The hardware and bandwidth for this mirror is donated by METANET, the Webhosting and Full Service-Cloud Provider.
If you wish to report a bug, or if you are interested in having us mirror your free-software or open-source project, please feel free to contact us at mirror[@]metanet.ch.

Type: Package
Date: 2024-02-02
License: GPL-3
Title: Multi-Site Stochastic Models for Daily Precipitation and Temperature
Version: 1.1.3
Author: Guillaume Evin [aut, cre]
Maintainer: Guillaume Evin <guillaume.evin@inrae.fr>
Imports: Rcpp (≥ 1.0.11), EnvStats, MASS, mvtnorm, nleqslv, fGarch, parallel, abind, foreach, doParallel, Renext, lmomco, methods, stats
LinkingTo: Rcpp, RcppArmadillo
Description: Application of multi-site models for daily precipitation and temperature data. This package is designed for an application to 105 precipitation and 26 temperature gauges located in Switzerland. It applies fitting procedures and provides weather generators described in the following references: - Evin, G., A.-C. Favre, and B. Hingray. (2018) <doi:10.5194/hess-22-655-2018>. - Evin, G., A.-C. Favre, and B. Hingray. (2018) <doi:10.1007/s00704-018-2404-x>.
Depends: R (≥ 2.10)
Encoding: UTF-8
LazyData: true
RoxygenNote: 7.2.3
NeedsCompilation: yes
Packaged: 2024-02-02 08:47:58 UTC; eving
Repository: CRAN
Date/Publication: 2024-02-02 09:00:02 UTC

EGPD.GI.fPWM

Description

Parameter estimation of the unified EGPD distribution with the PWM method. Set of equations which have to be equal to zero

Usage

EGPD.GI.fPWM(par, pwm, xi)

Arguments

par

vector of parameters kappa,sig,xi

pwm

set of probability weighted moments of order 0, 1 and 2

xi

shape parameter

Value

differences between expected and target weighted moments

Author(s)

Guillaume Evin

EGPD.GI.fit.PWM

Description

Parameter estimation of the unified EGPD distribution with the PWM method. Numerical solver of the system of nonlinear equations

Usage

EGPD.GI.fit.PWM(x, xi = 0.05)

Arguments

x

vector of parameters kappa,sig

xi

shape parameter

Value

estimated parameters kappa, sig, xi

Author(s)

Guillaume Evin

Class Gwex

Description

Defines a generic Gwex object. GWex objects contain two slots: - the version ('vX.X.X') - the type of variable ('Prec' or 'Temp')

Author(s)

Guillaume Evin

Class GwexFit

Description

Defines a GwexFit object which is a Gwex object containing 'fit', a list containing the fitted parameters, and 'p', the number of stations. See fitGwexModel for some examples.

Author(s)

Guillaume Evin

Constructor

Description

Constructor of class [GwexObs]

Usage

GwexObs(variable, date, obs)

Arguments

variable

'Prec' or 'Temp'

date

vector of class 'Date'

obs

matrix nTime x nStations of observations

Value

An object of class [GwexObs]

Examples

# Format dates corresponding to daily observations of precipitation and temperature
vecDates = seq(from=as.Date("01/01/2005",format="%d/%m/%Y"),
to=as.Date("31/12/2014",format="%d/%m/%Y"),by='day')

# build GwexObs object with precipitation data
myObsPrec = GwexObs(variable='Prec',date=vecDates,obs=dailyPrecipGWEX)

# print GwexObs object
myObsPrec 

# build GwexObs object with temperature data
myObsTemp = GwexObs(variable='Temp',date=vecDates,obs=dailyTemperGWEX)

# print GwexObs object
myObsTemp

Class GwexObs

Description

Defines a GwexObs object which is a Gwex object containing dates and a matrix of observations.

Author(s)

Guillaume Evin

Examples

# Format dates corresponding to daily observations of precipitation and temperature
vecDates = seq(from=as.Date("01/01/2005",format="%d/%m/%Y"),
to=as.Date("31/12/2014",format="%d/%m/%Y"),by='day')

# build GwexObs object with precipitation data
myObsPrec = GwexObs(variable='Prec',date=vecDates,obs=dailyPrecipGWEX)

# print GwexObs object
myObsPrec 

# build GwexObs object with temperature data
myObsTemp = GwexObs(variable='Temp',date=vecDates,obs=dailyTemperGWEX)

# print GwexObs object
myObsTemp

Defines a GwexSim object which is a Gwex object containing 'sim', an array containing the simulations, and 'dates', a vector of dates. See simGwexModel for some examples.

Description

Defines a GwexSim object which is a Gwex object containing 'sim', an array containing the simulations, and 'dates', a vector of dates. See simGwexModel for some examples.

Author(s)

Guillaume Evin

EGPD.GI.mu0, EGPD.GI.mu1, EGPD.GI.mu2

Description

Probability Weighted Moments of order 0, 1 and 2 of the unified EGPD distribution

Usage

EGPD.GI.mu0(kappa, sig, xi)

EGPD.GI.mu1(kappa, sig, xi)

EGPD.GI.mu2(kappa, sig, xi)

Arguments

kappa

transformation parameter greater than 0

sig

Scale parameter

xi

Shape parameter

Value

Probability Weighted Moments

Author(s)

Guillaume Evin

QtransMat2Array

Description

reshape Qtrans.mat to an array

Usage

QtransMat2Array(n, p, Qtrans.mat)

Arguments

n

matrix of precipitation

p

number of stations

Qtrans.mat

transition probabilities, 2 x ncomb matrix

Value

array

array of transition probabilities with dimension n x p x n.comb

Author(s)

Guillaume Evin

agg.matrix

Description

Simple accumulation of a matrix of precipitation

Usage

agg.matrix(mat, k, average = F)

Arguments

mat

matrix nDates x nStations to be aggregated

k

number of days for the accumulation

average

logical: should we average over the different periods (default=F)

Value

aggregated matrix

Author(s)

Guillaume Evin

autocor.emp.int

Description

Finds empirical autocorrelations (lag-1) between intensities corresponding to a degree of autocorrelation of an AR(1) process

Usage

autocor.emp.int(rho, nChainFit, Xt, parMargin, typeMargin)

Arguments

rho

autocorrelation of the AR(1) process

nChainFit

number of simulated variates

Xt

simulated occurrences, nChainFit x 2 matrix

parMargin

parameters of the margins 2 x 3

typeMargin

type of marginal distribution: 'EGPD' or 'mixExp'

Value

scalar

correlation between simulated intensities

Author(s)

Guillaume Evin

cor.emp.int

Description

Finds observed correlations between intensities corresponding to a degree of correlation of Gaussian multivariate random numbers

Usage

cor.emp.int(zeta, nChainFit, Xt, parMargin, typeMargin)

Arguments

zeta

correlation of Gaussian multivariates

nChainFit

number of simulated variates

Xt

simulated occurrences, n x 2 matrix

parMargin

parameters of the margins 2 x 3

typeMargin

type of marginal distribution: 'EGPD' or 'mixExp'

Value

scalar

correlation between simulated intensities

Author(s)

Guillaume Evin

cor.emp.occ

Description

Finds observed correlations between occurrences corresponding to a degree of correlation of Gaussian multivariate random numbers

Usage

cor.emp.occ(w, Qtrans.mat, mat.comb, nLag, nChainFit, myseed = 1)

Arguments

w

correlation of Gaussian multivariates

Qtrans.mat

transition probabilities, 2 x ncomb matrix

mat.comb

matrix of logical: ncomb x nlag

nLag

order of the Markov chain

nChainFit

number of simulated variates

myseed

seed of random variates

Value

scalar

correlation between occurrences

Author(s)

Guillaume Evin

cor.obs.occ

Description

provide observed correlations between occurrences for all pairs of stations see Mhanna et al. (2012)

Usage

cor.obs.occ(pi00, pi0, pi1)

Arguments

pi00

joint probability of having dry states

pi0

probability of having a dry state

pi1

probability of having a wet state

Value

scalar

matrix of observed correlations

Author(s)

Guillaume Evin

References

Mhanna, Muamaraldin, and Willy Bauwens. “A Stochastic Space-Time Model for the Generation of Daily Rainfall in the Gaza Strip.” International Journal of Climatology 32, no. 7 (June 15, 2012): 1098–1112. doi:10.1002/joc.2305.

daily observations of precipitation data

Description

Example of daily observations of precipitation (mm) for three fictive stations, for a period of ten years.

Usage

data(dailyPrecipGWEX)

Format

matrix of Observed precipitation: 3652 days x 3 stations

Author(s)

Guillaume Evin guillaume.evin@irstea.fr

References

Evin, G., A.-C. Favre, and B. Hingray. 2018. “Stochastic Generation of Multi-Site Daily Precipitation Focusing on Extreme Events". Hydrol. Earth Syst. Sci. 22 (1): 655–672.

daily observations of temperature data

Description

Example of daily observations of temperature (mm) for three fictive stations, for a period of ten years.

Usage

data(dailyTemperGWEX)

Format

matrix of Observed temperature: 3652 days x 3 stations

Author(s)

Guillaume Evin guillaume.evin@irstea.fr

References

Evin G., A.C. Favre, and B. Hingray. 2018. Stochastic Generators of Multi Site Daily Temperature: Comparison of Performances in Various Applications. Theoretical and Applied Climatology.

disag.3D.to.1D

Description

disag.3D.to.1D

Usage

disag.3D.to.1D(Yobs, YObsAgg, mObsAgg, YSimAgg, mSimAgg, prob.class)

Arguments

Yobs

matrix of observed intensities at 24h: (nTobs*3) x nStation

YObsAgg

matrix of observed 3-day intensities: nTobs x nStation

mObsAgg

vector of season corresponding to YobsAgg

YSimAgg

matrix of simulated intensities per 3-day period: nTsim x nStation

mSimAgg

vector of season corresponding to the period simulated

prob.class

vector of probabilities indicating class of "similar" mean intensities

Value

list

Ysim matrix of disagregated daily precipitation, codeDisag matrix of disagregation codes

Author(s)

Guillaume Evin

dEGPD.GI, pEGPD.GI, qEGPD.GI, rEGPD.GI

Description

Density function, distribution function, quantile function, random generation for the unified EGPD distribution

Usage

dEGPD.GI(x, kappa, sig, xi)

pEGPD.GI(x, kappa, sig, xi)

qEGPD.GI(p, kappa, sig, xi)

rEGPD.GI(n, kappa, sig, xi)

Arguments

x

Vector of quantiles

kappa

transformation parameter greater than 0

sig

Scale parameter

xi

Shape parameter

p

Vector of probabilities

n

Number of observations

Value

dEGPD.GI gives the density function, pEGPD.GI gives the distribution function, qEGPD.GI gives the quantile function, and rEGPD.GI generates random deviates.

Author(s)

Guillaume Evin

dry.day.frequency

Description

Estimate the dry day frequency (proportion of dry days) for all stations

Usage

dry.day.frequency(mat.prec, th)

Arguments

mat.prec

matrix of precipitation (possibly for one month/period)

th

threshold above which we consider that a day is wet (e.g. 0.2 mm)

Value

vector of numeric

dry day frequencies

Author(s)

Guillaume Evin

find.autocor

Description

finds the autocorrelation leading to observed autocorrelation

Usage

find.autocor(autocor.emp, nChainFit, Xt, parMargin, typeMargin)

Arguments

autocor.emp

target correlation between intensities

nChainFit

number of simulations

Xt

simulated occurrences, nChainFit x 2 matrix

parMargin

parameters of the margins 2 x 3

typeMargin

type of marginal distribution: 'EGPD' or 'mixExp'

Value

scalar

needed correlation

Author(s)

Guillaume Evin

find.omega

Description

finds the correlation between normal variates leading to correlation between occurrences

Usage

find.omega(rho.emp, Qtrans.mat, mat.comb, nLag, nChainFit)

Arguments

rho.emp

target correlation between occurences

Qtrans.mat

transition probabilities, 2 x ncomb matrix

mat.comb

matrix of logical: ncomb x nlag

nLag

order of the Markov chain

nChainFit

length of the simulated chains used during the fitting

Value

scalar

needed correlation

Author(s)

Guillaume Evin

find.zeta

Description

finds the correlation between normal variates leading to correlation between intensities

Usage

find.zeta(eta.emp, nChainFit, Xt, parMargin, typeMargin)

Arguments

eta.emp

target correlation between intensities

nChainFit

number of simulations

Xt

simulated occurrences, n x 2 matrix

parMargin

parameters of the margins 2 x 3

typeMargin

type of marginal distribution: 'EGPD' or 'mixExp'

Value

scalar

needed correlation

Author(s)

Guillaume Evin

fit.GWex.prec

Description

estimate all the parameters for the G-Wex model of precipitation

Usage

fit.GWex.prec(objGwexObs, parMargin, listOption = NULL)

Arguments

objGwexObs

object of class GwexObs

parMargin

if not NULL, list where each element parMargin[[iM]] corresponds to a month iM=1...12 and contains a matrix nStation x 3 of estimated parameters of the marginal distributions (EGPD or mixture of exponentials)

listOption

list with the following fields:

  • th: threshold value in mm above which precipitation observations are considered to be non-zero (=0.2 by default)

  • nLag: order of he Markov chain for the transitions between dry and wet states (=2 by default)

  • typeMargin: 'EGPD' (Extended GPD) or 'mixExp' (Mixture of Exponentials). 'EGPD' by default

  • copulaInt: 'Gaussian' or 'Student': type of dependence for amounts (='Student' by default)

  • isMAR: logical value, do we apply a Autoregressive Multivariate Autoregressive model (order 1) =TRUE by default

  • is3Damount: logical value, do we apply the model on 3D-amount. =FALSE by default

  • nChainFit: integer, length of the runs used during the fitting procedure. =100000 by default

  • nCluster: integer, number of clusters which can be used for the parallel computation

Value

a list containing the list of options listOption and the list of estimated parameters listPar. The parameters of the occurrence process are contained in parOcc and the parameters related to the precipitation amounts are contained in parInt. Each type of parameter is a list containing the estimates for each month. In parOcc, we find:

In parInt, we have:

Author(s)

Guillaume Evin

References

Evin, G., A.-C. Favre, and B. Hingray. 2018. 'Stochastic Generation of Multi-Site Daily Precipitation Focusing on Extreme Events.' Hydrol. Earth Syst. Sci. 22 (1): 655-672. doi.org/10.5194/hess-22-655-2018.

fit.MAR1.amount

Description

estimate parameters which control the dependence between intensities with a MAR(1) process

Usage

fit.MAR1.amount(P.mat, isPeriod, th, copulaInt, M0, A)

Arguments

P.mat

precipitation matrix

isPeriod

vector of logical n x 1 indicating the days concerned by a 3-month period

th

threshold above which we consider that a day is wet (e.g. 0.2 mm)

copulaInt

type of dependance between inter-site amounts: 'Gaussian' or 'Student'

M0

covariance matrix of gaussianized prec. amounts for all pairs of stations

A

Matrix containing the autocorrelation (temporal) correlations

Value

list with the following items

Author(s)

Guillaume Evin

References

Matalas, N. C. 1967. “Mathematical Assessment of Synthetic Hydrology.” Water Resources Research 3 (4): 937–45. https://doi.org/10.1029/WR003i004p00937.

Bárdossy, A., and G. G. S. Pegram. 2009. “Copula Based Multisite Model for Daily Precipitation Simulation.” Hydrology and Earth System Sciences 13 (12): 2299–2314. https://doi.org/10.5194/hess-13-2299-2009.

fit.copula.amount

Description

estimate parameters which control the spatial dependence between intensities using a copula

Usage

fit.copula.amount(P.mat, isPeriod, th, copulaInt, M0)

Arguments

P.mat

precipitation matrix

isPeriod

vector of logical n x 1 indicating the days concerned by a 3-month period

th

threshold above which we consider that a day is wet (e.g. 0.2 mm)

copulaInt

type of dependence between inter-site amounts: 'Gaussian' or 'Student'

M0

covariance matrix of gaussianized prec. amounts for all pairs of stations

Value

list

list of estimates (e.g., M0, dfStudent)

Author(s)

Guillaume Evin

fit.margin.cdf

Description

estimate parameters which control the marginal distribution of precipitation amounts

Usage

fit.margin.cdf(P.mat, isPeriod, th, type = c("EGPD", "mixExp"))

Arguments

P.mat

precipitation matrix

isPeriod

vector of logical n x 1 indicating the days concerned by a 3-month period

th

threshold above which we consider that a day is wet (e.g. 0.2 mm)

type

distribution: 'EGPD' or 'mixExp'

Value

matrix

matrix of estimates p x 3

Author(s)

Guillaume Evin

fitGwexModel: fit a GWex model to observations.

Description

fitGwexModel: fit a GWex model to observations.

Usage

fitGwexModel(objGwexObs, parMargin = NULL, listOption = NULL)

Arguments

objGwexObs

an object of class GwexObs

parMargin

(not required for temperature) list parMargin where and each element corresponds to a month (1...12) and contains a matrix nStation x 3 of pre-estimated parameters of the marginal distributions (EGPD or Mixture of Exponentials)

listOption

for precipitation, a list with the following fields:

  • th: threshold value in mm above which precipitation observations are considered to be non-zero (=0.2 by default)

  • nLag: order of the Markov chain for the transitions between dry and wet states (=2 by default)

  • typeMargin: 'EGPD' (Extended GPD) or 'mixExp' (Mixture of Exponentials). 'mixExp' by default

  • copulaInt: 'Gaussian' or 'Student': type of dependence for amounts (='Gaussian' by default)

  • isMAR: logical value, do we apply a Autoregressive Multivariate Autoregressive model (order 1) = FALSE by default

  • is3Damount: logical value, do we apply the model on 3D-amount. =FALSE by default

  • nChainFit: integer, length of the runs which are generated during the fitting procedure. =100000 by default

  • nCluster: integer, number of clusters which can be used for the parallel computation

and for temperature, a list with the following fields:

  • hasTrend: logical value, do we fit a linear trend for the long-term change, =FALSE by default

  • objGwexPrec: object of class GwexObs containing precipitation observations. If provided, we assume that temperature must be modelled and simulated according to the precipitation states 'dry' and 'wet'. For each state, a seasonal cycle is fitted (mean and sd).

  • typeMargin: 'SGED' (default) or 'Gaussian': type of marginal distribution.

  • depStation: 'MAR1' (default) or 'Gaussian': MAR1 (Multivariate Autoregressive model order 1) for the spatial and temporal dependence or 'Gaussian' for the spatial dependence only.

Value

Return an object of class GwexFit with:

Author(s)

Guillaume Evin

Examples

# Format dates corresponding to daily observations of precipitation and temperature
vecDates = seq(from=as.Date("01/01/2005",format="%d/%m/%Y"),
to=as.Date("31/12/2014",format="%d/%m/%Y"),by='day')

###############################################################
#               FIT THE PRECIPITATION MODEL
###############################################################

# Format observations: create a Gwex object for one station only to show a quick
# example. The syntax is similar for multi-site applications.
myObsPrec = GwexObs(variable='Prec',date=vecDates,obs=dailyPrecipGWEX[,1,drop=FALSE])

# Fit precipitation model with a threshold of 0.5 mm to distinguish wet and dry 
# states (th) and keep default options otherwise, e.g. a Gaussian
# copula for the spatial dependence (copulaInt) and a mixExp distribution for 
# marginal intensities ('typeMargin')
myParPrec = fitGwexModel(myObsPrec,listOption=list(th=0.5))
myParPrec # print object

###############################################################
#     FIT THE TEMPERATURE MODEL, COND. TO PRECIPITATION
###############################################################
# Format observations: create a G-Wex object
myObsTemp = GwexObs(variable='Temp',date=vecDates,obs=dailyTemperGWEX)

# Fit temperature model with a long-term linear trend ('hasTrend'), Gaussian margins 
# ('typeMargin') and Gaussian spatial dependence ('depStation')
myParTemp = fitGwexModel(myObsTemp,listOption=list(hasTrend=TRUE,typeMargin='Gaussian',
depStation='Gaussian'))
myParTemp # print object

EGPD.pGI, EGPD.dGI, EGPD.qGI

Description

First parametric family for G(v) = v^kappa: distribution, density and quantile function

Usage

EGPD.pGI(v, kappa)

EGPD.dGI(v, kappa)

EGPD.qGI(p, kappa)

Arguments

v

probability

kappa

transformation parameter greater than 0

p

probability

Value

distribution, density and quantile of EGPD

Author(s)

Guillaume Evin

get.M0

Description

find matrix of correlations leading to estimates cor between intensities

Usage

get.M0(
  cor.obs,
  infer.mat.omega.out,
  nLag,
  parMargin,
  typeMargin,
  nChainFit,
  isParallel
)

Arguments

cor.obs

matrix p x p of observed correlations between intensities for all pairs of stations

infer.mat.omega.out

output of infer.mat.omega

nLag

order of the Markov chain

parMargin

parameters of the margins p x 3

typeMargin

type of marginal distribution: 'EGPD' or 'mixExp'

nChainFit

integer indicating the length of simulated chains

isParallel

logical: indicate computation in parallel or not (easier for debugging)

Value

list with two items

Author(s)

Guillaume Evin

get.df.Student

Description

Estimates the nu parameter (degrees of freedom) of the multivariate Student distribution when the correlation matrix Sig is given

Usage

get.df.Student(P, Sig, max.df = 20)

Arguments

P

matrix of non-zero precipitation (zero precipitation are set to NA)

Sig

correlation matrix

max.df

maximum degrees of freedom tested (default=20)

Value

nu estimate

Author(s)

Guillaume Evin

References

McNeil et al. (2005) "Quantitative Risk Management"

get.df.Student

Description

get the cdf values (empirical distribution) of positive precipitation

Usage

get.emp.cdf.matrix(X)

Arguments

X

matrix of positive precipitation

Value

matrix with cdf values (NA if zero precipitation)

Author(s)

Guillaume Evin

get.list.month

Description

return a vector of 3-char tags of the 12 months

Usage

get.list.month()

get.list.season

Description

get the vector of the four seasons c('DJF','MAM','JJA','SON')

Usage

get.list.season()

Author(s)

Guillaume Evin

get.listOption

Description

get default options and check values proposed by the user

Usage

get.listOption(listOption)

Arguments

listOption

list containing fields corr. to the different options. Can be NULL if no options are set

Value

listOption

list of options

Author(s)

Guillaume Evin

get.mat.omega

Description

find omega correlation leading to estimates cor between occurrences

Usage

get.mat.omega(cor.obs, Qtrans.mat, mat.comb, nLag, nChainFit, isParallel)

Arguments

cor.obs

matrix p x p of observed correlations between occurrences for all pairs of stations

Qtrans.mat

transition probabilities, 2 x ncomb matrix

mat.comb

matrix of logical: ncomb x nlag

nLag

order of the Markov chain

nChainFit

length of the simulated chains used during the fitting

isParallel

logical: indicate computation in parallel or not (easier for debugging)

Value

matrix

omega correlations for all pairs of stations

Author(s)

Guillaume Evin

get.period.fitting.month

Description

get.period.fitting.month

Usage

get.period.fitting.month(m.char)

Arguments

m.char

3-letter name of a month (e.g. 'JAN')

return the 3 indices corresponding to the 3-month period of a month ('JAN')

get.vec.autocor

Description

find rho autocorrelation leading to empirical estimates

Usage

get.vec.autocor(vec.ar1.obs, Xt, parMargin, typeMargin, nChainFit, isParallel)

Arguments

vec.ar1.obs

vector of observed autocorrelations for all stations

Xt

simulated occurrences given model parameters of wet/dry states

parMargin

parameters of the margins p x 3

typeMargin

type of marginal distribution: 'EGPD' or 'mixExp'

nChainFit

integer indicating the length of the simulated chains

isParallel

logical: indicate computation in parallel or not (easier for debugging)

Value

vector

vector of rho parameters to simulate the MAR process

Author(s)

Guillaume Evin

getGwexFitPrec

Description

get object GwexFit derived from the parameters replicated for each month

Usage

getGwexFitPrec(
  listOption = NULL,
  p,
  condProbaWDstates,
  parMargin,
  vec.ar1 = NULL,
  M0 = NULL,
  mat.omega = NULL
)

Arguments

listOption

list of options (see fitGwexModel)

p

number of stations

condProbaWDstates

vector of length nLag^2 of transition probabilities corresponding to the nlag possible transitions between dry/wet states expand.grid(lapply(numeric(nLag), function(x) c(F,T)))

parMargin

parameters of the margins: vector of length 3

vec.ar1

vector of observed autocorrelations for all stations

M0

M0: covariance matrix of gaussianized prec. amounts for all pairs of stations

mat.omega

mat.omega: The spatial correlation matrix of occurrences \Omega

Value

Return an object of class GwexFit with:

Examples

exFitGwexPrec = getGwexFitPrec(p=2,condProbaWDstates=c(0.7,0.3,0.2,0.1),
parMargin=c(0.5,0.1,0.4),vec.ar1=rep(0.7,2),M0=rbind(c(1,0.6),c(0.6,1)),
mat.omega=rbind(c(1,0.8),c(0.8,1)))

infer.autocor.amount

Description

special case of infer.dep.amount where there is only one station

Usage

infer.autocor.amount(
  P.mat,
  pr.state,
  isPeriod,
  nLag,
  th,
  parMargin,
  typeMargin,
  nChainFit,
  isMAR,
  isParallel
)

Arguments

P.mat

precipitation matrix

pr.state

probabilities of transitions for a Markov chain with lag p.

isPeriod

vector of logical n x 1 indicating the days concerned by a 3-month period

nLag

order of he Markov chain for the transitions between dry and wet states (=2 by default)

th

threshold above which we consider that a day is wet (e.g. 0.2 mm)

parMargin

parameters of the margins 2 x 3

typeMargin

'EGPD' (Extended GPD) or 'mixExp' (Mixture of Exponentials). 'EGPD' by default

nChainFit

integer, length of the runs used during the fitting procedure. =100000 by default

isMAR

logical value, do we apply a Autoregressive Multivariate Autoregressive model (order 1) =TRUE by default

isParallel

logical: indicate computation in parallel or not (easier for debugging)

Value

list

list of estimates (e.g., M0, dfStudent)

Author(s)

Guillaume Evin

infer.dep.amount

Description

estimate parameters which control the spatial dependence between intensities using a copula

Usage

infer.dep.amount(
  P.mat,
  isPeriod,
  infer.mat.omega.out,
  nLag,
  th,
  parMargin,
  typeMargin,
  nChainFit,
  isMAR,
  copulaInt,
  isParallel
)

Arguments

P.mat

precipitation matrix

isPeriod

vector of logical n x 1 indicating the days concerned by a 3-month period

infer.mat.omega.out

output of infer.mat.omega

nLag

order of he Markov chain for the transitions between dry and wet states (=2 by default)

th

threshold above which we consider that a day is wet (e.g. 0.2 mm)

parMargin

parameters of the margins 2 x 3

typeMargin

'EGPD' (Extended GPD) or 'mixExp' (Mixture of Exponentials). 'EGPD' by default

nChainFit

integer, length of the runs used during the fitting procedure. =100000 by default

isMAR

logical value, do we apply a Autoregressive Multivariate Autoregressive model (order 1) =TRUE by default

copulaInt

'Gaussian' or 'Student': type of dependence for amounts (='Student' by default)

isParallel

logical: indicate computation in parallel or not (easier for debugging)

Value

list

list of estimates (e.g., M0, dfStudent)

Author(s)

Guillaume Evin

infer.mat.omega

Description

find omega correlation leading to estimates cor between occurrences

Usage

infer.mat.omega(P.mat, isPeriod, th, nLag, pr.state, nChainFit, isParallel)

Arguments

P.mat

matrix of precipitation n x p

isPeriod

vector of logical n x 1 indicating the days concerned by a 3-month period

th

threshold above which we consider that a day is wet (e.g. 0.2 mm)

nLag

order of the Markov chain

pr.state

output of function lagTransProbaMatrix

nChainFit

length of the simulated chains used during the fitting

isParallel

logical: indicate computation in parallel or not (easier for debugging)

Value

A list with different objects

Author(s)

Guillaume Evin

joint.proba.occ

Description

joint probabilities of occurrences for all pairs of stations

Usage

joint.proba.occ(P, th)

Arguments

P

matrix of precipitation

th

threshold above which we consider that a day is wet (e.g. 0.2 mm)

Value

list

list of joint probabilities

Author(s)

Guillaume Evin

lagTransProbaMatrix

Description

Estimate the transition probabilities between wet and dry states, for nlag previous days, for all stations

Usage

lagTransProbaMatrix(mat.prec, isPeriod, th, nlag)

Arguments

mat.prec

matrix of precipitation

isPeriod

vector of logical n x 1 indicating the days concerned by a 3-month period

th

threshold above which we consider that a day is wet (e.g. 0.2 mm)

nlag

number of lag days

Value

list

list with one item per station, where each item is a matrix nLag^2 x (nLag+1) of transition probability between dry/wet state. The first nLag columns indicate the wet/dry states for the previous nLag days

Author(s)

Guillaume Evin

lagTransProbaVector

Description

Estimate the transition probabilities between wet and dry states, for nlag previous days, for one station

Usage

lagTransProbaVector(vec.prec, isPeriod, th, nlag)

Arguments

vec.prec

vector nx1 of precipitation for one station

isPeriod

vector of logical n x 1 indicating the days concerned by a 3-month period

th

threshold above which we consider that a day is wet (e.g. 0.2 mm)

nlag

number of lag days

Value

matrix

matrix nLag^2 x (nLag+1) of transition probability between dry/wet state. The first nLag columns indicate the wet/dry states for the previous nLag days

Author(s)

Guillaume Evin

mask.GWex.Yt

Description

Mask intensities where there is no occurrence

Usage

mask.GWex.Yt(Xt, Yt)

Arguments

Xt

simulated occurrences

Yt

simulated intensities

Value

matrix

matrix n x p of simulated precipitations

Author(s)

Guillaume Evin

modify.cor.matrix

Description

Modify a non-positive definite correlation matrix in order to have a positive definite matrix

Usage

modify.cor.matrix(cor.matrix)

Arguments

cor.matrix

possibly non-positive definite correlation matrix

Value

positive definite correlation matrix

Author(s)

Guillaume Evin

References

Rousseeuw, P. J. and G. Molenberghs. 1993. Transformation of non positive semidefinite correlation matrices. Communications in Statistics: Theory and Methods 22(4):965-984.

Rebonato, R., & Jackel, P. (2000). The most general methodology to create a valid correlation matrix for risk management and option pricing purposes. J. Risk, 2(2), 17-26.

month2season

Description

transform vector of months to seasons

Usage

month2season(vecMonth)

Arguments

vecMonth

a vector of months given as integers 1:12

Author(s)

Guillaume Evin

print-methods: Create a method to print Gwex objects.

Description

print-methods: Create a method to print Gwex objects.

Usage

## S4 method for signature 'Gwex'
print(x)

## S4 method for signature 'GwexObs'
print(x)

## S4 method for signature 'GwexFit'
print(x)

## S4 method for signature 'GwexSim'
print(x)

Arguments

x

Gwex object

Examples

# Format dates corresponding to daily observations of precipitation and temperature
vecDates = seq(from=as.Date("01/01/2005",format="%d/%m/%Y"),
to=as.Date("31/12/2014",format="%d/%m/%Y"),by='day')

# build GwexObs object with temperature data
myObsTemp = GwexObs(variable='Temp',date=vecDates,obs=dailyTemperGWEX)

# print GwexObs object
myObsTemp

show-methods: Create a method to show Gwex objects.

Description

show-methods: Create a method to show Gwex objects.

Usage

## S4 method for signature 'Gwex'
show(object)

## S4 method for signature 'GwexObs'
show(object)

## S4 method for signature 'GwexFit'
show(object)

## S4 method for signature 'GwexSim'
show(object)

Arguments

object

Gwex object

Examples

# Format dates corresponding to daily observations of precipitation and temperature
vecDates = seq(from=as.Date("01/01/2005",format="%d/%m/%Y"),
to=as.Date("31/12/2014",format="%d/%m/%Y"),by='day')

# build GwexObs object with temperature data
myObsTemp = GwexObs(variable='Temp',date=vecDates,obs=dailyTemperGWEX)

# show GwexObs object
myObsTemp

sim.GWex.Yt

Description

Inverse PIT: from the probability space to the precipitation space

Usage

sim.GWex.Yt(objGwexFit, vecMonth, Yt.Pr)

Arguments

objGwexFit

object of class GwexFit

vecMonth

vector of integer indicating the months

Yt.Pr

uniform variates describing dependence between inter-site amounts

Value

matrix

matrix n x p of simulated non-zero precipitation intensities

Author(s)

Guillaume Evin

sim.GWex.Yt.Pr

Description

generate uniform variates which describe the dependence between intersite amount correlations

Usage

sim.GWex.Yt.Pr(objGwexFit, vecMonth)

Arguments

objGwexFit

object of class GwexFit

vecMonth

vector n x 1 of integer indicating the months

Value

matrix

matrix n x p of uniform dependent variates

Author(s)

Guillaume Evin

sim.GWex.Yt.Pr.get.param

Description

get relevant parameters

Usage

sim.GWex.Yt.Pr.get.param(objGwexFit, iM)

Arguments

objGwexFit

object of class GwexFit

iM

integer indicating the month

Value

list

list of parameters

Author(s)

Guillaume Evin

sim.GWex.occ

Description

generate boolean variates which describe the dependence between intersite occurrence correlations and wet/dry persistence

Usage

sim.GWex.occ(objGwexFit, vecMonth)

Arguments

objGwexFit

object of class GwexFit

vecMonth

vector n x 1 of integers indicating the months

Value

matrix of logical

occurrences simulated

Author(s)

Guillaume Evin

sim.GWex.prec.1it

Description

Simulate one scenario of precipitation from the GWex model

Usage

sim.GWex.prec.1it(objGwexFit, vecDates, myseed, objGwexObs, prob.class)

Arguments

objGwexFit

object of class GwexFit

vecDates

vector of continuous dates

myseed

seed of the random generation, to be fixed if the results need to be replicated

objGwexObs

optional: necessary if we need observations to simulate (e.g. disaggregation of 3-day periods)

prob.class

vector of probabilities indicating class of "similar" mean intensities

Value

matrix

Precipitation simulated for the dates contained in vec.Dates at the different stations

Author(s)

Guillaume Evin

sim.Zt.MAR

Description

generate gaussian variates which describe the spatial and temporal dependence between the sites (MAR(1) process)

Usage

sim.Zt.MAR(PAR, copulaInt, Zprev, p)

Arguments

PAR

parameters for this class

copulaInt

'Gaussian' or 'Student'

Zprev

previous Gaussian variate

p

number of stations

Value

matrix

matrix n x p of uniform dependent variates

Author(s)

Guillaume Evin

sim.Zt.Spatial

Description

generate gaussian variates which describe the spatial dependence between the sites

Usage

sim.Zt.Spatial(PAR, copulaInt, p)

Arguments

PAR

parameters for a class

copulaInt

'Gaussian' or 'Student'

p

number of stations

Value

matrix

matrix n x p of uniform dependent variates

Author(s)

Guillaume Evin

simGwexModel

Description

Simulate from a GWex model

Usage

simGwexModel(
  objGwexFit,
  nb.rep = 10,
  d.start = as.Date("01011900", "%d%m%Y"),
  d.end = as.Date("31121999", "%d%m%Y"),
  objGwexObs = NULL,
  prob.class = c(0.5, 0.75, 0.9, 0.99),
  objGwexSim = NULL,
  nCluster = 1
)

Arguments

objGwexFit

an object of class GwexFit

nb.rep

number of repetitions of scenarios

d.start

a starting date for the simulation

d.end

an ending date for the simulation

objGwexObs

optional: an object of class GwexObs if we need the observations to simulate (disaggregation prec 3D -> 1D)

prob.class

vector of probabilities indicating class of "similar" mean intensities

objGwexSim

optional: an object of class GwexSim if we need simulations to simulate (temp conditional to prec)

nCluster

optional, number of clusters which can be used for the parallel computation

Value

GwexSim

an object of class GwexSim. Contains sim (3D-array with the simulations) and a vector of dates

Author(s)

Guillaume Evin

Examples

# vector of dates
vecDates = seq(from=as.Date("01/01/2005",format="%d/%m/%Y"),
to=as.Date("31/12/2014",format="%d/%m/%Y"),by='day')

###############################################################
#               FIT AND SIMULATE FROM THE PRECIPITATION MODEL
###############################################################
# Format observations: create a G-Wex object
myObsPrec = GwexObs(variable='Prec',date=vecDates,obs=dailyPrecipGWEX[,1,drop=FALSE])

# Fit GWEX precipitation model, default options except for the threshold th
myParPrec = fitGwexModel(myObsPrec,listOption=list(th=0.5)) # fit model

# Generate 2 scenarios for one year, using the 'GwexFit' object
mySimPrec = simGwexModel(objGwexFit=myParPrec, nb.rep=2, d.start=vecDates[1],
d.end=vecDates[10])
mySimPrec # print object

###############################################################
#     FIT AND SIMULATE FROM THE TEMPERATURE MODEL
###############################################################
# Format observations: create a G-Wex object
myObsTemp = GwexObs(variable='Temp',date=vecDates,obs=dailyTemperGWEX)

# Fit GWEX temperature model
myParTemp = fitGwexModel(myObsTemp,listOption=list(hasTrend=TRUE,typeMargin='Gaussian',
depStation='Gaussian'))

# Generate 2 scenarios for one year, using an existing 'GwexFit' object
mySimTemp = simGwexModel(objGwexFit=myParTemp, nb.rep=2, d.start=vecDates[1], 
                          d.end=vecDates[365],objGwexObs=myObsPrec)
mySimTemp # print object

simPrecipOcc

Description

find matrix of correlations leading to estimates cor between intensities

Usage

simPrecipOcc(nLag, n, pr)

Arguments

nLag

order of the Markov chain

n

integer indicating the length of simulated chains

pr

vector of probabilies corr. to the conditional transition probabilities

Value

a vector Xt of length n with values 0/1 corr. to dry/wet states

Author(s)

Guillaume Evin

unif.to.prec

Description

from uniform variates to precipitation variates

Usage

unif.to.prec(pI, typeMargin, U)

Arguments

pI

vector of three parameters of the marginal distributions

typeMargin

type of marginal distribution: 'EGPD' or 'mixExp'

U

vector of uniform variates

Value

matrix

matrix of estimates p x 3

Author(s)

Guillaume Evin

wet.day.frequency

Description

Estimate the wet day frequency (proportion of wet days) for all stations

Usage

wet.day.frequency(mat.prec, th)

Arguments

mat.prec

matrix of precipitation (possibly for one month/period)

th

threshold above which we consider that a day is wet (e.g. 0.2 mm)

Value

vector of numeric

wet day frequencies

Author(s)

Guillaume Evin

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.