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mean_and_trend.m
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mean_and_trend.m
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function [mean_metric,annual_metric,trend_metric,p_metric]=mean_and_trend(MHW,mhw_ts,data_start,varargin)
%mean_and_trend - calculating mean states and trends of event metrics
% Syntax
% [mean_metric,annual_metric,trend_metric,p_metric]=mean_and_trend(MHW,mhw_ts,data_start);
% [mean_metric,annual_metric,trend_metric,p_metric]=mean_and_trend(MHW,mhw_ts,data_start,'Metric','Duration');
%
% Description
% [mean_metric,annual_metric,trend_metric,p_metric]=mean_and_trend(MHW,mhw_ts,data_start)
% returns the mean states and annual trends of MHW/MCS frequency (number
% of events per year) based on event table MHW and MHW/MCS time series
% MHW_TS. The start year (DATA_START) is the first year of MHW_TS.
%
% [mean_metric,annual_metric,trend_metric,p_metric]=mean_and_trend(MHW,mhw_ts,data_start,'Metric','Duration')
% returns the mean states and annual trends of MHW/MCS duration.
%
% Input Arguments
%
% MHW, mhw_ts - Outputs from function detect
%
% data_start - A numeric value indicating the start year of MHW_TS.
%
% 'Metric' - Default is 'Frequency'. The metric for which mean states and annual trends are
% calculated.
% 'Frequency' - The annual number of events.
% 'Duration' - The duration of events.
% 'MaxInt' - The maximum intensity of events.
% 'MeanInt' - The mean intensity of events.
% 'CumInt' - The cumulative intensity of events.
% 'Days' - The annual total MHW/MCS days.
%
% Output Arguments
%
% mean_metric - A 2D numeric matrix (m-by-n) containing the mean states
% of MHW/MCS metrics.
%
% annual_metric - A 3D numeric matrix (m-by-n-by-Y) containing annual
% mean MHW/MCS metrics, whre Y indicates the number of year based on the
% start year DATA_START and the size of MHW_TS.
%
% trend_metric - A 2D numeric matrix (m-by-n) containing linear trend
% calculated from ANNUAL_METRIC in unit of 'unit of metric/year'.
%
% p_metric - A 2D numeric matrix (m-by-n) containing p value of
% TREND_METRIC.
paramNames = {'Metric'};
defaults = {'Frequency'};
[vMetric]...
= internal.stats.parseArgs(paramNames, defaults, varargin{:});
MetricNames = {'Frequency','Duration','MaxInt','MeanInt','CumInt','Days'};
vMetric = internal.stats.getParamVal(vMetric,MetricNames,...
'''Metric''');
[x,y,~]=size(mhw_ts);
MHW=MHW{:,:};
switch vMetric
case 'Duration'
period_used=datenum(data_start,1,1):(datenum(data_start,1,1)+size(mhw_ts,3)-1);
period_used=datevec(period_used);
years_mhw=unique(period_used(:,1),'rows');
mean_metric=NaN(x,y);
trend_metric=NaN(x,y);
p_metric=NaN(x,y);
annual_metric=NaN(x,y,length(years_mhw));
loc_u=unique(MHW(:,8:9),'rows');
for i=1:size(loc_u)
ts_here=squeeze(mhw_ts(loc_u(i,1),loc_u(i,2),:));
bw=bwconncomp(~isnan(ts_here));
mean_metric(loc_u(i,1),loc_u(i,2))=nanmean(cellfun(@length,bw.PixelIdxList));
sd=datevec(cellfun(@nanmin,bw.PixelIdxList)-1+datenum(1982,1,1));
ed=datevec(cellfun(@nanmax,bw.PixelIdxList)-1+datenum(1982,1,1));
durc=cellfun(@length,bw.PixelIdxList);
for j=years_mhw(1):years_mhw(end)
annual_metric(loc_u(i,1),loc_u(i,2),j-years_mhw(1)+1)=nanmean(durc(sd(:,1)==j | ed(:,1)==j));
end
[b,bint]=regress(squeeze(annual_metric(loc_u(i,1),loc_u(i,2),:)),...
[ones(length(years_mhw),1) (1:length(years_mhw))']);
trend_metric(loc_u(i,1),loc_u(i,2))=b(2);
p_metric(loc_u(i,1),loc_u(i,2))=double((bint(2,1)*bint(2,2))>=0);
end
case 'MaxInt'
period_used=datenum(data_start,1,1):(datenum(data_start,1,1)+size(mhw_ts,3)-1);
period_used=datevec(period_used);
years_mhw=unique(period_used(:,1),'rows');
mean_metric=nanmax(mhw_ts,[],3);
trend_metric=NaN(x,y);
p_metric=NaN(x,y);
annual_metric=NaN(x,y,length(years_mhw));
loc_u=unique(MHW(:,8:9),'rows');
date_used=datevec(datenum(years_mhw(1),1,1):datenum(years_mhw(end),12,31));
for i=years_mhw(1):years_mhw(end)
index_here=date_used(:,1)==i;
annual_metric(:,:,i-years_mhw(1)+1)=nanmax(mhw_ts(:,:,index_here),[],3);
end
for i=1:size(loc_u)
[b,bint]=regress(squeeze(annual_metric(loc_u(i,1),loc_u(i,2),:)),...
[ones(length(years_mhw),1) (1:length(years_mhw))']);
trend_metric(loc_u(i,1),loc_u(i,2))=b(2);
p_metric(loc_u(i,1),loc_u(i,2))=double((bint(2,1)*bint(2,2))>=0);
end
case 'MeanInt'
period_used=datenum(data_start,1,1):(datenum(data_start,1,1)+size(mhw_ts,3)-1);
period_used=datevec(period_used);
years_mhw=unique(period_used(:,1),'rows');
mean_metric=nanmean(mhw_ts,3);
trend_metric=NaN(x,y);
p_metric=NaN(x,y);
annual_metric=NaN(x,y,length(years_mhw));
loc_u=unique(MHW(:,8:9),'rows');
date_used=datevec(datenum(years_mhw(1),1,1):datenum(years_mhw(end),12,31));
for i=years_mhw(1):years_mhw(end)
index_here=date_used(:,1)==i;
annual_metric(:,:,i-years_mhw(1)+1)=nanmean(mhw_ts(:,:,index_here),3);
end
for i=1:size(loc_u)
[b,bint]=regress(squeeze(annual_metric(loc_u(i,1),loc_u(i,2),:)),...
[ones(length(years_mhw),1) (1:length(years_mhw))']);
trend_metric(loc_u(i,1),loc_u(i,2))=b(2);
p_metric(loc_u(i,1),loc_u(i,2))=double((bint(2,1)*bint(2,2))>=0);
end
case 'CumInt'
period_used=datenum(data_start,1,1):(datenum(data_start,1,1)+size(mhw_ts,3)-1);
period_used=datevec(period_used);
years_mhw=unique(period_used(:,1),'rows');
mean_metric=NaN(x,y);
trend_metric=NaN(x,y);
p_metric=NaN(x,y);
annual_metric=NaN(x,y,length(years_mhw));
loc_u=unique(MHW(:,8:9),'rows');
for i=1:size(loc_u)
ts_here=squeeze(mhw_ts(loc_u(i,1),loc_u(i,2),:));
bw=bwconncomp(~isnan(ts_here));
mean_metric(loc_u(i,1),loc_u(i,2))=nanmean(cellfun(@(x)nansum(ts_here(x)),bw.PixelIdxList));
sd=datevec(cellfun(@nanmin,bw.PixelIdxList)-1+datenum(1982,1,1));
ed=datevec(cellfun(@nanmax,bw.PixelIdxList)-1+datenum(1982,1,1));
durc=cellfun(@(x)nansum(ts_here(x)),bw.PixelIdxList);
for j=years_mhw(1):years_mhw(end)
annual_metric(loc_u(i,1),loc_u(i,2),j-years_mhw(1)+1)=nanmean(durc(sd(:,1)==j | ed(:,1)==j));
end
[b,bint]=regress(squeeze(annual_metric(loc_u(i,1),loc_u(i,2),:)),...
[ones(length(years_mhw),1) (1:length(years_mhw))']);
trend_metric(loc_u(i,1),loc_u(i,2))=b(2);
p_metric(loc_u(i,1),loc_u(i,2))=double((bint(2,1)*bint(2,2))>=0);
end
case 'Days'
period_used=datenum(data_start,1,1):(datenum(data_start,1,1)+size(mhw_ts,3)-1);
period_used=datevec(period_used);
years_mhw=unique(period_used(:,1),'rows');
mean_metric=nansum(~isnan(mhw_ts),3)./length(years_mhw);
trend_metric=NaN(x,y);
p_metric=NaN(x,y);
annual_metric=NaN(x,y,length(years_mhw));
loc_u=unique(MHW(:,8:9),'rows');
date_used=datevec(datenum(years_mhw(1),1,1):datenum(years_mhw(end),12,31));
for i=years_mhw(1):years_mhw(end)
index_here=date_used(:,1)==i;
annual_metric(:,:,i-years_mhw(1)+1)=nansum(~isnan(mhw_ts(:,:,index_here)),3);
end
for i=1:size(loc_u)
[b,bint]=regress(squeeze(annual_metric(loc_u(i,1),loc_u(i,2),:)),...
[ones(length(years_mhw),1) (1:length(years_mhw))']);
trend_metric(loc_u(i,1),loc_u(i,2))=b(2);
p_metric(loc_u(i,1),loc_u(i,2))=double((bint(2,1)*bint(2,2))>=0);
end
case 'Frequency'
period_used=datenum(data_start,1,1):(datenum(data_start,1,1)+size(mhw_ts,3)-1);
period_used=datevec(period_used);
years_mhw=unique(period_used(:,1),'rows');
mean_metric=NaN(x,y);
trend_metric=NaN(x,y);
p_metric=NaN(x,y);
annual_metric=NaN(x,y,length(years_mhw));
loc_u=unique(MHW(:,8:9),'rows');
for i=1:size(loc_u)
ts_here=squeeze(mhw_ts(loc_u(i,1),loc_u(i,2),:));
bw=bwconncomp(~isnan(ts_here));
mean_metric(loc_u(i,1),loc_u(i,2))=length(bw.PixelIdxList)./length(years_mhw);
sd=datevec(cellfun(@nanmin,bw.PixelIdxList)-1+datenum(1982,1,1));
ed=datevec(cellfun(@nanmax,bw.PixelIdxList)-1+datenum(1982,1,1));
for j=years_mhw(1):years_mhw(end)
annual_metric(loc_u(i,1),loc_u(i,2),j-years_mhw(1)+1)=nansum(sd(:,1)==j | ed(:,1)==j);
end
[b,bint]=regress(squeeze(annual_metric(loc_u(i,1),loc_u(i,2),:)),...
[ones(length(years_mhw),1) (1:length(years_mhw))']);
trend_metric(loc_u(i,1),loc_u(i,2))=b(2);
p_metric(loc_u(i,1),loc_u(i,2))=double((bint(2,1)*bint(2,2))>=0);
end
end