cond_returnlevels {SpatialModelsZAMG} | R Documentation |
this function calculates conditional return levels.
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 .
cond_returnlevels(locations, GEVparam, q, cond_locations, cond_GEVparam, same_var, cor_coeff, cond_B, cond_B_2 = Inf, var = NULL, model = "ext-t", printObjectives = FALSE)
locations |
a matrix or vector with certain location characteristics as columns/entries. each row corresponds to one location, columns are for example: longitude, latitude and altitude |
GEVparam |
a named matrix or vector with the GEV parameters of the variable for which the conditional return levels are calculated.
each row corresponds to one location (same ones as in |
q |
the return period for the calculation of the conditional return levels – must be a number greater than 1 |
cond_locations |
a matrix or a vector with the location characteristics of the conditioned locations.
each row corresponds to one location, columns should be the same as in |
cond_GEVparam |
a named matrix or vector with the GEV parameters of the conditioned variable.
each row corresponds to one location (same ones as in |
same_var |
logical value; if |
cor_coeff |
a named vector with the correlation parameters. |
cond_B |
a vector of real numbers as the lower barriers of the conditioned variable (e.g. the return levels) |
cond_B_2 |
a vector of real numbers as the upper barriers of the conditioned variable. |
var |
a character string being either |
model |
a character string; chose which bivariate max-stable model should be used to calculate the conditional return levels. this should be either |
printObjectives |
logical value; if 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) (e.g. sd or swe) exceeds B, given that Z2(x2) (e.g. swe or sd) is in between cond_B and cond_B_2; |
a vector with the conditional return levels
Genton, M.G. & Padoan, S.A. & Sang, H. (2015): Multivariate max-stable spatial processes. Biometrika 102(1): 215-230.
http://repository.kaust.edu.sa/kaust/bitstream/10754/552385/1/2013.GPS.Biometrika.Rev_14.pdf
GEVparameters_from_models
,
cond_returnlevel_plot
,
cond_returnlevel_map
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returnlevels
# get covariables lon = get(data(lon.at)) lon = as.vector(t(lon)) lat = get(data(lat.at)) lat = as.vector(t(lat)) alt = get(data(alt.at)) alt = as.vector(t(alt)) x = get(data(sample_grid_data)) mdday = x$mdday sd_mmax = x$mmsd swe_mmax = x$mmswe # take only locations of the (Austrian) domain lon = lon[which(!is.na(mdday))] lat = lat[which(!is.na(mdday))] alt = alt[which(!is.na(mdday))] mdday = mdday[which(!is.na(mdday))] sd_mmax = sd_mmax[which(!is.na(sd_mmax))] swe_mmax = swe_mmax[which(!is.na(swe_mmax))] # define matrix 'covariables' covariables = cbind("lon" = lon, "lat" = lat, "alt" = alt, "mdday" = mdday, "sd_mmax" = sd_mmax, "swe_mmax" = swe_mmax) # load function output from GEVparameters_from_models sd_GEVparam = get(data("sd_GEVparam")) swe_GEVparam = get(data("swe_GEVparam")) # load function output from optimizer_biv_hr_model data("optim_hr") # define coefficients sd_coeff = optim_hr$coefficients$sd_coeff swe_coeff = optim_hr$coefficients$swe_coeff cor_coeff = optim_hr$coefficients$cor_coeff # define return period (same as in sd_GEVparam) q = 100 # calculate return levels sd_rl = returnlevels(GEVparam = sd_GEVparam, q = q) swe_rl = returnlevels(GEVparam = swe_GEVparam, q = q) # sd given swe at same locations cond_rl_sd = cond_returnlevels(locations = covariables, GEVparam = sd_GEVparam, q = q, cond_locations = covariables, cond_GEVparam = swe_GEVparam, same_var = FALSE, cond_B = swe_rl, cor_coeff = cor_coeff, model = "hr", printObjectives = TRUE) # swe given sd at same location cond_rl_swe = cond_returnlevels(locations = covariables, GEVparam = swe_GEVparam, q = q, cond_locations = covariables, cond_GEVparam = sd_GEVparam, same_var = FALSE, cond_B = sd_rl, cor_coeff = cor_coeff, model = "hr", printObjectives = TRUE) # sd given sd in ibk ibk = c("lon" = 11.392778, "lat" = 47.267222, "alt" = 574, "mdday" = 6.12, "sd_mmax" = 16.8, "swe_mmax" = 29) sd_GEVparam_ibk = GEVparameters_from_models(ibk, sd_coeff) sd_rl_ibk = returnlevels(GEVparam = sd_GEVparam_ibk, q = q) cond_rl_ibk = cond_returnlevels(locations = covariables, GEVparam = sd_GEVparam, q = q, cond_locations = ibk, cond_GEVparam = sd_GEVparam_ibk, same_var = TRUE, cond_B = sd_rl_ibk, cor_coeff = cor_coeff, model = "hr", printObjectives = TRUE)