GPDfitwaves_mod.m

clear
close all
%PF = it will plot something
load wave_height_banks_peninsula.mat
%
hs_obs = hs_obs(:); time_obs = time_obs(:);

cdfplot(hs_obs) % PF cdf = cumulative density function. find suitable thresholds to constrain GPthres.m. This is just a rough guide. looks like something between 2 and 6 metres would work (between 0.5 and 1)
%return

tolerance =0.0001; % sometimes gpfit doesn't like having zero values, so add a tiny (inconsequential) amount
tthr = 3; % peaks over threshold (POT) separated by at least 3 days. Most weather systems in NZ are separated by 4-7 days
ythr = GPthres(time_obs,hs_obs+tolerance,2,6,0.1,tthr,1); % Automate threshold selection
disp(['GPD threshold selected: H_s = ' num2str(ythr) ' m'])
ARI = [1 2 5 10 20 50 100]; % This specifies the Average Recurrence Intervals (ARI) for output. Change these to what you like. 

[GPD,gpp,gpci,Sy,ARI_POT,POT_sorted] = GPDfit(hs_obs+tolerance,time_obs,tthr,ythr,ARI); % PF

figure; clf
semilogx([0 0],[0 0],'r',[0 0],[0 0],'b'); hold on;
semilogx(ARI_POT,POT_sorted,'ok'), 
hold on
semilogx(ARI,GPD(1,:),'r',ARI,GPD(2,:),'--r',ARI,GPD(3,:),'--r')
title('GPD fitted to peaks over threshold'), xlabel('Average recurrence interval (years)'), ylabel('H_s')

% Compare to annual maxima method. Don't need this but sometimes useful to 
AMy = AMcalc(time_obs,hs_obs,1); AM = AMy(:,3);
[gev,gevci] = gevfit(AM);
GEV = gevinv(1-ARI2AEP(ARI),gev(1),gev(2),gev(3));
GEV(2,:) = gevinv(1-ARI2AEP(ARI),gevci(1,1),gevci(1,2),gevci(1,3));
GEV(3,:) = gevinv(1-ARI2AEP(ARI),gevci(2,1),gevci(2,2),gevci(2,3));

figure;[AMari,AMsorted] = gringorten(AM,1,1);  hold on
semilogx(AMari,AMsorted,'xb')
semilogx(ARI,GEV(1,:),'b','LineWidth',2)
semilogx(ARI,GEV(2,:),'--b',ARI,GEV(3,:),'--b')
hold off
title('GEV fitted to annual maxima'), xlabel('Average recurrence interval  (years)'), ylabel('H_s')

figure(2) 
hold on
semilogx(ARI,GEV(1,:),'b'), semilogx(ARI,GEV(2,:),'--b',ARI,GEV(3,:),'--b'), 
semilogx(AMari,AMsorted,'+b')
hold off

legend('GPD-POT','GEV-AM');