| 1 |
function [FLD]=diffsmooth2D_extrap_inv(fld,mskOut,varargin); |
| 2 |
%object: extrapolate an incomplete field to create a full field, by |
| 3 |
% solving for a diffusion equation equilibrium state. |
| 4 |
%inputs: fld incomplete field of interest (masked with NaN) |
| 5 |
% mskOut land mask (1s and NaNs) for the full field (output) |
| 6 |
%output: FLD full field |
| 7 |
%optional: doFormMatrix (1 by default) |
| 8 |
% if set to 1 then compute the dFLDdt_op matrix |
| 9 |
% if set to 0 then use precomputed one (global dFLDdt_op) |
| 10 |
% doMSKOUT (1 by default) |
| 11 |
% if set to 1 then first detect closed regions lacking |
| 12 |
% data points to extrapolate from (e.g. abyssal canions) |
| 13 |
% and restrict mskOut to MSKOUT accordingly |
| 14 |
% if set to 0 then omit this step |
| 15 |
%principle : |
| 16 |
%in points where mskFreeze is 1 solve diffusion equation |
| 17 |
%in points where mskFreeze is 0 solve the trivial FLD=fld |
| 18 |
|
| 19 |
gcmfaces_global; |
| 20 |
|
| 21 |
if nargin==3; doFormMatrix=varargin{1}; else; doFormMatrix=1; end; |
| 22 |
if nargin==4; doMSKOUT=varargin{2}; else; doMSKOUT=1; end; |
| 23 |
|
| 24 |
if doMSKOUT; |
| 25 |
%problematic regions will show MSKOUT==0; |
| 26 |
tmp1=1+0*fld; [MSKOUT]=diffsmooth2D_extrap_inv(tmp1,mskOut,doFormMatrix,0); |
| 27 |
%if no problematic region then no need to recompute dFLDdt_op |
| 28 |
if sum(MSKOUT==0)==0; doFormMatrix=0; end; |
| 29 |
%finalize MSKOUT |
| 30 |
MSKOUT(MSKOUT==0)=NaN; |
| 31 |
MSKOUT(~isnan(MSKOUT))=1; |
| 32 |
end; |
| 33 |
|
| 34 |
dxC=mygrid.DXC; dyC=mygrid.DYC; |
| 35 |
rA=mygrid.RAC; |
| 36 |
|
| 37 |
dxCsm=dxC; dyCsm=dyC; |
| 38 |
mskFreeze=fld; mskFreeze(find(~isnan(mskFreeze)))=0; mskFreeze(find(isnan(mskFreeze)))=1; |
| 39 |
|
| 40 |
%check for domain edge points where no exchange is possible: |
| 41 |
tmp1=mskOut; tmp1(:)=1; tmp2=exch_T_N(tmp1); |
| 42 |
for iF=1:mskOut.nFaces; |
| 43 |
tmp3=mskOut{iF}; tmp4=tmp2{iF}; |
| 44 |
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); |
| 45 |
if ~isempty(find(isnan(tmp4)&~isnan(tmp3))); fprintf('warning: mask was modified\n'); end; |
| 46 |
tmp3(isnan(tmp4))=NaN; mskOut{iF}=tmp3; |
| 47 |
end; |
| 48 |
|
| 49 |
%put 0 first guess if needed and switch land mask: |
| 50 |
fld(find(isnan(fld)))=0; fld=fld.*mskOut; |
| 51 |
|
| 52 |
%scale the diffusive operator: |
| 53 |
tmp0=dxCsm./dxC; tmp0(isnan(mskOut))=NaN; tmp00=nanmax(tmp0); |
| 54 |
tmp0=dyCsm./dyC; tmp0(isnan(mskOut))=NaN; tmp00=max([tmp00 nanmax(tmp0)]); |
| 55 |
smooth2D_nbt=tmp00; |
| 56 |
smooth2D_nbt=ceil(1.1*2*smooth2D_nbt^2); |
| 57 |
|
| 58 |
smooth2D_dt=1; |
| 59 |
smooth2D_T=smooth2D_nbt*smooth2D_dt; |
| 60 |
smooth2D_Kux=dxCsm.*dxCsm/smooth2D_T/2; |
| 61 |
smooth2D_Kvy=dyCsm.*dyCsm/smooth2D_T/2; |
| 62 |
|
| 63 |
%form matrix problem: |
| 64 |
tmp1=convert2array(mskOut); |
| 65 |
kk=find(~isnan(tmp1)); |
| 66 |
KK=tmp1; KK(kk)=kk; KK=convert2array(KK); |
| 67 |
nn=length(kk); |
| 68 |
NN=tmp1; NN(kk)=[1:nn]; %NN=convert2array(NN); |
| 69 |
|
| 70 |
global dFLDdt_op; |
| 71 |
if doFormMatrix==1; |
| 72 |
|
| 73 |
dFLDdt_op=sparse([],[],[],nn,nn,nn*5); |
| 74 |
|
| 75 |
for iF=1:fld.nFaces; for ii=1:3; for jj=1:3; |
| 76 |
FLDones=fld; FLDones(find(~isnan(fld)))=0; |
| 77 |
FLDones{iF}(ii:3:end,jj:3:end)=1; |
| 78 |
FLDones(find(isnan(fld)))=NaN; |
| 79 |
|
| 80 |
FLDkkFROMtmp=fld; FLDkkFROMtmp(find(~isnan(fld)))=0; |
| 81 |
FLDkkFROMtmp{iF}(ii:3:end,jj:3:end)=KK{iF}(ii:3:end,jj:3:end); |
| 82 |
FLDkkFROMtmp(find(isnan(fld)))=0; |
| 83 |
|
| 84 |
FLDkkFROM=exch_T_N(FLDkkFROMtmp); |
| 85 |
FLDkkFROM(find(isnan(FLDkkFROM)))=0; |
| 86 |
for iF2=1:fld.nFaces; |
| 87 |
tmp1=FLDkkFROM{iF2}; tmp2=zeros(size(tmp1)-2); |
| 88 |
for ii2=1:3; for jj2=1:3; tmp2=tmp2+tmp1(ii2:end-3+ii2,jj2:end-3+jj2); end; end; |
| 89 |
FLDkkFROM{iF2}=tmp2; |
| 90 |
end; |
| 91 |
%clear FLDkkFROMtmp; |
| 92 |
|
| 93 |
[dTdxAtU,dTdyAtV]=calc_T_grad(FLDones,0); |
| 94 |
tmpU=dTdxAtU.*smooth2D_Kux; |
| 95 |
tmpV=dTdyAtV.*smooth2D_Kvy; |
| 96 |
[fldDIV]=calc_UV_conv(tmpU,tmpV); |
| 97 |
dFLDdt=smooth2D_dt*fldDIV./rA; |
| 98 |
dFLDdt=dFLDdt.*mskFreeze; |
| 99 |
|
| 100 |
dFLDdt=convert2array(dFLDdt); FLDkkFROM=convert2array(FLDkkFROM); FLDkkTO=convert2array(KK); |
| 101 |
tmp1=find(dFLDdt~=0&~isnan(dFLDdt)); |
| 102 |
dFLDdt=dFLDdt(tmp1); FLDkkFROM=FLDkkFROM(tmp1); FLDkkTO=FLDkkTO(tmp1); |
| 103 |
dFLDdt_op=dFLDdt_op+sparse(NN(FLDkkTO),NN(FLDkkFROM),dFLDdt,nn,nn); |
| 104 |
|
| 105 |
end; end; end; |
| 106 |
|
| 107 |
end;%if doFormMatrix==1; |
| 108 |
|
| 109 |
%figure; spy(dFLDdt_op); |
| 110 |
|
| 111 |
FLD_vec=convert2array(fld);%right hand side of FLD=fld |
| 112 |
mskFreeze_vec=convert2array(mskFreeze); |
| 113 |
FLD_vec(find(mskFreeze_vec==1))=0;%right hand side of diffusion equation |
| 114 |
FLD_vec=FLD_vec(kk); |
| 115 |
|
| 116 |
INV_op=1-mskFreeze_vec(kk); |
| 117 |
INV_op=sparse([1:nn],[1:nn],INV_op,nn,nn);%identity where mskFreeze is 0 |
| 118 |
INV_op=INV_op+dFLDdt_op;%add diffusion operator where mskFreeze is 1 |
| 119 |
|
| 120 |
warning('off','MATLAB:nearlySingularMatrix'); |
| 121 |
warning('off','MATLAB:singularMatrix'); |
| 122 |
INV_vec=INV_op\FLD_vec;%solve |
| 123 |
warning('on','MATLAB:nearlySingularMatrix'); |
| 124 |
warning('on','MATLAB:singularMatrix'); |
| 125 |
|
| 126 |
INV_fld=convert2array(mskOut); |
| 127 |
INV_fld(find(~isnan(INV_fld)))=INV_vec; |
| 128 |
FLD=convert2array(INV_fld);%reformat |
| 129 |
|
| 130 |
if doMSKOUT; FLD=FLD.*MSKOUT; end;%mask problematic regions |
| 131 |
|
| 132 |
|
Parent Directory
| 
Revision Log
| 
Revision Graph