CCGamma function

This function extends continuity_ratio and adds the corresponding gaussian correlation matrix for no-precipitation occurrence.

CCGamma(
  data,
  lag = 0,
  p0_v1 = NULL,
  p = NA,
  valmin = 0.5,
  nearPD = (lag >= 0),
  interval = c(-1, 1),
  tolerance = .Machine$double.eps,
  only.matrix = FALSE,
  return.value = NULL,
  null.gcorrelation = 1e-05,
  sample = NULL,
  origin = "1961-1-1",
  ...
)

Arguments

• data: data frame or 'zoo' R object containing daily precipitation time series for several gauges (one gauge time series per column). See continuity_ratio.
• lag: numeric lag (expressed as number of days) used for computation for "cross" continuity ratio and joint probability of prercipitation (no)occurrence. See continuity_ratio.
• p0_v1: vector for marginal probablities, see omega and omega_inv.
• p: positive integer parameter. Default is NA, otherwise, lag is calculated as the vector 0:p.
• valmin: threshold precipitation value [mm] for wet/dry day indicator. If precipitation is lower than valmin, day is considered dry. Default is 0.5 mm. See continuity_ratio.
• nearPD: see omega_inv. Default is (lag==0).
• interval, tolerance: see omega_inv
• only.matrix: logical value. If TRUE the function returns only the gaussian correlaton matrix. Deafaul is FALSE.
• return.value: string. If it is not either NULL (Default) and NA, function returns only the argument indicated by this argument.
• null.gcorrelation: numerical value nooccurrence_gcorrelation under which is considered to be 0.
• sample: character string indicated if function must be calculated differently for subset of the year, e.g. monthly. Admitted values are NULL (Default), "all" or "monthly".
• origin: character string (yyyy-dd-mm) indicated the date of the first row of "data". It is used if data and sample are not NULL.
• ...: additional agruments of omega_inv or CCGamma

Returns

An object which is a list containing the following fields:

continuity_ratio : lag-day lagged continuity ratio, as returned by continuity_ratio;

occurrence : joint probability of lag-day lagged precipitation occurrence, as returned by continuity_ratio;

nooccurrence : joint probability of lag-day lagged no precipitation occurrence, as returned by continuity_ratio;

lag : number of days lagged between the two compared events (see argument lag);

p0_v1 : vector of marginal probability of no precipitation occurrence. If lag

is 0, it corresponds to the diagonal of nooccurrence matrix (see argument p0_v1);

nooccurrence_gcorrelation corresponding gaussian correlation for no precipitation occurrence obtained by applying omega_inv to nooccurrence,

If the argument only.matrix is TRUE, only nooccurrence_gcorrelation is returned as a matrix. In case the argument lag is a vector wirh length more than one, the function returns a list of the above-cited return object for each value of the vector lag.

Note

This functon is useful to generate the serial cross-correlation matrices for no precipitation occurrence for Yule-Walker Equations. In case lag is a vactor, nearPD must be a vector of the same size, default is (lag==0).

See the R code for major details

Examples

data(trentino)

year_min <- 1961
year_max <- 1990
origin <- paste(year_min,1,1,sep="-")

period <- PRECIPITATION$year>=year_min & PRECIPITATION$year<=year_max
station <- names(PRECIPITATION)[!(names(PRECIPITATION) %in% c("day","month","year"))]
prec_mes <- PRECIPITATION[period,station]  

## removing nonworking stations (e.g. time series with NA)
accepted <- array(TRUE,length(names(prec_mes)))
names(accepted) <- names(prec_mes)
for (it in names(prec_mes)) {
                 accepted[it]  <- (length(which(!is.na(prec_mes[,it])))==length(prec_mes[,it]))
}

prec_mes <- prec_mes[,accepted]
## the dateset is reduced!!! 
prec_mes <- prec_mes[,1:2]

CCGamma <- CCGamma(data=prec_mes,lag=0,tolerance=0.001,only.matrix=FALSE)

## Not Run in the examples, uncomment to run the following line
 CCGamma <- CCGamma(data=prec_mes,lag=0:2,tolerance=0.001,only.matrix=FALSE)

## Not Run in the examples, uncomment to run the following line
 CCGamma_monthly <- CCGamma(data=prec_mes,lag=0,tolerance=0.001,only.matrix=FALSE,
                     sample="monthly",origin=origin)

References

D.S. Wilks (1998), Multisite Generalization of a Daily Stochastic Precipitation Generation Model, Journal of Hydrology, Volume 210, Issues 1-4, September 1998, Pages 178-191, https://www.sciencedirect.com/science/article/pii/S0022169498001863

Muamaraldin Mhanna and Willy Bauwens (2011) A Stochastic Space-Time Model for the Generation of Daily Rainfall in the Gaza Strip, International Journal of Climatology, Volume 32, Issue 7, pages 1098-1112, tools:::Rd_expr_doi("10.1002/joc.2305") , https://rmets.onlinelibrary.wiley.com/doi/abs/10.1002/joc.2305

See Also

continuity_ratio,omega_inv,omega,CCGammaToBlockmatrix

Author(s)

Emanuele Cordano