Initial commit.

geo/dm2deci.m

+function [lond,latd] = dm2deci(londeg,lonmin,lonsec,EW,latdeg,latmin,latsec,NS)
+
+%
+% This function converts coordinates from deg/min/sec to decimal
+%
+% [lond,latd] = dm2deci(londeg,lonmin,lonsec,EW,latdeg,latmin,latsec,NS)
+%
+% Enter numbers for longitude degrees, minutes and seconds, and a string for cardinal direction ('E' or 'W')
+%                                              followed by
+%       numbers for latitude  degrees, minutes and seconds, and a string for cardinal direction ('N' or 'S')
+%
+% Written by Jean-Luc Shaw
+%
+
+if(strmatch(NS,'N')) ; lat_sign =  1. ; end
+if(strmatch(NS,'S')) ; lat_sign = -1. ; end
+if(strmatch(EW,'E')) ; lon_sign =  1. ; end
+if(strmatch(EW,'W')) ; lon_sign = -1. ; end
+
+lond = lon_sign*(londeg+lonmin./60+lonsec./3600) ;
+latd = lat_sign*(latdeg+latmin./60+latsec./3600) ;
+
+end

geo/globeGrid.m

+function [LNG,LAT] = globeGrid(lims,sz)
+% Synthax :         [LNG,LAT] = globeGrid(lims,sz)
+%
+% Takes as input longitude and latitude limits 'lims', in format :
+%
+%             lims = [lon_min lon_max lat_min lat_max]
+% 
+% and a grid size 'sz' in kilometers, and generates a grid uniform in
+% kilometer space, with the center of the x dimension aligned with the
+% center of the area specified by 'lims'. This is mostly designed for use
+% with small grids (~50-100km^2) where this representation looks almost
+% regular in coordinate space and kind of "looks nice"... at least to me it
+% does.
+%
+% 
+
+% EARTH RADIUS
+R       = 6371 ;
+
+% convert to km
+lng = [lims(1); lims(1); lims(2); lims(2)] ;
+lat = [lims(3); lims(4); lims(3); lims(4)] ;
+avl = mean(lng) ;
+lng = lng - avl ;                              % move to prime meridian
+
+% SINUSOIDAL PROJECTION
+y     = (            lat*R*pi / 180 ) ;
+x     = ( cosd(lat).*lng*R*pi / 180 ) ;
+
+avy   = mean(y) ;
+avx   = mean(x) ;
+
+% MAKE GRID VECTORS AROUND CENTER IN KM SPACE
+xg    = [flipud( [avx:-sz:min(x)]' ) ; [avx+sz:sz:max(x)]' ] ;
+yg    = [flipud( [avy:-sz:min(y)]' ) ; [avy+sz:sz:max(y)]' ] ;
+
+% GENERATE UNIFORM GRID IN KM SPACE
+[X,Y] = meshgrid(xg,yg) ;
+
+% CONVERT BACK TO GEOGRAPHICAL COORDINATES
+LAT   = 180*Y./(R*pi) ;
+LNG   = 180*X./(R*pi*cosd(LAT)) + avl ;   % moved back to average meridian
+
+end
\ No newline at end of file

geo/ll2area.m

+function A = ll2area(lng,lat,unit)
+% Synthax :                A = ll2area(lng,lat,unit)
+%
+% Takes as input the geographical coordinate vectors for longitude 'lng'
+% and latitude 'lat' in column format and returns the area inside the
+% non-intersecting polygon they form as ouput 'A' in units 'unit'. 
+% recognized unit options are 'm' for square meters and 'km' for square
+% kilometers.
+%
+% BASED ON:
+%
+% https://www.periscopedata.com/blog/polygon-area-from-latitude-and-longitude-using-sql
+%
+% and
+%
+% http://geomalgorithms.com/a01-_area.html
+
+% PARAMETERS
+switch unit
+	case 'km'
+		R   =  6371 ;    % earth radius (km)
+	case 'm'
+		R   =  6371000 ; % earth radius (m)
+end
+
+% CONVERT TO XY
+y     = (            lat*R*pi / 180 ) ;
+x     = ( cosd(lat).*lng*R*pi / 180 ) ;
+avx   = mean(x) ;
+avy   = mean(y) ;
+normx = x - avx ;
+normy = y - avy ;
+
+% GET ANGLE FOR EVERY VERTEX (0-360) and convert 
+ang            = atan2d(normy,normx); % + (-1*normx./abs(normx))*90 + 180 ;
+ang( ang < 0 ) = ang( ang < 0 ) + 360 ;
+ang            = ang - 90;
+ang            = 360 - ang ;
+ang(ang < 0)   = ang(ang < 0) + 360 ;
+ang            = mod(ang,360) ;
+
+% SORT TO AVOID SELF INTERSECTION
+[~,IA] = sort(ang,'descend') ;
+x      = x(IA) ;
+y      = y(IA) ;
+
+% APPEND FOR WRAPPING
+x1 = x(1); xn = x(end) ;
+y1 = y(1); yn = y(end) ;
+x  = [xn; x; x1] ;
+y  = [yn; y; y1] ;
+
+% COMPUTE THE SUM
+A      = 0 ;
+for ii = 2:numel(x)-1
+    A = A + 0.5*( x(ii).*( y(ii+1) - y(ii-1) ) ) ;
+end
+
+end

geo/llt2spd.m

+function [u,v,spd,head] = llt2spd(lon,lat,time)
+
+% Synthax : [u,v,spd,head] = llt2spd(lon,lat,time)
+% 
+% Returns the speed 'spd' and it's eastward/northward components 'u' and
+% 'v' in (m/s), and the heading 'head' in degrees with 0 as east increasing
+% towards the north (90 degrees). 
+%
+% Values are calculated from a latitude/longitude time series with 
+% coordinates in decimal degrees and time in days.
+% 
+% Values are estimated between longitude/latitude coordinates and then
+% interpolated linearly to the input 'time' vector. Begining and end
+% values are extrapolated using the "pchip" method.
+
+%% make everything column vectors
+if ~iscolumn(lon)  ; lon  = lon'  ; end
+if ~iscolumn(lat)  ; lat  = lat'  ; end
+if ~iscolumn(time) ; time = time' ; end
+
+%% make differential vectors
+dlon = diff(lon) ;
+dlat = diff(lat) ;
+dt   = diff(time) ;
+dl   = m_lldist(lon,lat)*1000 ; % (m)
+
+%% calculate norm of speed
+spd = dl./(dt*24*60*60) ;
+
+%% calculate heading
+head = range_pm180_2_360(atan2d(dlat,dlon)) ;
+
+%% decompose into eastward/northward
+u = spd.*cosd(head) ;
+v = spd.*sind(head) ;
+
+%% make the time vector
+t = time(1:end-1)+0.5*dt(1);
+
+%% interpolate to the input time grid
+u    = interp1(t,u,time,'linear','extrap') ;
+v    = interp1(t,v,time,'linear','extrap') ;
+spd  = interp1(t,spd,time) ;
+spd(1)   = sqrt(u(1).^2+v(1).^2);
+spd(end) = sqrt(u(end).^2+v(end).^2);
+head     = interp1(t,head,time) ;
+
+
+end

geo/range_360_2_pm180.m

+function output = range_360_2_pm180(input)
+
+I = find(input > 180) ;
+input(I) = input(I) - 360 ;
+
+output = input ;
+
+end

geo/range_pm180_2_360.m

+function output = range_pm180_2_360(input)
+
+I = find(input < 0) ;
+input(I) = input(I) + 360 ;
+
+output = input ;
+
+end

geo/theta2heading.m

+
+function output  = theta2heading(input)
+% Synthax :           output = theta2heading(input)
+%
+% Takes as input angle vector in cartesian coordinates running counter-
+% clockwise from 0 (east) to 360 degrees and transforms it into a heading
+% vector running clockwise from 0 to the north to 360 degrees. 
+%
+ 
+input            = input - 90;
+input            = 360 - input ;
+input(input < 0) = input(input < 0) + 360 ;
+output            = mod(input,360) ;
+
+end

math/SEplot.m

+function [bins,bs,m,M]=SEplot(dist)
+% Synthax :            [bins,bs,m,M]=SEplot(dist)
+%     
+% Produces a histogram plot of distribution 'dist' with a color code
+% identifying which portions of the distribution correspond to +-1 standard
+% error, +-2 standard error, +-3 standard error, and beyond. Limits are
+% included to the categories and standard error is calculated with the
+% built in matlab std function
+
+sigma = std(dist,'omitnan') ;
+mdist = mean(dist,'omitnan') ;
+
+M     = max(dist) ; 
+m     = min(dist) ;
+
+bs    = sigma./20 ;
+bins  = sort([mdist:-bs:m mdist+bs:bs:M]);
+
+figure ; 
+i = find(dist <= mdist + 1*sigma & dist >= mdist - 1.*sigma) ;
+histogram(dist(i),bins,'facecolor','b') ;
+
+hold on
+
+i = find(dist <= mdist + 2*sigma & dist >  mdist + 1.*sigma | ... 
+         dist <  mdist - 1*sigma & dist >= mdist - 2.*sigma) ;
+histogram(dist(i),bins,'facecolor','g') ;
+
+i = find(dist <= mdist + 3*sigma & dist >  mdist + 2.*sigma | ... 
+         dist <  mdist - 2*sigma & dist >= mdist - 3.*sigma) ;
+histogram(dist(i),bins,'facecolor','r') ;
+
+i = find(dist <= mdist - 3*sigma | dist >= mdist + 3.*sigma) ;
+histogram(dist(i),bins,'facecolor','c') ;
+
+end

math/SEtrunc.m

+function [dist,I] = SEtrunc(dist,thres)
+% Synthax :            [dist,I] = SEtrunc(dist,thres)
+% 
+% Replaces with nan the values in dist which are outside the range
+% 
+%                      +-'thres'*std('dist')
+%
+% where std is matlab built in function. Limits of the range are excluded.
+% also returns the index values 'I' of the values nan-ed.
+
+sigma = std(dist,'omitnan') ;
+mdist = mean(dist,'omitnan') ;
+
+I       = find(dist < mdist - thres.*sigma | dist > mdist + thres.*sigma) ;
+dist(I) = nan ;
+
+end
+
+

math/jlpca.m

+function [vals,vecs,stds] = jlpca(X)
+% Synthax :            [vals,vecs,stds] = jlpca(X)
+% 
+% Performs principal component analysis on input matrix 'X' . Input matrix
+% must be in a form where columns are different features of the data set
+% and rows are repetitions of the same measurement.
+%
+% Also returns the standard deviation of every feature projected in the space
+% of the eigenvectors found by the PCA.
+%
+
+
+[m,n] = size(X) ;
+
+
+%% De-trend
+F      = repmat(nan,size(X)) ;
+for ii = 1:n
+    F(:,ii) = X(:,ii) - mean(X(:,ii),'omitnan') ;
+end
+
+%% Build covariance matrix
+R = F'*F ;
+
+%% Find eigenvalues
+[C,L]     = eig(R) ;
+
+%% sort and normalise
+vals      = sort(diag(L),'descend') ;
+
+% eigenvectors in growing importance
+vecs = fliplr(C) ;
+
+%% Project in the space of the eigenvectors
+Fprime = inv(vecs)*F' ;
+
+%% Get the standard error in each "eigendimension"
+stds   = std(Fprime,[],2) ;
+
+end

math/nanmean.m

+function output = nanmean(input,varargin)
+
+%
+% Matlab is super cheap for not including this 
+%     in the student license. Seriously. 
+%
+
+I = find(isfinite(input)) ;
+output = mean(input(I),varargin{:}) ;
+end

math/nanmedian.m

+function out = nanmedian(in)
+
+I   = find(isfinite(in)) ;
+out = median(in(I)) ;
+
+end

math/nlinfit.m

+function [yfit,A] = nlinfit(rhs,x,y,pars,varargin)
+% 
+% Synthax :  [yfit,A] = nlinfit(rhs,x,y,pars,cst1,cst2,...,cstn)
+%
+% An idea found online and remodeled to make it more modular about how to
+% fminsearch.m to perform non-linear, multiple parameter function fitting.
+% Variables 'x' and 'y' are the input data, i.e., y = y(x) and must be
+% vectors. Variable 'rhs' is a function handle refering to te mathematical
+% form of the fitted function. For example, to fit a 1/6 power law, define:
+%
+%                 rhs = @(a,x) a(1)*x.^(1/6) + a(2) ;
+%
+% where 'a' is a vector formed of the parameters to fit and 'x' is the
+% input independent variable. If variable 'pars' is entered as an integer
+% it is interpreted as the number of parameters to fit, and sets the first
+% guess for all parameters to zero. If 'pars' is entered as a vector, then
+% it is interpreted as the first guess for all parameters.
+%
+% The function returns the fitted values at 'x' as well as the optimized
+% parameter vector 'A'.
+
+% Is pars first guess for parameters or number of parameters
+sz = size(pars) ;
+if     sz(1) == 1 & sz(2) == 1   
+            start = zeros([pars 1]) ;
+elseif sz(1) == 1 & sz(2) >  1 | sz(2) == 1 & sz(1) >  1
+            start = pars ;
+end
+
+% Minimize parameters
+         A     = fminsearch(@(a)sum( (y - rhs(a,x,varargin{:})).^2 ),start) ;
+         yfit  = rhs(A,x,varargin{:}) ;
+end

math/smooth2D.m

+function output = smooth2D(input,hs,vs)
+% Synthax :          output = smooth2D(input,hs,vs)
+%
+% 2D moving average. The window size is 'hs' in direction j and 'vs' in
+% direction i. Both 'hs' and 'vs' MUST be odd integers. Each element of
+% 'output' is calculated from the nanmean of a box of size 'hs' by 'vs' 
+% centered on the element of corresponding indices in 'input'.
+
+output = repmat(nan,size(input)) ;
+hpad   = (hs-1)/2 ;
+vpad   = (vs-1)/2 ;
+if vpad < 1 ; vpad = 0 ; end;
+if hpad < 1 ; hpad = 0 ; end;
+if iseven(vpad) ; vpad = vpad + 1 ; end
+if iseven(hpad) ; hpad = hpad + 1 ; end
+
+[II,JJ] = size(input); 
+
+for ii = 1:II
+    for jj = 1:JJ
+        if     ii <= vpad    & jj > hpad & jj <= JJ-hpad  % TOP 
+            box           = input(1:ii+vpad,jj-hpad:jj+hpad) ;
+        elseif ii >  II-vpad & jj > hpad & jj <= JJ-hpad  % BOTTOM
+            box           = input(ii-vpad:II,jj-hpad:jj+hpad) ;
+        elseif jj <= hpad    & ii > vpad & ii <= II-vpad  % LEFT   
+            box           = input(ii-vpad:ii+vpad,1:jj+hpad) ;
+        elseif jj >  JJ-hpad & ii > vpad & ii <= II-vpad  % RIGHT   
+            box           = input(ii-vpad:ii+vpad,jj-hpad:JJ) ;
+        elseif ii <= vpad    & jj <= hpad                 % TOP LEFT
+            box           = input(1:ii+vpad,1:jj+hpad) ;
+        elseif ii >  II-vpad & jj <= hpad                 % BOTTOM LEFT
+            box           = input(ii-vpad:II,1:jj+hpad) ;
+        elseif ii <= vpad    & jj >  JJ-hpad              % TOP RIGHT
+            box           = input(1:ii+vpad,jj-hpad:JJ) ;
+        elseif ii >  II-vpad & jj >  JJ-hpad              % BOTTOM RIGHT
+            box           = input(ii-vpad:II,jj-hpad:JJ) ;
+        else                                % INSIDE
+            box           = input(ii-vpad:ii+vpad,jj-hpad:jj+hpad) ;
+        end
+        output(ii,jj) = mean(box(:),'omitnan') ;
+    end
+end
+end

math/unifrnd.m

+function output = unifrnd(b_min,b_max,d_len,m,n)
+
+% Synthax :          output = unifrnd(b_min,b_max,d_len,m,n)
+%
+% Imitates the unifrnd function from the statistics toolbox. Generates a
+% 'm' by 'n' matrix of values chosen from a uniform distribution of minimum
+% 'b_min' and maximum 'b_max' . The parameter 'd_len' controls the number
+% of elements in the uniform distribution the 'output' values are chosen
+% from.
+%
+
+dist   = linspace(b_min,b_max,d_len)' ;
+I      = randi([1 d_len],[m n]) ;
+
+output = dist(I) ;
+
+end
\ No newline at end of file

math/vvangle.m

+function theta = vvangle(v1,v2)
+% Synthax :                theta = vvangle(v1,v2)
+%
+% Get the absolute angle between two line vectors, or between the vectors
+% described by the lines v1 and v2.
+%
+
+%% make sure the sizes are compatible
+if ~( isequal(size(v1),size(v2)) || isvector(v1) && isvector(v2) && numel(v1) == numel(v2) )
+    disp('    Error : v1 and v2 have different dimensions!') ;
+    return ;
+end
+
+%% get the vector norms
+nv1 = sum(abs(v1).^2,2).^(1/2) ;
+nv2 = sum(abs(v2).^2,2).^(1/2) ;
+
+%% calculate the angle
+theta = acosd( ( dot(v1,v2,2) ) ./ (nv1.*nv2) ) ;
+
+end
\ No newline at end of file

old/ADCP_gridding.m

+function ADCP_gridding(ADCP_file_name,G,Gstrt,Gstop,Fh,Fv,theta,corrtag,WD)
+
+disp('========== 2) Smoothing then griding ==========')
+
+CC             = strrep(num2str(theta),'.','') ; 
+
+load([WD 'data/ADCP_23237/' ADCP_file_name(1:end-4) '_CC' CC 'd_' corrtag '.mat']) ;
+
+paperwidth  = 20 ;
+paperheight = 6 ;
+
+suffix = ['_1DF' num2str(Fh) 'm_G' sprintf('%d',1000*G) 'm'] ;
+
+%% TRANSFORM FILTER SIZE -> NUMBER OF CASTS
+hsize = round(Fh./(mean(diff(S.time)*24*3600,'omitnan').*2));
+
+%% INITIALISE output structure
+C.along = [] ;
+C.cross = [] ;
+C.dist  = [] ;
+C.time  = [] ;
+C.lon   = [] ;
+C.lat   = [] ;
+sm_al   = [] ;
+sm_cr   = [] ;
+sm_time = [] ;
+
+%% Find index of extreme sides of transects
+[~,MAXs] = findpeaks( S.dist,'MinPeakHeight',3.7,'MinPeakProminence',0.01) ;
+[~,MINs] = findpeaks(-S.dist,'MinPeakHeight',-0.3,'MinPeakProminence',1) ;
+II       = sort([MAXs MINs]) ;
+II       = [1 II] ;
+
+% figure
+% plot(S.time,S.dist,'k.')
+% hold on
+% plot(S.time(II),S.dist(II),'o')
+% datetick('x','HH:MM:SS')
+
+%% SET GRID 
+grdist    = [Gstrt:G:Gstop]' ;
+
+for ii = 1:numel(II)-1
+
+    start = ii ;
+    stop = start + 1 ;
+
+    % % VIEW THIS TRANSECT
+    % figure ;
+    % pcolor(S.time(II(start):II(stop)),S.z,S.cross(:,II(start):II(stop)))
+    % hold on
+    % datetick('x','HH:MM')
+    % xlabel('Time')
+    % ylabel('Depth (m)')
+    % shading flat ;
+    % axis ij;
+    % ylim([0 80]) ; xlim([S.time(II(start)) S.time(II(stop))]) ;
+    % caxis([-1 1])
+    % jlcolorbar('u$_{cross}$') ;
+    
+    %% SELECT DATA FOR THIS TRANSECT
+    DIST   = S.dist(II(start):II(stop))' ;
+    LON    = S.plon(II(start):II(stop)) ;
+    LAT    = S.plat(II(start):II(stop)) ;
+    TIME   = S.time(II(start):II(stop)) ;
+    ALONG  = S.along(:,II(start):II(stop)) ;
+    CROSS  = S.cross(:,II(start):II(stop)) ;
+    pNAN   = S.pNanUnder(:,II(start):II(stop)) ;
+    
+    %% MAKE THE DATA REGULAR
+    if DIST(1) > DIST(end)
+        % Exclude data too close to boat turns
+        I = find(DIST <= Gstop + 0.1 & DIST >= Gstrt - 0.1 ) ;
+        DIST        = DIST(I) ;
+        LON         = LON(I) ;
+        LAT         = LAT(I) ;
+        TIME        = TIME(I) ;
+        ALONG       = ALONG(:,I) ;
+        CROSS       = CROSS(:,I) ;
+        pNAN        = pNAN(:,I) ;
+        
+        % Sort according to transect direction
+        [DIST,Is]   = sort(DIST,'descend') ;
+        % Clip double values
+        [DIST,IA,~] = unique(DIST,'stable') ;
+        TIME        = TIME(IA) ;
+        LON         = LON(IA) ;
+        LAT         = LAT(IA) ;
+        ALONG       = ALONG(:,IA) ;
+        CROSS       = CROSS(:,IA) ;
+        pNAN        = pNAN(:,IA) ;
+    else
+        % Exclude data too close to boat turns
+        I = find(DIST <= Gstop + 0.1 & DIST >= Gstrt - 0.1) ;
+        DIST        = DIST(I) ;
+        TIME        = TIME(I) ;
+        LON         = LON(I) ;
+        LAT         = LAT(I) ;
+        ALONG       = ALONG(:,I) ;
+        CROSS       = CROSS(:,I) ;
+        pNAN        = pNAN(:,I) ;        
+
+        % Sort according to transect direction
+        [DIST,Is]   = sort(DIST,'ascend') ;
+        % Clip double values
+        [DIST,IA,~] = unique(DIST,'stable') ;
+        TIME        = TIME(IA) ;
+        LON         = LON(IA) ;
+        LAT         = LAT(IA) ;
+        ALONG       = ALONG(:,IA) ;
+        CROSS       = CROSS(:,IA) ;
+        pNAN        = pNAN(:,IA) ;
+    end
+    
+    %% SMOOTH DATA
+    I        = find( pNAN >= 0.99) ;
+    ALONG    = movmean(ALONG,hsize,2,'omitnan') ;
+    ALONG    = movmean(ALONG,Fv,1,'omitnan');
+    ALONG(I) = nan ;
+    
+    I        = find( pNAN >= 0.99) ;    
+    CROSS    = movmean(CROSS,hsize,2,'omitnan') ;
+    CROSS    = movmean(CROSS,Fv,1,'omitnan') ;
+    CROSS(I) = nan ;
+    
+    % Save the smooth uninterpollated data to inspect
+    sm_al   = [sm_al repmat(nan,[numel(ALONG(:,1)) 1]) ALONG(:,2:end)] ;
+    sm_cr   = [sm_cr CROSS] ;
+    sm_time = [sm_time ; TIME] ;
+    
+    %% INTERPOLATE ON SPATIAL GRID with TIME TAGS
+    if DIST(1) > DIST(end)
+        tdist   = flipud(grdist) ;
+        grtime  = interp1(DIST,TIME,tdist) ;
+        Inonan  = find(~isnan(grtime)) ;
+        grtime  = grtime(Inonan) ;
+        tdist   = tdist(Inonan) ;
+        gralong = interp1(DIST,ALONG',tdist)' ;
+        grcross = interp1(DIST,CROSS',tdist)' ;
+        grlon   = interp1(DIST,LON,tdist) ;
+        grlat   = interp1(DIST,LAT,tdist) ;
+    else
+        tdist   =        grdist  ;
+        grtime  = interp1(DIST,TIME,tdist) ;
+        Inonan  = find(~isnan(grtime)) ;
+        grtime  = grtime(Inonan) ;
+        tdist   = tdist(Inonan) ;
+        gralong = interp1(DIST,ALONG',tdist)' ;
+        grcross = interp1(DIST,CROSS',tdist)' ;
+        grlon   = interp1(DIST,LON,tdist) ;
+        grlat   = interp1(DIST,LAT,tdist) ;
+    end
+    
+