matlab_class/gcmfaces_calc/calc_overturn.m

function [FLD]=calc_overturn(fldU,fldV,doFlip,list_factors);
%object:    compute meridional overturning streamfunction
%inputs:    fldU and fldV are the fields of grid point transport
%optional:  doFlip (default is 1). If 1 then flip the vertical 
%               axis back and forth, hence intergrating from the 
%               'bottom'. If 0 then dont.
%           list_factors (default is {'dh','dz'})
%output:    FLD is the streamfunction
%
%notes:     mygrid.LATS_MASKS is the set of quasi longitudinal lines along which
%               transports will integrated, as computed in gcmfaces_lines_zonal
%           the result is converted to Sv, and sign is changed.

gcmfaces_global;

if nargin<3; doFlip=1; end;
if nargin<4; list_factors={'dh','dz'}; end;

%check that LATS_MASKS has already been defined:
if ~isfield(mygrid,'LATS_MASKS');
    fprintf('one-time initialization of gcmfaces_lines_zonal: begin\n');
    gcmfaces_lines_zonal;
    fprintf('one-time initialization of gcmfaces_lines_zonal: end\n');
end;

%initialize output:
n3=max(size(fldU.f1,3),1); n4=max(size(fldV.f1,4),1);
FLD=NaN*squeeze(zeros(length(mygrid.LATS_MASKS),n3+1,n4));

%prepare fldU/fldV:
fldU(isnan(fldU))=0; fldV(isnan(fldV))=0;

dxg=mk3D(mygrid.DXG,fldU); dyg=mk3D(mygrid.DYG,fldU);
if size(fldU.f1,3)==length(mygrid.DRF); drf=mk3D(mygrid.DRF,fldU); else; drf=fldU; drf(:)=1; end;
facW=drf; facW(:)=1; facS=facW;
for ii=1:length(list_factors);
  tmp1=list_factors{ii};
  if strcmp(tmp1,'dh'); facW=facW.*dyg; facS=facS.*dxg;
  elseif strcmp(tmp1,'dz'); facW=facW.*drf; facS=facS.*drf;
  elseif strcmp(tmp1,'hfac'); facW=facW.*mygrid.hFacW; facS=facS.*mygrid.hFacS;
  elseif isempty(tmp1); 1;
  else; fprintf('error in calc_overturn : non supported factor\n'); return;
  end;
end;

for k4=1:n4;
fldU(:,:,:,k4)=fldU(:,:,:,k4).*facW;
fldV(:,:,:,k4)=fldV(:,:,:,k4).*facS;
end;

%use array format to speed up computation below:
fldU=convert2array(fldU); fldV=convert2array(fldV);

for iy=1:length(mygrid.LATS_MASKS); 

   %get list ofpoints that form a zonal band:
   mskW=mygrid.LATS_MASKS(iy).mskWedge;
   vecW=gcmfaces_subset(mskW,fldU);
   mskS=mygrid.LATS_MASKS(iy).mskSedge;
   vecS=gcmfaces_subset(mskS,fldV);
   trsp=nansum(vecW,1)+nansum(vecS,1);

   %store:
   if doFlip;
     FLD(iy,1:n3,:)=flipdim(cumsum(flipdim(trsp,2),2),2);
   else;
     FLD(iy,2:n3+1,:)=cumsum(trsp,2);
   end;

   %convert to Sv and change sign:
   FLD(iy,:,:)=-1e-6*FLD(iy,:,:);

end; 

if doFlip;
  FLD(:,end,:)=0;
else;
  FLD(:,1,:)=0;
end;

1	function [FLD]=calc_overturn(fldU,fldV,doFlip,list_factors);
2	%object: compute meridional overturning streamfunction
3	%inputs: fldU and fldV are the fields of grid point transport
4	%optional: doFlip (default is 1). If 1 then flip the vertical
5	% axis back and forth, hence intergrating from the
6	% 'bottom'. If 0 then dont.
7	% list_factors (default is {'dh','dz'})
8	%output: FLD is the streamfunction
9	%
10	%notes: mygrid.LATS_MASKS is the set of quasi longitudinal lines along which
11	% transports will integrated, as computed in gcmfaces_lines_zonal
12	% the result is converted to Sv, and sign is changed.
13
14	gcmfaces_global;
15
16	if nargin<3; doFlip=1; end;
17	if nargin<4; list_factors={'dh','dz'}; end;
18
19	%check that LATS_MASKS has already been defined:
20	if ~isfield(mygrid,'LATS_MASKS');
21	fprintf('one-time initialization of gcmfaces_lines_zonal: begin\n');
22	gcmfaces_lines_zonal;
23	fprintf('one-time initialization of gcmfaces_lines_zonal: end\n');
24	end;
25
26	%initialize output:
27	n3=max(size(fldU.f1,3),1); n4=max(size(fldV.f1,4),1);
28	FLD=NaN*squeeze(zeros(length(mygrid.LATS_MASKS),n3+1,n4));
29
30	%prepare fldU/fldV:
31	fldU(isnan(fldU))=0; fldV(isnan(fldV))=0;
32
33	dxg=mk3D(mygrid.DXG,fldU); dyg=mk3D(mygrid.DYG,fldU);
34	if size(fldU.f1,3)==length(mygrid.DRF); drf=mk3D(mygrid.DRF,fldU); else; drf=fldU; drf(:)=1; end;
35	facW=drf; facW(:)=1; facS=facW;
36	for ii=1:length(list_factors);
37	tmp1=list_factors{ii};
38	if strcmp(tmp1,'dh'); facW=facW.dyg; facS=facS.dxg;
39	elseif strcmp(tmp1,'dz'); facW=facW.drf; facS=facS.drf;
40	elseif strcmp(tmp1,'hfac'); facW=facW.mygrid.hFacW; facS=facS.mygrid.hFacS;
41	elseif isempty(tmp1); 1;
42	else; fprintf('error in calc_overturn : non supported factor\n'); return;
43	end;
44	end;
45
46	for k4=1:n4;
47	fldU(:,:,:,k4)=fldU(:,:,:,k4).*facW;
48	fldV(:,:,:,k4)=fldV(:,:,:,k4).*facS;
49	end;
50
51	%use array format to speed up computation below:
52	fldU=convert2array(fldU); fldV=convert2array(fldV);
53
54	for iy=1:length(mygrid.LATS_MASKS);
55
56	%get list ofpoints that form a zonal band:
57	mskW=mygrid.LATS_MASKS(iy).mskWedge;
58	vecW=gcmfaces_subset(mskW,fldU);
59	mskS=mygrid.LATS_MASKS(iy).mskSedge;
60	vecS=gcmfaces_subset(mskS,fldV);
61	trsp=nansum(vecW,1)+nansum(vecS,1);
62
63	%store:
64	if doFlip;
65	FLD(iy,1:n3,:)=flipdim(cumsum(flipdim(trsp,2),2),2);
66	else;
67	FLD(iy,2:n3+1,:)=cumsum(trsp,2);
68	end;
69
70	%convert to Sv and change sign:
71	FLD(iy,:,:)=-1e-6*FLD(iy,:,:);
72
73	end;
74
75	if doFlip;
76	FLD(:,end,:)=0;
77	else;
78	FLD(:,1,:)=0;
79	end;
80