkkFROM=FLDkkFROM(tmp1); FLDkkTO=FLDkkTO(tmp1); |
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dFLDdt_op=dFLDdt_op+sparse(NN(FLDkkTO),NN(FLDkkFROM),dFLDdt,nn,nn); |
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end; end; end; |
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%figure; spy(dFLDdt_op); |
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FLD_vec=convert2array(fld); |
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mskFreeze_vec=convert2array(mskFreeze); |
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FLD_vec(find(mskFreeze_vec==1))=0; |
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FLD_vec=FLD_vec(kk); |
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INV_op=1-mskFreeze_vec(kk); |
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INV_op=sparse([1:nn],[1:nn],INV_op,nn,nn); |
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INV_op=INV_op+dFLDdt_op; |
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INV_vec=INV_op\FLD_vec; |
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INV_fld=convert2array(mskOut); |
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INV_fld(find(~isnan(INV_fld)))=INV_vec; |
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FLD=convert2array(INV_fld,fld); |
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return; |
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%time step using matrix: |
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FLD_vec=convert2array(fld); |
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FLD_vec=FLD_vec(find(~isnan(FLD_vec))); |
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dFLDdt_vec=dFLDdt_op*FLD_vec; |
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dFLDdt_fld=convert2array(FLD); |
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dFLDdt_fld(find(~isnan(dFLDdt_fld)))=dFLDdt_vec; |
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dFLDdt_fld(find(isnan(dFLDdt_fld)))=0; |
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%time-stepping loop: |
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FLD=fld; |
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test1=0; it=0; |
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while ~test1; |
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it=it+1; |
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[dTdxAtU,dTdyAtV]=calc_T_grad(FLD,0); |
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tmpU=dTdxAtU.*smooth2D_Kux; |
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tmpV=dTdyAtV.*smooth2D_Kvy; |
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[fldDIV]=calc_UV_div(tmpU,tmpV); |
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dFLDdt=smooth2D_dt*fldDIV./rA; |
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dFLDdt=dFLDdt.*mskFreeze; |
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FLD=FLD-dFLDdt; |
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tmp1=max(abs(dFLDdt)); |
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if mod(it,10)==0; fprintf([num2str(it) ' del=' num2str(tmp1) ' eps=' num2str(eps) ' \n']); end; |
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test1=tmp1<eps; |
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FLDstore{it}=dFLDdt; |
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end; |
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if 1; |
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jj=1; FLDstore2=zeros([size(FLD{jj}) length(FLDstore)]); |
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for ii=1:length(FLDstore); FLDstore2(:,:,ii)=FLDstore{ii}{jj}; end; |
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tmp1=abs(FLDstore2(:,:,end)); [ii,jj]=find(tmp1==max(tmp1(:))); |
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figure; plot(cumsum(squeeze(FLDstore2(ii,jj,:)))); |
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end; |
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