Design_Event_2D_NEW: Derives a single or ensemble of bivariate design events

In CoRE-Lab-UCF/MultiHazard-R-Package: Tools for modeling compound events

Derives a single or ensemble of bivariate design events

Description

Calculates the isoline and relative probability of events on the isoline, given the observational data, for one or more user-specified return periods. Outputs the single "most-likely" design event or an ensemble of possible design events obtained by sampling along the isoline according to these relative probabilities. The design event under the assumption of full dependence is also computed.

Usage

Design_Event_2D_NEW(
  Data,
  Data_Con1,
  Data_Con2,
  u1,
  u2,
  Thres1 = NA,
  Thres2 = NA,
  Copula_Family1,
  Copula_Family2,
  Marginal_Dist1,
  Marginal_Dist2,
  GPD1,
  GPD2,
  Con1 = "Rainfall",
  Con2 = "OsWL",
  mu = 365.25,
  GPD_Bayes = TRUE,
  RP,
  Interval = 10000,
  x_lab = "Rainfall (mm)",
  y_lab = "O-sWL (mNGVD 29)",
  x_lim_min = NA,
  x_lim_max = NA,
  y_lim_min = NA,
  y_lim_max = NA,
  N = 10^6,
  N_Ensemble = 0,
  Sim_Max = 10,
  Plot_Quantile_Isoline = FALSE,
  Isoline_Type = "Combined"
)

Arguments

Data	Data frame of dimension nx2 containing two co-occurring time series of length n.
Data_Con1	Data frame containing the conditional sample (declustered excesses paired with concurrent values of other variable), conditioned on the variable in the first column.
Data_Con2	Data frame containing the conditional sample (declustered excesses paired with concurrent values of other variable), conditioned on the variable in the second column. Can be obtained using the Con_Sampling_2D function.
u1	Numeric vector of length one specifying the threshold, expressed as a quantile, above which the variable in the first column was sampled in Data_Con1.
u2	Numeric vector of length one specifying the threshold, expressed as a quantile, above which the variable in the second column was sampled in Data_Con2.
Thres1	Numeric vector of length one specifying the threshold above which the variable in the first column was sampled in Data_Con1. Only one of u1 and Thres1 should be supplied. Default is NA.
Thres2	Numeric vector of length one specifying the threshold above which the variable in the second column was sampled in Data_Con2. Only one of u2 and Thres2 should be supplied. Default is NA.
Copula_Family1	Numeric vector of length one specifying the copula family used to model the Data_Con1 dataset.
Copula_Family2	Numeric vector of length one specifying the copula family used to model the Data_Con2 dataset. Best fitting of 40 copulas can be found using the Copula_Threshold_2D function.
Marginal_Dist1	Character vector of length one specifying (non-extreme) distribution used to model the marginal distribution of the non-conditioned variable in Data_Con1.
Marginal_Dist2	Character vector of length one specifying (non-extreme) distribution used to model the marginal distribution of the non-conditioned variable in Data_Con2.
Con1	Character vector of length one specifying the name of variable in the first column of Data.
Con2	Character vector of length one specifying the name of variable in the second column of Data.
mu	Numeric vector of length one specifying the (average) occurrence frequency of events in Data. Default is 365.25, daily data.
GPD_Bayes	Logical; indicating whether to use a Bayesian approach to estimate GPD parameters. This involves applying a penalty to the likelihood to aid in the stability of the optimization procedure. Default is TRUE.
RP	Numeric vector specifying the return periods of interest.
Interval	Numeric vector specifying the number of equally spaced points comprising the combined isoline.
x_lab	Character vector specifying the x-axis label.
y_lab	Character vector specifying the y-axis label.
x_lim_min	Numeric vector of length one specifying x-axis minimum. Default is NA.
x_lim_max	Numeric vector of length one specifying x-axis maximum. Default is NA.
y_lim_min	Numeric vector of length one specifying y-axis minimum. Default is NA.
y_lim_max	Numeric vector of length one specifying y-axis maximum. Default is NA.
N	Numeric vector of length one specifying the size of the sample from the fitted joint distributions used to estimate the density along an isoline. Samples are collected from the two joint distribution with proportions consistent with the total number of extreme events conditioned on each variable. Default is 10^6
N_Ensemble	Numeric vector of length one specifying the number of possible design events sampled along the isoline of interest.
Sim_Max	Numeric vector of length one specifying the maximum value, given as a multiple of the largest observation of each variable, permitted in the sample used to estimate the (relative) probabilities along the isoline.
Plot_Quantile_Isoline	Logical; indicating whether to first plot the quantile isoline. Default is FALSE.
Isoline_Type	Character vector of length one specifying the type of isoline. For isolines obtained using the overlaying method in Bender et al. (2016) use "Combined" (default). For quantile isoline from the sample conditioned variable Con1|(Con2) on use "Con1"("Con2").

Value

Plot of all the observations (grey circles) as well as the declustered excesses above Thres1 (blue circles) or Thres2 (blue circles), observations may belong to both conditional samples. Also shown is the isoline associated with RP contoured according to their relative probability of occurrence on the basis of the sample from the two joint distributions, the "most likely" design event (black diamond), and design event under the assumption of full dependence (black triangle) are also shown in the plot. The function also returns a list comprising the design events assuming full dependence "FullDependence", as well as once the dependence between the variables is accounted for the "Most likley" "MostLikelyEvent" as well as an "Ensemble" of possible design events.

See Also

Copula_Threshold_2D Diag_Non_Con Diag_Non_Con_Trunc

Examples

S22.Rainfall<-Con_Sampling_2D(Data_Detrend=S22.Detrend.df[,-c(1,4)],
                             Data_Declust=S22.Detrend.Declustered.df[,-c(1,4)],
                             Con_Variable="Rainfall",u=0.97)
S22.OsWL<-Con_Sampling_2D(Data_Detrend=S22.Detrend.df[,-c(1,4)],
                         Data_Declust=S22.Detrend.Declustered.df[,-c(1,4)],
                         Con_Variable="OsWL",u=0.97)
S22.Copula.Rainfall<-Copula_Threshold_2D(Data_Detrend=S22.Detrend.df[,-c(1,4)],
                                        Data_Declust=S22.Detrend.Declustered.df[,-c(1,4)],u =0.97,
                                        y_lim_min=-0.075,y_lim_max=0.25,
                                        Upper=c(2,9),Lower=c(2,10),GAP=0.15)$Copula_Family_Var1
S22.Copula.OsWL<-Copula_Threshold_2D(Data_Detrend=S22.Detrend.df[,-c(1,4)],
                                    Data_Declust=S22.Detrend.Declustered.df[,-c(1,4)],u =0.97,
                                    y_lim_min=-0.075, y_lim_max =0.25,
                                    Upper=c(2,9),Lower=c(2,10),GAP=0.15)$Copula_Family_Var2
Design_Event_2D(Data=S22.Detrend.df[,-c(1,4)],
               Data_Con1=S22.Rainfall$Data, Data_Con2=S22.OsWL$Data,
               u1=0.97, u2=0.97,
               Copula_Family1=S22.Copula.Rainfall, Copula_Family2=S22.Copula.OsWL,
               Marginal_Dist1="Logis", Marginal_Dist2="Twe",
               RP=100,Interval=10000,N=10,N_Ensemble=10,
               Plot_Quantile_Isoline=FALSE)

CoRE-Lab-UCF/MultiHazard-R-Package documentation built on April 14, 2025, 8:31 a.m.