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#'Compute estimate of seasonal mean of Atlantic hurricane activity
#'
#'Compute one of G. Villarini's statistically downscaled measure of mean
#'Atlantic hurricane activity and its variance. The hurricane activity is
#'estimated using seasonal averages of sea surface temperature anomalies over
#'the tropical Atlantic (bounded by 10N-25N and 80W-20W) and the tropics at
#'large (bounded by 30N-30S). The anomalies are for the JJASON season.\cr
#'The estimated seasonal average is either 1) number of hurricanes, 2) number
#'of tropical cyclones with lifetime >=48h or 3) power dissipation index
#'(PDI; in 10^11 m^3 s^{-2}).\cr
#'The statistical models used in this function are described in\cr
#'
#'@param atlano Array of Atlantic sea surface temperature anomalies.
#' Must have the same dimension as tropano.
#'@param tropano Array of tropical sea surface temperature anomalies.
#' Must have the same dimension as atlano.
#'@param hrvar The seasonal average to be estimated. The options are either\cr
#' "HR" (hurricanes) \cr
#' "TC" (tropical cyclones with lifetime >=48h) \cr
#' "PDI" (power dissipation index) \cr
#'
#'@return A list composed of two matrices:\cr
#'\enumerate{
#' \item{
#' A matrix (mean) with the seasonal average values of the desired quantity.\cr
#' }
#' \item{
#' A matrix (var) of the variance of that quantity.\cr
#' }
#'}
#'The dimensions of the two matrices are the same as the dimensions of
#' atlano/tropano.
#'
#'@keywords datagen
#'@references
#'Villarini et al. (2010) Mon Wea Rev, 138, 2681-2705.\cr
#'Villarini et al. (2012) Mon Wea Rev, 140, 44-65.\cr
#'Villarini et al. (2012) J Clim, 25, 625-637.\cr
#'An example of how the function can be used in hurricane forecast studies
#' is given in\cr
#'Caron, L.-P. et al. (2014) Multi-year prediction skill of Atlantic hurricane
#' activity in CMIP5 decadal hindcasts. Climate Dynamics, 42, 2675-2690.
#' doi:10.1007/s00382-013-1773-1.
#'@author History:\cr
#'0.1 - 2015-11 (Louis-Philippe Caron) - Original code
#'@examples
#'# Let AtlAno represents 5 different 5-year forecasts of seasonally averaged
#'# Atlantic sea surface temperature anomalies.
#'AtlAno <- matrix(c(-0.31, -0.36, 0.26, -0.16, -0.16,
#' -0.06, -0.22, -0.31, -0.36, -0.39,
#' 0.20, -0.14, 0.12, 0.22, 0.02,
#' -0.28, 0.26, -0.10, 0.18, 0.33,
#' 0.45, 0.46, 0.04, 0.12, 0.21),
#' nrow = 5, ncol = 5)
#'# Let TropAno represents 5 corresponding 5-year forecasts of seasonally averaged
#'# tropical sea surface temperature anomalies.
#'TropAno <- matrix(c(-0.22, -.13, 0.07, -0.16, -0.15,
#' 0.00, -0.03, -0.22, -0.13, -0.10,
#' 0.07, -0.07, 0.17, 0.10, -0.15,
#' -0.01, 0.08, 0.07, 0.17, 0.13,
#' 0.16, 0.15, -0.09, 0.03, 0.27),
#' nrow = 5, ncol = 5)
#'# The seasonal average of hurricanes for each of the five forecasted years,
#'# for each forecast, would then be given by
#'hr_count <- StatSeasAtlHurr(atlano = AtlAno,
#' tropano = TropAno,
#' hrvar = 'HR')
#'print(hr_count$mean)
#'
#'@export
StatSeasAtlHurr <- function(atlano = NULL, tropano = NULL, hrvar = "HR") {
# Verify that variables are either TC, HR or PDI.
# -----------------------------------------------
if (hrvar != "HR" && hrvar != "TC" && hrvar != "PDI") {
stop("Hurricane variable not recognized.")
}
# Verify that both Atl and Trop SSTA are present.
# -----------------------------------------------
if (is.null(atlano)) {
stop("Atlantic SST missing.")
}
if (is.null(tropano)) {
stop("Tropical SST missing.")
}
# Verify that Atl and Trop SSTA are of the same dimensions.
# ---------------------------------------------------------
if (length(dim(atlano)) != length(dim(tropano))) {
stop("Input arrays are of different dimensions.")
} else {
for (i in 1:length(dim(atlano))) {
if (dim(atlano)[i] != dim(tropano)[i]) {
stop("Input arrays are of different sizes.")
}
}
}
# Get the values of the betas according to the hurricane
# activity measure we specified.
# ------------------------------------------------------
if (hrvar == "HR") {
# beta's are derived from Villarini et al. (2012), Mon Wea
# Rev, 140, 44-65. beta's are for corrected hurricane data +
# ERSST with SBC criteria (table 2)
beta0 <- 1.85
betaAtl <- 1.05
betaTrop <- -1.17
} else if (hrvar == "TC") {
# beta's are from Villarini et al. (2010), Mon Wea Rev, 138,
# 2681-2705. beta's are for corrected TC data (lifetime >=
# 48h) + ERSST (table 5)
beta0 <- 2.1
betaAtl <- 1.02
betaTrop <- -1.05
} else if (hrvar == "PDI") {
# beta's are from Villarini et al. (2012), J Clim, 25,
# 625-637. beta's are from ERSST, with SBC penalty criterion
# (table 1)
beta0 <- 0.76
betaAtl <- 1.94
betaTrop <- -1.78
}
# Create matrix of similar dimension as atlano for beta0.
# -------------------------------------------------------
intercept <- array(beta0, dim(atlano))
# Compute statistical relationship b/w SSTAs and mean
# hurricane activity.
# ---------------------------------------------------
atl <- betaAtl * atlano
trop <- betaTrop * tropano
#
temp <- intercept + atl + trop
#
statval <- list(mean = array(NA, dim(atl)), var = array(NA, dim(atl)))
statval$mean[] <- vapply(X = temp, FUN = exp, numeric(1))
# Compute the variance of the distribution. TC and HR follow
# a Poisson distribution, so the variance is equal to the
# mean. PDI follows a gamma distribution, with sigma =
# -0.57. (variance = sigma^2 * mean^2).
# -----------------------------------------------------------
if (hrvar == "HR" | hrvar == "TC") {
statval$var <- statval$mean
} else {
sigma <- -0.57
statval$var[] <- sigma^2 * vapply(X = statval$mean, FUN = function(x) x^2,
numeric(1))
}
# Output
# ~~~~~~~~
statval
}
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