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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%% SUB-FUNCTIONS %% |
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%% USED BY: VOLBET2ISO %% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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% USE DIRECTLY AT YOUR OWN RISK ! % |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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% Master sub-function: |
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function varargout = subfct_getvol(CHP,Z,Y,X,LIMITS) |
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% Limits: |
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%disp(strcat('Limits: ',num2str(LIMITS))); |
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O = LIMITS(1); |
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MZ = LIMITS(2); |
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MY = sort( LIMITS(3:4) ); |
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MX = sort( LIMITS(5:6) ); |
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|
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% Compute the volume: |
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[V Vmat dV] = getvol(Z,Y,X,O,MZ,MY,MX,CHP); |
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% Outputs: |
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switch nargout |
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case 1 |
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varargout(1) = {V}; |
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case 2 |
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varargout(1) = {V}; |
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varargout(2) = {Vmat}; |
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case 3 |
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varargout(1) = {V}; |
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varargout(2) = {Vmat}; |
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varargout(3) = {dV}; |
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end %switch nargout |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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% This function computes the volume limited southward by |
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% MY(1), northward by iso-O (or MY(2) if iso-O reaches it), |
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% eastward by MX(1), westward by MX(2) and downward by iso-O |
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% (or MZ if iso-O reaches it). |
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% |
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% Updates: |
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% 20060615: add a default meridional gradient (negative) |
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% test on x,y,z limits |
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% |
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function varargout = getvol(Z,Y,X,O,MZ,MY,MX,CHP) |
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%% Dim: |
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nz = length(Z); |
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ny = length(Y); |
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nx = length(X); |
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%disp(num2str([nz ny nx])); |
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%% Indices: |
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izmax = min( find( Z>MZ ) ); if isempty(izmax),izmax=nz;end; |
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iymin = max( find( Y<MY(1) ) ); if isempty(iymin),iymin=1; end; |
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iymax = min( find( Y>MY(2) ) ); if isempty(iymax),iymax=ny;end; |
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ixmin = max( find( X<MX(1) ) ); if isempty(ixmin),ixmin=1; end; |
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ixmax = min( find( X>MX(2) ) ); if isempty(ixmax),ixmax=nx;end; |
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%disp(num2str([1 izmax iymin iymax ixmin ixmax])); |
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%% 1- determine the 3D matrix of volume elements defined by |
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% the grid: |
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dV = getdV(Z,Y,X); |
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%% 2- compute the 3D volume matrix where 1 means dV must be |
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% counted and 0 must not: |
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V = ones(nz,ny,nx); % initialy keep all points |
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|
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% Exclude northward iso-O limits: |
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% NB: here the test depends on the meridional gradient of CHP |
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% if CHP increase (resp. decreases) with LAT then we must |
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% keep lower (resp. higher) values than O limit |
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% a: determine test type: |
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N = iymax - iymin + 1; % Number of Y points in the domain |
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CHPsouth = nanmean(nanmean(squeeze(CHP(1,iymin:iymin+fix(N/2),ixmin:ixmax)))); |
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CHPnorth = nanmean(nanmean(squeeze(CHP(1,iymin+fix(N/2):iymax,ixmin:ixmax)))); |
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SNgrad = (CHPnorth - CHPsouth)./abs(CHPnorth - CHPsouth); |
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if isnan(SNgrad), SNgrad=-1; end % Assume negative gradient by default |
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%disp(strcat('Northward gradient sign is:',num2str(SNgrad))); |
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switch SNgrad |
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case 1, testype = 'le'; % Less than or equal |
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case -1, testype = 'ge'; % Greater than or equal |
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end %switch |
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% b: exclude points |
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for iz=1:izmax |
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chpZ = squeeze(CHP(iz,:,:)); |
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V(iz,:,:)=double(feval(testype,chpZ,O)); |
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end %for iz |
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% Exclude southward limit: |
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V(:,1:iymin,:) = zeros(nz,iymin,nx); |
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% Exclude northward limit: |
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V(:,iymax:ny,:) = zeros(nz,(ny-iymax)+1,nx); |
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% Exclude westward limit: |
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V(:,:,1:ixmin) = zeros(nz,ny,ixmin); |
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% Exclude eastward limit: |
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V(:,:,ixmax:nx) = zeros(nz,ny,(nx-ixmax)+1); |
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% Exclude downward limit: |
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V(izmax:nz,:,:) = zeros((nz-izmax)+1,ny,nx); |
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%% 3- Then compute the volume by summing dV elements |
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% for non 0 V points |
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Vkeep = V.*dV; |
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Vkeep = sum(sum(sum(Vkeep))); |
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%% 4- Outputs: |
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switch nargout |
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case 1 |
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varargout(1) = {Vkeep}; % Volume single value |
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case 2 |
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varargout(1) = {Vkeep}; |
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varargout(2) = {V}; % Logical V matrix with included/excluded points |
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case 3 |
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varargout(1) = {Vkeep}; |
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varargout(2) = {V}; |
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varargout(3) = {dV}; % Volume elements matrix |
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end %switch nargout |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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% This function computes the 3D dV volume elements. |
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function dv = getdV(Z,Y,X); |
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nz = length(Z); |
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ny = length(Y); |
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nx = length(X); |
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%%% Compute the DY: |
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% Assuming Y is independant of ix: |
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d = m_lldist([1 1]*X(1),Y); |
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dy = [d(1)/2 (d(2:length(d))+d(1:length(d)-1))/2 d(length(d))/2]; |
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dy = meshgrid(dy,X)'; |
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%%% Compute the DX: |
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clear d |
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for iy = 1 : ny |
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d(:,iy) = m_lldist(X,Y([iy iy])); |
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end |
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dx = [d(1,:)/2 ; ( d(2:size(d,1),:) + d(1:size(d,1)-1,:) )./2 ; d(size(d,1),:)/2]; |
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dx = dx'; |
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%% Compute the horizontal DS surface element: |
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ds = dx.*dy; |
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%% Compute the DZ: |
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d = diff(Z); |
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dz = [d(1)/2 ( d(2:length(d)) + d(1:length(d)-1) )./2 d(length(d))/2]; |
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%% Then compute the DV volume elements: |
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dv = ones(nz,ny,nx)*NaN; |
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for iz=1:nz |
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dv(iz,:,:) = dz(iz).*ds; |
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end |
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