Conditional_RP_2D: Calculates joint and conditional return periods

In rjaneUCF/MultiHazard: Tools for modeling compound events

Calculates joint and conditional return periods

Description

Univariate return period events are obtained from the GPDs to be consistent with the isolines produced by the Design_Event_2D function. To find the conditional probabilities 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

Conditional_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,
  Con_Var,
  RP_Con,
  RP_Non_Con,
  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
)

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 (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.
Con_Var	Character vector of length one specifying the (column) name of the conditioning variable.
RP_Con	Numeric vector of length one specifying the return period of the conditioning variable Con_Var.
RP_Non_Con	Numeric vector of length one specifying the return period of the non-conditioning variable.
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:

• Con_Var Name of the conditioning variable

• RP_Var1 Return period of variable Con1 i.e., variable in second column of Data

• RP_Var2 Return period of variable Con2 i.e., variable in third column of Data

• Var1 Value of Con1 at the return period of interest i.e. RP_Var1

• Var2 Value of Con2 at the return period of interest i.e. RP_Var2

• RP_Full_Dependence Joint return period of the (Var1,Var2) event under full dependence

• RP_Independence Joint return period of the (Var1,Var2) event under independence

• RP_Copula Joint return period of the (Var1,Var2) event according to the two sided conditional sampling - copula theory approach

• Prob Probability associated with RP_Copula

• N_Excess Number of realizations of the Con_Var above RP_Con-year return period value

• Non_Con_Var_X Values of the non-conditioned variable of the (conditional) Cummulative Distribution Function (CDF) i.e. x-axis of bottom left plot

• Con_Prob Con_Prob CDF of the non-conditioned variable given the return period of Con_Var exceeds RP_Con

• Con_Prob_Est Probability the non-conditioned variable is less than or equal to RP_Non_Con given the return period of Con_Var exceeds RP_Con

Graphical output:

• Top left: Sample conditioned on Con1 (red crosses) and Con2 (blue circles). Black dot is the event with a marginal return period of the conditioned variable Var_Con and non-conditioned variable equal to RP_Con and RP_Non_Con, respectively. The joint return period of the event using the conditional sampling - copula theory approach and under the assumptions of full dependence and independence between the variables are printed.

• Top right: Sample conditioned on Con1 (red crosses) and Con2 (blue circles). Only the region where Con_Var exceeds RP_Con is visible. This is the region for which the conditional distribution (of the non-conditioned variable given Con_Var exceeds RP_Con) and in turn conditional return periods are calculated.

• Bottom left: Conditional Cumulative Distribution Function (CDF) of the non-conditioned variable given the marginal return period of the conditioned variable Var_Con exceeds RP_Con years i.e. the points visible in the top right plot.

• Bottom right: Conditional return period of the non-conditioned variable given the conditioned variable Var_Con has a return period longer than RP_Con.

See Also

Design_Event_2D

Examples

#Under a 10yr (or greater) rainfall event condition, what is the joint probability that a 10yr
#O-sWLevent occurs simultaneously?  What is the cumulative probability of events with the
#frequency equal to or less than a 10yr O-sWL event?
Conditional_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,
                  Con_Var="Rainfall",
                  RP_Con=10, RP_Non_Con=10,
                  x_lab = "Rainfall (Inches)", y_lab = "O-sWL (ft NGVD 29)",
                  y_lim_max = 10,
                  N=10^7)

rjaneUCF/MultiHazard documentation built on April 20, 2024, 12:48 a.m.