# title : Mann-Kendall trend test of raster time series
# Date : Jan 2018
# Version : 0.2
# Licence : GPL v3
# Maintainer : Federico Filipponi <federico.filipponi@gmail.com>
#
#######################################################################
#
#' @title Raster time series Mann-Kendall trend test
#'
#' @description This function conducts Mann-Kendall trend test from raster time series
#' using "Kendall" package especially designed to handle gappy time series.
#'
#' @param rasterts Input raster time series as \code{\linkS4class{RasterStackTS}} or \code{\linkS4class{RasterBrickTS}} object.
#' @param rastermask Either a \code{\linkS4class{RasterLayer}} or "compute". Raster layer to use as a mask. When "compute"
#' is set raster mask is computed to remove all pixels with incomplete time series.
#' @param gapfill Character. Defines the algorithm to be used to interpolate pixels with incomplete temporal profiles.
#' Accepts argument supported as method in function \code{\link[rtsa]{rtsa.gapfill}}.
#' @param cores Integer. Defines the number of CPU to be used for multicore processing. Default to "1" core for
#' singlecore processing.
#' @param ... Additional arguments to be passed through to function \code{\link[Kendall]{MannKendall}}.
#'
#' @return Object of class \code{\link{MKstack-class}} containing the following components:
#' \tabular{rll}{
#' \tab \code{tau} \tab Kendall tau statistic\cr
#' \tab \code{pvalue} \tab Kendall two-sided p-value\cr
#' \tab \code{score} \tab Kendall Score\cr
#' \tab \code{variance} \tab Variance of Kendall Score\cr
#' }
#'
#' @details
#'
#' @author Federico Filipponi
#'
#' @references
#'
#' Mann, H.B. (1945). Non-parametric tests against trend. Econometrica, 13, 163-171.
#' Kendall, M.G. (1975). Rank Correlation Methods, 4th edition. Charles Griffin, London.
#' Gilbert, R.O. (1987) . Statistical Methods for Environmental Pollution Monitoring. Wiley, NY.
#' Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application. Cambridge University Press.
#' Hipel, K.W. and McLeod, A.I., (2005). Time Series Modelling of Water Resources and Environmental Systems.
#' Electronic reprint of our book orginally published in 1994. \href{http://www.stats.uwo.ca/faculty/aim/1994Book/}{book}
#'
#' @keywords Mann-Kendall trend test time series analysis
#'
#' @seealso \code{\link[Kendall]{MannKendall}}, \code{\link[rtsa]{rtsa.stl}}, \code{\link[rtsa]{rtsa.seas}}, \code{\link[rtsa]{rtsa.gapfill}}
#'
#' @examples
#' \dontrun{
#' ## create raster time series using the 'pacificSST' data from 'remote' package
#' require(remote)
#'
#' data(pacificSST)
#' pacificSST[which(getValues(pacificSST == 0))] <- NA # set NA values
#' # create rts object
#' rasterts <- rts(pacificSST, seq(as.Date('1982-01-15'), as.Date('2010-12-15'), 'months'))
#'
#' ## generate raster mask
#' raster_mask <- pacificSST[[1]] # create raster mask
#' names(raster_mask) <- "mask"
#' values(raster_mask) <- 1 # set raster mask values
#' raster_mask[which(is.na(getValues(pacificSST[[1]])))] <- 0 # set raster mask values
#'
#' # compute Mann-Kendall trend test
#' MannKendall_result <- rtsa.mk(rasterts=rasterts, rastermask=raster_mask)
#' # compute Mann-Kendall trend test using multiple cores on monthly time series
#' ### create monthly averages
#' rasterts_monthly_mean <- apply.monthly(rasterts, mean)
#' MannKendall_monhtly_result <- rtsa.mk(rasterts=rasterts_monthly_mean, rastermask=raster_mask)
#' }
#'
#' @import raster
#' @import rts
#' @import parallel
#' @import doParallel
#' @importFrom Kendall MannKendall
#' @importFrom Kendall SeasonalMannKendall
#' @importFrom xts xts
#' @importFrom xts periodicity
#' @importFrom parallel detectCores
#' @importFrom parallel makePSOCKcluster
#' @importFrom parallel clusterExport
#' @importFrom parallel parCapply
#' @importFrom parallel stopCluster
#' @importFrom doParallel registerDoParallel
#' @importFrom methods new
#' @importFrom stats time
#' @importFrom stats ts
#' @export
# define rsta.stl function
rtsa.mk <- function(rasterts, rastermask=NULL, gapfill="none", cores=1L, verbose=FALSE){
# set environment
options(scipen=7)
# check if gapfill argument is set
if(!(gapfill %in% c("none", "dineof", "linear", "spline", "stine")))
stop("'gapfill' argument must be one of the following options: 'none', 'dineof', 'linear', 'spline', 'stine'")
# require the 'stlplus' package
if(!requireNamespace("Kendall", quietly = TRUE))
stop("Package 'Kendall' is required to run this function.\nYou can install using the command:\ninstall.packages('Kendall', dependencies=TRUE)")
# check if input file is an object of class 'RasterStackTS', 'RasterBrickTS'
if(!(class(rasterts) %in% c("RasterStackTS", "RasterBrickTS")))
stop("'rasterts' argument must be an object of class 'RasterStackTS' or 'RasterBrickTS'.\nUse 'rts()' function to generate 'rasterts' input")
# set time periodicity
# define table for periodicity to deltat conversion
deltatable <- data.frame(scale=c("yearly", "quarterly", "monthly", "weekly", "daily", "hourly", "minute", "seconds"),
deltat=c(1, 1.0/3, 1.0/12, 1.0/52.17857, 1.0/365, 1.0/8760, 1.0/525600, 1.0/31536000),
periodicity=c(1, 3, 12, 52.17857, 365, 8760, 525600, 31536000))
# convert periodicity to deltat
periodicity_tprofile <- xts::periodicity(rasterts@time)$scale
deltats <- as.double(deltatable$deltat[which(deltatable$scale == periodicity_tprofile)])
seasonal_periodicity <- as.double(deltatable$periodicity[which(deltatable$scale == periodicity_tprofile)])
# set 'mk_seasonal' variable based on periodicity
if(seasonal_periodicity == 12){
mk_seasonal <- TRUE
} else {
mk_seasonal <- FALSE
}
# set raster mask
# check if 'rastermask' argument is present
if(!(is.null(rastermask))){
if(class(rastermask) %in% c("character")){
if(rastermask %in% c("compute")){
# computer raster mask from raster time series (pixels)
if(verbose){
message("Mask raster will be computed from input raster time series\nPixel temporal profiles with missing data will be masked")
}
# create matrix with raster time series values
matrice_full <- as.matrix(getValues(rasterts))
# define function to mask incomplete pixel temporal profiles
generateMask <- function(x){
m <- as.integer(!anyNA(x))
return(m)
}
# generate raster mask
if(cores>1){
if(!requireNamespace("parallel", quietly = TRUE)){
warning("Package 'parallel' is required to run this function.\nGoing on using one core")
generated_mask <- as.vector(apply(X=matrice_full, FUN=generateMask, MARGIN=1))
} else {
# check that machine has available cores
if(cores > as.integer(parallel::detectCores())){
cores <- as.integer(parallel::detectCores())
}
cl <- parallel::makePSOCKcluster(cores)
parallel::clusterExport(cl, varlist=c("generateMask"), envir=environment())
generated_mask <- parallel::parApply(cl=cl, X=matrice_full, FUN=generateMask, MARGIN=1)
parallel::stopCluster(cl)
}
} else {
generated_mask <- as.vector(apply(X=matrice_full, FUN=generateMask, MARGIN=1))
}
# set not NaN pixel list
na_index_mask <- as.vector(which(generated_mask==1))
}
} else {
if(!(class(rastermask) %in% c("RasterLayer"))){
warning("'rastermask' argument is not an object of class 'raster'.\nNo raster mask will be used to clip the input raster time series")
na_index_mask <- as.vector(1:ncell(rasterts))
} else {
# compare mask raster extent with the input raster time series
mask_correspondence <- as.logical(compareRaster(rasterts@raster, rastermask, extent=TRUE, rowcol=TRUE, crs=TRUE, res=TRUE, rotation=TRUE, values=FALSE, stopiffalse=FALSE))
if(!(mask_correspondence)){
warning("'rastermask' extent does not correspond to 'rasterts'.\nNo mask will be used to clip the input raster time series")
na_index_mask <- as.vector(1:ncell(rasterts))
} else {
# check mask raster values
if(length(which(getValues(rastermask)==1))<1){
warning("'rastermask' does not contain valid pixels for masking purpose (mask pixel values equal to 1).\nNo mask will be used to clip the input raster time series")
na_index_mask <- as.vector(1:ncell(rasterts))
} else {
# import raster time series applying raster mask
if(verbose){
message("Mask raster is used to mask input raster time series")
}
na_index_mask <- as.vector(which(getValues(rastermask)==1))
}
}
}
}
} else {
na_index_mask <- as.vector(1:ncell(rasterts))
if(verbose){
message("Mask raster not supplied. Using the full raster time series")
}
}
# import raster time series values
if(verbose){
message("Importing dataset")
}
matrice <- as.matrix(rasterts[na_index_mask])
if(verbose){
message("Masked raster time series has ", ncol(matrice), " pixels and ", nrow(matrice), " temporal observations")
}
# check if there are NAs in the masked dataset
na_check <- anyNA(matrice)
if(na_check){
if(gapfill == "none"){
warning("Raster time series still contain NA values after masking.\nChange input raster mask or consider the use of the available options\nfor 'gapfill' argument to select a gap-filling method before the STL computation.\nGoing on however using gappy input raster time series for the STL computation")
}
} else {
if(verbose){
message("Raster time series does not contain NA values after masking: OK.\nGap-filling will be not performed before the Mann-Kendall trend test computation")
}
}
# perform gap-filling
if(na_check){
if(gapfill != "none"){
# check if gapfill argument is set
if(!(gapfill %in% c("none", "dineof", "gapfill", "linear", "spline", "stine")))
stop("'gapfill' argument must be one of the following options: 'none', 'dineof', 'gapfill', 'linear', 'spline', 'stine'")
# generate rastermask layer for gap-filling procedure
rastermask_gapfill <- raster(rasterts@raster[[1]])
values(rastermask_gapfill) <- 0
rastermask_gapfill[na_index_mask] <- 1
names(rastermask_gapfill) <- "mask"
# perform gap-filling
if(verbose){
message("Gap-filling using '", gapfill, "' method will be applied to masked raster time series")
}
rasterts <- rtsa.gapfill(x=rasterts, rastermask=rastermask_gapfill, method=gapfill)
}
}
# check number of NAs in time series
if(na_check){
# define 'countValid' function
countValid <- function(x){
output <- as.integer(length(which(!is.na(x))))
return(output)
}
# count consecutive NAs
if(cores>1){
if(!requireNamespace("doParallel", quietly = TRUE)){
warning("Package 'doParallel' is required to run this function.\nYou can install using the command:\ninstall.packages('doParallel', dependencies=TRUE)\nGoing on using one core")
res_countValid <- apply(X=matrice, MARGIN=2, FUN=countValid)
} else {
# check that machine has available cores
if(cores > as.integer(parallel::detectCores())){
cores <- as.integer(parallel::detectCores())
}
# start cluster for parallel computation
cl <- parallel::makePSOCKcluster(cores)
doParallel::registerDoParallel(cl)
# perform count of valid pixels
res_countValid <- parallel::parCapply(cl=cl, x=matrice, FUN=countValid)
# stop cluster
parallel::stopCluster(cl)
}
} else {
res_countValid <- apply(X=matrice, MARGIN=2, FUN=countValid)
}
# stop cluster
#parallel::stopCluster(cl) ### check why it is not stopping inside the function
# check if there are pixel profiles exceeding minimum number of valid observations for function 'MannKendall' (5)
min_res_countValid <- min(res_countValid)
if(min_res_countValid < 5){
na_index_mask <- na_index_mask[-(which(min_res_countValid < 5))]
if(length(na_index_mask) == 0){
stop("Raster time series contain too many missing values and no pixel has a valid temporal profile.\nConsider the use of argument 'gapfill' to perform gapfilling before STL computation")
}
matrice <- as.matrix(rasterts[na_index_mask])
if(verbose){
message("Raster mask has been refined to deal with minumum number of time series oservations (minimum: 5 / found: ", min_res_countValid, ")")
message("Final masked raster time series has ", ncol(matrice), " pixels and ", nrow(matrice), " temporal observations")
}
}
}
# compute Mann-Kendall test using 'Kendall' package
# define parallel 'rtsa.mkpar' function
# create time variable for the computation
rtime <- as.integer(time(rasterts@time))
# define Mann-Kendall function for parallel computing
if(mk_seasonal){
rtsa.mkpar <- function(x){
tprofile <- xts::xts(as.vector(x), as.Date(rtime, origin="1970-01-01", tz="GMT"))
tprofile2 <- stats::ts(data=as.vector(tprofile), start=c(as.integer(format(time(tprofile[1]), "%Y")), as.integer(format(time(tprofile[1]), "%m")), as.integer(format(time(tprofile[1]), "%d"))), end=c(as.integer(format(time(tprofile[length(tprofile)]), "%Y")), as.integer(format(time(tprofile[length(tprofile)]), "%m")), as.integer(format(time(tprofile[length(tprofile)]), "%d"))), deltat=deltats)
mk_result <- Kendall::SeasonalMannKendall(tprofile2)
output <- as.vector(c(as.double(mk_result$tau), as.double(mk_result$sl), as.integer(mk_result$S), as.integer(mk_result$varS)))
return(output)
}
} else {
rtsa.mkpar <- function(x){
tprofile <- xts::xts(as.vector(x), as.Date(rtime, origin="1970-01-01", tz="GMT"))
tprofile2 <- ts(data=as.vector(tprofile), start=c(as.integer(format(time(tprofile[1]), "%Y")), as.integer(format(time(tprofile[1]), "%m")), as.integer(format(time(tprofile[1]), "%d"))), end=c(as.integer(format(time(tprofile[length(tprofile)]), "%Y")), as.integer(format(time(tprofile[length(tprofile)]), "%m")), as.integer(format(time(tprofile[length(tprofile)]), "%d"))), deltat=deltats)
mk_result <- Kendall::MannKendall(tprofile2)
output <- as.vector(c(as.double(mk_result$tau), as.double(mk_result$sl), as.integer(mk_result$S), as.integer(mk_result$varS)))
return(output)
}
}
if(verbose){
message(paste(c("Mann-Kendall trend test started at: "), Sys.time(), sep=""))
}
ptm <- proc.time()
if(cores>1){
if(!requireNamespace("doParallel", quietly = TRUE)){
warning("Package 'doParallel' is required to run this function.\nYou can install using the command:\ninstall.packages('doParallel', dependencies=TRUE)\nGoing on using one core")
res_mk <- apply(X=matrice, MARGIN=2, FUN=rtsa.mkpar)
} else {
# check that machine has available cores
if(cores > as.integer(parallel::detectCores())){
cores <- as.integer(parallel::detectCores())
}
if(verbose){
message("Running Mann-Kendall trend test analysis using ", cores, " cores")
}
# run 'stl' computation in parallel
# start cluster for parallel computation
cl <- parallel::makePSOCKcluster(cores)
doParallel::registerDoParallel(cl)
# export 'stlplus' arguments to the cluster environment
parallel::clusterExport(cl=cl, varlist=c("rtime", "deltats"), envir=environment())
# perform 'stl' computation
res_mk <- parallel::parCapply(cl=cl, x=matrice, FUN=rtsa.mkpar)
# stop cluster
parallel::stopCluster(cl)
}
} else {
# run function using one core
res_mk <- apply(X=matrice, MARGIN=2, FUN=rtsa.mkpar)
}
# stop cluster
#parallel::stopCluster(cl) ### check why it is not stopping inside the function
if(verbose){
message(paste(c("Mann-Kendall trend test computation ended at: "), Sys.time(), sep=""))
message(paste("Elapsed time ", as.character(paste(as.integer(as.numeric(proc.time() - ptm)[3]/3600), ":", sprintf("%02i", as.integer((as.numeric(proc.time() - ptm)[3]/3600 - as.integer(as.numeric(proc.time() - ptm)[3]/3600)) * 60)), ":", sprintf("%02i", as.integer((as.numeric(proc.time() - ptm)[3]/60 - as.integer(as.numeric(proc.time() - ptm)[3]/60)) * 60)), sep="")), " hours", sep=""))
}
# create output object
# assemble results to matrix object
res_mk_matrix <- matrix(data=res_mk, nrow=ncol(matrice), ncol=4, byrow=TRUE)
# create empty 'rts' object to store results
void_raster <- raster(rasterts@raster[[1]])
values(void_raster) <- NA
# assemble results in a object of class 'STDstack' (Seasonal Trend Decomposition)
mkreturn <- new("MKstack")
void_raster[na_index_mask] <- as.vector(res_mk_matrix[,1])
mkreturn@tau <- void_raster
values(void_raster) <- NA
void_raster[na_index_mask] <- as.vector(res_mk_matrix[,2])
mkreturn@pvalue <- void_raster
values(void_raster) <- NA
void_raster[na_index_mask] <- as.vector(res_mk_matrix[,3])
mkreturn@score <- void_raster
values(void_raster) <- NA
void_raster[na_index_mask] <- as.vector(res_mk_matrix[,4])
mkreturn@variance <- void_raster
# return function result
return(mkreturn)
# stop cluster
on.exit(stopCluster(cl))
}
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.