# This function extends `continuity_ratio` and adds the corresponding gaussian correlation matrix for no-precipitation occurrence. ```r 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 ```r 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](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](https://rmets.onlinelibrary.wiley.com/doi/abs/10.1002/joc.2305) ## See Also `continuity_ratio`,`omega_inv`,`omega`,`CCGammaToBlockmatrix` ## Author(s) Emanuele Cordano

CCGamma function