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TSE_Buoy_Example.m

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+%%%%%%%%%%%%%%% Input Data %%%%%%%%%%%%%%%%
+%%% Longitude: vector of lon positions %%%%
+%%% Latitude: vector of lat positions %%%%%
+%%% time: vector of GPS sampling times %%%%
+%%%         - units of days            %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%% User Variables %%%%%%%%%%%%%%%%
+Integration_Time = 3;                     % Number of days for summing TSE and \bar{TSE}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%% Generate buoy speed times series from lat/lon %%%%
+ds=abs(time(2)-time(1));        % Assuming uniform timestep. Units of days.
+window = floor(Integration_Time/ds);
+Distances=gc_dist_length(Longitdue(1:end-2),Latitude(1:end-2),Longitude_(3:end),Latitude(3:end));   %km
+Speed_sqrd=(Distances.^2)/(ds).^2;    %km/day
+
+%%%% Calculate instantaneous TSE measurements %%%%
+TSE_Instant=log((Speed_sqrd(2:end))./(Speed_sqrd(1:end-1)));
+TSE_Instant(abs(TSE_Instant)==Inf)=NaN;
+
+%%%% Sum up TSE and \bar{TSE} %%%%
+TSE_Bar=1/(time(window+1)-time(1)) * movsum(abs(TSE_Instant),[0 window],'Endpoints','fill');
+TSE=1/(time(window+1)-time(1)) * log((Speed_sqrd(window+1:end))./(Speed_sqrd(1:end-window)));
+TSE_Bar(end+1:numel(TSE_Instant))=NaN;
+TSE(end+1:numel(TSE_Instant))=NaN;
+
+%%%% Great circle distance assuming spherical earth %%%%
+function [d]=gc_dist_length(long_initial,lat_initial,long_final,lat_final)
+r=6371;     %km
+d=r*2*asin(sqrt(sind((lat_initial-lat_final)/2).^2 + cosd(lat_initial).*cosd(lat_final).*sind((long_initial-long_final)/2).^2) );
+end