Calculates joint return periods

Calculates joint return periods via simulation. A large number of realizations are simulated from the copulas fit to the conditioned samples, in proportion with the sizes of the conditional samples. The realizations are transformed to the original scale and the relevant probabilities estimated empirically.

Usage

Joint_RP_2D(
  Data,
  Data_Con1,
  Data_Con2,
  u1,
  u2,
  Thres1 = NA,
  Thres2 = NA,
  Copula_Family1,
  Copula_Family2,
  Marginal_Dist1,
  Marginal_Dist2,
  Con1 = "Rainfall",
  Con2 = "OsWL",
  mu = 365.25,
  RP_Var1,
  RP_Var2,
  Var1 = NA,
  Var2 = NA,
  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,
  DecP = 2,
  N = 10^6
)

Arguments

Data: Data frame containing two co-occurring time series.
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 (quantile) threshold above which the variable in the first column was sampled in Data_Con1.
u2: Numeric vector of length one specifying the (quantile) threshold 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.
RP_Var1: Numeric vector of length one specifying the univariate return period of variable Con1.
RP_Var2: Numeric vector of length one specifying the univariate return period of variable Con2.
Var1: Numeric vector specifying the values of the variable in the first column of Data. Default is NA.
Var2: Numeric vector specifying the values of the variable in the second column of Data. Default is NA.
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.
DecP: Numeric vector of length one specifying the number of decimal places to round the data in the conditional samples to in order to identify observations in both conditional samples. Default is 2.
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

Value

Console output is a vector RP_Copula of the joint return period of the specified (Var1,Var2) events according to the conditional sampling - copula theory approach.

Examples

con.sample.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)
con.sample.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)
con.sample.OsWL$Data$Rainfall <- con.sample.OsWL$Data$Rainfall +
                                     runif(length(con.sample.OsWL$Data$Rainfall),0.001,0.01)
cop.Rainfall<-Copula_Threshold_2D(Data_Detrend=S22.Detrend.df[,-c(1,4)],
                                  Data_Declust=S22.Detrend.Declustered.df[,-c(1,4)],u1 =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

cop.OsWL<-Copula_Threshold_2D(Data_Detrend=S22.Detrend.df[,-c(1,4)],
                              Data_Declust=S22.Detrend.Declustered.df[,-c(1,4)],u2 =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

#Joint excedence probability of a 5 inch rainfall and 2 ft O-sWL at S-22.
Joint_RP_2D(Data=S22.Detrend.df,
            Data_Con1=con.sample.Rainfall$Data, Data_Con2=con.sample.OsWL$Data,
            u1=0.98, u2=0.98,
            Copula_Family1=cop.Rainfall,Copula_Family2=cop.OsWL,
            Marginal_Dist1="Logis", Marginal_Dist2="BS",
            Con1 = "Rainfall", Con2 = "OsWL",
            mu = 365.25,
            RP_Var1 =10, RP_Var2 =10,
            x_lab = "Rainfall (Inches)", y_lab = "O-sWL (ft NGVD 29)",
            y_lim_max = 10,
            N=10^7)
#> Warning: NaNs produced
#> Warning: NaNs produced
#> Warning: NaNs produced
#> Warning: NaNs produced
#> [1] 50.79394

Usage

Arguments

Value

See also

Examples