ProbPlot {FloodFreqPlot}

Flood Probability Plotting

Description

ProbPlot checks that a probability distribution fits a set of flood data.

Usage

ProbPlot(
  data_obs,
  probs = NULL,
  PP = NULL,
  dist = NULL,
  T_rp = NULL,
  beta_CL = NULL,
  T_lim = NULL,
  Q_lim = NULL,
  main_title = NULL,
  x_lab = NULL,
  y_lab = NULL,
  Pcol = "black",
  Ppch = 1,
  Pcex = 1,
  Lcol = "blue",
  Lty = 1,
  Lwd = 1.5,
  CPlot = TRUE,
  CLcol = "red",
  CLty = 2,
  CLwd = 1.5,
  QTcol = "green",
  QTpch = 15,
  QTcex = 1.5,
  GumbRV = FALSE,
  P3SkewCheck = TRUE
)

Arguments

data_obs

A vector, data frame or matrix containing observed data or flood quantiles.

probs

Optional. The vector of plotting position probability values corresponding to the quantiles. If probs = NULL, then a Weibull plotting position formula is used to calculate probability values for quantiles.

PP

Optional. A character string that represents the plotting position formula used to calculate the empirical probability. The formula can be chosen from the list: "Blom", "California_1", "California_2", "Chegodayev", "Gringorten", "Hazen", "Tukey", and "Weibull". If PP = NULL, then PP = 'Weibull'.

dist

Optional. A string that represents CDF and it can be 'Norm' for Normal distribution, 'LNorm' for Log-Normal distribution, 'Gumb' for Gumbel distribution, 'Pea3' for Pearson type III distribution, and 'LPea3' for Log-Pearson type III distribution. If dist = NULL, then dist = 'Norm'.

T_rp

Optional. A numeric vector including the return periods of interest for the flood quantile estimation.

beta_CL

Optional. A numeric scalar that represents the confidence level for calculating and plotting the confidence limits (bounds). If beta_CL = NULL, then beta_CL = 0.95. It means that the significance level is equal to 0.05.

T_lim

Optional. A two-member numeric vector including the lower and upper return period limits determining the horizontal (x) axis range.

Q_lim

Optional. A two-member numeric vector including the lower and upper limits determining the vertical (y) axis range to show quantile values.

main_title

Optional. A character string representing the main title of the plot. The default title denotes the name of the theoretical probability distribution chosen to fit the data.

x_lab

Optional. A character string representing the label of horizontal axis. The default label of the axis is F(x) = P(X <= x).

y_lab

Optional. A character string representing the label of vertical axis. The default label of the axis is "Quantile".

Pcol

Optional. A specification for the observed flood quantile points color. Defaults to "black".

Ppch

Optional. Either an integer specifying a symbol or a single character to be used as the default in plotting observed flood quantile points. See points for possible values and their interpretation. Defaults to 1.

Pcex

Optional. A numerical value giving the amount by which plotting point symbols should be magnified relative to the default. Defaults to 1.

Lcol

Optional. A specification for the theoretical probability line color. Defaults to "blue".

Lty

Optional. The theoretical probability line type. Line types can either be specified as an integer (0=blank, 1=solid (default), 2=dashed, 3=dotted, 4=dotdash, 5=longdash, 6=twodash) or as one of the character strings "blank", "solid", "dashed", "dotted", "dotdash", "longdash", or "twodash", where "blank" uses 'invisible lines' (i.e., does not draw them). Defaults to 1.

Lwd

Optional. The theoretical probability line width, a positive number, defaulting to 1.5.

CPlot

Logical. If CPlot = TRUE, the confidence limits (bounds) are plotted. Defaults to TRUE.

CLcol

Optional. A specification for the confidence limits (bounds) color. Defaults to "red".

CLty

Optional. The confidence limits (bounds) line type. Line types can either be specified as an integer (0=blank, 1=solid (default), 2=dashed, 3=dotted, 4=dotdash, 5=longdash, 6=twodash) or as one of the character strings "blank", "solid", "dashed", "dotted", "dotdash", "longdash", or "twodash", where "blank" uses 'invisible lines' (i.e., does not draw them). Defaults to 1.

CLwd

Optional. The confidence limits (bounds) line width, a positive number, defaulting to 1.5.

QTcol

Optional. A specification for the T-year flood quantile estimate point color. Defaults to "green".

QTpch

Optional. Either an integer specifying a symbol or a single character to be used as the default in plotting the T-year flood quantile estimate points. See points for possible values and their interpretation. Defaults to 15.

QTcex

Optional. A numerical value giving the amount by which the T-year flood quantile estimate point symbols should be magnified. Defaults to 1.5.

GumbRV

Logical. If dist = 'Gumb' and GumbRV = 'TRUE', an extra horizontal axis is plotted to show Reduced Variable values.

P3SkewCheck

Logical. If P3SkewCheck = 'TRUE' (default), the skewness of data is checked and if the coefficient of skewness is greater than 2.5, the confidence limits are not plotted for some data in the left tail of the dataset.

Details

This is a function for frequency analysis by a graphical method. The flood data are plotted on an appropriate probability paper that linearizes the cumulative distribution function. Then the plotted flood data are fitted with a straight line for interpolation and extrapolation purposes. If probs = NULL, then a Weibull plotting position formula is used to calculate probability values for quantiles. If PP = NULL, then a Weibull plotting position formula is used to calculate the probabilities corresponding to the quantiles. If dist = NULL, then Normal distribution is used as the default frequency distribution. It should be noted that the distribution parameters are estimated by Method Of Moments (MOM). If beta_CL = NULL, then the confidence level is considered equal to 0.95 (that means the significance level is equal to 1-0.95=0.05).

Value

The function returns a graph including the plotted flood data and the fitted distribution and the confidence limits (bounds). Also, it returns and shows the flood quantile estimates corresponding to the return period(s) T_rp.

See Also

PlotPos for the plotting position probability.

Examples

# First Example
data('Harricana')
ProbPlot(data_obs = Harricana, PP = 'Cunnane', dist = 'LPea3', T_rp = c(100, 1000))

# Second Example
data('AH_Tab12_1_1')
ProbPlot(data_obs = AH_Tab12_1_1, PP = 'Weibull', dist = 'Gumb', T_rp = 250, T_lim = c(2, 1000))