#' Indices describing timing of average flow events.
#' @description Calculates 3 indices used to describe the timing of average flow conditions.
#' See Table X in the EflowStats package vignette for a full description of indices.
#' @param x A dataframe containing a vector of date values in the first column and vector of numeric flow values in the second column.
#' @param yearType A charcter of either "water" or "calendar" indicating whether to use water years or calendar years, respectively.
#' @param wyMonth A numeric. The month of the year in which the water year starts
#' (1=January, 12=December). The water year begins on the first day of wyMonth.
#' @param digits A numeric. Number of digits to round indice values
#' @param pref A character of either "mean" or "median", indicating whether to use mean or median. See details.
#' @param floodThreshold Numeric flood threshold as the flow equivalent for a flood recurrence of 1.67 years
#' @param ... Optional arguments needed for \code{calc_allHIT} function
#' @details Descriptions of indices.
#' \itemize{
#' \item ta1; Constancy. Constancy is computed via the formulation of Colwell (see example in
#' Colwell, 1974). A matrix of values is compiled where the columns are 11 flow
#' categories and the rows are 365 days of the year (no leap years) defined as either calendar or water year. February 29th is removed on leap years. The cell
#' values are the number of times that a flow falls into a category on each day. The
#' categories are listed below. The row totals, column totals, and grand total are computed. Using the equations for
#' Shannon information theory parameters, constancy is computed as 1-(uncertainty with respect to state)/log10(number of state)
#' \itemize{
#' \item log(flow) < .1 x log(mean flow)
#' \item .1 x log(mean flow) <= log(flow) < .25 x log(mean flow)
#' \item .25 x log(mean flow) <= log(flow) < .5 x log(mean flow)
#' \item .5 x log(mean flow) <= log(flow) < .75 x log(mean flow)
#' \item .75 x log(mean flow) <= log(flow) < 1.0 x log(mean flow)
#' \item 1.0 x log(mean flow) <= log(flow) < 1.25 x log(mean flow)
#' \item 1.25 x log(mean flow) <= log(flow) < 1.5 x log(mean flow)
#' \item 1.5 x log(mean flow) <= log(flow) < 1.75 x log(mean flow)
#' \item 1.75 x log(mean flow) <= log(flow) < 2.0 x log(mean flow)
#' \item 2.0 x log(mean flow) <= log(flow) < 2.25 x log(mean flow)
#' \item log(flow) >= 2.25 x log(mean flow)
#' }
#' \item ta2; Predictability. Predictability is computed from the same matrix as constancy (see
#' example in Colwell, 1974). It is computed as: 1- (uncertainty with respect to interaction of time and state - uncertainty with respect to time)/log10(number of state)
#' \item ta3; Seasonal predictability of flooding. Divide years up into 2-month periods (that is,
#' Oct-Nov, Dec-Jan, and so forth). Count the number of flood days (flow events with
#' flows > 1.67-year flood) in each period over the entire flow record. TA3 is the
#' maximum number of flood days in any one period divided by the total number of
#' flood days.
#' }
#' @return A data.frame of flow statistics
#' @importFrom lubridate year
#' @importFrom lubridate month
#' @export
#' @examples
#' x <- sampleData[c("date","discharge")]
#' yearType = "water"
#' floodThreshold = 1158
#' calc_timingAverage(x=x,yearType = yearType,floodThreshold =floodThreshold)
calc_timingAverage <- function(x,yearType = "water",wyMonth=10L,digits=3,pref="mean",floodThreshold=NULL,...) {
#Check data inputs
x <- validate_data(x,yearType=yearType,wyMonth=wyMonth)
if(isFALSE(x)) stop("input data not valid")
check_preference(pref)
#calculate some stuff for use later
x$month_val <- lubridate::month(x$date)
x$dayom_val <- lubridate::mday(x$date)
meanFlow <- mean(x$discharge)
# remove all February 29th from the time series to calculate
# Colwell matrix
x <- x[!((x$month_val == 2) & (x$dayom_val == 29)),]
# #Get a new julian day value that does not count leap years
# after removing the 29th of Feb, we can count the rows sequentially
# for each unique water year; https://stackoverflow.com/a/46613159
x$day <- sequence(rle(x$year_val)$lengths)
#Calculate the colwell matrix...
log_meanFlow = log10(meanFlow)
x$log_discharge = log10(x$discharge)
#...using findInterval
break_pts = c(.1, seq(0.25, 2.25, by=.25)) * log_meanFlow
x$interv = findInterval(x$log_discharge, sort(break_pts))
colwellMatrix = table(x$day, x$interv)
#ta1.2
XJ <- rowSums(colwellMatrix)
YI <- colSums(colwellMatrix)
Z <- sum(colwellMatrix)
XJ_sub <- XJ[XJ>0]
HX <- -sum((XJ_sub/Z)*log10(XJ_sub/Z))
YI_sub <- YI[YI>0]
HY <- -sum((YI_sub/Z)*log10(YI_sub/Z))
colwell_sub <- colwellMatrix[colwellMatrix>0]
HXY <- -sum((colwell_sub/Z)*log10(colwell_sub/Z))
HxY <- HXY - HX
ta1 <- 1-(HY/log10(11))
ta2 <- 100*(1-(HxY/log10(11)))
#ta3
countsYearMon <- dplyr::summarize(dplyr::group_by(x,year_val,month_val),
counts = length(discharge[discharge>floodThreshold])
)
countsYearMon <- dplyr::arrange(countsYearMon,year_val,month_val)
rollSum <- RcppRoll::roll_sum(countsYearMon$counts,n=2)
ta3 <- max(rollSum)/sum(countsYearMon$counts)
#output results
taOut <- data.frame(indice = c(paste0("ta",1:3)),
statistic = c(ta1,
ta2,
ta3),
stringsAsFactors = F
)
taOut$statistic <- round(taOut$statistic,digits=digits)
return(taOut)
}
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