Nothing
#-----------------------------------------------------------------------------------------------------------------#
#-----------------------------------------------------------------------------------------------------------------#
#---------------------------------------- function: cond_returnlevel_plot ----------------------------------------#
#-----------------------------------------------------------------------------------------------------------------#
#-----------------------------------------------------------------------------------------------------------------#
cond_returnlevel_plot = function(location, GEVparam, cond_location, cond_GEVparam, same_var,
cor_coeff, cond_B, cond_B_2 = Inf, obs = NULL, var = NULL,
period_range = c(1,128), model = "ext-t", printObjectives = FALSE,
plottitle = NULL, save_name = NULL, save_dir = getwd(),
printPlot = TRUE) {
# Information ---------------------------------------------------------------------------------------------------
# example: cond_returnlevel_plot(location = arl, GEVparam = sd_GEVparam_arl, cond_location = ibk,
# cond_GEVparam = swe_GEVparam_ibk, same_var = FALSE, cond_B = cond_B,
# cor_coeff = cor_coeff, model = "hr",
# plottitle = "sd cond rl at arlberg given swe > swe_rl50 in ibk",
# printPlot = FALSE)
# output: a conditional return level plot
#
# --- this function creates a conditional return level plot
# the q-year conditional return level of variable Z1 at location x1 given variable Z2 at location x2 is
# defined as the threshold B, such that the conditional probability that Z1(x1) exceeds this threshold,
# given that Z2(x2) is in the interval ('cond_B','cond_B_2'), is 1/q :
# Pr[Z1(x1) > B | Z2(x2) in (cond_B,cond_B_2)] = 1/q
#
# --- input:
# 1. 'location': a vector with certain location characteristics as entries
# characteristics are for example: longitude, latitude and altitude
# 2. 'GEVparam': a named vector with the GEV parameters of the variable for which
# conditional return levels are calculated
# names are 'loc', 'scale' and 'shape'
# 3. 'cond_location': a vector with the characteristics of the conditioned location
# characteristics should be the same as in 'location'
# 4. 'cond_GEVparam': a named vector with the GEV parameters of the conditioned variable
# names are 'loc', 'scale' and 'shape'
# 5. 'same_var': logical value
# if TRUE, the conditioned variable is the same as the unconditioned variable
# this has to be known in order to use the right correlation function
# 6. 'cor_coeff': a named vector with the correlation parameters
# for the Huesler-Reiss model: 'alpha', 'kappa' and 'lambda12'
# for the Extremal-Gaussian model: 'alpha', 'sd_kappa', 'swe_kappa' and 'rho12'
# for the Extremal-t model: 'alpha', 'sd_kappa', 'swe_kappa', 'rho12' and 'nu'
# 7. 'cond_B': a real number as the lower barrier of the conditioned variable
# (e.g. the return level)
# --- optional input:
# 8. 'cond_B_2': a real number as the upper barrier of the conditioned variable
# default (if this input is missing) is Inf
# 9. 'obs': a vector with empirical observations
# if provided, sample quantiles of this vector are added to the plot as points
# 10. 'var': a character string being 'sd' or 'swe' if 'same_var' is TRUE and model is
# 'ext-t' or 'ext-gauss'
# that is, if the conditioned variable is the same as the unconditioned variable,
# for the Extremal-Gaussian and Extremal-t model it has to be known which variable it is
# 11. 'period_range': the range of the return period to be plotted
# a vector with start and end point, which should be numbers greater or equal than 1
# default (if this input is missing) is 'c(1,128)'
# 12. 'model': a character string
# chose which bivariate max-stable model should be used to calculate the conditional
# return levels; either 'hr' for the Huesler-Reiss, 'ext-gauss' for the Extremal-Gaussian or
# 'ext-t' for the Extremal-t model
# default (if this input is missing) is 'ext-t'
# 13. 'printObjectives': logical value
# if TRUE, a summary of the values
# f(B) = abs(1/q - Pr[Z1(x1) > B | Z2(x2) in (cond_B,cond_B_2)])
# is printed, where B is the found conditional return level and
# Pr[Z1(x1) > B | Z2(x2) in (cond_B,cond_B_2)] is the conditional probability that Z1(x1)
# (eg. sd or swe) exceeds B, given that Z2(x2) (eg. swe or sd) is in between cond_B and cond_B_2;
# by the minimaization of the function f we find the 1/q quantile of this conditional
# distribution, thus we want small values
# default (if this input is missing) is FALSE
# 14. 'plottitle': a character string defining the title of the plot
# default (if this input is missing) is 'conditional return level plot'
# 15. 'save_name': a character string defining the saving name of the plot
# default (if this input is missing) is 'cond_return_level_plot'
# 16. 'save_dir': a character string defining the directory for the plot to be saved
# default (if this input is missing) is the working directory
# 17. 'print_plot': logical value
# if TRUE, the plot is printed
# default (if this input is missing) is TRUE
#---------------------------------------------------------------------------------------------------------------#
# Check required packages and input parameters ------------------------------------------------------------------
# # load required package 'SpatialExtremes'
# if (inherits(try(library(SpatialExtremes, warn.conflicts = FALSE, quietly = TRUE),
# silent = TRUE), "try-error")) {
# message("required package 'SpatialExtremes' is not installed yet -- trying to install package")
# install.packages("SpatialExtremes", quiet = TRUE)
# if (inherits(try(library(SpatialExtremes, warn.conflicts = FALSE, quietly = TRUE),
# silent = TRUE), "try-error")) {
# stop("package 'SpatialExtremes' couldn't be installed")
# } else {
# message("package successfully installed and loaded")
# }
# }
#
# # load required package 'ggplot2'
# if (inherits(try(library(ggplot2, warn.conflicts = FALSE, quietly = TRUE), silent = TRUE), "try-error")) {
# message("required package 'ggplot2' is not installed yet -- trying to install package")
# install.packages("ggplot2", quiet = TRUE)
# if (inherits(try(library(ggplot2, warn.conflicts = FALSE, quietly = TRUE), silent = TRUE), "try-error")) {
# stop("package 'ggplot2' couldn't be installed")
# } else {
# message("package successfully installed and loaded")
# }
# }
# check whether 'location' and 'cond_location' are vectors
if (!is.vector(location) || !is.vector(cond_location)) {
stop("'location' and 'cond_location' have to be vectors")
}
# check whether the length of 'location' and 'cond_location' coincide
if (length(location) != length(cond_location)) {
stop("'location' and 'cond_location' must have the same length")
}
# check whether 'GEVparam' and 'cond_GEVparam' are vectors
if (!is.vector(GEVparam) || !is.vector(cond_GEVparam)) {
stop("'GEVparam' and 'cond_GEVparam' have to be vectors")
}
# names of 'GEVparam' must be 'loc', 'scale' and 'shape'
if (!(all(c("loc","scale","shape") %in% names(GEVparam)))) {
stop("names of 'GEVparam' must be 'loc', 'scale' and 'shape'")
}
# names of 'cond_GEVparam' must be 'loc', 'scale' and 'shape'
if (!(all(c("loc","scale","shape") %in% names(cond_GEVparam)))) {
stop("names of 'cond_GEVparam' must be 'loc', 'scale' and 'shape'")
}
# 'cond_B' has to be a real number
if (!is.vector(cond_B) || length(cond_B) != 1 || !is.numeric(cond_B)) {
stop("'cond_B' has to be a real number")
}
# 'cond_B_2' has to be a real number
if (!is.vector(cond_B_2) || length(cond_B_2) != 1 || !is.numeric(cond_B_2)) {
stop("'cond_B_2' has to be a real number")
}
# 'cond_B_2' has to be greater than 'cond_B'
if (cond_B_2 <= cond_B) {
stop("'cond_B_2' has to be greater than 'cond_B'")
}
# 'model' has to be either 'hr', 'ext-gauss' or 'ext-t'
if (!(model %in% c("hr","ext-gauss","ext-t"))) {
stop(sprintf("'model' has to be either 'hr', 'ext-gauss' or 'ext-t' -- '%s' is not allowed",model))
}
# 'cor_coeff' must be a named vector with the correlation coefficients according to the chosen model
if (model == "hr" && !all(c("alpha","kappa","lambda12") %in% names(cor_coeff))) {
stop(c("for the Huesler-Reiss model 'cor_coeff' must be a named vector with the correlation coefficients",
"\n 'alpha', 'kappa' and 'lambda12' -- you might change input argument 'model'"))
} else if (model == "ext-gauss" && !all(c("alpha","sd_kappa","swe_kappa","rho12") %in% names(cor_coeff))) {
stop(c("for the Extremal-Gaussian model 'cor_coeff' must be a named vector with the correlation coefficients",
"\n 'alpha', 'sd_kappa', 'swe_kappa' and 'rho12' -- you might change input argument 'model'"))
} else if (model == "ext-t" && !all(c("alpha","sd_kappa","swe_kappa","rho12","nu") %in% names(cor_coeff))) {
stop(c("for the Extremal-t model 'cor_coeff' must be a named vector with the correlation coefficients",
"\n 'alpha', 'sd_kappa', 'swe_kappa', 'rho12' and 'nu' -- you might change input argument 'model'"))
}
# check whether 'obs' is a vector
if (!missing(obs) && !is.vector(obs)) {
stop("'obs' has to be a vector")
}
# 'printObjectives' has to be a logical value
if (!(is.logical(printObjectives))) {
stop(sprintf("'printObjectives' has to be TRUE or FALSE -- '%s' is not allowed",printObjectives))
}
# 'period_range' has to be a vector of length 2 with numbers greater or equal than 1
if (length(period_range) != 2) {
stop("please state start and end point of return level period: 'period_range = c(start,end)'")
}
if (any(period_range < 1)) {
stop("numbers in 'period_range' have to be greater or equal than 1")
}
if (period_range[1] >= period_range[2]) {
stop("endpoint of 'period_range' is less or equal its startpoint")
}
# 'printPlot' has to be a logical value
if (!(is.logical(printPlot))) {
stop(sprintf("'printPlot' has to be TRUE or FALSE -- '%s' is not allowed",printPlot))
}
# 'same_var' has to be a logical value
if (!(is.logical(same_var))) {
stop(sprintf("'same_var' has to be TRUE or FALSE -- '%s' is not allowed",same_var))
}
# if 'same_var' is TRUE, the variable has to be named for the 'ext-gauss' or 'ext-t' model,
# this can be done with the input argument 'var' being 'sd' or 'swe'
if (same_var && (model %in% c("ext-gauss","ext-t"))) {
if (missing(var)) {
stop(c("if 'same_var' is TRUE, the variable has to be named",
"\n this can be done with the input argument 'var' being 'sd' or 'swe'"))
} else{
if (!(var %in% c("sd","swe"))) {
stop(sprintf("'var' has to be either 'sd' or 'swe' -- '%s' is not allowed",var))
}
}
}
rl <- NULL
#---------------------------------------------------------------------------------------------------------------#
# Perform calculations ------------------------------------------------------------------------------------------
# calculate the spatial lag between the two locations
h = sqrt(sum(location - cond_location)^2)
# if 'same_var' is TRUE, 'locations' and 'cond_locations' can't be the same (h != 0)
if (same_var) {
if (h == 0) {
stop(c("same variable ('same_var = TRUE') can't be conditioned on same location",
"\n either condition on different location or use different variables"))
}
}
# define non equidistant sequence of return level period
a = period_range[1]:period_range[2]
# define number of grid points with n
n = period_range[2] - period_range[1]
# partition the logarithmized intervall into equidistant points
loga = log(a)
log_int = max(loga) - min(loga)
log_equi = loga[1] + log_int*(1:n)/n
# transform log intervall back (q has to be greater than 1)
if (period_range[1] == 1) {
q = exp(log_equi)
} else {
q = c(period_range[1], exp(log_equi))
}
# transform conditional barriers 'cond_B' and 'cond_B_2' to unit Frechet
b1 = gev2frech(cond_B, loc = as.numeric(cond_GEVparam["loc"]), scale = as.numeric(cond_GEVparam["scale"]),
shape = as.numeric(cond_GEVparam["shape"]))
b2 = gev2frech(cond_B_2, loc = as.numeric(cond_GEVparam["loc"]), scale = as.numeric(cond_GEVparam["scale"]),
shape = as.numeric(cond_GEVparam["shape"]))
# depending on the model calculate the conditional return levels
if (model == "hr") {
# define the correlation function for the Huesler-Reiss model
lambda_h = function(h,alpha,kappa) {
as.numeric(sqrt((h/alpha)^kappa))
}
lambda12_h = function(h,alpha,kappa,lambda12) {
as.numeric(sqrt(lambda12^2 + lambda_h(h,alpha,kappa)^2))
}
# define the correlation parameters
alpha = cor_coeff["alpha"]
kappa = cor_coeff["kappa"]
lambda12 = cor_coeff["lambda12"]
# calculate correlations or cross-correlations, depending on 'same_var'
if (same_var) {
lh = lambda_h(h,alpha,kappa)
} else {
lh = lambda12_h(h, alpha, kappa, lambda12)
}
# predefine conditional return level and objectives vector
cond_rl = rep(NA,times = length(q))
objectives = rep(NA,times = length(q))
# find the conditional return level for every return period in q
for (k in 1:length(q)) {
# define function f calculating abs(1/q[k] - the conditional probability),
# which will be minimized in order to find the 1-q[k] quantil of the conditional distribution
f = function(B) {
a = gev2frech(B, loc = as.numeric(GEVparam["loc"]), scale = as.numeric(GEVparam["scale"]),
shape = as.numeric(GEVparam["shape"]))
help1 = log(b1/a)/lh
help2 = log(b2/a)/lh
P_sd_swe_1 = exp(-1/a*pnorm(lh/2 + help1) - 1/b1*pnorm(lh/2 - help1))
P_sd_swe_2 = exp(-1/a*pnorm(lh/2 + help2) - 1/b2*pnorm(lh/2 - help2))
ans = abs(1/q[k] - (exp(-1/b2) - exp(-1/b1) - P_sd_swe_2 + P_sd_swe_1)/(exp(-1/b2) - exp(-1/b1)))
ans[which(ans == 1/q[k])] = Inf
return(ans)
}
# define the starting value for the optimization to find the conditional return level
start_val = returnlevels(GEVparam = GEVparam, q = q[k])
# calculate conditional return levels
opt = suppressWarnings(nlminb(start_val, f))
# if optimization was not successful (value of f >= 1e-03)),
# try to find better solution with different starting value
opt1 = opt
j = 0
while (opt$objective >= 1e-03 && j <= 17) {
l = 1.5 + (-1)^j*floor((j+1)/2)*0.1
start_val_new = start_val*l
if (!is.infinite(f(start_val_new))) {
opt = suppressWarnings(nlminb(start_val_new, f))
}
j = j + 1
}
if (opt1$objective <= opt$objective) {
opt = opt1
}
if (opt$objective >= 1e-03) {
opt_seq = seq(0.8*start_val[k], 1.5*start_val[k], by = 0.001)
opt_ind = which.min(f(opt_seq))
if (all(is.na(f(opt_seq)))) {
cond_rl[k] = NA
objectives[k] = NA
warning("probability that conditioned variable is greater than 'cond_B' is zero -- change 'cond_B'")
} else if (f(opt_seq[opt_ind]) <= opt$objective) {
cond_rl[k] = opt_seq[opt_ind]
objectives[k] = f(opt_seq[opt_ind])
} else {
cond_rl[k] = opt$par
objectives[k] = opt$objective
}
} else {
cond_rl[k] = opt$par
objectives[k] = opt$objective
}
}
} else if (model == "ext-gauss") {
# define the correlation function for the Extremal-Gaussian model
matern_h = function(h,alpha,kappa) {
2^(1-kappa)/gamma(kappa)*(h/alpha)^kappa*besselK(h/alpha, kappa)
}
# define the correlation parameters
alpha = cor_coeff["alpha"]
sd_kappa = cor_coeff["sd_kappa"]
swe_kappa = cor_coeff["swe_kappa"]
rho12 = cor_coeff["rho12"]
# calculate correlations or cross-correlations, depending on 'same_var'
if (same_var) {
if (var == "sd") {
matern = matern_h(h,alpha,sd_kappa)
} else if (var == "swe") {
matern = matern_h(h,alpha,swe_kappa)
}
} else{
matern = rho12*matern_h(h,alpha,1/2*(sd_kappa + swe_kappa))
matern[which(is.na(matern))] = rho12
}
# predefine conditional return level and objectives vector
cond_rl = rep(NA,times = length(q))
objectives = rep(NA,times = length(q))
# find the conditional return level for every return period in q
for (k in 1:length(q)) {
# define function f calculating abs(1/q[k] - the conditional probability),
# which will be minimized in order to find the 1-q[k] quantil of the conditional distribution
f = function(B) {
a = gev2frech(B, loc = as.numeric(GEVparam["loc"]), scale = as.numeric(GEVparam["scale"]),
shape = as.numeric(GEVparam["shape"]))
help = (2/(1 - matern^2))^(1/2)
P_sd_swe_1 = exp(-1/a*pt(help*(b1/a - matern), df = 2) -
1/b1*pt(help*(a/b1 - matern), df = 2))
P_sd_swe_2 = exp(-1/a*pt(help*(b2/a - matern), df = 2) -
1/b2*pt(help*(a/b2 - matern), df = 2))
ans = abs(1/q[k] - (exp(-1/b2) - exp(-1/b1) - P_sd_swe_2 + P_sd_swe_1)/(exp(-1/b2) - exp(-1/b1)))
ans[which(ans == 1/q[k])] = Inf
return(ans)
}
# define the starting value for the optimization to find the conditional return level
start_val = returnlevels(GEVparam = GEVparam, q = q[k])
# calculate conditional return levels
opt = suppressWarnings(nlminb(start_val, f))
# if optimization was not successful (value of f >= 1e-03)),
# try to find better solution with different starting value
opt1 = opt
j = 0
while (opt$objective >= 1e-03 && j <= 17) {
l = 1.5 + (-1)^j*floor((j+1)/2)*0.1
start_val_new = start_val*l
if (!is.infinite(f(start_val_new))) {
opt = suppressWarnings(nlminb(start_val_new, f))
}
j = j + 1
}
if (opt1$objective <= opt$objective) {
opt = opt1
}
if (opt$objective >= 1e-03) {
opt_seq = seq(0.8*start_val[k], 1.5*start_val[k], by = 0.001)
opt_ind = which.min(f(opt_seq))
if (all(is.na(f(opt_seq)))) {
cond_rl[k] = NA
objectives[k] = NA
warning("probability that conditioned variable is greater than 'cond_B' is zero -- change 'cond_B'")
} else if (f(opt_seq[opt_ind]) <= opt$objective) {
cond_rl[k] = opt_seq[opt_ind]
objectives[k] = f(opt_seq[opt_ind])
} else {
cond_rl[k] = opt$par
objectives[k] = opt$objective
}
} else {
cond_rl[k] = opt$par
objectives[k] = opt$objective
}
}
} else if (model == "ext-t") {
# define the correlation function for the Extremal-t model
matern_h = function(h,alpha,kappa) {
2^(1-kappa)/gamma(kappa)*(h/alpha)^kappa*besselK(h/alpha, kappa)
}
# define the correlation parameters
alpha = cor_coeff["alpha"]
sd_kappa = cor_coeff["sd_kappa"]
swe_kappa = cor_coeff["swe_kappa"]
rho12 = cor_coeff["rho12"]
nu = cor_coeff["nu"]
# calculate correlations or cross-correlations, depending on 'same_var'
if (same_var) {
if (var == "sd") {
matern = matern_h(h,alpha,sd_kappa)
} else if (var == "swe") {
matern = matern_h(h,alpha,swe_kappa)
}
} else{
matern = rho12*matern_h(h,alpha,1/2*(sd_kappa + swe_kappa))
matern[which(is.na(matern))] = rho12
}
# predefine conditional return level and objectives vector
cond_rl = rep(NA,times = length(q))
objectives = rep(NA,times = length(q))
# find the conditional return level for every return period in q
for (k in 1:length(q)) {
# define function f calculating abs(1/q[k] - the conditional probability),
# which will be minimized in order to find the 1-q[k] quantil of the conditional distribution
f = function(B) {
a = gev2frech(B, loc = as.numeric(GEVparam["loc"]), scale = as.numeric(GEVparam["scale"]),
shape = as.numeric(GEVparam["shape"]))
help = ((nu + 1)/(1 - matern^2))^(1/2)
P_sd_swe_1 = exp(-1/a*pt(help*((b1/a)^(1/nu) - matern), df = nu + 1) -
1/b1*pt(help*((a/b1)^(1/nu) - matern), df = nu + 1))
P_sd_swe_2 = exp(-1/a*pt(help*((b2/a)^(1/nu) - matern), df = nu + 1) -
1/b2*pt(help*((a/b2)^(1/nu) - matern), df = nu + 1))
ans = abs(1/q[k] - (exp(-1/b2) - exp(-1/b1) - P_sd_swe_2 + P_sd_swe_1)/(exp(-1/b2) - exp(-1/b1)))
ans[which(ans == 1/q[k])] = Inf
return(ans)
}
# define the starting value for the optimization to find the conditional return level
start_val = returnlevels(GEVparam = GEVparam, q = q[k])
# calculate conditional return levels
opt = suppressWarnings(nlminb(start_val, f))
# if optimization was not successful (value of f >= 1e-03)),
# try to find better solution with different starting value
opt1 = opt
j = 0
while (opt$objective >= 1e-03 && j <= 17) {
l = 1.5 + (-1)^j*floor((j+1)/2)*0.1
start_val_new = start_val*l
if (!is.infinite(f(start_val_new))) {
opt = suppressWarnings(nlminb(start_val_new, f))
}
j = j + 1
}
if (opt1$objective <= opt$objective) {
opt = opt1
}
if (opt$objective >= 1e-03) {
opt_seq = seq(0.8*start_val[k], 1.5*start_val[k], by = 0.001)
opt_ind = which.min(f(opt_seq))
if (all(is.na(f(opt_seq)))) {
cond_rl[k] = NA
objectives[k] = NA
warning("probability that conditioned variable is greater than 'cond_B' is zero -- change 'cond_B'")
} else if (f(opt_seq[opt_ind]) <= opt$objective) {
cond_rl[k] = opt_seq[opt_ind]
objectives[k] = f(opt_seq[opt_ind])
} else {
cond_rl[k] = opt$par
objectives[k] = opt$objective
}
} else {
cond_rl[k] = opt$par
objectives[k] = opt$objective
}
}
}
if (printObjectives) {
print(summary(objectives))
}
# define dataframe with 'cond_rl' and 'q'
df = data.frame(cond_rl = cond_rl, q = q)
# define plottitle
if (missing(plottitle)) {
plottitle = "conditional return level plot"
}
# define breaks and labels
b = period_range[1]*2^(0:10)
b = c(b[which(b < period_range[2])],period_range[2])
l = b
# prepare GEV parameters for the ggplot
GEV = paste0("loc = ",round(GEVparam["loc"], digits = 2),
", scale = ",round(GEVparam["scale"], digits = 2),
", shape = ",round(GEVparam["shape"], digits = 2))
# create plot
if (missing(obs)) {
plot = ggplot(df,aes(x = q, y = cond_rl)) +
geom_line() +
scale_x_log10(name = "return period",
breaks = b,
labels = l) +
scale_y_continuous(name = "conditional return level") +
geom_label(aes(label = GEV, x = b[1], y = max(cond_rl, na.rm = TRUE)), hjust = 0, vjust = 1, size = 3) +
ggtitle(plottitle)
} else {
r = quantile(obs, 1-1/q, names = FALSE)
df.obs = data.frame(rl = r, q = q)
plot = ggplot(df,aes(x = q, y = cond_rl)) +
geom_line() +
geom_point(data = df.obs, aes(x = q, y = rl)) +
scale_x_log10(name = "return period",
breaks = b,
labels = l) +
scale_y_continuous(name = "conditional return level") +
geom_label(aes(label = GEV, x = b[1], y = max(max(df$cond_rl, na.rm = TRUE), max(df.obs$rl, na.rm = TRUE))),
hjust = 0, vjust = 1, size = 3) +
ggtitle(plottitle)
}
# define save name
if (!missing(save_name)) {
plotname = paste0(save_name,".pdf",sep = "")
# plot is saved to given directory
path = save_dir
message(sprintf("plot was saved as '%s' to directory: \n '%s'",plotname,path))
# save plot
ggsave(filename = plotname, plot = plot, path = path, width = 7, height = 7)
}
# print plot if 'printPlot' is TRUE
if (printPlot) {
print(plot)
}
#---------------------------------------------------------------------------------------------------------------#
}
Any scripts or data that you put into this service are public.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.