,
S. Saeid Mousavi Nadoushani [aut]| Title: | Flood Probability Plotting and Graphical Frequency Analysis |
|---|---|
| Description: | Plotting flood quantiles and their corresponding probabilities (return periods) on the probability papers. The details of relevant methods are available in Chow et al (1988, ISBN: 007070242X, 9780070702424), and Bobee and Ashkar (1991, ISBN: 0918334683, 9780918334688). |
| Authors: | Ali Ahani [aut, cre] ,
S. Saeid Mousavi Nadoushani [aut] |
| Maintainer: | Ali Ahani <[email protected]> |
| License: | GPL (>= 3) |
| Version: | 0.1.0 |
| Built: | 2025-01-24 04:39:02 UTC |
| Source: | https://github.com/cran/FloodFreqPlot |
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.
A dataset containing annual maximum discharges (in cfs) of the Guadalupe River near Victoria, Texas, during 1935-1978, in cfs extracted from TABLE 12.1.1 of "Applied Hydrology" (Chow et al., 1987).
A data frame with 44 rows and 1 variable:
annual maximum discharges in cfs
...
Chow, V. T., Maidment, D. R., & Mays, L. W. (1988). Applied Hydrology. McGraw-Hill, New York, U. S.
A dataset containing annual maximum 10-minute rainfall (in inches) at Chicago, Illinois, during 1913-1947 extracted from TABLE 12.2.1 of "Applied Hydrology" (Chow et al., 1987).
A data frame with 35 rows and 1 variable:
annual maximum 10-minute rainfall in inches
...
Chow, V. T., Maidment, D. R., & Mays, L. W. (1988). Applied Hydrology. McGraw-Hill, New York, U. S.
A dataset containing the U.S. Geological Survey gage 01614000 Back Creek near Jones Springs, West Virginia annual peak-flow record consisting of 56 peaks during 1929-2012, including the 1936 historical flood, extracted from Table 10.10 in "Guidelines for determining flood flow frequency - Bulletin 17C" (England et al., 2019)
A data frame with 56 rows and 1 variable:
peak flows in cfs
This table contains the date of the annual peak recorded at the gage, the water year of the annual peak, and the corresponding annual peak in cubic feet per second (ft3/s).
England, J. F., Jr., Cohn, T. A., Faber, B. A., Stedinger, J. R., Thomas, W. O., Jr., Veilleux, A. G., Kiang, J. E., & Mason, R. R., Jr. (2019). Guidelines for determining flood flow frequency - Bulletin 17C. U.S. Geological Survey.
A dataset containing the U.S. Geological Survey gage 07099500 (and others) Arkansas River annual peak-flow record consisting of 85 peaks from 1864 to 1976 extracted from Table 10.14 in "Guidelines for determining flood flow frequency - Bulletin 17C" (England et al., 2019)
A data frame with 85 rows and 1 variable:
peak flows in cfs
This table contains the water year of the annual peak and the corresponding annual peak in cubic feet per second (ft3/s).
England, J. F., Jr., Cohn, T. A., Faber, B. A., Stedinger, J. R., Thomas, W. O., Jr., Veilleux, A. G., Kiang, J. E., & Mason, R. R., Jr. (2019). Guidelines for determining flood flow frequency - Bulletin 17C. U.S. Geological Survey.
A dataset containing the U.S. Geological Survey gage 05489490 Bear Creek at Ottumwa, Iowa annual peak-flow record consisting of 49 peaks from 1965 to 2014 extracted from Table 10.18 in "Guidelines for determining flood flow frequency - Bulletin 17C" (England et al., 2019)
A data frame with 50 rows and 1 variable:
peak flows in cfs
This table contains the date of the annual peak recorded at the gage, the water year of the annual peak, and the corresponding annual peak in cubic feet per second (ft3/s).
England, J. F., Jr., Cohn, T. A., Faber, B. A., Stedinger, J. R., Thomas, W. O., Jr., Veilleux, A. G., Kiang, J. E., & Mason, R. R., Jr. (2019). Guidelines for determining flood flow frequency - Bulletin 17C. U.S. Geological Survey.
A dataset containing the U.S. Geological Survey gage 01134500 Moose River at Victory, Vermont annual peak-flow record consisting of 68 peaks from 1947 to 2014 extracted from Table 10.2 in "Guidelines for determining flood flow frequency - Bulletin 17C" (England et al., 2019)
A data frame with 68 rows and 1 variable:
peak flows in cfs
This table contains the date of the annual peak recorded at the gage, the water year of the annual peak, and the corresponding annual peak in cubic feet per second (ft3/s).
England, J. F., Jr., Cohn, T. A., Faber, B. A., Stedinger, J. R., Thomas, W. O., Jr., Veilleux, A. G., Kiang, J. E., & Mason, R. R., Jr. (2019). Guidelines for determining flood flow frequency - Bulletin 17C. U.S. Geological Survey.
A dataset containing the U.S. Geological Survey gage 09480000 Santa Cruz River near Lochiel, Arizona annual peak-flow record consisting of 65 peaks from 1949 to 2013 extracted from Table 10.18 in "Guidelines for determining flood flow frequency - Bulletin 17C" (England et al., 2019)
A data frame with 65 rows and 1 variable:
peak flows in cfs
This table contains the date of the annual peak recorded at the gage, the water year of the annual peak, and the corresponding annual peak in cubic feet per second (ft3/s).
England, J. F., Jr., Cohn, T. A., Faber, B. A., Stedinger, J. R., Thomas, W. O., Jr., Veilleux, A. G., Kiang, J. E., & Mason, R. R., Jr. (2019). Guidelines for determining flood flow frequency - Bulletin 17C. U.S. Geological Survey.
A dataset containing the U.S. Geological Survey gage 11274500 Orestimba Creek near Newman, California annual peak-flow record consisting of 82 peaks from 1932 to 2013 extracted from Table 10.6 in "Guidelines for determining flood flow frequency - Bulletin 17C" (England et al., 2019)
A data frame with 82 rows and 1 variable:
peak flows in cfs
This table contains the date of the annual peak recorded at the gage, the water year of the annual peak, and the corresponding annual peak in cubic feet per second (ft3/s).
England, J. F., Jr., Cohn, T. A., Faber, B. A., Stedinger, J. R., Thomas, W. O., Jr., Veilleux, A. G., Kiang, J. E., & Mason, R. R., Jr. (2019). Guidelines for determining flood flow frequency - Bulletin 17C. U.S. Geological Survey.
A dataset containing the summary of concurrent observed annual peak data for the Etowah River and Suwanee Creek from 1985-2004 extracted from Table 8.1 in "Guidelines for determining flood flow frequency - Bulletin 17C" (England et al., 2019)
A data frame with 20 rows and 2 variables:
name of the crop
the crop coefficient in the growth initial stage
England, J. F., Jr., Cohn, T. A., Faber, B. A., Stedinger, J. R., Thomas, W. O., Jr., Veilleux, A. G., Kiang, J. E., & Mason, R. R., Jr. (2019). Guidelines for determining flood flow frequency - Bulletin 17C. U.S. Geological Survey.
A dataset containing the MOVE extended record for 13 years (1972-1984) for Suwanee Creek at Suwanee, Georgia (station 02334885) extracted from Table 8.2 in "Guidelines for determining flood flow frequency - Bulletin 17C" (England et al., 2019)
A data frame with 13 rows and 1 variable:
peak flows in cfs
England, J. F., Jr., Cohn, T. A., Faber, B. A., Stedinger, J. R., Thomas, W. O., Jr., Veilleux, A. G., Kiang, J. E., & Mason, R. R., Jr. (2019). Guidelines for determining flood flow frequency - Bulletin 17C. U.S. Geological Survey.
A dataset containing the flood records for 93 years (1892-1984) for the Etowah River at Canton, Georgia (station 02335000) extracted from Table 8.3 in "Guidelines for determining flood flow frequency - Bulletin 17C" (England et al., 2019)
A data frame with 93 rows and 1 variable:
peak flows in cfs
England, J. F., Jr., Cohn, T. A., Faber, B. A., Stedinger, J. R., Thomas, W. O., Jr., Veilleux, A. G., Kiang, J. E., & Mason, R. R., Jr. (2019). Guidelines for determining flood flow frequency - Bulletin 17C. U.S. Geological Survey.
A dataset containing the Maximum annual peak discharge values in cubic meter per second (cms), observed at Harricana River at Amos (Quebec, Canada) as displayed by the program HFA extracted from Table 1.2 in "The Gamma Family and Derived Distributions Applied in Hydrology" (Bobee and Ashkar, 1991).
A data frame with 72 rows and 1 variable:
peak flows
Bobee, B. & Ashkar, F. (1991). The Gamma Family and Derived Distributions Applied in Hydrology. Water Resources Publications.
PlotPos returns the empirical probability values corresponding to
the observed data of hydrological extreme events as a vector of numerics.
PlotPos(data_obs, PP)PlotPos(data_obs, PP)
data_obs |
A vector, data frame or matrix containing observed data or flood quantiles. |
PP |
A character string that determines the empirical formula used to calculate the probability.
The formula can be chosen from the list: |
This is a function to calculate the emprical probability values assigned to the observed data of hydrological extreme events to be plotted.
The function returns the probabilities assigned to the observed data as a vector of numerics.
Chow, V. T., Maidment, D. R., & Mays, L. W. (1988). Applied Hydrology. McGraw-Hill, New York, U.S.
ProbPlot for graphical frequency analysis.
# First Example data('Harricana') PlotPos(data_obs = Harricana, PP = 'Weibull') # Second Example data('B17C_Tab8_1') PlotPos(data_obs = B17C_Tab8_1, PP = 'Cunnane')# First Example data('Harricana') PlotPos(data_obs = Harricana, PP = 'Weibull') # Second Example data('B17C_Tab8_1') PlotPos(data_obs = B17C_Tab8_1, PP = 'Cunnane')
ProbPlot checks that a probability distribution fits a set of flood data.
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 )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 )
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 |
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: |
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 |
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 |
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 |
y_lab |
Optional. A character string representing the label of vertical axis. The default label of
the axis is |
Pcol |
Optional. A specification for the observed flood quantile points color. Defaults to
|
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 |
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 |
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 |
Lwd |
Optional. The theoretical probability line width, a positive number, defaulting to 1.5. |
CPlot |
Logical. If |
CLcol |
Optional. A specification for the confidence limits (bounds) color. Defaults to |
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 |
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
|
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 |
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 |
P3SkewCheck |
Logical. If |
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).
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.
PlotPos for the plotting position probability.
# 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))# 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))