matlab_class/gcmfaces_smooth/diffsmooth2D_extrap_fwd.m

function [FLD]=diffsmooth2D_extrap_fwd(fld,mskOut,eps);
%object:        extrapolate an incomplete field to create a full field, by 
%                       time-stepping a diffusion equation to near-equilibrium.
%inputs:        fld     incomplete field of interest (masked with NaN)
%               mskOut  land mask (1s and NaNs) for the full field (output)
%               eps     convergence criterium
%output:        FLD     full field

global mygrid;

dxC=mygrid.DXC; dyC=mygrid.DYC; 
rA=mygrid.RAC;

dxCsm=dxC; dyCsm=dyC;

%mask of points which values will evolve 
doStep=1*(isnan(fld));

%put first guess:
x=convert2array(mygrid.XC);
y=convert2array(mygrid.YC);
z=convert2array(fld);
m=convert2array(mskOut);
tmp1=find(~isnan(z));
tmp2=find(~isnan(m));
zz=z;
zz(tmp2) = griddata(x(tmp1),y(tmp1),z(tmp1),x(tmp2),y(tmp2),'nearest');
fld=convert2array(zz);

%put 0 first guess if needed and switch land mask:
fld(find(isnan(fld)))=0; fld=fld.*mskOut;

%scale the diffusive operator:
tmp0=dxCsm./dxC; tmp0(isnan(mskOut))=NaN; tmp00=nanmax(tmp0);
tmp0=dyCsm./dyC; tmp0(isnan(mskOut))=NaN; tmp00=max([tmp00 nanmax(tmp0)]);
smooth2D_nbt=tmp00;
smooth2D_nbt=ceil(1.1*2*smooth2D_nbt^2);

smooth2D_dt=1;
smooth2D_T=smooth2D_nbt*smooth2D_dt;
smooth2D_Kux=dxCsm.*dxCsm/smooth2D_T/2;
smooth2D_Kvy=dyCsm.*dyCsm/smooth2D_T/2;

%setup problem:
myOp.dt=1;
myOp.eps=eps;
myOp.Kux=smooth2D_Kux;
myOp.Kvy=smooth2D_Kvy;
myOp.doStep=doStep;

%time step problem:
FLD=gcmfaces_timestep(myOp,fld);


1	function [FLD]=diffsmooth2D_extrap_fwd(fld,mskOut,eps);
2	%object: extrapolate an incomplete field to create a full field, by
3	% time-stepping a diffusion equation to near-equilibrium.
4	%inputs: fld incomplete field of interest (masked with NaN)
5	% mskOut land mask (1s and NaNs) for the full field (output)
6	% eps convergence criterium
7	%output: FLD full field
8
9	global mygrid;
10
11	dxC=mygrid.DXC; dyC=mygrid.DYC;
12	rA=mygrid.RAC;
13
14	dxCsm=dxC; dyCsm=dyC;
15
16	%mask of points which values will evolve
17	doStep=1*(isnan(fld));
18
19	%put first guess:
20	x=convert2array(mygrid.XC);
21	y=convert2array(mygrid.YC);
22	z=convert2array(fld);
23	m=convert2array(mskOut);
24	tmp1=find(~isnan(z));
25	tmp2=find(~isnan(m));
26	zz=z;
27	zz(tmp2) = griddata(x(tmp1),y(tmp1),z(tmp1),x(tmp2),y(tmp2),'nearest');
28	fld=convert2array(zz);
29
30	%put 0 first guess if needed and switch land mask:
31	fld(find(isnan(fld)))=0; fld=fld.*mskOut;
32
33	%scale the diffusive operator:
34	tmp0=dxCsm./dxC; tmp0(isnan(mskOut))=NaN; tmp00=nanmax(tmp0);
35	tmp0=dyCsm./dyC; tmp0(isnan(mskOut))=NaN; tmp00=max([tmp00 nanmax(tmp0)]);
36	smooth2D_nbt=tmp00;
37	smooth2D_nbt=ceil(1.12smooth2D_nbt^2);
38
39	smooth2D_dt=1;
40	smooth2D_T=smooth2D_nbt*smooth2D_dt;
41	smooth2D_Kux=dxCsm.*dxCsm/smooth2D_T/2;
42	smooth2D_Kvy=dyCsm.*dyCsm/smooth2D_T/2;
43
44	%setup problem:
45	myOp.dt=1;
46	myOp.eps=eps;
47	myOp.Kux=smooth2D_Kux;
48	myOp.Kvy=smooth2D_Kvy;
49	myOp.doStep=doStep;
50
51	%time step problem:
52	FLD=gcmfaces_timestep(myOp,fld);
53
54