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eddy2_track_eddies.m
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%% eddy tracking
% if not on first timestep
% check each eddy on this timestep for distance from previous eddies
% if distance < eddy_track_dist_param
% andif same winding dir as before
% then this eddy is a continuation of the last eddy
% check if this eddy track exists
% if it does, add new data point
% else look back eddy_track_time_param hours/timesteps for eddy
% else if no previous eddy, make new eddy track
%
% Douglas Cahl, PhD
% University of South Carolina 2023
%% parameters
params_eddy2;
%% directory setup
name_dir = dout_data; % results folder
name_pre = [region '_' num2str(radar_km_resolution) 'km_']; % name prefix, e.g., data2_1.mat , data2_2.mat , ...
outfile = [tracks_dir name_pre 'tracks'];
%% load data
j = 0;
f = dir(name_dir);
for i = 3:length(f)
fn = f(i).name;
if ~strcmp(fn(end-3:end),'.mat') || ~contains(fn,name_pre) || contains(fn,'tracks')
continue
end
disp(fn)
data = load([name_dir fn]);
if ~isempty(data.eddy_streamlines_lat)
j = j + 1;
tmp.eddy_angular_vel{j} = data.eddy_angular_vel;
tmp.eddy_center_lat{j} = data.eddy_center_lat;
tmp.eddy_center_lon{j} = data.eddy_center_lon;
tmp.eddy_dir{j} = data.eddy_dir;
tmp.eddy_ellipse_theta{j} = data.eddy_ellipse_theta;
tmp.eddy_length_x{j} = data.eddy_length_x;
tmp.eddy_length_y{j} = data.eddy_length_y;
tmp.eddy_streamlines{j} = data.eddy_streamlines;
tmp.time(j) = data.time;
end
clear data
end
if ~exist('tmp','var')
return
end
%% sort by time
[time,timei] = sort(tmp.time);
for i = 1:length(timei)
j = timei(i);
eddy_angular_vel{i} = tmp.eddy_angular_vel{j};
eddy_center_lat{i} = tmp.eddy_center_lat{j};
eddy_center_lon{i} = tmp.eddy_center_lon{j};
eddy_dir{i} = tmp.eddy_dir{j};
eddy_ellipse_theta{i} = tmp.eddy_ellipse_theta{j};
eddy_length_x{i} = tmp.eddy_length_x{j};
eddy_length_y{i} = tmp.eddy_length_y{j};
eddy_streamlines{i} = tmp.eddy_streamlines{j};
end
clear tmp
%%
j = 0;
for i = 1:length(eddy_dir)
j = j + length(eddy_dir{i});
jj(i) = length(eddy_dir{i});
mxstreams = max(eddy_streamlines{i});
if ~isempty(mxstreams)
jjstreams(i) = max(eddy_streamlines{i});
else
jjstreams(i) = 0;
end
end
disp(['Total eddies = ' num2str(j)])
disp(['Max eddies in a single timestep = ' num2str(max(jj))])
disp(['Max streamlines for an eddy = ' num2str(max(jjstreams))])
%% no tracking for first timestep
it = 1; % timestep 1
i_cluster = length(eddy_center_lat{it}); % i_eddy is the cluster
for i = 1:i_cluster
lat_center{i} = eddy_center_lat{it}(i);
lon_center{i} = eddy_center_lon{it}(i);
ellipse_theta{i} = eddy_ellipse_theta{it}(i);
eig1{i} = eddy_length_x{it}(i);
eig2{i} = eddy_length_y{it}(i);
omega{i} = eddy_angular_vel{it}(i); % rads per sec
direction{i} = eddy_dir{it}(i); % +1 is cyclonic, -1 is anticyclonic
num_streams{i} = eddy_streamlines{it}(i); % intensity
Time{i} = time(it);
timegap(i) = 1;
end
if i_cluster == 0
timegap = 1;
end
%%
i1_start = 1;
total_tracks = i_cluster;
disp('Starting track finding routine')
disp(['Total number of timestep to analyze = ' num2str(length(time))])
% disp(['Timestep = ' num2str(it)])
for it = 2:length(time)
% disp(['Timestep = ' num2str(it)])
i_cluster = length(eddy_center_lat{it}); % number of eddies at this timestep
for i=1:i_cluster
curr_lat_center = eddy_center_lat{it}(i);
if isnan(curr_lat_center)
continue
end
curr_lon_center = eddy_center_lon{it}(i);
curr_ellipse_x = eddy_length_x{it}(i);
curr_ellipse_y = eddy_length_y{it}(i);
curr_ellipse_th = eddy_ellipse_theta{it}(i);
% check over all tracks with timesteps from before
succ = 0;
i1_start = find(timegap <= eddy_track_time_param,1);
for i1=i1_start:total_tracks
eddy_continuation = 0; %
if new_dist_thres % Cahl et al., 2023 method (if center is within another streamline, they are the same eddy)
% in km
i_ellipse = 30:30:360;
ellipse_x = eig1{i1}(end)*cosd(i_ellipse);
ellipse_y = eig2{i1}(end)*sind(i_ellipse);
ellipse_th = ellipse_theta{i1}(end);
% Create rotation matrix
R = [cosd(ellipse_th) -sind(ellipse_th); sind(ellipse_th) cosd(ellipse_th)];
% Rotate points
eddypts = R*[ellipse_x ; ellipse_y];
ellipse_x = eddypts(1,:);
ellipse_y = eddypts(2,:);
% in km
[x,y,UTMzone] = geog2utm_nodisp(lon_center{i1}(end),lat_center{i1}(end),curr_lon_center,curr_lat_center);
ellipse_x = ellipse_x + x;
ellipse_y = ellipse_y + y;
% is old center within new eddy ellipse
in1 = inpolygon(0,0,ellipse_x,ellipse_y);
% in km
i_ellipse = 30:30:360;
% Create rotation matrix
R = [cosd(curr_ellipse_th) -sind(curr_ellipse_th); sind(curr_ellipse_th) cosd(curr_ellipse_th)];
% Rotate points
eddypts = R*[curr_ellipse_x ; curr_ellipse_y];
ellipse_x1 = eddypts(1,:);
ellipse_y1 = eddypts(2,:);
% is new center within old eddy ellipse
in2 = inpolygon(x,y,ellipse_x1,ellipse_y1);
if in1 || in2 %
eddy_continuation = 1;
else
% in km
[x,y,UTMzone] = geog2utm_nodisp(lon_center{i1}(end),lat_center{i1}(end),curr_lon_center,curr_lat_center);
dist = sqrt(x^2+y^2);
% if centers are close and winding direction is the same
if dist < eddy_track_dist_param
eddy_continuation = 1;
end
end
else % Sadarjoen and Post 2000 method
% in km
[x,y,UTMzone] = geog2utm_nodisp(lon_center{i1}(end),lat_center{i1}(end),curr_lon_center,curr_lat_center);
dist = sqrt(x^2+y^2);
if dist < eddy_track_dist_param
eddy_continuation = 1;
end
end
if eddy_continuation
for i_tgap = 1:eddy_track_time_param
if timegap(i1) <= i_tgap
lat_center{i1} = [lat_center{i1} ; eddy_center_lat{it}(i)];
lon_center{i1} = [lon_center{i1} ; eddy_center_lon{it}(i)];
ellipse_theta{i1} = [ellipse_theta{i1} ; eddy_ellipse_theta{it}(i)];
eig1{i1} = [eig1{i1} ; eddy_length_x{it}(i)];
eig2{i1} = [eig2{i1} ; eddy_length_y{it}(i)];
omega{i1} = [omega{i1} ; eddy_angular_vel{it}(i)];
direction{i1} = [direction{i1}; eddy_dir{it}(i)]; % +1 is cyclonic, -1 is anticyclonic
num_streams{i1} = [num_streams{i1} ; eddy_streamlines{it}(i)]; % intensity
Time{i1} = [Time{i1} ; time(it)];
timegap(i1) = 0; % zero because it's gonna add one right after this loop
succ = 1;
break;
end
end
end
end
% if not close to others, create new track
if succ == 0
total_tracks = total_tracks + 1;
lat_center{total_tracks} = eddy_center_lat{it}(i);
lon_center{total_tracks} = eddy_center_lon{it}(i);
ellipse_theta{total_tracks} = eddy_ellipse_theta{it}(i);
eig1{total_tracks} = eddy_length_x{it}(i);
eig2{total_tracks} = eddy_length_y{it}(i);
omega{total_tracks} = eddy_angular_vel{it}(i);
direction{total_tracks} = eddy_dir{it}(i); % +1 is cyclonic, -1 is anticyclonic
num_streams{total_tracks} = eddy_streamlines{it}(i); % intensity
Time{total_tracks} = time(it);
timegap(total_tracks) = 0; % zero because it's gonna add one right after this loop
end
end
% add 1 timestep to the counter
for i1=i1_start:total_tracks
timegap(i1) = timegap(i1) + 1;
end
end
disp('Finished eddy track finding')
%% save here
save(outfile,'total_tracks','lat_center','lon_center','ellipse_theta',...
'eig1','eig2','omega','direction','num_streams','Time','timegap',...
'eddy_track_dist_param','eddy_track_time_param')