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# File baseflow.R
# File plot_p_q.R
# Part of the hydroTSM R package, https://github.com/hzambran/hydroTSM ;
# https://CRAN.R-project.org/package=hydroTSM
# http://www.rforge.net/hydroTSM/
# Copyright 2012-2018 Mauricio Zambrano-Bigiarini
# Distributed under GPL 2 or later
################################################################################
# 'baseflow' #
################################################################################
# Purpose: Given a complete (without missing values) series of streamflow, #
# this function computes the baseflow using the filter proposed by #
# Arnold & Allen in 1999 #
################################################################################
# Reference: Arnold, J. G., & Allen, P. M. (1999). Automated methods for #
# estimating baseflow and ground water recharge from streamflow #
# records. JAWRA Journal of the American Water Resources Association,
# 35(2), 411-424. doi: 10.1111/j.1752-1688.1999.tb03599.x #
################################################################################
# Author : Mauricio Zambrano-Bigiarini #
# Started: 2013 #
# Updates: 16-May-2018 #
# 26-Nov-2023 #
# 17-Jan-2024 #
################################################################################
# 'x' : zoo object with streamflow records. The suggested time
# frequency should be hourly or daily, but the algorithm will work
# with any time frequency
# 'beta' : numeric representing the filter parameter. Default value is 0.925
# as recommended by Arnold & Allen (1999)
# 'from' : Character indicating the starting date for creating the regularly
# spaced zoo object. The default value corresponds to the date of
# the first element of \code{x} \cr
# It has to be in the format indicated by \code{date.fmt}.
# 'to' : Character indicating the ending date for creating the regularly
# spaced zoo object. The default value corresponds to the date of
# the last element of \code{x} \cr
# It has to be in the format indicated by \code{date.fmt}.
# 'date.fmt' : Character indicating the format in which the dates are stored in
# \code{from} and \code{to}, e.g. \kbd{\%Y-\%m-\%d}.
# See \sQuote{Details} section in \code{\link[base]{strptime}}.
# By default, \code{date.fmt} is missing, and it is automatically
# set to \kbd{\%Y-\%m-\%d} when \code{time(x)} is \code{Date}
# object, and set to \kbd{\%Y-\%m-\%d \%H:\%M:\%S} when \code{x}
# is a sub-daily zoo object.
# 'tz' : Character, with the specification of the time zone used for
# \code{from}, \code{to}. System-specific (see time zones),
# but \code{""} is the current time zone, and \code{"GMT"} is
# UTC (Universal Time, Coordinated).
# See \code{\link[base]{Sys.timezone}} and
# \code{\link[base]{as.POSIXct}}. \cr
# If \code{tz} is missing (the default), it is automatically set
# to the time zone used in \code{time(x)}. \cr
# This argument can be used when working with sub-daily zoo objects
# to force using time zones other than the local time zone for
# \code{from} and \code{to}. It should be used with caution,
# being well aware of the time zone of the data. See examples.
# 'na.fill' : Character indicating how to fill any NA present in 'x'.
# Valid values are:
# -) "none" => NAs are not removed, and therefore the algorithm is
# not executed
# -) "linear" => NAs are removed by linear interpolation, using
# \code{\link[zoo]{na.approx}}
# -) "spline" => NAs are removed by spline interpolation, using
# \code{\link[zoo]{na.spline}}
# 'out.type': Character indicating the type of result that is given by this function.
# Valid values are:
# -) "last" => only the baseflow computed after the third pass
# of the filter is returned
# -) "all " => the 3 baseflows computed after each pass of the
# filter are returned in a matrix or zoo object
# 'plot' : logical. Indicates if the baseflow should be plotted or not.
# If plotted, the original 'x' values are plotted as well
# 'xcol' : character, representing the color to be used for ploting the
# streamflow time series
# Only used when \code{plot=TRUE}.
# 'bfcol' : character of lenght 3, representing the color(s) to be used for
# ploting the baseflow time series. The first, second and third
# element are used to represent the baseflow after the third,
# second and first pass of the filter, respectively.
# Only used when \code{plot=TRUE}.
# 'pch' : numeric, representing the symbols used for ploting the streamflow
# time series (both, the original series and the baseflow).
# Only used when \code{plot=TRUE}.
# 'cex' : a numerical vector giving the amount by which plotting characters
# and symbols should be scaled relative to the default.
# This works as a multiple of par("cex").
# See \code{\link[graphics]{plot.default}}.
# Only used when \code{plot=TRUE}.
# '...' : further arguments passed to or from other methods. Not used yet.
baseflow <- function(x, ...) UseMethod("baseflow")
baseflow.zoo <- function(x,
beta=0.925,
from=start(x),
to=end(x),
date.fmt,
tz,
na.fill=c("none", "linear", "spline"),
out.type=c("last", "all"),
plot=TRUE,
xcol="black",
bfcol=c("blue", "darkcyan", "darkorange3"),
pch=15,
cex=0.3,
...) {
# Checking 'out.type'
out.type <- match.arg(out.type)
# Checking 'na.fill'
na.fill <- match.arg(na.fill)
# sampling frequency of 'x'
x.freq <- sfreq(x)
# Checking if 'x is a sub-daily zoo object
if (x.freq %in% c("minute","hourly") ) {
subdaily.ts <- TRUE
} else subdaily.ts <- FALSE
####################################################################################
# Lines 119-202 are taken from izoo2rzoo.R to check 'from' and 'to'
####################################################################################
# Automatic detection of 'date.fmt'
if ( missing(date.fmt) ) {
if ( subdaily.ts ) {
date.fmt <- "%Y-%m-%d %H:%M:%S"
} else date.fmt <- "%Y-%m-%d"
} # IF end
# Automatic detection of 'tz'
missingTZ <- FALSE
if (missing(tz)) {
missingTZ <- TRUE
tz <- ""
} # IF end
ifelse ( grepl("%H", date.fmt, fixed=TRUE) | grepl("%M", date.fmt, fixed=TRUE) |
grepl("%S", date.fmt, fixed=TRUE) | grepl("%I", date.fmt, fixed=TRUE) |
grepl("%p", date.fmt, fixed=TRUE) | grepl("%X", date.fmt, fixed=TRUE),
subdaily.date.fmt <- TRUE, subdaily.date.fmt <- FALSE )
# If the index of 'x' is character, it is converted into a Date object
if ( class(time(x))[1] %in% c("factor", "character") )
#ifelse(subdaily.date.fmt, time(x) <- as.POSIXct(time(x), format=date.fmt, tz=tz),
ifelse(subdaily.date.fmt, time(x) <- as.POSIXct(time(x), format=date.fmt),
time(x) <- as.Date(time(x), format=date.fmt) )
# If 'from' was given as Date, but 'x' is sub-daily
if (!missing(from)) {
if (from > to) stop("Invalid argument: 'from > to' !")
if (from > end(x)) stop("Invalid argument: 'from > end(x)' !")
if ( subdaily.date.fmt & !(grepl(":", from, fixed=TRUE) ) )
from <- paste(from, "00:00:00")
if ( subdaily.date.fmt & missingTZ )
from <- as.POSIXct(from, tz=tz)
} # IF end
# If 'to' was given as Date, but 'x' is sub-daily
if (!missing(to)) {
if (to < from ) stop("Invalid argument: 'to < from' !")
if (to < start(x) ) stop("Invalid argument: 'to < start(x)' !")
if ( subdaily.date.fmt & !(grepl(":", to, fixed=TRUE) ) )
to <- paste(to, "00:00:00")
if ( subdaily.date.fmt & missingTZ )
to <- as.POSIXct(to, tz=tz)
} # IF end
# checking that date.fmt and the sampling frequency of 'x' are compatible
if ( subdaily.ts ) {
if (!subdaily.date.fmt)
stop("Invalid argument: 'date.fmt' (", date.fmt,
") is not compatible with a sub-daily time series !!")
} else {
if (subdaily.date.fmt) {
#time(x) <- as.POSIXct(time(x), tz=tz)
time(x) <- as.POSIXct(time(x))
warning("'date.fmt' (", date.fmt, ") is sub-daily, while 'x' is a '",
x.freq, "' ts => 'time(x)=as.POSIXct(time(x), tz)'")
} # IF end
} # ELSE end
if (subdaily.ts) {
dt <- try(as.POSIXct(from, format=date.fmt, tz=tz))
#dt <- try(as.POSIXct(from, format=date.fmt))
} else dt <- try(as.Date(from, format=date.fmt))
if("try-error" %in% class(dt) || is.na(dt)) {
stop("Invalid argument: format of 'from' is not compatible with 'date.fmt' !")
} else if (subdaily.ts) {
from <- as.POSIXct(from, format=date.fmt, tz=tz)
#from <- as.POSIXct(from, format=date.fmt)
} else from <- as.Date(from, format=date.fmt)
if (subdaily.ts) {
dt <- try(as.POSIXct(to, format=date.fmt, tz=tz))
} else dt <- try(as.Date(to, format=date.fmt))
if("try-error" %in% class(dt) || is.na(dt)) {
stop("Invalid argument: format of 'to' is not compatible with 'date.fmt' !")
} else if (subdaily.ts) {
to <- as.POSIXct(to, format=date.fmt, tz=tz)
} else to <- as.Date(to, format=date.fmt)
####################################################################################
# Selecting only those data within the time period between 'from' and 'to'
x <- window(x, start=from, end=to)
# Checking that 'x' does not have any missing value
na.index <- which(is.na(x))
if (length(na.index) > 0) {
if (na.fill == "none") {
stop("Invalid argument: 'x' has some NA values. See 'na.fill' argument !!")
} else if (na.fill == "linear") {
x <- zoo::na.approx(x)
} else x <- zoo::na.spline(x)
} # IF end
# Storing and then removing the possible time attribute
HasTime <- FALSE
if ( is.zoo(x) ) {
HasTime <- TRUE
xtime <- time(x)
x <- zoo::coredata(x)
} # if END
# Initializing some parameters of the algorithm
n <- length(x)
f1 <- beta
f2 <- (1+beta) / 2
# Initializing quickflow values
quickflow <- rep(NA, n)
quickflow[1] <- x[1] / 2
# Initializing baseflow values after the first ('baseflow1'),
# second ('baseflow2') and third ('baseflow3') pass of the filter
baseflow1 <- rep(NA, n)
baseflow2 <- rep(NA, n)
baseflow3 <- rep(NA, n)
# 1) First pass of the filter (forward)
for (i in 2:n) {
quickflow[i] <- f1 * quickflow[i-1] + f2 * ( x[i] - x[i-1] )
if ( quickflow[i] < 0) quickflow[i] <- 0
} # FOR end
# baseflow1 computation
baseflow1 <- x - quickflow
# Removing any possible negative values
neg.index <- which(baseflow1 < 0)
if (length(neg.index) > 0) baseflow1[neg.index] <- 0
# Removing any possible baseflow1 values larger than its corresponding streamflow
larger.index <- which(baseflow1 > x)
if (length(larger.index) > 0) baseflow1[larger.index] <- x[larger.index]
# 2) Second pass of the filter (backward)
baseflow2[n-1] <- baseflow1[n-1]
for (i in (n-2):1) {
quickflow[i] <- f1 * quickflow[i+1] + f2 * ( baseflow1[i] - baseflow1[i+1] )
if ( quickflow[i] < 0) quickflow[i] <- 0
} # FOR end
# baseflow2 computation
baseflow2 <- baseflow1 - quickflow
# Removing any possible negative values
neg.index <- which(baseflow2 < 0)
if (length(neg.index) > 0) baseflow2[neg.index] <- 0
# Removing any possible baseflow2 values larger than its previous baseflow1
larger.index <- which(baseflow2 > baseflow1)
if (length(larger.index) > 0) baseflow2[larger.index] <- baseflow1[larger.index]
# 3) Third pass of the filter (forward)
baseflow3[n-1] <- baseflow1[n-1]
for (i in 2:n) {
quickflow[i] <- f1 * quickflow[i-1] + f2 * ( baseflow2[i] - baseflow2[i-1] )
if ( quickflow[i] < 0) quickflow[i] <- 0
} # FOR end
# baseflow3 computation
baseflow3 <- baseflow2 - quickflow
# Removing any possible negative values
neg.index <- which(baseflow3 < 0)
if (length(neg.index) > 0) baseflow3[neg.index] <- 0
# Removing any possible baseflow3 values larger than its previous baseflow2
larger.index <- which(baseflow3 > baseflow2)
if (length(larger.index) > 0) baseflow3[larger.index] <- baseflow2[larger.index]
# Giving back the time attribute if the orignal 'x' object had one
if ( HasTime ) {
x <- zoo(x, xtime)
baseflow1 <- zoo(baseflow1, xtime)
baseflow2 <- zoo(baseflow2, xtime)
baseflow3 <- zoo(baseflow3, xtime)
} # if END
# Creating the output object
if (out.type=="last") {
out <- baseflow3
} else out <- cbind(baseflow3, baseflow2, baseflow1)
# Plotting, if necessary
if (plot) {
if (HasTime) {
plot(x, ylab="Q", type="n", xaxt="n", xlab="Time")
drawTimeAxis(x)
grid()
points(x, type="o", col=xcol, pch=15, lty=1, cex=cex)
if (out.type=="all") {
points(baseflow1, type="o", col=bfcol[3], pch=pch, lty=1, cex=cex)
points(baseflow2, type="o", col=bfcol[2], pch=pch, lty=1, cex=cex)
legend.text <- c("Streamflow", "Baseflow 3rd pass", "Baseflow 2nd pass", "Baseflow 1st pass")
legend.cols <- c(xcol, bfcol[1], bfcol[2], bfcol[3])
} else {
legend.text <- c("Streamflow", "Baseflow")
legend.cols <- c(xcol, bfcol[1])
} # ELSE end
points(baseflow3, type="o", col=bfcol[1], pch=pch, lty=1, cex=cex)
} else { # HasTime == FALSE
plot(1:n, x, ylab="Q", type="n", xlab="Time")
grid()
points(1:n, x, type="o", col=xcol, pch=pch, lty=1, cex=cex)
if (out.type=="all") {
points(1:n, baseflow1, type="o", col=bfcol[3], pch=pch, lty=1, cex=cex)
points(1:n, baseflow2, type="o", col=bfcol[2], pch=pch, lty=1, cex=cex)
legend.text <- c("Streamflow", "Baseflow 3rd pass", "Baseflow 2nd pass", "Baseflow 1st pass")
legend.cols <- c(xcol, bfcol[1], bfcol[2], bfcol[3])
} else {
legend.text <- c("Streamflow", "Baseflow")
legend.cols <- c(xcol, bfcol[1])
} # ELSE end
points(1:n, baseflow3, type="o", col=bfcol[1], pch=pch, lty=1, cex=cex)
} # ELSE end
legend("topright", legend = legend.text, bty="n",
lty=c(1,1), pch=c(pch, pch), col=legend.cols,
#lty = 1:2, xjust = 1, yjust = 1,
title = "")
} # IF end
return(out)
} # 'baseflow' END
#setwd("/dataMZB/2018-UFRO/work/Investigacion/Colaboracion_de_estudiantes/Cristobal_Soto/data/ts")
#library(zoo)
#x <- read.csv(file="Caudales_Curacautin_en_Rari_Ruca.csv")
#dates <- as.Date(x[,1], format="%d-%m-%Y")
#q <- x[1:3597, 2]
#dates <- dates[1:3597]
#q.na.filled <- na.approx(q)
#bf <- baseflow(q.na.filled)
#bf <- zoo(bf, dates)
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