# This script provides a demonstration of how a weather generator can be designed:
# ESD is used to predict thanges in the pdfs for temperature and precipitation.
# Temperature: mean, stdv.
# Precipitation: mu, fw (assume similar spell statistics as in present time).
#
# (more advanced method may perhaps predict changes to the spell-statistics).
#
# Rasmus Benestad
#' Weather generators for conditioned on simulated climate aggregated
#' statistics.
#'
#' Weather generators for conditional simulation of daily temperature and/or
#' precipitation, given mean and/or standard deviation. The family of WG
#' functions procude stochastic time series with similar characteristics as the
#' station series provided (if none if provided, it will use either ferder or
#' bjornholt provided by the esd-package). Here characteristics means similar
#' mean value, standard deviation, and spectral properties. \code{FTscramble}
#' takes the Fourier components (doing a Fourier Transform - FT) of a series
#' and reassigns random phase to each frequency and then returns a new series
#' through an inverse FT. The FT scrambling is used for temperature, but not
#' for precipitation that is non-Gaussian and involves sporadic events with
#' rain. For precipitation, a different approach is used, taking the wet-day
#' frequency of each year and using the wet-day mean and ranomly generated
#' exponentially distributed numbers to provide similar aggregated annual
#' statistics as the station or predicted though downscaling. The precipitation
#' WG can also take into account the number of consequtive number-of-dry-days
#' statistics, using either a Poisson or a gemoetric distribution.
#'
#' The weather generater produces a series with similar length as the provided
#' sample data, but with shifted dates according to specified scenarios for
#' annual mean mean/standard deviation/wet-day mean/wet-day frequency.
#'
#' \code{WG.FT.day.t2m} generates daily temperature from seasonal means and
#' standard deviations. It is given a sample station series, and uses
#' \code{FTscramble} to generate a series with random phase but similar (or
#' predicted - in the future) spectral characteristics. It then uses a quantile
#' transform to prescribe predicted mean and standard deviation, assuming the
#' distributions are normal. The temperal structure (power spectrum) is
#' therefore similar as the sample provided.
#'
#' \code{WG.fw.day.precip} uses the annual wet-day mean and the wet-day
#' frequency as input, and takes a sample station of daily values to
#' stochastically simulate number consequtive wet days based on its annual mean
#' number. If not specified, it is taken from the sample data after being phase
#' scrambeled (\code{FTscramble}) The number of wet-days per year is estimated
#' from the wed-day frequency, it too taken to be phase scrambled estimates
#' from the sample data unless specifically specified. The daily amount is
#' taken from stochastic values generated with \code{\link{rexp}}. The number
#' of consequtive wet days can be approximated by a geometric distribution
#' (\code{\link{rgeom}}), and the annual mean number was estimated from the
#' sample series.
#'
#' @aliases WG WG.station WG.fw.day.precip WG.FT.day.t2m
#' WG.pca.day.t2m.precip FTscramble
#'
#' @importFrom stats start end approx pnorm qnorm qqnorm sd dgeom rgeom rexp qexp pexp dpois
#' fft runif
#' @importFrom graphics hist
#'
#' @param x station object
#' @param option Define the type of WG
#' @param amean annual mean values. If NULL, use those estimated from x; if NA,
#' estimate using \code{\link{DSensemble.t2m}}, or if provided, assume a
#' 'dsensemble' object.
#' @param asd annual standard deviation. If NULL, use those estimated from x;
#' if NA, estimate using \code{\link{DSensemble.t2m}}, or if provided, assume a
#' 'dsensemble' object.
#' @param t Time axis. If null, use the same as x or the last interval of same
#' length as x from downscaled results.
#' @param ip passed on to \code{\link{DSensemble.t2m}}
#' @param select passed on to \code{\link{DSensemble.t2m}}
#' @param lon passed on to \code{\link{DSensemble.t2m}}
#' @param lat passed on to \code{\link{DSensemble.t2m}}
#' @param plot if TRUE, plot results
#' @param biascorrect passed on to \code{\link{DSensemble.t2m}}
#' @param verbose passed on to \code{\link{DSensemble.t2m}}
#' @param mu annual wet-mean values. If NULL, use those estimated from x; if
#' NA, estimate using \code{\link{DSensemble.t2m}}, or if provided, assume a
#' 'dsensemble' object.
#' @param fw annual wet-day frequency. If NULL, use those estimated from x; if
#' NA, estimate using \code{\link{DSensemble.t2m}}, or if provided, assume a
#' 'dsensemble' object.
#' @param ndd annual mean dry spell length. If NULL, use those estimated from
#' x; if NA, estimate using \code{\link{DSensemble.t2m}}, or if provided,
#' assume a 'dsensemble' object.
#' @param threshold Definition of a rainy day.
#' @param method Assume a gemoetric or a poisson distribution. Can also define
#' ownth methods.
#' @param t2m station object with temperature
#' @param precip station object with precipitation.
#' @param \dots additional arguments
#' @author R.E. Benestad
#' @keywords manip
#' @examples
#'
#' data(ferder)
#' t2m <- WG(ferder)
#' data(bjornholt)
#' pr <- WG(bjornholt)
#'
#' @export WG
WG <- function(x,...) UseMethod("WG")
#' @exportS3Method
#' @export WG.station
WG.station <- function(x,...,option='default') {
if (inherits(x,'day')) {
if (length(varid(x))==1) {
if (varid(x)=='t2m') y <- WG.FT.day.t2m(x,...) else
if (varid(x)=='precip') y <- WG.fw.day.precip(x,...)
}
}
return(y)
}
#' @exportS3Method
#' @export WG.FT.day.t2m
WG.FT.day.t2m <- function(x=NULL,...,amean=NULL,asd=NULL,t=NULL,ip=1:4,
select=NULL,lon=c(-20,20),lat=c(-20,20),
plot=FALSE,biascorrect=TRUE,verbose=FALSE) {
if (verbose) print('WG.FT.day.t2m')
## Single function for just temperature.
## The arguments mean and sd are time series predicted through ESD or
## adopted from a zoo or station object (x).
if (is.null(x)) {
## If no stations objects is given, use default
if (verbose) print("use default: Ferder, Norway")
ferder <- NULL
data("ferder",envir=environment())
x <- ferder
rm('ferder')
}
## Different options for annual mean temperature. Default - estimate from the station
if (is.null(amean)) amean <- annual(x) else
## If NA, then compute using DSensemble
if (is.na(amean)) {
if (verbose) print('Estimate mean change')
T2M <- retrieve('~/data/ERAINT/ERAINT_t2m_mon.nc',
lon=lon(x) + lon,lat=lat(x) + lat)
ztm <- DSensemble.t2m(x,predictor=T2M,biascorrect=biascorrect,
plot=plot,lon=lon,lat=lat,ip=ip,
select=select,verbose=verbose)
amean <- zoo(rowMeans(ztm,na.rm=TRUE) - mean(ztm,na.rm=TRUE),
order.by=index(ztm))
} else if (inherits(amean,'dsensemble'))
## Or use prescribed projections
amean <- rowMeans(amean,na.rm=TRUE) - mean(amean,na.rm=TRUE)
if(verbose) print(paste('mean(amean)=',mean(amean)))
## Also select annual standard deviations estimated from daly anomalies -
## repeat the same procedure as for the mean.
if (is.null(asd)) asd <- annual(anomaly(x,verbose=verbose),FUN='sd') else
if (is.na(asd)) {
if (verbose) print('Estimate standard deviation change')
SLP <- retrieve('~/data/ERAINT/ERAINT_slp_mon.nc',
lon=lon(x) + lon,lat=lat(x) + lat)
coredata(SLP) <- 100*coredata(SLP) # The CMIP5 units are in Pa!
if (plot) dev.new()
# zts <- DSensemble.t2m(x,predictor=SLP,biascorrect=biascorrect,
# FUN='sd',plot=plot,lon=lon,lat=lat,ip=ip,
# path='data/CMIP5.mslp/',pattern='psl_Amon_ens',
# select=select,verbose=verbose)
zts <- DSensemble.t2m(x,predictor=T2M,biascorrect=biascorrect,
FUN='sd',plot=plot,lon=lon,lat=lat,ip=ip,
FUNX='sd',select=select,verbose=verbose)
asd <- zoo(rowMeans(zts,na.rm=TRUE) - mean(zts,na.rm=TRUE),
order.by=index(zts))
} else if (inherits(asd,'dsensemble'))
asd <- rowMeans(asd,na.rm=TRUE) - mean(asd,na.rm=TRUE)
## Get the daily anomalies and the climatology
xa <- anomaly(x); clim <- x - xa
## Define time axis for projection based on the annual mean data either from station or
## downscaled projections
if (is.null(t)) {
if (verbose) print("set the time index")
ly <- max(year(amean)); ny <- length(rownames(table(year(amean))))
interval <- c(ly-ny+1,ly)
if(verbose) print(interval)
t <- seq.Date(as.Date(paste(interval[1],substr(start(x),5,10),sep='')),
as.Date(paste(interval[2],substr(end(x),5,10),sep='')),
by="day")
#browser()
#str(t); print(paste(interval[1],month(x)[1],day(x)[1],sep='-'))
#t <- t - julian(t[1]) +
# julian(as.Date(paste(interval[1],month(x)[1],day(x)[1],sep='-')))
}
## Estimate a smooth curve for the annual mean and standard deviation that has a daily resolution
if (verbose) print("Estimate smooth day-by-day changes in mean and sd:")
ym <- approx(julian(as.Date(index(amean))),coredata(amean),xout=julian(as.Date(t)),rule=2)$y
#print(summary(ym))
ys <- approx(julian(as.Date(index(asd))),coredata(asd),xout=julian(as.Date(t)),rule=2)$y
## New object y that contains random variable as original data but with same spectral
## characteristics and same climatology
if (verbose) print("Construct a station object with random timing but original time structure:")
y <- zoo(FTscramble(xa,t),order.by=t)
if (verbose) print("add climatology")
y <- y + matchdate(clim,y)
if (plot) {
dev.new()
plot(merge(zoo(xa),zoo(anomaly(y))),plot.type='single',lwd=c(2,1),
col=c('black','grey'))
}
## qq-transform to transform the temperature distribution from present shape to future shape
## assuming a normal distribution: ~N(m1,s1) -> ~N(m2,s2). Estimate probabilities based on the
## scrambeled series y and use these probabilities to derive new quantiles based on the shifted
## pdf.
cdf <- pnorm(q=y,mean=mean(y,na.rm=TRUE),sd=sd(y,na.rm=TRUE))
q2 <- qnorm(cdf,mean=ym,sd=ys)
#print(summary(cdf)); print(summary(q2))
#hist(cdf); browser()
z <- zoo(q2,order.by=t)
#print(summary(z))
if (verbose) print("Attach attributes")
z <- attrcp(x,z)
attr(z,'mean') <- ym
attr(z,'sd') <- ys
attr(z,'aspect') <- paste(attr(z,'aspect'),'weather_generator',sep=', ')
attr(z,'history') <- history.stamp(x)
return(z)
}
## Fuure considerations -lso allow for estimating the AR(1) coefficient of the Hurst coefficient?
## Fractional Gaussian noise...?
## --- Precipitation
#' @exportS3Method
#' @export WG.fw.day.precip
WG.fw.day.precip <- function(x=NULL,...,mu=NULL,fw=NULL,
ncwd=NULL,ndbr=NULL,t=NULL,
threshold=1,select=NULL,
ip=1:6,lon=c(-10,10),lat=c(-10,10),
plot=FALSE,biascorrect=TRUE,
verbose=FALSE) {
if (verbose) print('WG.fw.day.precip')
# Single function for just precipitation
if (is.null(x)) {
bjornholt <- NULL
data("bjornholt",envir=environment())
x <- bjornholt
rm('bjornholt')
}
# use fw to estimate the number of rainy days per year:
x.fw <- as.annual(x,'wetfreq',threshold=threshold)
# Use predicted mu to generate exponentially distributed data:
x.mu <- as.annual(x,'exceedance',threshold=threshold)
# according to a geometric (default) or Poisson distribution
ncdd.cwd <- spell(x,threshold=threshold)
## Annual mean number of consecutive wet days
x.nd <- subset(annual(ncdd.cwd),is=1)
# extract the time interval between the start of each dry spell
ndbr <- diff(julian(as.Date(index(ncdd.cwd[is.finite(ncdd.cwd[,1]),1]))))
if (plot) {
dev.new()
f.k <- dgeom(0:max(ndbr), prob=1/(mean(ndbr)+1))
hist(ndbr,freq=FALSE,col="grey",xlab="days",
main="The time between the start of each precipitation event",
sub="Test: Red curve is the fitted geometric distribution")
lines(0:max(ndbr),f.k,lwd=5,col="red")
}
## Annual mean number of days between start of each rain event
ndbram <- annual(zoo(x=ndbr,order.by=index(ncdd.cwd)[-1]))
# Estimate number of wet events each year:
wet <- subset(ncdd.cwd,is=1)
## Annual number of of events
nawe <- aggregate(wet,by=year(wet),FUN="nv")
attributes(nawe) <- NULL
if (verbose) print(coredata(nawe))
if (plot) {
dev.new()
hist(coredata(nawe),breaks=seq(0,100,by=5),freq=FALSE,col="grey",
main="Number of wet events per year",xlab="days",
sub="Test: Red curve is the fitted Poisson distribution")
lines(seq(0,100,by=1),dpois(seq(0,100,by=1),lambda=mean(coredata(nawe))),
col="red",lwd=3)
}
# Wet-day mean: from DS or from observations
if (verbose) print('wet-day mean')
if (is.null(mu))
mu <- zoo(FTscramble(x.mu),order.by=index(x.mu))
# Wet-day frequency: from DS or from observations
if (verbose) print('wet-day frequency')
if (is.null(fw))
fw <- zoo(FTscramble(x.fw),order.by=index(x.fw))
# Number of consecutive wet days: from DS or from observations
if (verbose) print('random annual mean number of n_cwd:')
## Stochastic annual mean wet-spell duration:
rnd <- rnorm(length(mu),mean=mean(coredata(x.nd),na.rm=TRUE),
sd=sd(coredata(x.nd),na.rm=TRUE))
## Constraint: at least one wet event per year
rnd[rnd < 1] <- 1;
if (verbose) print(rnd)
## success probability
prob <- 1/rnd
if (verbose) print('the annual mean probability of successive wet days: prob')
if (verbose) print(prob)
if (verbose) print('the annual mean number of consecutive wet days: ncwd')
if (is.null(ncwd)) ncwd <- rgeom(length(mu),prob=prob)+1
# Time axis for projection:
if (verbose) print('Time axis for projection')
if (is.null(t)) {
ly <- max(year(mu))
ny <- length(rownames(table(year(mu))))
interval <- c(ly-ny+1,ny)
t <- index(x)
t <- t - julian(as.Date(t[1])) +
julian(as.Date(paste(interval[1],month(x)[1],day(x)[1],sep='-')))
if (verbose) print(interval)
}
n <- length(t)
yrs <- rownames(table(year(t)))
# Estimate the number of rainy days for each year
if (verbose) print('Number of wet days each year:')
nwet <- round( ( julian(as.Date(paste(year(fw),'12-31',sep='-'))) -
julian(as.Date(paste(year(fw),'01-01',sep='-'))) + 1) *
coredata(fw) )
#print(rbind(nwet,coredata(mu)))
# Errorbars for mu: var = mu**2 for exponential distrib:
mu.err <- mu/sqrt(nwet -1)
# set up a record with no rain:
z <- zoo(rep(0,length(t)),order.by=t)
# add rain events:
if (verbose) print(paste('loop over year:',1,'-',ny))
for ( i in 1:ny ) {
# Simulate precipitation amount: reduce to one decimal point and add
# threshold to mimic the original data...
## Use mean values if there is missing data for the specific year
## The wet-day mean precipitation
if (!is.finite(mu[i])) mu[i] <- mean(mu,na.rm=TRUE)
## Time between the start of each event
if (!is.finite(ndbram[i])) ndbram[i] <- mean(ndbram,na.rm=TRUE)
## number of wet events each year
if (!is.finite(nwet[i])) nwet[i] <- mean(nwet,na.rm=TRUE)
## The daily amounts for wet days
y <- round(rexp(366,1/coredata(mu[i])),1)
# Simulate the start of each rain event:
# nave = annual number of of events
# nbram = Annual mean number of days between start of each rain event
t0 <- cumsum(rgeom(max(coredata(nawe),na.rm=TRUE),
prob=1/(coredata(ndbram[i]))))
if (verbose) {print('times between events');print(t0)}
# simulate the duration of wet events:
nwd <- rgeom(2*length(t0),prob=prob[i])+1
#nwd <- nwd[cumsum(nwd <= nwet[i])]
t0 <- t0[1:length(nwd)]
# add rain to the appropriate year:
ii <- is.element(year(t),yrs[i])
rain <- rep(0,sum(ii)); iii <- 0
# simulate the rain-event occurrences which start at t0 and vary in duration: nwd
for (iv in 1:length(nwd)) {
iii <- max(iii) + (1:nwd[iv])
v <- t0[iv] + 0:(nwd[iv]-1)
v <- v[v <= length(rain)]
iii <- iii[iii <= length(y)]
if (verbose) print(c(iv,min(v),max(v),nwd[iv]))
if (sum(is.finite(v))>0) rain[v] <- y[iii]
## Simulate dry spell
}
if (verbose) print(paste(i,yrs[i],' total rain=',sum(rain,na.rm=TRUE),
' #wet days=',sum(nwd),'mu[i]=',round(mu[i],1),
'sum(is.finite(rain))=',sum(is.finite(rain)),
'nwet[i]=',nwet[i],' #events=',length(nwd)))
z[ii] <- rain
}
z <- attrcp(x,z)
attr(z,'original fw') <- fw
attr(z,'ncc') <- nwd
attr(z,'original mu') <- mu
attr(z,'mu.err') <- mu.err
attr(z,'aspect') <- paste(attr(z,'aspect'),'weather_generator',sep=', ')
attr(z,'history') <- history.stamp(x)
return(z)
}
# This weather generator assumes that the past covariate structure between
# temperature and precipitation is constant and doesn't change in the future.
# Moreover, the method also assumes that the spell-statistics will stay the same.
#' @exportS3Method
#' @export WG.pca.day.t2m.precip
WG.pca.day.t2m.precip <- function(x=NULL,...,precip=NULL,threshold=1,select=NULL,
wetfreq.pred=FALSE,spell.stats=FALSE,
verbose=FALSE) {
if(verbose) print("WG.pca.day.t2m.precip")
t2m <- x
if (is.null(t2m)) {
ferder <- NULL
data("ferder",envir=environment())
t2m <- ferder
rm('ferder')
}
if (is.null(precip)) {
bjornholt <- NULL
data("bjornholt",envir=environment())
pr <- bjornholt
rm('bjornholt')
}
lon <- lon(t2m) + c(-10,10)
lat <- lat(t2m) + c(-10,10)
SLP <- retrieve('~/data/ERAINT/ERAINT_slp_mon.nc',lon=lon,lat=lat)
coredata(SLP) <- 100*coredata(SLP) # The CMIP5 units are in Pa!
T2M <- retrieve('~/data/ERAINT/ERAINT_t2m_mon.nc',lon=lon,lat=lat)
PRE <- retrieve('~/data/ERAINT/ERAINT_pr_mon.nc',lon=lon,lat=lat)
ztm = DSensemble.t2m(t2m,predictor=T2M,biascorrect=TRUE,plot=FALSE,
lon=c(-10,10),lat=c(-10,10),select=select)
zts = DSensemble.t2m(t2m,FUN='sd',predictor=SLP,biascorrect=TRUE,plot=FALSE,
path='data/CMIP5.mslp/',pattern='psl_Amon_ens',
lon=c(-10,10),lat=c(-10,10),select=select)
zpm = DSensemble.precip(pr,FUN='wetmean',predictor=PRE,biascorrect=TRUE,
plot=FALSE,select=select)
if (wetfreq.pred) {
zpf = DSensemble.precip(pr,FUN='wetfreq',predictor=SLP,biascorrect=TRUE,plot=FALSE,
path='data/CMIP5.mslp/',pattern='psl_Amon_ens',select=select)
}
# select an equal number of years at the end of the downscaled results if none is specified
if (is.null(interval)) {
interval <- c(max(year(ztm))-ny+1,max(year(ztm)))
}
ztm <- subset(ztm,it=interval)
zts <- subset(zts,it=interval)
zpm <- subset(zpm,it=interval)
# Generate the daily variability from the observations:
t2ma <- anomaly(t2m); t2mc <- t2m - t2ma
xy <- merge(zoo(t2m),zoo(pr),zoo(t2mc),all=FALSE)
years <- as.numeric(rownames(table(year(xy))))
ny <- length(years)
wet <- (xy[,2] > threshold) & (is.finite(xy[,1])) & (is.finite(xy[,2]))
dry <- (xy[,2] <= threshold) & (is.finite(xy[,1])) & (is.finite(xy[,2]))
if (spell.stats) L <- spell(pr,threshold=threshold)
# Rainy days:
# Find the co-variate structures in daily temperature and precipitation
X <- coredata(xy[wet,1:2])
X[,2] <- log(X[,2])
qqnorm(X[,2])
pca <- svd(X)
# scramble the principal components:
z1 <- FTscramble(pca$u[,1])
z2 <- FTscramble(pca$u[,2])
pca$u <- cbind(z1,z2)
X <- pca$u %*% diag(pca$d) %*% t(pca$v)
X[,2] <- exp(X[,2])
# All days: set up date string
t <- julian(as.Date(paste(year(xy)-year(xy)[1]+interval[1],
month(xy),day(xy),sep='-')))
x <- zoo(coredata(xy[,1]),order.by=t)
attributes(x) <- NULL
# initialise temperature and precip - for t2m, add observed daily climatology
n <- length(x)
pr.x <- rep(0,n)
# shoehorn the rainy day temperature and precipitation into series
t2m.x[wet] <- X[,1]
# generate time series for predicted mean and sd with same length as the scrambled
# daily series: use the seasonal estimates
tensm <- rowMeans(ztm,na.rm=TRUE) - mean(ztm,na.rm=TRUE)
tenss <- rowMeans(zts,na.rm=TRUE) - mean(zts,na.rm=TRUE)
penss <- rowMeans(zpm,na.rm=TRUE) - mean(zpm,na.rm=TRUE)
ytm <- approx(julian(as.Date(index(ztm))),tensm,xout=julian(as.Date(t)),rule=2)$y
yts <- approx(julian(as.Date(index(zts))),tensm,xout=julian(as.Date(t)),rule=2)$y
ypm <- approx(julian(as.Date(index(ztm))),tensm,xout=julian(as.Date(t)),rule=2)$y
#qq-transform: temp(N1 -> N2) - year by year or for a given interval?
t2m.x <- qnorm(pnorm(q=t2m.x,mean=mean(t2m.x,na.rm=TRUE),sd=sd(t2m.x,na.rm=TRUE)),
mean=ytm,sd=yts)
#qq-transform: precip(exp1 -> exp2)
pr.x.wet <- qexp(pexp(q=X[,2],rate=1/mean(xy[,2],na.rm=TRUE)),
rate=1/ypm)
#empirical adjustment to precipitation?
# shoehorn the rainy day temperature and precipitation into series
pr.x[wet] <- pr.x.wet
t2m.x <- zoo(t2m.x,order.by=t)
t2m.x <- attrcp(t2m)
attr(t2m.x,'method') <- 'DShydro'
attr(t2m.x,'type') <- 'result: ESD + WG'
attr(t2m.x,'activity') <- 'CMIP5'
attr(t2m.x,'experiment') <- 'RCP 4.5'
pr.x <- zoo(pr.x,order.by=t)
pr.x <- attrcp(pr)
attr(pr.x,'method') <- 'DShydro'
attr(pr.x,'type') <- 'result: ESD + WG'
attr(pr.x,'activity') <- 'CMIP5'
attr(pr.x,'experiment') <- 'RCP 4.5'
y <- list(t2m=t2m.x,pr=pr.x)
attr(y,'history') <- history.stamp(t2m)
class(y) <- class(t2m)
return(y)
}
#' @export
FTscramble <- function(x,t=NULL,interval=NULL,spell.stats=FALSE,
wetfreq.pred=FALSE) {
attributes(x) <- NULL
n <- length(x)
# This function scramles the phase information of the FT components of a
# time series, maintaining the same spectral and time structure
if (sum(is.na(x))>0) {
ok <- is.finite(x)
y <- approx((1:n)[ok],x[ok],xout=1:n,rule=2)$y
x <- y
rm('y')
}
# Fourier transform (FT) to obtain power and phase information
X <- fft(x)
#print(summary(Re(X))); print(summary(Im(X)))
# Z contains the phase information
Z <- Mod(X)
#print(summary(Z))
ReX <- Re(X)
ImX <- Im(X)
phiX <- Arg(X)
#plot(phiX)
# Set new phase information to random
phiY <- runif(n,min=-pi,max=pi)
ReY <- Z*cos(phiY)
ImY <- Z*sin(phiY)
ReY[1] <- ReX[1]; ImY[1] <- ImX[1]
# ReY[n] <- ReX[n]; ImY[n] <- ImX[n]
Y <- complex(real=ReY, imaginary=ImY)
# Inverse FT to generate new time series:
y <- Re(fft(Y,inverse=TRUE))/n
# Make sure that the new scrambled series has the same mean and standard deviation
# as the original data:
y <- sd(x,na.rm=TRUE)*(y - mean(y,na.rm=TRUE))/sd(y,na.rm=TRUE) + mean(x,na.rm=TRUE)
if (!is.null(t)) {
if (length(t) <= length(y)) y <- y[1:length(t)] else
y <- c(y,rep(NA,length(t)-length(y)))
}
invisible(y)
}
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