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SDI_cal.m
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SDI_cal.m
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% Yiwen Mei ([email protected])
% SEAS, University of Michigan
% Last update: 1/15/2021
%% Functionality
% This code is used to calculate standardized drought index (e.g., SPI, SPEI).
%% Input
% Obj : a spatiotemporal class object (V2DTCls) or a Matlab timetable for the
% input variable (e.g. monthly precipitation, monthly water deficit);
% Nm : number of month to calculate the accumulations;
% DType: distribution assumed to the cummulative variable for calculation of
% the drought index (see Additional note section for distribution available);
% pth : path to store the output drought index files;
% fn : a name for the output drought index files (the output files will have
% the name fn.Nm.DType.yyyymm.tif in pth);
% pflg: parallel flag (false - default, squential; true - parallel).
%% Output
% If Obj is V2DTCls, the 2D drought index for every time step is outputted as
% geotiff files with the name fn.Nm.DType.yyyymm.tif in pth;
% If Obj is table, the drought index time series for every station is outputted
% as Matlab table with the name fn.Nm.DType.Sid.mat in pth.
%% Additional note
% Requrie matV2tif.m and V2DTCls.m.
% Available distribution for drought index calculation:
% 'Empirical' - empirical CDF
% 'Exponential' - exponential distribution
% 'Gamma' - gamma distribution
% 'Gaussian' - normal distribution
% 'Log-normal' - log normal distribution
% 'Log-logistic' - log logistic distribution
% 'Weibull' - Weibull distribution
function SDI_cal(Obj,Nm,DType,pth,fn,varargin)
%% Check the inputs
narginchk(5,6);
ips=inputParser;
ips.FunctionName=mfilename;
addRequired(ips,'Obj',@(x) validateattributes(x,{'V2DTCls','timetable'},{'nonempty'},mfilename,'Obj'));
addRequired(ips,'Nm',@(x) validateattributes(x,{'double'},{'scalar'},mfilename,'Nm'));
addRequired(ips,'DType',@(x) validateattributes(x,{'char'},{'nonempty'},mfilename,'DType'));
addRequired(ips,'pth',@(x) validateattributes(x,{'char'},{'nonempty'},mfilename,'pth'));
addRequired(ips,'fn',@(x) validateattributes(x,{'char'},{'nonempty'},mfilename,'fn'));
addOptional(ips,'pflg',false,@(x) validateattributes(x,{'logical'},{'nonempty'},mfilename,'pflg'));
parse(ips,Obj,Nm,DType,pth,fn,varargin{:});
pflg=ips.Results.pflg;
clear ips varargin
%% Time line and spatial info
if isa(Obj,'V2DTCls')
mk=Obj.readCls(1);
mk=~isnan(mk);
xll=Obj.GIf(1,1)-Obj.GIf(3,1)/2;
yll=Obj.GIf(2,2)-Obj.GIf(3,2)/2;
TL=Obj.TimeCls('begin');
elseif isa(Obj,'timetable')
mk=1;
xll=[];
yll=[];
TL=datenum(Obj.Time);
Obj=Obj(:,1:end);
end
[y,m,~]=datevec(TL);
TL=[TL y m];
%% Calculate the index
ofl=[];
switch pflg
case true
parfor mi=1:12
ofn=SDI_cal_sub(TL,mi,Nm,Obj,mk,DType,pth,fn,xll,yll);
ofl=[ofl;ofn];
end
case false
for mi=1:12
ofn=SDI_cal_sub(TL,mi,Nm,Obj,mk,DType,pth,fn,xll,yll);
ofl=[ofl;ofn];
end
end
clear TL y mk xll yll mi Nm
%% Concatenate the time series for stations
if isa(Obj,'timetable')
SDI=[];
for m=1:12
sdi=matfile(ofl(m,:));
sdi=sdi.SDI;
SDI=[SDI;sdi];
% delete(ofl(m,:));
end
SDI=sortrows(SDI,'Time','ascend');
clear sdi Obj
% Output the resulting TS
stn=SDI.Properties.VariableNames;
for s=1:length(stn)
ofn=[ofl(1,1:length(pth)+length(fn)+length(DType)+6) stn{s} ofl(1,end-3:end)];
sdi=SDI(:,s);
save(ofn,'sdi');
[~,ofn,~]=fileparts(ofn);
fprintf('%d. %s saved\n',s,ofn);
end
end
end
function ofn=SDI_cal_sub(TL,mi,Nm,Obj,mk,DType,pth,fn,xll,yll)
%% Cumulative variable
fprintf('Execute variable accumulation');
ei=find(TL(:,3)==mi);
si=ei-Nm+1;
ei(si<=0)=[];
si(si<=0)=[];
Cvb=[];
for y=1:length(si)
if isa(Obj,'V2DTCls')
Obj1=Obj;
Obj1.Fnm=Obj.Fnm(si(y):ei(y));
FX=[];
for m=1:length(Obj1.Fnm)
vb=Obj1.readCls(m); % vb is 2D
vb(~mk)=[]; % flatten vb to 1-by-Nloc
FX=[FX vb']; % flip vb to Nloc-by-1, FX is Nloc-by-Mmonth
end
elseif isa(Obj,'timetable')
FX=Obj{si(y):ei(y),:}';
end
Cvb=[Cvb sum(FX,2)]; % sum over month
end
clear Obj1 vb si cvb
fprintf(' ---- Done\n');
%% Calculate the drought index
fprintf('Execute DI calculation - assume %s distribution',DType);
FX=nan(size(Cvb));
switch DType
case 'Empirical'
for y=1:length(ei)
FX(:,y)=sum(Cvb<=repmat(Cvb(:,y),1,length(ei)),2);
end
FX(isnan(Cvb))=NaN;
FX=FX./(repmat(sum(~isnan(Cvb),2),1,length(ei))+1); % Probability
case 'Exponential'
for i=1:size(Cvb,1)
X=Cvb(i,:);
k=isnan(X);
X(k)=[];
prm=expfit(X);
FX(i,~k)=expcdf(X,prm);
end
case 'Gamma'
for i=1:size(Cvb,1)
X=Cvb(i,:);
k=isnan(X);
X(k)=[];
prm=gamfit(X(X~=0));
q=sum(X==0)/length(X);
FX(i,~k)=q+(1-q)*gamcdf(X,prm(1),prm(2));
end
case 'Gaussian'
for i=1:size(Cvb,1)
X=Cvb(i,:);
k=isnan(X);
X(k)=[];
[prm1,prm2]=normfit(X);
FX(i,~k)=normcdf(X,prm1,prm2);
end
case 'Log-normal'
for i=1:size(Cvb,1)
X=Cvb(i,:);
k=isnan(X);
X(k)=[];
prm=lognfit(X(X~=0));
q=sum(X==0)/length(X);
FX(i,~k)=q+(1-q)*logncdf(X,prm(1),prm(2));
end
case 'Log-logistic'
Cvb=Cvb-repmat(min(Cvb,[],2),1,size(Cvb,2))+1;
for i=1:size(Cvb,1)
X=Cvb(i,:);
k=isnan(X);
X(k)=[];
prm=fitdist(X','loglogistic');
FX(i,~k)=cdf(prm,X);
end
case 'Weibull'
for i=1:size(Cvb,1)
X=Cvb(i,:);
k=isnan(X);
X(k)=[];
prm=wblfit(X(X~=0));
q=sum(X==0)/length(X);
FX(i,~k)=q+(1-q)*wblcdf(X,prm(1),prm(2));
end
otherwise
error('Please choose from the available list of distribution');
end
FX=norminv(FX); % Drought index
clear Cvb prm X
fprintf(' ---- Done\n');
%% Output the index
if isa(Obj,'V2DTCls')
for y=1:length(ei)
SDI=nan(size(mk)); % Reshape to the land mask (recycle Cvb)
SDI(mk)=FX(:,y);
ofn=fullfile(pth,sprintf('%s.%02i.%s.%d%02i.tif',fn,Nm,DType,TL(ei(y),2),mi));
matV2tif(ofn,SDI,xll,yll,Obj.GIf(3,1),Obj.ndv,Obj.srs,pth);
% fprintf('Output %s\n',ofn);
end
ofn=[];
elseif isa(Obj,'timetable')
ofn=fullfile(pth,sprintf('%s.%02i.%s.%02i.mat',fn,Nm,DType,mi));
SDI=array2timetable(FX','RowTimes',datetime(TL(ei,2),TL(ei,3),1),...
'VariableNames',Obj.Properties.VariableNames);
save(ofn,'SDI');
end
end