MITgcm_contrib/gmaze_pv/subfct_getsurf.m

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%        SUB-FUNCTIONS          %%
%% USED BY: SURFBET2OUTCROPS     %%
%%          INTBET2OUTCROPS      %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% USE DIRECTLY AT YOUR OWN RISK ! %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Master sub-function:
function varargout = subfct_getsurf(CHP,Y,X,LIMITS)

% Limits:
%disp(strcat('Limits: ',num2str(LIMITS)));
O  = LIMITS(1);
MY = sort( LIMITS(2:3) );
MX = sort( LIMITS(4:5) );

% Compute the surface:
[S Smat dS] = getsurf(Y,X,O,MY,MX,CHP);

% Outputs:
switch nargout
 case 1
  varargout(1) = {S};
 case 2
  varargout(1) = {S};
  varargout(2) = {Smat};
 case 3
  varargout(1) = {S};
  varargout(2) = {Smat};
  varargout(3) = {dS};
end %switch nargout


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This function computes the surface limited southward by
% MY(1), northward by iso-O (or MY(2) if iso-O reaches it),
% eastward by MX(1), westward by MX(2) 
%
% Updates: 
% 20060615: add a default meridional gradient (negative)
%           test on x,y limits
%
function varargout = getsurf(Y,X,O,MY,MX,CHP)

%% Dim:
ny = length(Y);
nx = length(X);
%disp(num2str([ny nx]));

%% Indices:
iymin = max( find( Y<MY(1) ) ); if isempty(iymin),iymin=1; end;
iymax = min( find( Y>MY(2) ) ); if isempty(iymax),iymax=ny;end;
ixmin = max( find( X<MX(1) ) ); if isempty(ixmin),ixmin=1; end;
ixmax = min( find( X>MX(2) ) ); if isempty(ixmax),ixmax=nx;end;
%disp(num2str([iymin iymax ixmin ixmax]));

%% 1- determine the 2D matrix of surface elements defined by
% the grid:
dS = getdS(Y,X);

%% 2- compute the 2D surface matrix where 1 means dS must be 
% counted and 0 must not:

S = ones(ny,nx); % initialy keep all points

% Exclude northward iso-O limits:
% NB: here the test depends on the meridional gradient of CHP
%     if CHP increase (resp. decreases) with LAT then we must
%     keep lower (resp. higher) values than iso-O limit
% a: determine test type:
N = iymax - iymin + 1; % Number of Y points in the domain
CHPsouth = nanmean(nanmean(squeeze(CHP(iymin:iymin+fix(N/2),ixmin:ixmax))));
CHPnorth = nanmean(nanmean(squeeze(CHP(iymin+fix(N/2):iymax,ixmin:ixmax))));
SNgrad = (CHPnorth - CHPsouth)./abs(CHPnorth - CHPsouth);
if isnan(SNgrad), SNgrad=-1; end % Assume negative gradient by default
%disp(strcat('Northward gradient sign is:',num2str(SNgrad)));
switch SNgrad
 case  1, testype = 'le'; % Less than  or equal 
 case -1, testype = 'ge'; % Greater than or equal
end %switch
% b: exclude points
S = double(feval(testype,CHP,O));

% Exclude southward limit:
S(1:iymin,:) = zeros(iymin,nx);

% Exclude northward limit:
S(iymax:ny,:) = zeros((ny-iymax)+1,nx);

% Exclude westward limit:
S(:,1:ixmin) = zeros(ny,ixmin);

% Exclude eastward limit:
S(:,ixmax:nx) = zeros(ny,(nx-ixmax)+1);


%% 3- Then compute the surface by summing dS elements 
%     for non nul S points
Skeep = S.*dS;
Skeep = sum(sum(sum(Skeep)));

%% 4- Outputs:
switch nargout
 case 1
  varargout(1) = {Skeep}; % Surface single value
 case 2
  varargout(1) = {Skeep};
  varargout(2) = {S};     % Logical S matrix with included/excluded points
 case 3
  varargout(1) = {Skeep};
  varargout(2) = {S};
  varargout(3) = {dS};    % Surface elements matrix
end %switch nargout


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This function computes the 2D dS surface elements.
function ds = getdS(Y,X);

ny = length(Y);
nx = length(X);

%%% Compute the DY:
% Assuming Y is independant of ix:
d  = m_lldist([1 1]*X(1),Y);
dy = [d(1)/2  (d(2:length(d))+d(1:length(d)-1))/2 d(length(d))/2];
dy = meshgrid(dy,X)';

%%% Compute the DX:
clear d
for iy = 1 : ny
   d(:,iy) = m_lldist(X,Y([iy iy]));
end
dx = [d(1,:)/2 ;  ( d(2:size(d,1),:) + d(1:size(d,1)-1,:) )./2 ; d(size(d,1),:)/2];
dx = dx';

%% Compute the horizontal DS surface element:
ds = dx.*dy;

1	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2	%% SUB-FUNCTIONS %%
3	%% USED BY: SURFBET2OUTCROPS %%
4	%% INTBET2OUTCROPS %%
5	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
6	% USE DIRECTLY AT YOUR OWN RISK ! %
7	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
8
9	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
10	% Master sub-function:
11	function varargout = subfct_getsurf(CHP,Y,X,LIMITS)
12
13	% Limits:
14	%disp(strcat('Limits: ',num2str(LIMITS)));
15	O = LIMITS(1);
16	MY = sort( LIMITS(2:3) );
17	MX = sort( LIMITS(4:5) );
18
19	% Compute the surface:
20	[S Smat dS] = getsurf(Y,X,O,MY,MX,CHP);
21
22	% Outputs:
23	switch nargout
24	case 1
25	varargout(1) = {S};
26	case 2
27	varargout(1) = {S};
28	varargout(2) = {Smat};
29	case 3
30	varargout(1) = {S};
31	varargout(2) = {Smat};
32	varargout(3) = {dS};
33	end %switch nargout
34
35
36	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
37	% This function computes the surface limited southward by
38	% MY(1), northward by iso-O (or MY(2) if iso-O reaches it),
39	% eastward by MX(1), westward by MX(2)
40	%
41	% Updates:
42	% 20060615: add a default meridional gradient (negative)
43	% test on x,y limits
44	%
45	function varargout = getsurf(Y,X,O,MY,MX,CHP)
46
47	%% Dim:
48	ny = length(Y);
49	nx = length(X);
50	%disp(num2str([ny nx]));
51
52	%% Indices:
53	iymin = max( find( Y<MY(1) ) ); if isempty(iymin),iymin=1; end;
54	iymax = min( find( Y>MY(2) ) ); if isempty(iymax),iymax=ny;end;
55	ixmin = max( find( X<MX(1) ) ); if isempty(ixmin),ixmin=1; end;
56	ixmax = min( find( X>MX(2) ) ); if isempty(ixmax),ixmax=nx;end;
57	%disp(num2str([iymin iymax ixmin ixmax]));
58
59	%% 1- determine the 2D matrix of surface elements defined by
60	% the grid:
61	dS = getdS(Y,X);
62
63	%% 2- compute the 2D surface matrix where 1 means dS must be
64	% counted and 0 must not:
65
66	S = ones(ny,nx); % initialy keep all points
67
68	% Exclude northward iso-O limits:
69	% NB: here the test depends on the meridional gradient of CHP
70	% if CHP increase (resp. decreases) with LAT then we must
71	% keep lower (resp. higher) values than iso-O limit
72	% a: determine test type:
73	N = iymax - iymin + 1; % Number of Y points in the domain
74	CHPsouth = nanmean(nanmean(squeeze(CHP(iymin:iymin+fix(N/2),ixmin:ixmax))));
75	CHPnorth = nanmean(nanmean(squeeze(CHP(iymin+fix(N/2):iymax,ixmin:ixmax))));
76	SNgrad = (CHPnorth - CHPsouth)./abs(CHPnorth - CHPsouth);
77	if isnan(SNgrad), SNgrad=-1; end % Assume negative gradient by default
78	%disp(strcat('Northward gradient sign is:',num2str(SNgrad)));
79	switch SNgrad
80	case 1, testype = 'le'; % Less than or equal
81	case -1, testype = 'ge'; % Greater than or equal
82	end %switch
83	% b: exclude points
84	S = double(feval(testype,CHP,O));
85
86	% Exclude southward limit:
87	S(1:iymin,:) = zeros(iymin,nx);
88
89	% Exclude northward limit:
90	S(iymax:ny,:) = zeros((ny-iymax)+1,nx);
91
92	% Exclude westward limit:
93	S(:,1:ixmin) = zeros(ny,ixmin);
94
95	% Exclude eastward limit:
96	S(:,ixmax:nx) = zeros(ny,(nx-ixmax)+1);
97
98
99	%% 3- Then compute the surface by summing dS elements
100	% for non nul S points
101	Skeep = S.*dS;
102	Skeep = sum(sum(sum(Skeep)));
103
104	%% 4- Outputs:
105	switch nargout
106	case 1
107	varargout(1) = {Skeep}; % Surface single value
108	case 2
109	varargout(1) = {Skeep};
110	varargout(2) = {S}; % Logical S matrix with included/excluded points
111	case 3
112	varargout(1) = {Skeep};
113	varargout(2) = {S};
114	varargout(3) = {dS}; % Surface elements matrix
115	end %switch nargout
116
117
118
119	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
120	% This function computes the 2D dS surface elements.
121	function ds = getdS(Y,X);
122
123	ny = length(Y);
124	nx = length(X);
125
126	%%% Compute the DY:
127	% Assuming Y is independant of ix:
128	d = m_lldist([1 1]*X(1),Y);
129	dy = [d(1)/2 (d(2:length(d))+d(1:length(d)-1))/2 d(length(d))/2];
130	dy = meshgrid(dy,X)';
131
132	%%% Compute the DX:
133	clear d
134	for iy = 1 : ny
135	d(:,iy) = m_lldist(X,Y([iy iy]));
136	end
137	dx = [d(1,:)/2 ; ( d(2:size(d,1),:) + d(1:size(d,1)-1,:) )./2 ; d(size(d,1),:)/2];
138	dx = dx';
139
140	%% Compute the horizontal DS surface element:
141	ds = dx.*dy;
142