Package 'RtsEva'

Description

A time series of simulated river discharge of the Ardeche river close to its confluence with the Rhone (longitude = 4.658 \ latitude = 44.258) from 1951 to 2020. Time series extracted from the HERA dataset: https://data.jrc.ec.europa.eu/dataset/a605a675-9444-4017-8b34-d66be5b18c95. The Ardèche is Mediterranean river mostly known for tourism due to its scenic gorges, but floods and droughts can impact the local economy and environment.

Usage

data(ArdecheStMartin)

Format

Two column dataframe: #'

• time (POSIXct timestamp with 6-hourly resolution)

• Q (6-houry mean discharge in cubic meter per second)

Source

https://data.jrc.ec.europa.eu/dataset/a605a675-9444-4017-8b34-d66be5b18c95

Description

This function checks if all years specified in a given time series are present.

Usage

check_timeseries(timeseries, yro)

Arguments

Value

A logical value indicating whether all years in the time series are present.

Examples

ts_data <- seq(as.POSIXct("2000-01-01"), as.POSIXct("2004-12-31"), by = "year")
check_timeseries(ts_data, c(2000, 2004))
# Output: TRUE

check_timeseries(ts_data, c(2000, 2005))
# Output: FALSE

Description

computeAnnualMaxima is a function that computes the annual maxima of a time series.

Usage

computeAnnualMaxima(timeAndSeries)

Arguments

Value

A list containing the annual maximum values, their corresponding dates, and their indices.

annualMax

A numeric vector of annual maximum values.

annualMaxDate

A vector of dates corresponding to the annual maximum values.

annualMaxIndx

A vector of indices indicating the positions of the annual maximum values in the original time series.

Examples

timeAndSeries <- ArdecheStMartin
computeAnnualMaxima(timeAndSeries)

Description

computeMonthlyMaxima is a function that computes the monthly maxima of a time series.

Usage

computeMonthlyMaxima(timeAndSeries)

Arguments

Value

A list containing the monthly maxima, corresponding dates, and indices.

monthlyMax

A vector of the monthly maximum values.

monthlyMaxDate

A vector of the dates corresponding to the monthly maximum values.

monthlyMaxIndx

A vector of the indices of the monthly maximum values in the original series.

Examples

timeAndSeries <- ArdecheStMartin
computeMonthlyMaxima(timeAndSeries)

Description

A time series of simulated river discharge of the Danube river in Vienna (longitude = 16.64 \ latitude = 48.13) from 1951 to 2020. Time series extracted from the HERA dataset: https://data.jrc.ec.europa.eu/dataset/a605a675-9444-4017-8b34-d66be5b18c95. The Danube is the longest river in the EU and is an important waterway for international trade, connecting several countries in Central and Eastern Europe.

Usage

data(DanubeVienna)

Format

Two column dataframe: #'

• time (POSIXct timestamp with 6-hourly resolution)

• Q (6-houry mean discharge in cubic meter per second)

Source

https://data.jrc.ec.europa.eu/dataset/a605a675-9444-4017-8b34-d66be5b18c95

Description

declustpeaks is a function that takes in a data vector, minimum peak distance, minimum run distance, and a threshold value. It finds peaks in the data vector based on the minimum peak distance and threshold value. It then declusters the peaks based on the minimum run distance and threshold value. The function returns a data frame with information about the peaks, including the peak value, start and end indices, duration, and cluster information.

Usage

declustpeaks(data, minpeakdistance = 10, minrundistance = 7, qt)

Arguments

Value

A data frame with information about the peaks, including:

Q

the peak value

max

max time index

start

start time index

end

end time index

dur

duration

cluster

cluster information

Examples

data <- c(1, 2, 3, 4, 5, 4, 3, 2, 1)
declustpeaks(data, minpeakdistance = 2, minrundistance = 2, qt = 3)

Description

A time series of simulated river discharge of the Ebro river at Zaragoza (longitude = -0.825 \ latitude = 41.608) from 1951 to 2020. Time series extracted from the HERA dataset: https://data.jrc.ec.europa.eu/dataset/a605a675-9444-4017-8b34-d66be5b18c95. The Ebro is Spain's longest river, with low and high water levels alternating throughout the year, influenced by winter snowmelt and summer evaporation/human usage. The river is vital for agriculture.

Usage

data(EbroZaragoza)

Format

Two column dataframe: #'

• time (POSIXct timestamp with 6-hourly resolution)

• Q (6-houry mean discharge in cubic meter per second)

Source

https://data.jrc.ec.europa.eu/dataset/a605a675-9444-4017-8b34-d66be5b18c95

Description

empdis is a function that calculates the empirical distribution function for a given dataset.

Usage

empdis(x, nyr)

Arguments

Value

A data frame containing:

emp.RP

empirical return period

haz.RP

Hazen return period

cun.RP

Cunnane return period

gumbel

Gumbel values

emp.f

empirical cumulative density

emp.hazen

Hazen cumulative density

emp.cunnan

Cunnane cumulative density

Q

original data

timestamp

time component

Examples

x <- c(1, 2, 3, 4, 5)
nyr <- 5
empdis(x, nyr)

Description

This function calculates the empirical distribution function for a given dataset, with a focus on low values

Usage

empdisl(x, nyr)

Arguments

Value

A data frame containing the following columns:

emp.RP

Empirical return period

haz.RP

Hazen return period

gumbel

Gumbel frequency

emp.f

Empirical frequency

emp.hazen

Empirical Hazen frequency

Q

Discharge values

Examples

x <- c(10, 20, 30, 40, 50)
nyr <- 5
empdisl(x, nyr)

Description

findMax is a function that takes a subset of a vector and returns the index of the maximum value in that subset.

Usage

findMax(subIndxs, srs)

Arguments

Value

The index of the maximum value in the subset.

Examples

srs <- c(10, 20, 30, 40, 50)
findMax(c(1, 3, 5),srs)
#result is 5.

Description

This function calculates percentiles for a given dataset

Usage

initPercentiles(subsrs, percentM, percent, percentP)

Arguments

Value

A list containing the calculated percentiles and probabilities.

See Also

tsEvaNanRunningPercentiles()

Examples

timeAndSeries <- ArdecheStMartin
timeStamps <- ArdecheStMartin[,1]
series <- ArdecheStMartin[,2]
initPercentiles(series, 89, 90, 91)

Description

This function converts a 6-hourly time series to a daily time series and calculates the maximum value for each day.

Usage

max_daily_value(timeseries)

Arguments

Value

A data frame containing the daily maximum values.

Examples

# Example usage:
timeseries <- ArdecheStMartin
max_daily_value(timeseries)

Description

A time series of simulated river discharge of the Rhone river close to its confluence with the Saone (longitude = 4.891 \ latitude = 45.772) from 1951 to 2020. Time series extracted from the HERA dataset: https://data.jrc.ec.europa.eu/dataset/a605a675-9444-4017-8b34-d66be5b18c95. The Rhône is France's most powerful river,characterized by a significant seasonal variation in flow rates. The Rhône River is crucial for transportation, hydropower generation, and irrigation in the region.

Usage

data(RhoneLyon)

Format

Two column dataframe: #'

• time (POSIXct timestamp with 6-hourly resolution)

• Q (6-houry mean discharge in cubic meter per second)

Source

https://data.jrc.ec.europa.eu/dataset/a605a675-9444-4017-8b34-d66be5b18c95

Description

This function takes a list of named arguments and assigns their values to a predefined argument structure. The argument structure is a list with named elements representing the available arguments. If an argument is present in the list of named arguments, its value is assigned to the corresponding element in the argument structure. If an argument is not present, its value in the argument structure remains unchanged.

Usage

tsEasyParseNamedArgs(args, argStruct)

Arguments

Value

A modified argument structure with values assigned from the list of named arguments.

Examples

args <- list(arg1 = 10, arg2 = "tanargue")
argStruct <- list(arg1 = 0, arg2 = "", arg3 = TRUE)
modifiedArgStruct <- tsEasyParseNamedArgs(args, argStruct)
modifiedArgStruct

Description

This function estimates the average seasonality of a time series based on the given parameters.

Usage

tsEstimateAverageSeasonality(timeStamps, seasonalitySeries, timeWindow)

Arguments

Value

A list containing the estimated regime and the seasonality series:

regime

The estimated regime of the time series.

Seasonality

A data frame containing the average and varying seasonality series.

averageSeasonalitySeries

The average seasonality series.

varyingSeasonalitySeries

The varying seasonality series.

Examples

timeAndSeries <- ArdecheStMartin
timeStamps <- ArdecheStMartin[,1]
series  <- ArdecheStMartin[,2]
timeWindow <- 30*365  # 30 years
rs <- tsEvaDetrendTimeSeries(timeStamps, series, timeWindow)
nRunMn <- rs@nRunMn
cat("computing trend seasonality ...\n")
seasonalitySeries <- rs@detrendSeries
result <- tsEstimateAverageSeasonality(timeStamps, seasonalitySeries, timeWindow=rs@nRunMn)
plot(result$regime, type = "l", xlab = "Day", ylab = "Regime", main = "Estimated Regime")
plot(result$Seasonality$averageSeasonalitySeries, type = "l", xlab = "Day",
ylab = "Seasonality", main = "Average Seasonality")
plot(result$Seasonality$varyingSeasonalitySeries, type = "l", xlab = "Day",
ylab = "Seasonality", main = "Varying Seasonality")

Description

This function applies the PELT method for change point detection in a time series. It returns the mean and variance of the series segments between change points.

Usage

tsEvaChangepts(series, timeWindow, timeStamps)

Arguments

Value

A list containing:

trend

A numeric vector of the same length as series, with each segment between change points filled with its mean value

variance

A numeric vector of the same length as series, with each segment between change points filled with its variance

changepoints

A vector of timestamps at which change points were detected

Examples

timeAndSeries <- ArdecheStMartin
timeStamps <- ArdecheStMartin[,1]
series <- ArdecheStMartin[,2]
timeWindow <- 30*365 # 30 years
result <- tsEvaChangepts(series, timeWindow, timeStamps)
plot(timeAndSeries, type = "l")
lines(timeStamps,result$trend,col=2)
points(timeStamps[result$changepoints], result$trend[result$changepoints], col = "red")

Description

tsEvaComputeReturnPeriodsGPDis a function that calculates the return levels for a Generalized Extreme Value (GEV) distribution given the GEV parameters and their standard errors. The return periods are specified in a time unit that corresponds to the size of the time segments for evaluating the maxima.

Usage

tsEvaComputeReturnLevelsGEV(
  epsilon,
  sigma,
  mu,
  epsilonStdErr,
  sigmaStdErr,
  muStdErr,
  returnPeriodsInDts
)

Arguments

Value

A list containing the following components:

returnLevels

A matrix of return levels corresponding to the specified return periods.

returnLevelsErr

A matrix of standard errors for the return levels.

See Also

empdis

Examples

# Example usage with some sample data
epsilon <- c(0.1)
sigma <- c(2.3)
mu <- c(1.3)
epsilonStdErr <- c(0.01)
sigmaStdErr <- c(0.11)
muStdErr <- c(0.011)
returnPeriodsInDts <- c( 5, 10, 20, 50)
results <- tsEvaComputeReturnLevelsGEV(epsilon, sigma, mu, epsilonStdErr,
sigmaStdErr, muStdErr, returnPeriodsInDts)
head(results$returnLevels)
head(results$returnLevelsErr)

Description

tsEvaComputeReturnLevelsGEVFromAnalysisObjis a function that calculates the return levels for a Generalized Extreme Value (GEV) distribution using the parameters obtained from a non-stationary extreme value analysis. It supports non-stationary analysis by considering different parameters for each time index.

Usage

tsEvaComputeReturnLevelsGEVFromAnalysisObj(
  nonStationaryEvaParams,
  returnPeriodsInYears,
  timeIndex = -1
)

Arguments

Value

A list containing the following components:

returnLevels

A matrix of return levels corresponding to the specified return periods.

returnLevelsErr

A matrix of standard errors for the return levels.

returnLevelsErrFit

A matrix of standard errors for the return levels obtained from fitting the non-stationary model.

returnLevelsErrTransf

A matrix of standard errors for the return levels obtained from the transformed data.

See Also

tsEvaComputeReturnLevelsGEV

Examples

# Example usage with some sample data
nonStationaryEvaParams <- list(list(
parameters = list(
  epsilon = 0.1,
  sigma = c(2.1, 2.2, 2.3),
  mu = c(1.1, 1.2, 1.3),
  timeHorizonStart=as.POSIXct("1951-01-01"),
  timeHorizonEnd=as.POSIXct("2020-12-31"),
  nPeaks=90

),
paramErr = list(
  epsilonErr = 0.01,
  sigmaErr = c(0.11, 0.12, 0.13),
  muErr = c(0.011, 0.012, 0.013)
),NA
)
)
returnPeriodsInYears <- c(1, 5, 10, 20, 50)
timeIndex=1
results <- tsEvaComputeReturnLevelsGEVFromAnalysisObj(nonStationaryEvaParams, returnPeriodsInYears)
head(results$returnLevels)

Description

#' tsEvaComputeReturnLevelsGPDis a function that compute the return levels for a Generalized Pareto Distribution (GPD) using the parameters of the distribution and their standard errors.

Usage

tsEvaComputeReturnLevelsGPD(
  epsilon,
  sigma,
  threshold,
  epsilonStdErr,
  sigmaStdErr,
  thresholdStdErr,
  nPeaks,
  sampleTimeHorizon,
  returnPeriods
)

Arguments

Details

sampleTimeHorizon and returnPeriods must be in the same units, e.g. years

Value

A list containing the following components:

returnLevels

A vector of return levels corresponding to the specified return periods.

returnLevelsErr

A vector of standard errors for the return levels.

Examples

# Example usage with some sample data
epsilon <- c(0.1)
sigma <- c(2.3)
threshold <- c(1.3)
epsilonStdErr <- c(0.01)
sigmaStdErr <- c(0.11)
thresholdStdErr <- c(0.011)
returnPeriodsInDts <- c( 5, 10, 20, 50)
nPeaks=70
SampleTimeHorizon=70
results <- tsEvaComputeReturnLevelsGPD(epsilon, sigma, threshold, epsilonStdErr,
sigmaStdErr, thresholdStdErr, nPeaks, SampleTimeHorizon, returnPeriodsInDts)
head(results$returnLevels)
head(results$returnLevelsErr)

Description

tsEvaComputeReturnLevelsGPDFromAnalysisObj is a function that calculates the return levels for a Generalized Pareto Distribution (GPD) using the parameters obtained from an analysis object. It takes into account non-stationarity by considering time-varying parameters and their associated standard errors.

Usage

tsEvaComputeReturnLevelsGPDFromAnalysisObj(
  nonStationaryEvaParams,
  returnPeriodsInYears,
  timeIndex = -1
)

Arguments

Value

A list with the following components:

returnLevels

A vector of return levels corresponding to the specified return periods.

returnLevelsErrFit

A vector of standard errors for the return levels estimated based on the fit.

returnLevelsErrTransf

A vector of standard errors for the return levels estimated based on the transformed parameters.

See Also

tsEvaComputeReturnLevelsGPD

Examples

# Example usage with some sample data
nonStationaryEvaParams <- list(NA,list(
 parameters = list(
   epsilon = 0.1,
   sigma = c(2.1, 2.2, 2.3),
   threshold = c(1.1, 1.2, 1.3),
   timeHorizonStart=as.POSIXct("1951-01-01"),
   timeHorizonEnd=as.POSIXct("2020-12-31"),
   nPeaks=90

 ),
 paramErr = list(
   epsilonErr = 0.01,
   sigmaErr = c(0.11, 0.12, 0.13),
   thresholdErr = c(0.011, 0.012, 0.013)
 )
)
)
returnPeriodsInYears <- c(1, 5, 10, 20, 50)
timeIndex=1
results <- tsEvaComputeReturnLevelsGPDFromAnalysisObj(nonStationaryEvaParams, returnPeriodsInYears)
head(results$returnLevels)

Description

tsEvaComputeReturnPeriodsGEVis a function that computes the return periods of a set of observations (can be Annual maxima or others) for a Generalized Extreme Value (GEV) distribution, given the GEV parameters and their standard error. The return levels represent the values of annual maxima with a certain probability, while the return periods indicate the average time between exceedances of those threshold values.

Usage

tsEvaComputeReturnPeriodsGEV(epsilon, sigma, mu, BlockMax)

Arguments

Value

A list containing the following components:

GevPseudo

A matrix of pseudo observations obtained from the GEV distribution for each annual extreme at every time step.

returnPeriods

A matrix of return periods corresponding to the pseudo observations.

PseudoObs

The pseudo observation corresponding to the maximum value used in the computation.

See Also

empdis

Examples

# Example usage with some sample data
epsilon <- 0.1
sigma <- 2.2
mu <- 1.3
BlockMax <- c(10, 20, 30, 40, 50)

results <- tsEvaComputeReturnPeriodsGEV(epsilon, sigma, mu, BlockMax)
head(results$GevPseudo)
head(results$returnPeriods)
head(results$PseudoObs)

Description

tsEvaComputeReturnPeriodsGPDis a function that computes the return periods of a set of observations (peaks) for a Generalized Pareto Distribution (GPD), given the GPD parameters, threshold, peaks data, and sample time horizon.

Usage

tsEvaComputeReturnPeriodsGPD(
  epsilon,
  sigma,
  threshold,
  peaks,
  nPeaks,
  peaksID,
  sampleTimeHorizon
)

Arguments

Value

A list containing the following components:

GpdPseudo

A matrix of pseudo observations obtained from the GPD for each peak value at every time step.

returnPeriods

A matrix of return periods corresponding to the pseudo observations.

PseudoObs

A data frame containing the pseudo observations and their corresponding identifiers.

See Also

empdis

Examples

# Example usage with some sample data
epsilon <- 0.1
sigma <- 2.2
threshold <- 1.3
peaks <- c(10, 20, 30, 40, 50)
nPeaks=5
peaksID=c(230,550,999,1540,3012)
SampleTimeHorizon = 70

results <- tsEvaComputeReturnPeriodsGPD(epsilon, sigma, threshold, peaks,
nPeaks, peaksID, SampleTimeHorizon)
head(results$GpdPseudo)
head(results$returnPeriods)
head(results$PseudoObs)

Description

tsEvaComputeRLsGEVGPD is a function that calculates the return levels and their associated errors for a Generalized Extreme Value (GEV) and Generalized Pareto (GPD) distribution using the parameters obtained from a non-stationary extreme value analysis. It supports non-stationary analysis by considering different parameters for each time index.

Usage

tsEvaComputeRLsGEVGPD(nonStationaryEvaParams, RPgoal, timeIndex, trans = NA)

Arguments

Value

A list containing the following components:

Fit

A character string indicating whether the EVD could be fitted to the data ("No fit") or the EVD was successfully fitted to the data ("Fitted").

ReturnLevels

A data frame containing the target return period (ReturnPeriod), GEV return level (GEV), GPD return level (GPD), GEV return level error (errGEV), and GPD return level error (errGPD) for the specified time index.

Params

A list containing the GEV and GPD parameters for the specified time index, including their standard errors.

See Also

tsEvaComputeReturnLevelsGEV, tsEvaComputeReturnLevelsGPD

Description

tsEvaComputeTimeRPis a function that calculates the return period of a given event for GEV and GPD distributions at a given time index.

Usage

tsEvaComputeTimeRP(params, RPiGEV, RPiGPD)

Arguments

Value

A vector with the calculated return period for GEV and GPD distributions.

Examples

#Parameter vector:
params <- t(data.frame(epsilonGEV = 0.2, muGEV = 3, sigmaGEV = 1,
                  epsilonGPD = 0.2, thresholdGPD = 3, sigmaGPD = 1,
                  nPeaks = 70, SampleTimeHorizon = 70))

tsEvaComputeTimeRP(params, RPiGEV = 10, RPiGPD = 10)

Description

This function detrends a time series by subtracting the trend component from the original series.

Usage

tsEvaDetrendTimeSeries(
  timeStamps,
  series,
  timeWindow,
  percent = NA,
  fast = TRUE
)

Arguments

Value

An object of class "tsTrend" with the following components:

originSeries

The original time series

detrendSeries

The detrended time series

trendSeries

The trend component of the time series

nRunMn

The number of data points in the moving window used to calculate the trend

Examples

timeAndSeries <- ArdecheStMartin
timeStamps <- ArdecheStMartin[,1]
series  <- ArdecheStMartin[,2]
timeWindow <- 365*30
detrended <- tsEvaDetrendTimeSeries(timeStamps, series, timeWindow)

Description

This function takes a vector of timestamps and a corresponding series with missing values, and fills the missing values by taking the average of the surrounding values.

Usage

tsEvaFillSeries(timeStamps, series)

Arguments

Value

A vector with missing values filled using a moving average approach.

Examples

timeStamps <- c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
series <- c(1, 2, NA, 4, 5, NA, 7, 8, NA, 10)
filledSeries <- tsEvaFillSeries(timeStamps, series)
filledSeries

Description

This function calculates the optimal trend threshold for a given time series.

Usage

tsEvaFindTrendThreshold(series, timeStamps, timeWindow)

Arguments

Details

This function iterates over different percentiles and calculates the threshold based on each percentile. It then removes data points below the threshold and detrends the time series using the specified time window. The function calculates the correlation between the normalized trend and the time series and stores the correlation coefficient for each percentile. It performs a changepoint analysis to determine if there is a significant change in the correlation coefficients. If a change point is found, the function returns the percentile corresponding to the change point. If no change point is found, the function returns the percentile with the highest correlation coefficient. If there are negative values in the detrended time series, the function returns the percentile with the fewest negative values.

Value

The trend threshold value.

Examples

timeAndSeries <- ArdecheStMartin
#go from six-hourly values to daily max
timeAndSeries <- max_daily_value(timeAndSeries)
#keep only the 30 last years
yrs <- as.integer(format(timeAndSeries[,1], "%Y"))
tokeep <- which(yrs>=1990)
timeAndSeries <- timeAndSeries[tokeep,]
timeWindow <- 10*365 # 10 years
timeStamps <- timeAndSeries[,1]
series <- timeAndSeries[,2]
tsEvaFindTrendThreshold(series, timeStamps, timeWindow)

Description

This function calculates the return period of low flow for a given time series based on a threshold and window size. It uses a sliding window approach to count the number of values below the threshold within each window, and then calculates the return period based on the proportion of values below the threshold. Assumes that the input data has a 7 days timestep.

Usage

tsEvaNanRunnigBlowTh(series, threshold, windowSize)

Arguments

Value

A data frame with two columns: "time" representing the time points corresponding to the sliding windows, and "RP" representing the calculated return period of low flow.

Examples

series <- c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
threshold <- 5
windowSize <- 3
tsEvaNanRunnigBlowTh(series, threshold, windowSize)

Description

This function calculates the running mean of a time series, taking into account NaN values. It uses a sliding window approach to calculate the mean, where the window size is specified by the user. If the number of non-NaN values within the window is greater than a threshold, the mean is calculated. Otherwise, NaN is returned.

Usage

tsEvaNanRunningMean(series, windowSize)

Arguments

Value

A vector containing the running mean of the time series

Examples

series <- c(1,2,NaN,4,5,6,NaN,8,9,4,5,6,7,3,9,1,0,4,5,2)
windowSize <- 3
result <- tsEvaNanRunningMean(series, windowSize)
print(result)

Description

Computes a running percentile for a given series using a window with a specified size.

Usage

tsEvaNanRunningPercentiles(timeStamps, series, windowSize, percent)

Arguments

Details

This function computes a running percentile for a given series using a window with a specified size. The running percentile is computed by interpolating the percentile value for the requested percentage based on the quitting values and incoming values in the window. The function also performs smoothing on the output and calculates the standard error.

The function uses the following label parameters:

percentDelta

Delta for the computation of a percentile interval around the requested percentage. If the windowSize is greater than 2000, percentDelta is set to 1. If the windowSize is between 1000 and 2000, percentDelta is set to 2. If the windowSize is between 100 and 1000, percentDelta is set to 5.

nLowLimit

Minimum number of non-NA elements for a window for percentile computation

Value

A list containing the approximated running percentile (rnprcnt) and the standard error (stdError).

Examples

timeAndSeries <- ArdecheStMartin
timeStamps <- ArdecheStMartin[,1]
series  <- ArdecheStMartin[,2]
windowSize <- 365
percent <- 90
result <- tsEvaNanRunningPercentiles(timeStamps, series, windowSize, percent)
print(result$rnprcnt)
print(result$stdError)

Description

Returns the moving statistical momentums to the forth.

Usage

tsEvaNanRunningStatistics(series, windowSize)

Arguments

Details

This function calculates the running variance, running third statistical momentum, and running fourth statistical momentum for a given time series data using a moving window approach. The window size determines the number of observations used to calculate the statistics at each point.

Value

A data frame containing the following running statistics:

rnvar

running variance

rn3mom

running third statistical momentum

rn4mom

running fourth statistical momentum

Examples

series <- c(1,2,NaN,4,5,6,NaN,8,9,4,5,6,7,3,9,1,0,4,5,2)
windowSize <- 3
tsEvaNanRunningStatistics(series, windowSize)

Description

This function calculates the running variance of a time series, taking into account NaN values. The series must be zero-averaged before passing it to this function.

Usage

tsEvaNanRunningVariance(series, windowSize)

Arguments

Value

A vector containing the running variance values.

Examples

series <- c(1,2,NaN,4,5,6,NaN,8,9,4,5,6,7,3,9,1,0,4,5,2)
windowSize <- 3
tsEvaNanRunningVariance(series, windowSize)

Description

This function performs non-stationary extreme value analysis (EVA) on a time series data.

Usage

TsEvaNs(
  timeAndSeries,
  timeWindow,
  transfType = "trendPeaks",
  minPeakDistanceInDays = 10,
  seasonalityVar = NA,
  minEventsPerYear = -1,
  gevMaxima = "annual",
  ciPercentile = 90,
  gevType = "GEV",
  evdType = c("GEV", "GPD"),
  tail = "high",
  epy = -1,
  lowdt = 7,
  trans = NULL,
  TrendTh = NA
)

Arguments

Details

The function takes a time series data and performs non-stationary EVA using various transformation types and parameters depending on the input data provided. Results are returned as a list containing the non-stationary EVA parameters and the transformed data for stationary EVA and can be used as input for further analysis. In particular for the following function

Value

A list containing the results of the non-stationary EVA. Containing the following components:

nonStationaryEvaParams

The estimated parameters for non-stationary EVA. Parameters include GEV and GPD parameters for each timestep, confidence intervals, and other statistical measures

stationaryTransformData

The transformed data for stationary EVA. Includes the stationary series, trend, and standard deviation series

References

Mentaschi, L., Vousdoukas, M., Voukouvalas, E., Sartini, L., Feyen, L., Besio, G., and Alfieri, L. (2016). The transformed-stationary approach: a generic and simplified methodology for non-stationary extreme value analysis. Hydrology and Earth System Sciences, 20(9), 3527-3547. doi:10.5194/hess-20-3527-2016.

Examples

# Example usage of TsEvaNs function
timeAndSeries <- ArdecheStMartin
#go from six-hourly values to daily max
timeAndSeries <- max_daily_value(timeAndSeries)
#keep only the 30 last years
yrs <- as.integer(format(timeAndSeries$date, "%Y"))
tokeep <- which(yrs>=1990)
timeAndSeries <- timeAndSeries[tokeep,]
timeWindow <- 10*365 # 10 years
result <- TsEvaNs(timeAndSeries, timeWindow,
transfType = 'trendPeaks',tail = 'high')

Description

tsEvaPlotAllRLevelsGEV is a function that generates a beam plot of return levels for a Generalized Extreme Value (GEV) distribution based on the provided parameters and data. The plot showcases the evolving relationship between return periods and return levels through time, allowing for visual analysis of extreme events and their probabilities.

Usage

tsEvaPlotAllRLevelsGEV(
  nonStationaryEvaParams,
  stationaryTransformData,
  rlvmax,
  timeIndex,
  timeStamps,
  tstamps,
  trans,
  ...
)

Arguments

Value

A plot object showing the relationship between return periods and return levels for the GEV distribution at different timesteps.

See Also

tsEvaComputeReturnLevelsGEV

Examples

# Example usage of TsEvaNs function
timeAndSeries <- ArdecheStMartin
#go from six-hourly values to daily max
timeAndSeries <- max_daily_value(timeAndSeries)
#keep only the 20 last years
yrs <- as.integer(format(timeAndSeries$date, "%Y"))
tokeep <- which(yrs>=2000)
timeAndSeries <- timeAndSeries[tokeep,]
timeWindow <- 5*365 # 5 years
TSEVA_data <- TsEvaNs(timeAndSeries, timeWindow,
transfType = 'trendPeaks',tail = 'high')
nonStationaryEvaParams <- TSEVA_data[[1]]
stationaryTransformData <- TSEVA_data[[2]]
amax <- nonStationaryEvaParams[[1]]$parameters$annualMax
amaxID <- nonStationaryEvaParams[[1]]$parameters$annualMaxIndx
timeStamps <- stationaryTransformData$timeStamps
trendPeaks <- stationaryTransformData$trendSeries[amaxID]
stdPeaks <- stationaryTransformData$stdDevSeries[amaxID]
amaxCor <- (amax - trendPeaks) / stdPeaks
nYears <- length(amaxCor)
rlvlmax <- empdis(amaxCor, nYears)
rlvlmax$QNS <- amax[order(amax)]
rlvlmax$Idt <- stationaryTransformData$timeStamps[amaxID][order(amax)]
timeIndex <- 2
tstamps <- "Example Timestamps"
trans <- "ori"
# Call the function with the defined arguments
result <- tsEvaPlotAllRLevelsGEV(
  nonStationaryEvaParams, stationaryTransformData,
  rlvlmax, timeIndex, timeStamps, tstamps,
  trans)
result

Description

tsEvaPlotAllRLevelsGPD is a function that generates a plot of return levels for a Generalized Pareto Distribution (GPD) based on the provided parameters and data. The plot showcases the evolving relationship between return periods and return levels, allowing for visual analysis of extreme events and their probabilities.

Usage

tsEvaPlotAllRLevelsGPD(
  nonStationaryEvaParams,
  stationaryTransformData,
  rlvmax,
  timeIndex,
  timeStamps,
  tstamps,
  trans,
  ...
)

Arguments

Value

A plot object showing the relationship between return periods and return levels for the GPD distribution at different timest

See Also

tsEvaComputeReturnLevelsGPD

Examples

# Example usage of TsEvaNs function
timeAndSeries <- ArdecheStMartin
#go from six-hourly values to daily max
timeAndSeries <- max_daily_value(timeAndSeries)
#keep only the 20 last years
yrs <- as.integer(format(timeAndSeries$date, "%Y"))
tokeep <- which(yrs>=2000)
timeAndSeries <- timeAndSeries[tokeep,]
timeWindow <- 5*365 # 5 years
TSEVA_data <- TsEvaNs(timeAndSeries, timeWindow,
                      transfType = 'trendPeaks',tail = 'high')
nonStationaryEvaParams <- TSEVA_data[[1]]
stationaryTransformData <- TSEVA_data[[2]]
peax <- nonStationaryEvaParams[[2]]$parameters$peaks
peaxID <- nonStationaryEvaParams[[2]]$parameters$peakID
timeStamps <- stationaryTransformData$timeStamps
trendPeaks <- stationaryTransformData$trendSeries[peaxID]
stdPeaks <- stationaryTransformData$stdDevSeries[peaxID]
peaksCor <- (peax - trendPeaks) / stdPeaks
nYears <- round(length(timeStamps) / 365.25 )
rlvlmax <- empdis(peaksCor, nYears)
rlvlmax$QNS <- peax[order(peax)]
rlvlmax$Idt <- stationaryTransformData$timeStamps[peaxID][order(peax)]
timeIndex <- 2
tstamps <- "Example Timestamps"
trans <- "ori"
# Call the function with the defined arguments
result <- tsEvaPlotAllRLevelsGPD(
  nonStationaryEvaParams, stationaryTransformData,
  rlvlmax, timeIndex, timeStamps, tstamps,
  trans)
# Plot the result
result

Description

tsEvaPlotGEVImageScis a function that generates a plot of the Generalized Extreme Value (GEV) distribution with evolving parameters using the provided data.

Usage

tsEvaPlotGEVImageSc(
  Y,
  timeStamps,
  serix,
  epsilon,
  sigma,
  mu,
  returnPeriodInDts,
  maxObs,
  trans,
  varargin
)

Arguments

Value

A ggplot object representing the GEV plot with a raster image.

See Also

tsEvaPlotGEVImageScFromAnalysisObj

Description

tsEvaPlotGEVImageScFromAnalysisObjis a function that generates a GEV (Generalized Extreme Value) time-varying distribution through time as and show the evolution of exceedance probabilities.

Usage

tsEvaPlotGEVImageScFromAnalysisObj(
  Y,
  nonStationaryEvaParams,
  stationaryTransformData,
  trans,
  ...
)

Arguments

Value

The GEV image scatter plot.

See Also

tsEvaPlotGEVImageSc

Examples

# Example usage of TsEvaNs function
timeAndSeries <- ArdecheStMartin
#go from six-hourly values to daily max
timeAndSeries <- max_daily_value(timeAndSeries)
#keep only the 20 last years
yrs <- as.integer(format(timeAndSeries$date, "%Y"))
tokeep <- which(yrs>=2000)
timeAndSeries <- timeAndSeries[tokeep,]
timeWindow <- 5*365 # 10 years
TSEVA_data <- TsEvaNs(timeAndSeries, timeWindow,
transfType = 'trendPeaks',tail = 'high')

# Define the required function arguments
stationaryTransformData <- TSEVA_data[[2]]
nonStationaryEvaParams <- TSEVA_data[[1]]
trans='ori'

ExRange= c(min(nonStationaryEvaParams$potObj$parameters$peaks),
max(nonStationaryEvaParams$potObj$parameters$peaks))
Y <- c(seq(min(ExRange),max(ExRange),length.out=700))

result = tsEvaPlotGEVImageScFromAnalysisObj(Y,nonStationaryEvaParams,
stationaryTransformData, trans)
result

Description

tsEvaPlotGPDImageScis a function that generates a time series plot of the Generalized Pareto Distribution (GPD) with evolving parameters using the provided data.

Usage

tsEvaPlotGPDImageSc(
  Y,
  timeStamps,
  serix,
  epsilon,
  sigma,
  threshold,
  peakplot,
  trans,
  varargin
)

Arguments

Value

A ggplot object representing the GPD plot.

See Also

tsEvaPlotGPDImageScFromAnalysisObj

Description

tsEvaPlotGPDImageScFromAnalysisObjis a function that plots the GPD (Generalized Pareto Distribution) time-varying distribution through time as and show the evolution of exceedance probabilities.

Usage

tsEvaPlotGPDImageScFromAnalysisObj(
  Y,
  nonStationaryEvaParams,
  stationaryTransformData,
  trans,
  ...
)

Arguments

Details

This function takes the input data Y, non-stationary evaluation parameters nonStationaryEvaParams, stationary transform data stationaryTransformData, transformation method trans, and additional arguments .... It then updates the arguments with the passed-in values, calculates the time stamps, and performs necessary transformations. Finally, it plots the GPD image score using the tsEvaPlotGPDImageSc function and returns the plot object.

Value

The plot object.

See Also

tsEvaPlotGPDImageSc

Examples

# Example usage of TsEvaNs function
timeAndSeries <- ArdecheStMartin
#go from six-hourly values to daily max
timeAndSeries <- max_daily_value(timeAndSeries)
#keep only the 20 last years
yrs <- as.integer(format(timeAndSeries$date, "%Y"))
tokeep <- which(yrs>=2000)
timeAndSeries <- timeAndSeries[tokeep,]
timeWindow <- 5*365 # 5 years
TSEVA_data <- TsEvaNs(timeAndSeries, timeWindow,
transfType = 'trendPeaks',tail = 'high')
nonStationaryEvaParams <- TSEVA_data[[1]]
stationaryTransformData <- TSEVA_data[[2]]
trans='ori'
ExRange= c(min(nonStationaryEvaParams$potObj$parameters$peaks),
max(nonStationaryEvaParams$potObj$parameters$peaks))
Y <- c(seq(min(ExRange),max(ExRange),length.out=700))
result = tsEvaPlotGEVImageScFromAnalysisObj(Y, nonStationaryEvaParams,
stationaryTransformData, trans)
result

Description

tsEvaPlotReturnLevelsGEV is a function that plots the return levels using the Generalized Extreme Value (GEV) distribution.

Usage

tsEvaPlotReturnLevelsGEV(
  epsilon,
  sigma,
  mu,
  epsilonStdErr,
  sigmaStdErr,
  muStdErr,
  rlvmax,
  tstamps,
  trans,
  ...
)

Arguments

Value

A ggplot object representing the plot of return levels.

See Also

tsEvaComputeReturnLevelsGEV tsEvaPlotReturnLevelsGEVFromAnalysisObj

Examples

# Define the required function arguments
epsilon <- 0.2
sigma <- 0.5
mu <- 10
epsilonStdErr <- 0.05
sigmaStdErr <- 0.05
muStdErr <- 0.1
rlvmax <- data.frame(
  haz.RP = c(2, 5, 10, 20, 50, 100, 200, 500, 1000),
  Idt = as.POSIXct(as.Date("2000-01-01") + round(runif(9, 0, 21 * 365.25)),
    origin = "1970-01-01"
  ),
  QNS = c(10, 12, 13, 13.2, 14, 15.7, 16, 16.2, 18)
)
tstamps <- "Example Timestamps"
trans <- "ori"
# Call the function with the defined arguments
result <- tsEvaPlotReturnLevelsGEV(
  epsilon, sigma, mu, epsilonStdErr, sigmaStdErr, muStdErr,
  rlvmax, tstamps, trans
)

# Plot the result
result

Description

tsEvaPlotReturnLevelsGEVFromAnalysisObj is a function that plots the return levels for a Generalized Extreme Value (GEV) distribution using the parameters obtained from an analysis object. It considers non-stationarity by considering time-varying parameters and their associated standard errors.

Usage

tsEvaPlotReturnLevelsGEVFromAnalysisObj(
  nonStationaryEvaParams,
  stationaryTransformData,
  timeIndex,
  trans,
  ...
)

Arguments

Value

Plot 1

RLtstep: return level curve with confidence interval for the selected timeIndex

Plot 2

beam: beam of return level curve for all with highlited curve for selected timeIndex

References

Mentaschi, L., Vousdoukas, M., Voukouvalas, E., Sartini, L., Feyen, L., Besio, G., and Alfieri, L. (2016). The transformed-stationary approach: a generic and simplified methodology for non-stationary extreme value analysis. Hydrology and Earth System Sciences, 20, 3527-3547. doi:10.5194/hess-20-3527-2016.

See Also

tsEvaPlotReturnLevelsGEV() and tsEvaPlotAllRLevelsGEV()

Examples

# Example usage of TsEvaNs function
timeAndSeries <- ArdecheStMartin
#go from six-hourly values to daily max
timeAndSeries <- max_daily_value(timeAndSeries)
#keep only the 30 last years
yrs <- as.integer(format(timeAndSeries$date, "%Y"))
tokeep <- which(yrs>=1990)
timeAndSeries <- timeAndSeries[tokeep,]
timeWindow <- 10*365 # 10 years
TSEVA_data <- TsEvaNs(timeAndSeries, timeWindow,
transfType = 'trendPeaks',tail = 'high')
nonStationaryEvaParams <- TSEVA_data[[1]]
stationaryTransformData <- TSEVA_data[[2]]
timeIndex=2
trans='ori'
result = tsEvaPlotReturnLevelsGEVFromAnalysisObj(nonStationaryEvaParams, stationaryTransformData,
timeIndex, trans)
result

Description

tsEvaPlotReturnLevelsGPD is a function that plots the return levels using the Generalized Pareto Distribution (GPD).

Usage

tsEvaPlotReturnLevelsGPD(
  epsilon,
  sigma,
  threshold,
  epsilonStdErr,
  sigmaStdErr,
  thresholdStdErr,
  nPeaks,
  timeHorizonInYears,
  rlvmax,
  tstamps,
  trans,
  ...
)

Arguments

Value

A ggplot object representing the plot of return levels.

See Also

tsEvaComputeReturnLevelsGPD tsEvaPlotReturnLevelsGPDFromAnalysisObj

Examples

# Define the required function arguments
epsilon <- 0.2
sigma <- 0.5
threshold <- 10
epsilonStdErr <- 0.05
sigmaStdErr <- 0.05
thresholdStdErr <- 0.1
rlvmax <- data.frame(
  haz.RP = c(2, 5, 10, 20, 50, 100, 200, 500, 1000),
  Idt = as.POSIXct(as.Date("2000-01-01") + round(runif(9, 0, 21 * 365.25)),
    origin = "1970-01-01"
  ),
  QNS = c(10, 12, 13, 13.2, 14, 15.7, 16, 16.2, 18)
)
tstamps <- "Example Timestamps"
trans <- "ori"
nPeaks=70
SampleTimeHorizon=70
# Call the function with the defined arguments
result <- tsEvaPlotReturnLevelsGPD(
  epsilon, sigma, threshold, epsilonStdErr, sigmaStdErr, thresholdStdErr,nPeaks,
  SampleTimeHorizon,rlvmax, tstamps, trans
)
# Plot the result
result

Description

tsEvaPlotReturnLevelsGPDFromAnalysisObj is a function that plots the return levels for a Generalized Pareto Distribution (GPD) using the parameters obtained from an analysis object. It considers non-stationarity by considering time-varying parameters and their associated standard errors.

Usage

tsEvaPlotReturnLevelsGPDFromAnalysisObj(
  nonStationaryEvaParams,
  stationaryTransformData,
  timeIndex,
  trans,
  ...
)

Arguments

Value

Plot 1

RLtstep: return level curve with confidence interval for the selected timeIndex

Plot 2

beam: beam of return level curve for all with highlited curve for selected timeIndex

References

Mentaschi, L., Vousdoukas, M., Voukouvalas, E., Sartini, L., Feyen, L., Besio, G., and Alfieri, L. (2016). The transformed-stationary approach: a generic and simplified methodology for non-stationary extreme value analysis. Hydrology and Earth System Sciences, 20, 3527-3547. doi:10.5194/hess-20-3527-2016.

See Also

tsEvaPlotReturnLevelsGPD() and tsEvaPlotAllRLevelsGPD()

Examples

# Example usage of TsEvaNs function
timeAndSeries <- ArdecheStMartin
#go from six-hourly values to daily max
timeAndSeries <- max_daily_value(timeAndSeries)
#keep only the 30 last years
yrs <- as.integer(format(timeAndSeries$date, "%Y"))
tokeep <- which(yrs>=1990)
timeAndSeries <- timeAndSeries[tokeep,]
timeWindow <- 10*365 # 10 years
TSEVA_data <- TsEvaNs(timeAndSeries, timeWindow,
transfType = 'trendPeaks',tail = 'high')
nonStationaryEvaParams <- TSEVA_data[[1]]
stationaryTransformData <- TSEVA_data[[2]]
timeIndex=2
trans='ori'
result = tsEvaPlotReturnLevelsGPDFromAnalysisObj(nonStationaryEvaParams, stationaryTransformData,
timeIndex, trans)
result

Description

tsEvaPlotTrendStdDevFromAnalysisObjis a function that plots a time series along with its trend and standard deviation.

Usage

tsEvaPlotSeriesTrendStdDevFromAnalyisObj(
  nonStationaryEvaParams,
  stationaryTransformData,
  trans,
  ...
)

Arguments

Value

A ggplot object representing the plot.

Examples

# Example usage of TsEvaNs function
timeAndSeries <- ArdecheStMartin
#go from six-hourly values to daily max
timeAndSeries <- max_daily_value(timeAndSeries)
#keep only the 30 last years
yrs <- as.integer(format(timeAndSeries$date, "%Y"))
tokeep <- which(yrs>=1990)
timeAndSeries <- timeAndSeries[tokeep,]
timeWindow <- 10*365 # 10 years
TSEVA_data <- TsEvaNs(timeAndSeries, timeWindow,
transfType = 'trendPeaks',tail = 'high')
nonStationaryEvaParams <- TSEVA_data[[1]]
stationaryTransformData <- TSEVA_data[[2]]
trans='ori'
result = tsEvaPlotSeriesTrendStdDevFromAnalyisObj(nonStationaryEvaParams,
stationaryTransformData, trans)
result

Description

tsEvaPlotTransfToStatis a function that creates a line plot of time series data along with statistical measures.

Usage

tsEvaPlotTransfToStat(
  timeStamps,
  statSeries,
  srsmean,
  stdDev,
  st3mom,
  st4mom,
  varargin
)

Arguments

Value

A ggplot object representing the line plot.

See Also

tsEvaPlotTransfToStatFromAnalysisObj

Description

tsEvaPlotTransfToStatFromAnalysisObjis a function that takes the parameters of a non-stationary time series evaluation, along with the transformed stationary data, and plots the converted stationary series.

Usage

tsEvaPlotTransfToStatFromAnalysisObj(
  nonStationaryEvaParams,
  stationaryTransformData,
  ...
)

Arguments

Value

The plot object representing the converted stationary series.

See Also

tsEvaPlotTransfToStat

Examples

# Example usage of TsEvaNs function
timeAndSeries <- ArdecheStMartin
#go from six-hourly values to daily max
timeAndSeries <- max_daily_value(timeAndSeries)
#keep only the 30 last years
yrs <- as.integer(format(timeAndSeries$date, "%Y"))
tokeep <- which(yrs>=1990)
timeAndSeries <- timeAndSeries[tokeep,]
timeWindow <- 10*365 # 10 years
TSEVA_data <- TsEvaNs(timeAndSeries, timeWindow,
transfType = 'trendPeaks',tail = 'high')
# Define the required function argumentsnonStationaryEvaParams <- TSEVA_data[[1]]
stationaryTransformData <- TSEVA_data[[2]]
nonStationaryEvaParams <- TSEVA_data[[1]]
trans='ori'
ExRange= c(min(nonStationaryEvaParams$potObj$parameters$peaks),
max(nonStationaryEvaParams$potObj$parameters$peaks))
Y <- c(seq(min(ExRange),max(ExRange),length.out=700))
result = tsEvaPlotTransfToStatFromAnalysisObj (nonStationaryEvaParams,
stationaryTransformData)
result

Description

This function calculates the running mean trend of a given time series using a specified time window.

Usage

tsEvaRunningMeanTrend(timeStamps, series, timeWindow)

Arguments

Value

A list containing the running mean trend series and the number of observations used for each running mean calculation.

Examples

timeAndSeries <- ArdecheStMartin
timeStamps <- ArdecheStMartin[,1]
series  <- ArdecheStMartin[,2]
timeWindow <- 365*30
result <- tsEvaRunningMeanTrend(timeStamps, series, timeWindow)
result$trendSeries
result$nRunMn

Description

tsEvaSampleData is a function that calculates various statistics and data for time series evaluation.

Usage

tsEvaSampleData(
  ms,
  meanEventsPerYear,
  minEventsPerYear,
  minPeakDistanceInDays,
  tail = NA
)

Arguments

Value

A list containing the following elements:

completeSeries

The complete time series data.

POT

The data for Peaks Over Threshold (POT) analysis.

years

The years in the time series data.

Percentiles

The desired percentiles and their corresponding values.

annualMax

The annual maximum values.

annualMaxDate

The dates corresponding to the annual maximum values.

annualMaxIndx

The indices of the annual maximum values.

monthlyMax

The monthly maximum values.

monthlyMaxDate

The dates corresponding to the monthly maximum values.

monthlyMaxIndx

The indices of the monthly maximum values.

See Also

tsGetPOT()

Examples

# Generate sample data
data <- ArdecheStMartin
colnames(data) <- c("Date", "Value")
#select only the 5 latest years
yrs <- as.integer(format(data$Date, "%Y"))
tokeep <- which(yrs>=2015)
data <- data[tokeep,]
timeWindow <- 365 # 1 year
# Calculate statistics and data
result <- tsEvaSampleData(data, meanEventsPerYear=3, minEventsPerYear=0,
minPeakDistanceInDays=7, "high")
# View the result
print(result)

Description

This function decomposes a time series into a season-dependent trend and a season-dependent standard deviation.It performs a transformation from non-stationary to stationary.

Usage

tsEvaTransformSeriesToStationaryMultiplicativeSeasonality(
  timeStamps,
  series,
  timeWindow,
  seasonalityVar = TRUE
)

Arguments

Value

A list containing the transformed data and various statistics and errors.

runningStatsMulteplicity

The size of the moving window used for trend estimation

stationarySeries

The transformed stationary series

trendSeries

The trend component of the transformed series

trendSeriesNonSeasonal

The trend component of the original series without seasonality

stdDevSeries

The standard deviation component of the transformed series

stdDevSeriesNonSeasonal

The standard deviation component of the original series without seasonality

trendNonSeasonalError

The error on the non-seasonal trend component

stdDevNonSeasonalError

The error on the non-seasonal standard deviation component

trendSeasonalError

The error on the seasonal trend component

stdDevSeasonalError

The error on the seasonal standard deviation component

trendError

The overall error on the trend component

stdDevError

The overall error on the standard deviation component

Regime

The estimated regime of the trend seasonality

timeStamps

The input timestamps

nonStatSeries

The original non-stationary series

statSer3Mom

The third moment of the transformed stationary series

statSer4Mom

The fourth moment of the transformed stationary series

transformation non stationary -> stationary

transformation stationary -> non stationary y(t) = stdDev(t)*ssn_stdDev(t)*x(t) + trend(t) + ssn_trend(t) trasfData.trendSeries = trend(t) + ssn_trend(t) trasfData.stdDevSeries = stdDev(t)*ssn_stdDev(t)

Examples

timeAndSeries <- ArdecheStMartin
timeStamps <- ArdecheStMartin[,1]
series <- ArdecheStMartin[,2]
#select only the 5 latest years
yrs <- as.integer(format(timeStamps, "%Y"))
tokeep <- which(yrs>=2015)
timeStamps <- timeStamps[tokeep]
series <- series[tokeep]
timeWindow <- 365 # 1 year
TrendTh <- NA
result <- tsEvaTransformSeriesToStationaryMultiplicativeSeasonality(timeStamps,
series, timeWindow,seasonalityVar=FALSE)
plot(result$trendSeries)

Description

tsEvaTransformSeriesToStationaryPeakTrend transforms a time series to a stationary one by focusing on extremes. The trend and slowly varying amplitude are computed on values above a threshold defined by the user or automatically with the function tsEvaFindTrendThreshold.

Usage

tsEvaTransformSeriesToStationaryPeakTrend(
  timeStamps,
  series,
  timeWindow,
  TrendTh
)

Arguments

Value

A list containing the following components:

runningStatsMulteplicity

The multiplicity of running statistics.

stationarySeries

The stationary series after removing the trend.

trendSeries

The trend component of the series.

trendSeriesNonSeasonal

NULL (not used).

trendError

The error on the trend component.

stdDevSeries

The standard deviation series.

stdDevSeriesNonSeasonal

NULL (not used).

stdDevError

The error on the standard deviation series.

timeStamps

The time stamps.

nonStatSeries

The original non-stationary series.

statSer3Mom

The running mean of the third moment of the stationary series.

statSer4Mom

The running mean of the fourth moment of the stationary series.

See Also

tsEvaFindTrendThreshold()

Examples

timeAndSeries <- ArdecheStMartin
timeStamps <- ArdecheStMartin[,1]
series <- ArdecheStMartin[,2]
#select only the 5 latest years
yrs <- as.integer(format(timeStamps, "%Y"))
tokeep <- which(yrs>=2015)
timeStamps <- timeStamps[tokeep]
series <- series[tokeep]
timeWindow <- 365 # 1 year
TrendTh <- NA
result <- tsEvaTransformSeriesToStationaryPeakTrend(timeStamps,
series, timeWindow, TrendTh)
plot(result$trendSeries)

Description

This function takes a time series and transforms it into a stationary trend series by removing the trend component and detecting change points. It computes the slowly varying standard deviation and normalizes the stationary series before detecting step changes. It also calculates the error on the trend and standard deviation.

Usage

tsEvaTransformSeriesToStationaryTrendAndChangepts(
  timeStamps,
  series,
  timeWindow
)

Arguments

Value

A list containing the following elements:

runningStatsMulteplicity

The running statistics multiplicity.

stationarySeries

The transformed stationary series.

trendSeries

The trend series.

trendonlySeries

The trend series without the stationary component.

ChpointsSeries2

The trend component of the change points.

changePoints

The detected change points.

trendSeriesNonSeasonal

The trend series without the seasonal component.

trendError

The error on the trend.

stdDevSeries

The slowly varying standard deviation series.

stdDevSeriesNonStep

The slowly varying standard deviation series without step changes.

stdDevError

The error on the standard deviation.

timeStamps

The time stamps.

nonStatSeries

The original non-stationary series.

statSer3Mom

The running mean of the third moment of the stationary series.

statSer4Mom

The running mean of the fourth moment of the stationary series.

Examples

timeAndSeries <- ArdecheStMartin
timeStamps <- ArdecheStMartin[,1]
series <- ArdecheStMartin[,2]
#select only the 5 latest years
yrs <- as.integer(format(timeStamps, "%Y"))
tokeep <- which(yrs>=2015)
timeStamps <- timeStamps[tokeep]
series <- series[tokeep]
timeWindow <- 365 # 1 year
percentile <- 90
result <- tsEvaTransformSeriesToStationaryTrendAndChangepts(timeStamps,
series, timeWindow)
plot(result$trendSeries)

Description

This function takes a time series and transforms it into a stationary trend series with change points and confidence intervals.

Usage

tsEvaTransformSeriesToStationaryTrendAndChangepts_ciPercentile(
  timeStamps,
  series,
  timeWindow,
  percentile
)

Arguments

Value

A list containing the following elements:

runningStatsMulteplicity

The running statistics multiplicity

stationarySeries

The transformed stationary series

trendSeries

The trend series

trendonlySeries

The trend series without the stationary component

ChpointsSeries2

The trend series with change points

changePoints

The detected change points

trendSeriesNonSeasonal

The trend series without the seasonal component

trendError

The error on the trend

stdDevSeries

The standard deviation series

stdDevSeriesNonStep

The standard deviation series without the step change component

stdDevError

The error on the standard deviation

timeStamps

The time stamps

nonStatSeries

The original non-stationary series

statSer3Mom

The running mean of the third moment of the stationary series

statSer4Mom

The running mean of the fourth moment of the stationary series

Examples

timeAndSeries <- ArdecheStMartin

#go from six-hourly values to daily max
timeAndSeries <- max_daily_value(timeAndSeries)
timeStamps <- timeAndSeries[,1]
series <- timeAndSeries[,2]

#select only the 5 latest years
yrs <- as.integer(format(timeStamps, "%Y"))
tokeep <- which(yrs>=2015)
timeStamps <- timeStamps[tokeep]
series <- series[tokeep]
timeWindow <- 365 # 1 year
percentile <- 90
result <- tsEvaTransformSeriesToStationaryTrendAndChangepts_ciPercentile(timeStamps,
series, timeWindow, percentile)
plot(result$trendSeries)

Description

tsEvaTransformSeriesToStationaryTrendOnly is the original detrending function implemented in Mentaschi et al.(2016). It takes a time series and transforms it into a stationary one. It computes the trend as a running average of the time series, the slowly varying amplitude as its standard deviation, and other statistical measures.

Usage

tsEvaTransformSeriesToStationaryTrendOnly(timeStamps, series, timeWindow)

Arguments

Value

A list containing the following elements:

runningStatsMulteplicity

The running statistics multiplicity.

stationarySeries

The transformed stationary series.

trendSeries

The trend series.

trendSeriesNonSeasonal

The non-seasonal trend series.

trendError

The error on the trend.

stdDevSeries

The slowly varying standard deviation series.

stdDevSeriesNonSeasonal

The non-seasonal slowly varying standard deviation series.

stdDevError

The error on the standard deviation.

timeStamps

The time stamps.

nonStatSeries

The original non-stationary series.

statSer3Mom

The third moment of the transformed stationary series.

statSer4Mom

The fourth moment of the transformed stationary series.

Examples

timeAndSeries <- ArdecheStMartin
timeStamps <- ArdecheStMartin[,1]
series <- ArdecheStMartin[,2]
timeWindow <- 30*365 # 30 years
#select only the 5 latest years
yrs <- as.integer(format(timeStamps, "%Y"))
tokeep <- which(yrs>=2015)
timeStamps <- timeStamps[tokeep]
series <- series[tokeep]
timeWindow <- 365 # 1 year
result <- tsEvaTransformSeriesToStationaryTrendOnly(timeStamps, series, timeWindow)
plot(result$trendSeries)

Description

tsEvaTransformSeriesToStationaryTrendOnly_ciPercentile transforms a time series to a stationary ones using a moving average as the trend and a running percentiles to represent the slowly varying amplitude of the distribution

Usage

tsEvaTransformSeriesToStationaryTrendOnly_ciPercentile(
  timeStamps,
  series,
  timeWindow,
  percentile
)

Arguments

Value

A list containing the following elements:

runningStatsMulteplicity

The running statistics multiplicity

stationarySeries

The transformed stationary trend only series

trendSeries

The trend series

trendSeriesNonSeasonal

The non-seasonal trend series

trendError

The error on the trend

stdDevSeries

The standard deviation series

stdDevSeriesNonSeasonal

The non-seasonal standard deviation series

stdDevError

The error on the standard deviation

timeStamps

The time stamps

nonStatSeries

The original non-stationary series

statSer3Mom

The running mean of the third moment of the stationary series

statSer4Mom

The running mean of the fourth moment of the stationary series

Examples

timeAndSeries <- ArdecheStMartin
timeStamps <- ArdecheStMartin[,1]
series <- ArdecheStMartin[,2]
#select only the 5 latest years
yrs <- as.integer(format(timeStamps, "%Y"))
tokeep <- which(yrs>=2015)
timeStamps <- timeStamps[tokeep]
series <- series[tokeep]
timeWindow <- 365 # 1 year
percentile <- 90
result <- tsEvaTransformSeriesToStationaryTrendOnly_ciPercentile(timeStamps,
series, timeWindow, percentile)
plot(result$trendSeries)

Description

This function decomposes a time series into a season-dependent trend and a season-dependent standard deviation. The season-dependent amplitude is given by a seasonal factor multiplied by a slowly varying percentile.

Usage

tsEvaTransformSeriesToStatSeasonal_ciPercentile(
  timeStamps,
  series,
  timeWindow,
  percentile
)

Arguments

Value

A list containing the following components:

runningStatsMulteplicity

The size of each sample used to compute the average

stationarySeries

The transformed stationary series

trendSeries

The trend series

trendSeriesNonSeasonal

The non-seasonal trend series

stdDevSeries

The season-dependent standard deviation series

stdDevSeriesNonSeasonal

The non-seasonal standard deviation series

trendError

The error on the trend

stdDevError

The error on the standard deviation

statSer3Mom

The 3rd moment of the transformed stationary series

statSer4Mom

The 4th moment of the transformed stationary series

nonStatSeries

The original non-stationary series

Regime

The regime of the trend seasonality

timeStamps

The time stamps

trendNonSeasonalError

The error on the non-seasonal trend

stdDevNonSeasonalError

The error on the non-seasonal standard deviation

trendSeasonalError

The error on the seasonal trend

stdDevSeasonalError

The error on the seasonal standard deviation

this function decomposes the series into a season-dependent trend and a

season-dependent standard deviation. The season-dependent standard deviation is given by a seasonal factor multiplied by a slowly varying standard deviation. transformation non stationary -> stationary x(t) = (y(t) - trend(t) - ssn_trend(t))/(stdDev(t)*ssn_stdDev(t)) transformation stationary -> non stationary y(t) = stdDev(t)*ssn_stdDev(t)*x(t) + trend(t) + ssn_trend(t) trasfData.trendSeries = trend(t) + ssn_trend(t) trasfData.stdDevSeries = stdDev(t)*ssn_stdDev(t)

Examples

timeAndSeries <- ArdecheStMartin
timeStamps <- ArdecheStMartin[,1]
series <- ArdecheStMartin[,2]
#select only the 5 latest years
yrs <- as.integer(format(timeStamps, "%Y"))
tokeep <- which(yrs>=2015)
timeStamps <- timeStamps[tokeep]
series <- series[tokeep]
timeWindow <- 365 # 1 year
percentile <- 90
result <- tsEvaTransformSeriesToStatSeasonal_ciPercentile(timeStamps,
series, timeWindow, percentile)
plot(result$trendSeries)

Description

tsEvstatistics is a function that calculates the Generalized Extreme Value (GEV) and Generalized Pareto Distribution (GPD) statistics and return levels for a given dataset of extreme values.

Usage

tsEVstatistics(
  pointData,
  alphaCI = 0.95,
  gevMaxima = "annual",
  gevType = "GEV",
  evdType = c("GEV", "GPD"),
  shape_bnd = c(-0.5, 1)
)

Arguments

Value

A list containing the following components:

EVmeta

A list containing metadata about the analysis. It includes Tr, A vector of return periods for which return levels are calculated

EVdata

A list containing the calculated statistics and return levels. It includes the following components:

GEVstat

A list containing the GEV statistics and return levels:

method

The method used for fitting the GEV distribution.

values

A vector of return levels calculated using the GEV distribution.

parameters

A vector of parameter estimates for the GEV distribution.

paramCIs

A matrix of confidence intervals for the parameter estimates.

GPDstat

list containing the GPD statistics and return levels:

method

The method used for fitting the GPD distribution

values

A vector of return levels calculated using the GPD distribution

parameters

A vector of parameter estimates for the GPD distribution

paramCIs

A matrix of confidence intervals for the parameter estimates

isValid

A logical value indicating whether the analysis was performed or not.

Examples

# Create a sample dataset
data <- ArdecheStMartin
colnames(data) <- c("Date", "Value")
yrs <- as.integer(format(data$Date, "%Y"))
tokeep <- which(yrs>=2015)
data <- data[tokeep,]
pointData <- tsEvaSampleData(data, meanEventsPerYear=3, minEventsPerYear=0,
minPeakDistanceInDays=7, "high")
result <- tsEVstatistics(pointData)
result$EVdata$GEVstat$values
result$EVdata$GPDstat$values

Description

tsGetNumberPerYear is a function that calculates the number of events per year based on a given time series and a set of locations.

Usage

tsGetNumberPerYear(ms, locs)

Arguments

Value

A data frame with two columns: "year" and "Freq". The "year" column contains the years, and the "Freq" column contains the number of events per year.

Examples

# Create a sample time series data frame
set.seed(123)
ms <- data.frame(date = seq(as.Date("2000-01-01"), as.Date("2022-12-31"), by = "day"),
                values=rnorm(8401))
# Generate random events
events <- match(sample(ms$date, 100),ms$date)
# Get the number of events per year
tsGetNumberPerYear(ms, events)

Description

tsGetPOT is a function that calculates the Peaks Over Threshold (POT) for a given time series data.

Usage

tsGetPOT(
  ms,
  pcts,
  desiredEventsPerYear,
  minEventsPerYear,
  minPeakDistanceInDays,
  tail
)

Arguments

Value

A list containing the following fields:

threshold

The threshold value used for identifying peaks

thresholdError

The error associated with the threshold value

percentile

The percentile value used as the threshold.

peaks

The values of the identified peaks.

stpeaks

The start indices of the identified peaks.

endpeaks

The end indices of the identified peaks.

ipeaks

The indices of the identified peaks.

time

The time values corresponding to the identified peaks.

pars

The parameters of the Generalized Pareto Distribution (GPD) fitted to the peaks.

See Also

tsEvaSampleData()

Examples

# Create a sample time series data
ms <- ArdecheStMartin

# Calculate the POT using the tsGetPOT function
pcts <- c(90, 95, 99)
desiredEventsPerYear <- 5
minEventsPerYear <- 2
minPeakDistanceInDays <- 10
tail <- "high"
POTdata <- tsGetPOT(ms, pcts, desiredEventsPerYear, minEventsPerYear, minPeakDistanceInDays, tail)
# Print the results
print(POTdata)