IDF.R 41.6 KB
Newer Older
1
##############################################################
Rust Henning's avatar
Rust Henning committed
2
## IDF package 
Christoph Ritschel's avatar
Christoph Ritschel committed
3
## Authors: Sarah Joedicke, Carola Detring, Christoph Ritschel
4
5
6
## Update: 15.09.2017
## revise for integration of covariates Sep. 2018
##############################################################
Rust Henning's avatar
Rust Henning committed
7

8
9
10
##############################################################
## Read data
##############################################################
Rust Henning's avatar
Rust Henning committed
11

Christoph Ritschel's avatar
Christoph Ritschel committed
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
#' @title Reading precipitation data 
#' @description The function \code{IDF.read} reads a file in table format and creates a \code{data.frame} from it
#' and adds some attributes (station information, aggregation time, data source). The only data values used are: 
#' date, precipitation
#' The \code{data.frame} will have the following format:
#' | year | mon | day | hour | min | RR |
#' |------+-----+-----+------+-----+----+
#' |      |     |     |      |     |    |
#' @usage IDF.read(file, type) 
#' @param file a \code{character string} naming the file from which the data is to be read. 
#' @param type a \code{character string} defining the type of data to be read: either "stadtmessnetz" or "webwerdis", depending on if the data comes from the Stadtmessnetz Berlin
#' or WebWerdis. If type = "webwerdis", the data will be read, then sorted, formatted and missing lines added, 
#' while if type = "stadtmessnetz", the data will just be read and formatted. 
#' Both source types have a different layout in the original file.
#' @return Liste a \code{data.frame} of date and time information and precipitation values for each time step
#' @details This function is designed to prepare a data file for doing an estimation on IDF parameters in function \code{IDF.fit}.
#' The time given in the data is the end time, so the precipitation was measured up to that time.  
#' @seealso read.table, IDF.fit
#' @author Sarah Joedicke \email{sarah.joedicke@@fu-berlin.de}
#' @author Christoph Ritschel \email{christoph.ritschel@@met.fu-berlin.de}
Rust Henning's avatar
Rust Henning committed
32
33
34
35
36
37
38
39
40
41
42
IDF.read <- function(file,type){
  
  if(type != "stadtmessnetz" && type != "webwerdis") {
    
    cat("Warning: wrong type declared for input file")
    stop()
  }
  
  if (type == "stadtmessnetz") {
    
    Tab_MN <- read.csv2(file)  #STADTMESSNETZ
Christoph Ritschel's avatar
Christoph Ritschel committed
43
    new_time <- strptime(Tab_MN$Zeitstempel,format="%d.%m.%Y %H:%M")   #STADTMESSNETZ date vector
Rust Henning's avatar
Rust Henning committed
44
45
46
47
48
49
50
51
52
53
  }
  
  # Da die Stadtmessnetzdaten (bisher) konstistent aussehen, wird auf das Erstellen einer neuen Tabelle mit sicher allen
  # Zeiten verzichtet, da die Minutendaten sehr gross sind. Sollte es inkonsistente Tabellen geben, sollte man diese seperat behandeln,
  # sonst wird viel Rechenzeit fuer die kompletten Tabellen verschwendet. 
  
  if (type == "webwerdis") {
    Tab <- read.table(file,header=TRUE,sep=";")   #WEBWERDIS
    Tab_kurz <- Tab[,c("Date","precipitation")]
    
Christoph Ritschel's avatar
Christoph Ritschel committed
54
    ## Sort table in output format
Rust Henning's avatar
Rust Henning committed
55
56
57
58
59
    time <- strptime(Tab_kurz$Date,format="%Y-%m-%d T %H:%M:%S")
    Tab_sort <- Tab_kurz[order(as.character(time)),]
    time_sort <- strptime(Tab_sort$Date,format="%Y-%m-%d T %H:%M:%S")
    Tab_sort$Date <- as.character(time_sort)
    
Christoph Ritschel's avatar
Christoph Ritschel committed
60
    ## If dates are missing, add lines containing NA preicipitation measurments for these time steps. 
Rust Henning's avatar
Rust Henning committed
61
    h_diff <- as.numeric(difftime(format(time_sort[length(time_sort)],"%Y-%m-%d T %H:%M:%S") , 
Christoph Ritschel's avatar
Christoph Ritschel committed
62
                                  format(time_sort[1],"%Y-%m-%d T %H:%M:%S"),units="hours")) #h_diff is the difference in time steps
Rust Henning's avatar
Rust Henning committed
63
    new_time <- seq(time_sort[1], length = h_diff+1, by = "hour")
Christoph Ritschel's avatar
Christoph Ritschel committed
64
    new_tab <- data.frame(Date=as.character(new_time), precipitation=NA)  # predefine table with NAs and every time steps
Rust Henning's avatar
Rust Henning committed
65
66
    
    Tab_na <- (merge(Tab_sort, new_tab, "Date", all.y=TRUE))[,1:2]
Christoph Ritschel's avatar
Christoph Ritschel committed
67
  }
Rust Henning's avatar
Rust Henning committed
68
69
70
71
72
73
74
75
76
77
78
79
  
  new_timect <- as.POSIXct(new_time)
  
  J <- as.numeric(format(new_timect,'%Y'))
  M <- as.numeric(format(new_timect,'%m'))
  d <- as.numeric(format(new_timect,'%d'))
  h <- as.numeric(format(new_timect,'%H'))
  m <- as.numeric(format(new_timect,'%M'))
  
  if (type == "webwerdis") Tab_end <- data.frame(J,M,d,h,m,Tab_na$precipitation.x) #WEBWERDIS
  if (type == "stadtmessnetz") Tab_end <- data.frame(J,M,d,h,m,Tab_MN[,2]) #STADTMESSNETZ
  
Christoph Ritschel's avatar
Christoph Ritschel committed
80
  ## Name table attributes: 
Rust Henning's avatar
Rust Henning committed
81
82
83
  
  colnames(Tab_end) <- c("year","mon","day","hour","min","RR")
  attr(Tab_end,"accumulation time (min)") <- as.numeric(difftime(new_timect[2],new_timect[1], units="mins"))
Christoph Ritschel's avatar
Christoph Ritschel committed
84
  # Liste <- list(t1=Tab_end)
Christoph Ritschel's avatar
Christoph Ritschel committed
85
  Liste <- Tab_end 
Christoph Ritschel's avatar
Christoph Ritschel committed
86
  
Rust Henning's avatar
Rust Henning committed
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
  if (type == "webwerdis"){
    # WEBWERDIS:
    attr(Liste,"StationName") <- as.character(Tab$Stationname[1])
    attr(Liste,"StationID") <- "NA"
    attr(Liste,"Long (deg N)")  <- Tab$Longitude[1]
    attr(Liste,"Lat (deg E)") <- Tab$Latitude[1]
    attr(Liste,"Heigth (m)")   <- Tab$StationHeight[1]
    attr(Liste,"Source") <- "Web-WERDIS"
  } #Listen-Attribute benennen
  
  if (type == "stadtmessnetz"){
    # STADTMESSNETZ:
    attr(Liste,"StationName") <- colnames(Tab_MN)[2]
    attr(Liste,"StationID") <- "NA"
    attr(Liste,"Long (deg N)")  <- "NA"
    attr(Liste,"Lat (deg E)") <- "NA"
    attr(Liste,"Height (m)")   <- "NA"
    attr(Liste,"Source") <- "Stadtmessnetz"
  } #Listen-Attribute benennen
  
  cat(paste("read.data of", file , "done \n"))
  str(Liste)   # optional; so sieht man beim Einlesen, womit man es zu tun hat und ob alles geklappt hat
  
  return(Liste)
} 
112
## End of function IDF.read
Rust Henning's avatar
Rust Henning committed
113

114
115
116
##############################################################
## Accumulation
##############################################################
Rust Henning's avatar
Rust Henning committed
117

Christoph Ritschel's avatar
Christoph Ritschel committed
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
#' \code{TS.acc} accumulates a given time series \code{x} at a given accumulation level \code{acc.val}. Minimum value
#' for acc.val is 2 [unit time]. Option for using moving sum is given.
#' @title Accumulation of a time series
#' @param x \code{vector} of a time series
#' @param acc.val \code{value} specifying the accumulation level, minimum value is 2
#' @param moving.sum \code{logical} 'TRUE' means moving sum will be applied
#' @return x.acc \code{TS.acc} returns a \code{vector} of an accumulated time series 
#' @usage TS.acc(x,acc.val,moving.sum="FALSE")
#' @examples
#' TS <- rgamma(n=1000,shape=1)
#' acc.2 <- TS.acc(TS,acc.val=2)
#' \donttest{
#' acc.24 <- TS.acc(TS,acc.val=24,moving.sum=TRUE)
#' }
#' @author Christoph Ritschel \email{christoph.ritschel@@met.fu-berlin.de}
#' @author Carola Detring \email{carola.detring@@met.fu-berlin.de}
TS.acc <- function(x,acc.val=2,moving.sum="FALSE") {
  
  ## check for input value of acc.val
  if(acc.val<1) cat(paste("Warning: accumulation value acc.val too small for accumulation of the time series \n"))
  
  if(moving.sum){
Christoph Ritschel's avatar
Christoph Ritschel committed
140
    
Christoph Ritschel's avatar
Christoph Ritschel committed
141
    x.acc <- as.numeric(filter(x,filter=rep(1,acc.val),method="convolution",sides=1))
Christoph Ritschel's avatar
Christoph Ritschel committed
142
    
Christoph Ritschel's avatar
Christoph Ritschel committed
143
  }else{
Christoph Ritschel's avatar
Christoph Ritschel committed
144
145
146
147
148
149
150
151
152
153
    
    l.new <- length(x)%/%acc.val ## calculate new length of accumulated time series
    l.rest <- length(x)%%acc.val ## calculate values left over
    if(l.rest==0) {
      x.acc <- apply(matrix(x,nrow=l.new,byrow=T),1,sum) 
    }else{
      x.acc <- apply(matrix(x[1:(length(x)-l.rest)],nrow=l.new,byrow=T),1,sum)   
      #cat(paste("Warning: ",l.rest,"time steps left and not used for accumulation \n"))
    }
    
Rust Henning's avatar
Rust Henning committed
154
155
  }
  
Christoph Ritschel's avatar
Christoph Ritschel committed
156
157
  ## return accumulated time series
  return(x.acc)
Christoph Ritschel's avatar
Christoph Ritschel committed
158
  
159
160
}
## End of function TS.acc
Rust Henning's avatar
Rust Henning committed
161

162
163
164
##############################################################
## Define duration dependent GEV, d/p/q/rgev.d
##############################################################
Rust Henning's avatar
Rust Henning committed
165

Christoph Ritschel's avatar
Christoph Ritschel committed
166
167
168
169
170
171
172
173
174
175
176
177
178
#'@title Density function of modified generalized extreme value distribution
#'@description The function \code{dgev.d} is a modified version of the function \code{dgev} for different durations \code{d} developed by Koutsoyiannis et al. (1998).
#'@param q Vector of quantiles
#'@param mu location value
#'@param sigma scale value
#'@param xi shape value
#'@param theta value defining the curvature of the IDF
#'@param eta value defining the slope of the IDF
#'@param d vector of durations
#'@param log \code{logical} option to use logarithmic parameter values, default=FALSE
#'@seealso \code{\link[evd]{dgev}}
#'@return dgev.d gives the density function
#' @author Christoph Ritschel \email{christoph.ritschel@@met.fu-berlin.de}
Rust Henning's avatar
Rust Henning committed
179
180
181

dgev.d <- function(q,mu=0,sigma=1,xi=0,theta=0,eta=1,d=1,log=FALSE) {
  sigma.d <- sigma/(d+theta)^eta
Christoph Ritschel's avatar
Christoph Ritschel committed
182
183
184
185
186
  ##problem if sigma.d is NaN (d+theta) negative and eta smaller than 1 --> cant calculate root of negative value 
  sigma.d[which(is.nan(sigma.d))] <- Inf
  dens <- dgev(q,loc=mu*sigma.d,scale=sigma.d,shape=xi,log=log)
  dens[which(is.nan(dens))] <- NA
  return(dens)
Rust Henning's avatar
Rust Henning committed
187
188
189
}


Christoph Ritschel's avatar
Christoph Ritschel committed
190
191
192
193
194
195
196
197
198
199
200
201
202
#'@title Quantile function of modified generalized extreme value distribution
#'@description The function \code{qgev.d} is a modified version of the function \code{qgev} for different durations \code{d} developed by Koutsoyiannis et al. (1998).
#'@param p Vector of probabilities
#'@param mu location value
#'@param sigma scale value
#'@param xi shape value
#'@param theta value defining the curvature of the IDF
#'@param eta value defining the slope of the IDF
#'@param d vector of durations
#'@param lower.tail \code{logical} if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]
#'@seealso \code{\link[evd]{qgev}}
#'@return qgev.d gives the quantile function
#' @author Christoph Ritschel \email{christoph.ritschel@@met.fu-berlin.de}
Rust Henning's avatar
Rust Henning committed
203
204
205
qgev.d <- function(p,mu=0,sigma=1,xi=0,theta=0,eta=1,d=1,lower.tail=TRUE) {
  
  sigma.d <- sigma/(d+theta)^eta
Christoph Ritschel's avatar
Christoph Ritschel committed
206
207
208
209
210
  ##problem if sigma.d is NaN (d+theta) negative and eta smaller than 1 --> cant calculate root of negative value 
  sigma.d[which(is.nan(sigma.d))] <- Inf
  quant <- qgev(p,loc=mu*sigma.d,scale=sigma.d,shape=xi,lower.tail=lower.tail)
  quant[is.infinite(quant)] <- NA
  return(quant)
Rust Henning's avatar
Rust Henning committed
211
212
}

Christoph Ritschel's avatar
Christoph Ritschel committed
213
214
215
216
217
218
219
220
221
222
223
224
#'@title Random generation for the modified generalized extreme value distribution
#'@description The function \code{rgev.d} is a modified version of the function \code{rgev} for different durations \code{d} developed by Koutsoyiannis et al. (1998).
#'@param n Number of observations
#'@param mu location value
#'@param sigma scale value
#'@param xi shape value
#'@param theta value defining the curvature of the IDF
#'@param eta value defining the slope of the IDF
#'@param d vector of durations
#'@seealso \code{\link[evd]{rgev}}
#'@return rgev.d generates random derivates
#' @author Christoph Ritschel \email{christoph.ritschel@@met.fu-berlin.de}
Rust Henning's avatar
Rust Henning committed
225
226
227
rgev.d <- function(n,mu=0,sigma=1,xi=0,theta=0,eta=1,d=1) {
  ## gumbel
  sigma.d <- sigma/(d+theta)^eta
Christoph Ritschel's avatar
Christoph Ritschel committed
228
229
230
231
232
233
  ##problem if sigma.d is NaN (d+theta) negative and eta smaller than 1 --> cant calculate root of negative value 
  sigma.d[which(is.nan(sigma.d))] <- Inf
  x <- rgev(n, loc=mu*sigma.d,scale=sigma.d,shape=xi)
  x[which(is.nan(x))] <- NA
  return(x)
  
Christoph Ritschel's avatar
Christoph Ritschel committed
234
}
Rust Henning's avatar
Rust Henning committed
235

236
237
238
239
##############################################################
## Define negative log-likelihood
##############################################################

Rust Henning's avatar
Rust Henning committed
240
#######################################################################
Christoph Ritschel's avatar
Christoph Ritschel committed
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
#' @title Negativ log-likelihood of modified GEV
#' @description The function \code{IDF.nll} calculates the negative log-likelihood for a given set of model parameters
#' \code{mu,sigma,xi,theta,eta}, given observations \code{x} and given durations \code{d}. Options for the usage of
#' logartihmic values \code{use.log} and a debugging function \code{DEBUG} are available.
#'@param mu location value
#'@param sigma scale value
#'@param xi shape value
#'@param theta value defining the curvature of the IDF
#'@param eta value defining the slope of the IDF
#'@param x vector of observations at different durations d
#'@param d vector of durations
#'@param use.log \code{logical} value for usage of logarithmic values, default is \code{FALSE}
#'@param DEBUG \code{logical} value for usage of debugging, if \code{TRUE} the input parameters and the value of negative
#'log-likelihood are printed on console.
#'@return retruns weightes negative log-likelihood by number of observatons uesd
#' @author Christoph Ritschel \email{christoph.ritschel@@met.fu-berlin.de}
Rust Henning's avatar
Rust Henning committed
257

258
IDF.nll <- function(mu=0,sigma=1,xi=0,theta=0,eta=1,x,d,DEBUG=F) {
Rust Henning's avatar
Rust Henning committed
259
260
  ## mu is the mu~ from Koutsoyiannis
  
Christoph Ritschel's avatar
Christoph Ritschel committed
261
  sigma.d <- sigma/((d+theta)^eta) 
Rust Henning's avatar
Rust Henning committed
262
263
  if(DEBUG) debug.values <- c(mu,sigma,xi,theta,eta)
  
Christoph Ritschel's avatar
Christoph Ritschel committed
264
265
  if(sum(is.nan(sigma.d))==0) {
    
Christoph Ritschel's avatar
Christoph Ritschel committed
266
267
268
269
270
271
272
273
274
275
276
277
278
279
    ## Weibull und Frechet
    if(xi!=0){
      C <- 1 + xi * (x/sigma.d - mu )
      nll <- switch((sum(C<0,na.rm=T)>0)+1,
                    sum(log(sigma.d),na.rm=T)+(1+1/xi)*sum(log(C),na.rm=T)+sum((C)^(-1/xi),na.rm=T),
                    NA)
      #       + penalty*(sum(C[C<0]^2))
      ## Gumbel
    }else if(xi==0){# & sigma<1 & eta<1) 
      Y <- x/sigma.d-mu
      nll <- -(-sum(log(sigma.d),na.rm=T)-sum((Y),na.rm=T)-sum(exp(-Y),na.rm=T))
    }
  }else{ nll <- NA}
  
Rust Henning's avatar
Rust Henning committed
280
281
282
283
284
285
286
  if(DEBUG){ 
    cat(debug.values,nll,"\n")
    options(digits.secs=6)
    ##    debug.values <- c(debug.values,nll,as.character(Sys.time()))
    ##    write(debug.values,file="optim.log",append=TRUE,ncolumns=length(debug.values))
    ##    cat(debug.values,nll,sum(A<0),"\n")
  }
Christoph Ritschel's avatar
Christoph Ritschel committed
287
  
Rust Henning's avatar
Rust Henning committed
288
289
  return(nll/length(x))
  
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
}
## end of function IDF.nll

### copied gev.fit from ismev to be adapted to IDF.nll
gev.d.fit <- function (xdat, ds, ydat = NULL, 
                       mul = NULL, sigl = NULL, shl = NULL, thetal = NULL, etal = NULL,
                       mulink = identity, siglink = identity, shlink = identity, thetalink = identity, etalink = identity, 
                       muinit = NULL, siginit = NULL, shinit = NULL, thetainit = NULL, etainit = NULL,
                       show = TRUE, method = "Nelder-Mead", maxit = 10000, ...) {
    z <- list()
    npmu <- length(mul) + 1
    npsc <- length(sigl) + 1
    npsh <- length(shl) + 1
    npth <- length(thetal) + 1
    npet <- length(etal) + 1
    z$trans <- FALSE

    ### guess initial values, this is done by Christoph's routine
    init.vals <- IDF.init(xdat,ds)
    
    if (is.null(mul)) {
        mumat <- as.matrix(rep(1, length(xdat)))
        if (is.null(muinit)) 
            muinit <- init.vals$mu
    }else {
        z$trans <- TRUE
        mumat <- cbind(rep(1, length(xdat)), ydat[, mul])
        if (is.null(muinit)) 
            muinit <- c(init.vals$mu, rep(0, length(mul)))
    }
    if (is.null(sigl)) {
        sigmat <- as.matrix(rep(1, length(xdat)))
        if (is.null(siginit)) 
            siginit <- init.vals$sigma
    }else {
        z$trans <- TRUE
        sigmat <- cbind(rep(1, length(xdat)), ydat[, sigl])
        if (is.null(siginit)) 
            siginit <- c(init.vals$sigma, rep(0, length(sigl)))
    }
    if (is.null(shl)) {
        shmat <- as.matrix(rep(1, length(xdat)))
        if (is.null(shinit)) 
            shinit <- init.vals$xi #0.1
    }else {
        z$trans <- TRUE
        shmat <- cbind(rep(1, length(xdat)), ydat[, shl])
        if (is.null(shinit)) 
            shinit <- c(init.vals$xi, rep(0, length(shl)))
    }
    if (is.null(thetal)) {
        thmat <- as.matrix(rep(1, length(xdat)))
        if (is.null(thetainit)) 
            thetainit <- 0
    }else {
        z$trans <- TRUE
        thmat <- cbind(rep(1, length(xdat)), ydat[, thetal])
        if (is.null(thetainit)) 
            thetainit <- c(0, rep(0, length(thetal)))
    }
    if (is.null(etal)) {
        etmat <- as.matrix(rep(1, length(xdat)))
        if (is.null(etainit)) 
            etainit <- init.vals$eta
    }else {
        z$trans <- TRUE
        etmat <- cbind(rep(1, length(xdat)), ydat[, etal])
        if (is.null(etainit)) 
            etainit <- c(init.vals$eta, rep(0, length(thetal)))
    }
    
    z$model <- list(mul, sigl, shl, thetal, etal)
    z$link <- deparse(substitute(c(mulink, siglink, shlink, thetalink, etalink)))
    init <- c(muinit, siginit, shinit, thetainit, etainit)

    ### define the likelihood function for the gev.d
    gev.d.lik <- function(a) {
        mu <- mulink(mumat %*% (a[1:npmu]))
        sigma <- siglink(sigmat %*% (a[seq(npmu + 1, length = npsc)]))
        xi <- shlink(shmat %*% (a[seq(npmu + npsc + 1, length = npsh)]))
        theta <- shlink(thmat %*% (a[seq(npmu + npsc + npsh + 1, length = npth)]))
        eta <- shlink(etmat %*% (a[seq(npmu + npsc + npsh + npth + 1, length = npet)]))
        return(IDF.nll(mu,sigma,xi,theta,eta,xdat,ds))
    }
    x <- optim(init, gev.d.lik, hessian = TRUE, method = method, 
        control = list(maxit = maxit, ...))
    z$conv <- x$convergence
    mu <- mulink(mumat %*% (x$par[1:npmu]))
    sc <- siglink(sigmat %*% (x$par[seq(npmu + 1, length = npsc)]))
    xi <- shlink(shmat %*% (x$par[seq(npmu + npsc + 1, length = npsh)]))
    theta <- thlink(thmat %*% (x$par[seq(npmu + npsc + npsh + 1, length = npth)]))
    eta <- etlink(etmat %*% (x$par[seq(npmu + npsc + npsh + npth + 1, length = npet)]))
    z$nllh <- x$value
    z$data <- xdat
    if (z$trans) {
        zdata <- NULL
        ### Here I need to adjust the formular for d.gev
                                        #        z$data <- -log(as.vector((1 + (xi * (xdat - mu))/sc)^(-1/xi)))
    }
    z$mle <- x$par
    z$cov <- solve(x$hessian)
    z$se <- sqrt(diag(z$cov))
    z$vals <- cbind(mu, sc, xi, theta, eta)
    if (FALSE) { ## this is if(show) but I don't understand the lower part
        if (z$trans) 
            print(z[c(2, 3, 4)])
        else print(z[4])
        if (!z$conv) 
            print(z[c(5, 7, 9)])
    }
    class(z) <- "gev.d.fit"
    invisible(z)
}
Rust Henning's avatar
Rust Henning committed
403

Christoph Ritschel's avatar
Christoph Ritschel committed
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
#' @title Fitting function to optimize IDF model parameters
#' @description The function \code{fit.fun} fits IDF model parameters \code{mu,sigma,xi,theta,eta} to a set of given observations \code{obs}, 
#' typically a series of yearly maxima at different durations \code{d}. Options for using logarithmic parameter values and debugging
#' are given. Also the \code{optim} parameters \code{method} and \code{upper,lower} can be defined.
#' @param obs vector of yearly intensity maxima at different durations. Order: Y1D1, Y2D1,...,YnD1,Y1D2,...YnD2,Y1D3,...,YnDk
#' @param dur vector of durations with same length as \code{obs}. Order: n x D1, n x D2, ... n x Dk 
#' @param mu location value
#' @param sigma scale value
#' @param xi shape value
#' @param theta value defining the curvature of the IDF
#' @param eta value defining the slope of the IDF
#' @param use.log \code{logical} value for usage of logarithmic values, default is \code{FALSE}
#' @param DEBUG \code{logical} value for usage of debugging, if \code{TRUE} the input parameters and the value of negative
#' log-likelihood are printed on console for each iteration during optimization.
#' @param method \code{character} defining the method to be used in \code{optim}, preferences are: "Nelder-Mead", "BFGS", "L-BFGS-B"e
#' @param lower \code{vector} specifying the lower boundary of parameters for "L-BFGS-B" method
#' @param upper \code{vector} specifying the upper boundary of parameters for "L-BFGS-B" method
#' @return $min value of negative log-likelihood at optimization minimum
#' @return $par vector of IDF parameters at optimization minimum
#' @author Christoph Ritschel \email{christoph.ritschel@@met.fu-berlin.de}
Rust Henning's avatar
Rust Henning committed
424

425
fit.fun <- function(obs,dur,mu=1,sigma=1,xi=0.5,theta=1,eta=1,use.log=F,DEBUG=F,method="Nelder-Mead",upper=Inf,lower=-Inf,...) {
Christoph Ritschel's avatar
Christoph Ritschel committed
426
  
Rust Henning's avatar
Rust Henning committed
427
428
429
  use.log=use.log
  
  if(use.log) {
Christoph Ritschel's avatar
Christoph Ritschel committed
430
431
432
    if(sigma<=0){sigma <- 1E-10}
    if(theta<=0){theta <- 1E-10}
    if(eta<=0){eta <- 1E-10}
Rust Henning's avatar
Rust Henning committed
433
434
435
436
    sigma <- log(sigma)
    theta <- log(theta)
    eta <- log(eta)
    
Christoph Ritschel's avatar
Christoph Ritschel committed
437
    if(method=="L-BFGS-B") {
Christoph Ritschel's avatar
Christoph Ritschel committed
438
439
440
441
442
443
444
      upper[2] <- log(upper[2])
      upper[4] <- log(upper[4])
      upper[5] <- log(upper[5])
      
      lower[2] <- log(lower[2])
      lower[4] <- log(lower[4])
      lower[5] <- log(lower[5])
Rust Henning's avatar
Rust Henning committed
445
446
447
448
449
450
    }
    
  }
  
  ## check initial value of negative log-Likelihood function
  nll <- IDF.nll(mu,sigma,xi,theta,eta,x=obs,d=dur,use.log=use.log,DEBUG=DEBUG)
451

Rust Henning's avatar
Rust Henning committed
452
453
454
455
456
457
458
459
460
  ## if initial value is acceptable...
  if(!is.infinite(nll)&!is.na(nll)) {
    
    
    if(method=="L-BFGS-B") {
      
      ## problem: optimization algrorithm often has difficulities concerning infinite or NA-difference values betweeen iterations
      ## solution: ignore this error message using functon tryCatch and return NULL if there was an error during optimization
      fit <- tryCatch(mle(IDF.nll,start=list(mu=mu,sigma=sigma,xi=xi,theta=theta,eta=eta),fixed=list(x=obs,d=dur,use.log=use.log,DEBUG=DEBUG),
461
                          control=list(...),
Rust Henning's avatar
Rust Henning committed
462
463
464
465
466
467
468
469
                          method=method,upper=upper,lower=lower), error=function(e) NULL)#,
      #upper=upper,lower=lower)
      
    }else{
      
      ## problem: optimization algrorithm often has difficulities concerning infinite or NA-difference values betweeen iterations
      ## solution: ignore this error message using functon tryCatch and return NULL if there was an error during optimization
      fit <- tryCatch(mle(IDF.nll,start=list(mu=mu,sigma=sigma,xi=xi,theta=theta,eta=eta),fixed=list(x=obs,d=dur,use.log=use.log,DEBUG=DEBUG),
470
                          control=list(...),
Rust Henning's avatar
Rust Henning committed
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
                          method=method), error=function(e) NULL)#,
      #upper=upper,lower=lower)
      
      
      
    }
    
    ## if there was no error
    if(!is.null(fit)) {
      fit.min <- fit@min
      fit.par <- fit@coef
    }else { ## else return NA
      fit.min <- NA
      fit.par <- rep(NA,5)  
    } ## end if error
    
  }else { ## else retunr NA
    
    fit.min <- NA
    fit.par <- rep(NA,5)  
    
  } ## end if initial value..
  
  if(use.log){
    fit.par[2] <- exp(fit.par[2])
    fit.par[4] <- exp(fit.par[4])
    fit.par[5] <- exp(fit.par[5])
  }
  names(fit.par) <- c("mu","sigma","xi","theta","eta")
  
  return(list("min"=fit.min,"par"=fit.par))
  
503
504
505
506
}
## end of function fit.fun


Rust Henning's avatar
Rust Henning committed
507
##################################################################################
Christoph Ritschel's avatar
Christoph Ritschel committed
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
#' @title Data aggregation for IDF parameter estimation
#' @description The function \code{IDF.agg} aggregates a data.frame of observations \code{data} with temporal inforamtion (at least years) and values of precipitation
#' at a given temporal resoultion at given aggregation levels \code{agg.lev} and yearly maxima of intensity are caluclated for a specific month or the whole year/dataset. 
#' @param data a \code{data,frame}, preferably generated by function \code{IDF.read}. It should at least contain a \code{$RR} and \code{$year} element for the 
#' function tow work properly. Also an option to use \code{moving.sum} is given. The function returns a vector of intensities and durations as well as the number of years of data.
#' @param agg.lev a vector of aggregation levels used to fit the IDF curves.
#' @param month \code{integer} value specifying the month to be used for estimating the IDF parameters. Type "all" for all months or if
#' the whole time series should be fitted.
#' @param moving.sum \code{logical} specifying if moving sum filtering should be applied for time series aggregation.
#' @return $ints.vec vector of sorted intensities for selected aggregation levels
#' @return $durs vector of sorted aggregation levels
#' @return $n.y number of years of data
#' @examples 
#' RR <- rgamma(10*30*24,shape=1)
#' year <- sort(rep(1:(10),30*24))
#' data <- data.frame(RR,year)
#' data.agg <- IDF.agg(data)
#' @author Christoph Ritschel \email{christoph.ritschel@@met.fu-berlin.de}
Rust Henning's avatar
Rust Henning committed
526

Henning Rust's avatar
Henning Rust committed
527
IDF.agg <- function(data,agg.lev=c(2,3,6,12,24,48,72,96),month="all",moving.sum="FALSE",DEBUG=FALSE) {
Christoph Ritschel's avatar
Christoph Ritschel committed
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
  
  RR <- data$RR ## get precipitation time series from data.frame
  years <- unique(data$year) # get years from data.frame
  n.y <- length(years) # number of years
  n.a <- length(agg.lev) # number of aggregation times
  
  ## initilise arrays 
  agg.1 <- array(NA,dim=c(n.y)) 
  ints <- array(NA,dim=c(n.y*n.a))
  
  ###loop over years
  for(y in 1:n.y) {
    
    if(month[1]=="all") { 
      index <- which(data$year==years[y])
    }else if(is.integer(month) | is.numeric(month)) {
      index <- which(data$year==years[y] & data$mon >= min(month) & data$mon <= max(month))    
    }
    if(length(index)>0) {
      RR.year <- RR[index]
      agg.1[y] <- max(RR.year,na.rm=T) 
      
      ###loop over agg.lev
      for(a in 1:n.a) {
Henning Rust's avatar
Henning Rust committed
552
        
Christoph Ritschel's avatar
Christoph Ritschel committed
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
        ints[y+((a-1)*n.y)] <-  max(TS.acc(RR.year,agg.lev[a],moving.sum=moving.sum),na.rm=T)/agg.lev[a]
        
      } # end for all aggregation times
    } # end if lenght
  } # end for all years
  
  ## vector of all intensities
  int.vec <- c(agg.1,ints)
  
  ## vector of all durations (single)
  d.all <- c(1,agg.lev)
  ## long vector of all durations (repeated for each year to have same length as intensity vector)
  durs <- rep(d.all,each=n.y)
  
  return(list(int.vec=int.vec,durs=durs,n.y=n.y))
} #
569

Christoph Ritschel's avatar
Christoph Ritschel committed
570
571
572
573
574
###############################################################################
#' @title Estimation of initial values for IDF fitting.
#' @description The function \code{IDF.init} estimates inital values for  \code{mu,sigma,xi and eta} assuming \code{theta} 
#' equals zero. A generalized extreme value distribution is fitted individually for each year and then the inital values
#' for the duration dependent gev fit are estimated from those by applying a linear regression to the scale parameters of each year.
575
576
577
#' @param xdat a \code{vector} of yearly maxima of intensity sorted by year and aggregatin level
#' @param ds a \code{vector} of durations used to fit the model. Has to have same length and order as \code{int.vec}

Christoph Ritschel's avatar
Christoph Ritschel committed
578
579
580
581
582
#' @return $mu initial estimation of location parameter
#' @return $sigma initial estimation of scale parameter
#' @return $xi inital estimation of shape parameter
#' @return $eta intial estimation of slope parameter for sigma-power law.
#' @author Christoph Ritschel \email{christoph.ritschel@@met.fu-berlin.de}
583
#' @author Henning Rust \email{henning.rust@fu-berlin.de}
Christoph Ritschel's avatar
Christoph Ritschel committed
584

585
IDF.init <- function(xdat,ds) {
Christoph Ritschel's avatar
Christoph Ritschel committed
586
  
587
588
589
    ## Fit a generalized extreme value distribution to the maximum intensities of each year for a single 
    ## aggregation level and write the estimated parameters in an array for further analyisis.
    pars <- simplify2array(tapply(xdat,ds,function(xdat) gev.fit(xdat,show=FALSE)$mle,simplify=TRUE))
Christoph Ritschel's avatar
Christoph Ritschel committed
590
    
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
    if(anyNA(pars)){
        cat("Warning: optimization did not converge in some cases and no parameters were estimated.\n")
        mu <- sigma <- xi <- eta <- NA
    }else{
        
#############################################################
### Derive starting parameters for duration-dependent GEV ###
#############################################################
        
        ## Fit a linear model to the individual sigmas for individual aggregation times in a log-log environment
        ## The slope coefficient is an estimate for the slope in the duration-dependent GEV, namely parameter eta
        ## The intersection is an estimation of the starting parameter sigma
        ## Parameter mu is estimated as mean value of individual mus divided by indiviudal sigmas
        ## The initial value for xi will be the mean of all individual xi, since it is approximately independent of duration
        formel <- lm(log(pars[2,]) ~ log(as.numeric(dimnames(pars)[[2]])))
        sigma <- as.numeric(exp(formel$coefficients[1]))
        mu <- mean(pars[1,]/pars[2,])
        eta <- as.numeric(-formel$coefficients[2])
        
        xi <- max(0,mean(pars[3,],na.rm=T))
    }
Christoph Ritschel's avatar
Christoph Ritschel committed
612
613
614
    
  return(list("mu"=mu,"sigma"=sigma,"xi"=xi,"eta"=eta))
  
615
616
}
                                        
Christoph Ritschel's avatar
Christoph Ritschel committed
617
618
619


#################################################################################
Henning Rust's avatar
Henning Rust committed
620

Christoph Ritschel's avatar
Christoph Ritschel committed
621
#' @title Fitting IDF model parameters to observations at different durations
622
#' @description The function \code{IDF} fits the IDF model parameters \code{mu,sigma,xi,eta,theta}
Christoph Ritschel's avatar
Christoph Ritschel committed
623
624
625
626
627
628
629
630
631
632
633
634
#' to a data.frame of observations \code{data} with temporal inforamtion (at least years) and values of precipitation
#' at a given temporal resoultion. This precipitation time series gets aggregated at given aggregation levels.
#' \code{agg.lev} and yearly maxima of intensity are caluclated for a specific month or the whole year/dataset. 
#' The starting values of the IDF model parameters can be determined by the user as well as specific options to use
#' during optimization. Logartihmic transformation, debugging, the optimization method, and an option to plot the
#' IDF curves.
#' @param data a \code{data,frame}, preferably generated by function \code{IDF.read}. It should at least contain a \code{$RR} and \code{$year} element for the 
#' function tow work properly.
#' @param agg.lev a vector of aggregation levels used to fit the IDF curves.
#' @param month \code{integer} value specifying the month to be used for estimating the IDF parameters. Type "all" for all months or if
#' the whole time series should be fitted.
#' @param moving.sum \code{logical} specifying if moving sum filtering should be applied for time series aggregation.
Christoph Ritschel's avatar
Christoph Ritschel committed
635
636
637
638
#' @param mu.init initial estimation of location parameter, default is NA. Initial value estimated by fitting individual gev parameters
#' @param sigma.init initial estimation of scale parameter,default is NA. Initial value estimated by fitting individual gev parameters
#' @param xi.init inital estimation of shape parameter, default is NA. Initial value estimated by fitting individual gev parameters
#' @param eta.init intial estimation of slope parameter for sigma-power law, default is NA. Initial value estimated by fitting individual gev parameters
Christoph Ritschel's avatar
Christoph Ritschel committed
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
#' @param theta.init inital value defining the curvature of the IDF, default is zero, it is not recommended to change it
#' @param use.log \code{logical} value for usage of logarithmic values, default is \code{FALSE}
#' @param DEBUG \code{logical} value for usage of debugging, if \code{TRUE} the input parameters and the value of negative
# 'log-likelihood are printed on console for each iteration during optimization.
#' @param method \code{character} defining the method to be used in \code{optim}, preferences are: "Nelder-Mead", "BFGS", "L-BFGS-B"e
#' @param lower \code{vector} specifying the lower boundary of parameters for "L-BFGS-B" method
#' @param upper \code{vector} specifying the upper boundary of parameters for "L-BFGS-B" method
#' @param plot \code{logical} option of creating a plot of IDF curves with estimated parameters.
#' @param probs a vector of probabilities for which the IDF curves are calculated
#' @param cols a vector of colors for the seperate IDF curves, needs same length as \code{probs}
#' @param station.name \code{character} overall naming of the IDF plot, e.g. name of location or model name
#' @param data.name \code{character} naming the data points, e.g. obs or model name
#' @return $ints vector of sorted intensities for selected aggregation levels
#' @return $durs vector of sorted aggregation levels
#' @return $min minimum value of negative log-likelihood during optimization
#' @return $par vector of estimated IDF model parameters mu,sigma,xi,theta,eta at minimum value of negative log-likelihood.
#' @examples 
#' RR <- rgamma(10*30*24,shape=1)
#' year <- sort(rep(1:(10),30*24))
#' data <- data.frame(RR,year)
#' fit <- IDF.fit(data)
#' pars <- fit$par 
#' @author Christoph Ritschel \email{christoph.ritschel@@met.fu-berlin.de}
Rust Henning's avatar
Rust Henning committed
662

Christoph Ritschel's avatar
Christoph Ritschel committed
663
664
IDF <- function(data,agg.lev=c(2,3,6,12,24,48,72,96),month="all",moving.sum="FALSE",mu.init=NA,sigma.init=NA,xi.init=NA,theta.init=0,eta.init=NA,
                use.log=FALSE,DEBUG=FALSE,method="Nelder-Mead",upper=Inf,lower=-Inf,plot=FALSE,
665
                probs=c(0.5,0.9,0.99),cols=c(rgb(1,0,0,1),rgb(0,1,0,1),rgb(0,0,1,1)),station.name="Berlin",data.name="obs",...) {
Christoph Ritschel's avatar
Christoph Ritschel committed
666
667
668
669
  
  #########################################################################
  ### Calculate extreme values for each year and each aggregation level ###
  #########################################################################
Christoph Ritschel's avatar
Christoph Ritschel committed
670
671
672
673
674
675
676
677
678
679
  dummy.list <- IDF.agg(data,agg.lev,month,moving.sum,DEBUG=FALSE)
  int.vec <- dummy.list$int.vec
  durs <- dummy.list$durs
  n.y <- dummy.list$n.y
  
  d.all <- unique(durs)
  ###################################################################################
  ### Estimate Parameters for single duration if not given initial values by user ###
  ###################################################################################
  if(is.na(mu.init) | is.na(sigma.init) | is.na(xi.init) | is.na(eta.init)) {
Christoph Ritschel's avatar
Christoph Ritschel committed
680
    
Christoph Ritschel's avatar
Christoph Ritschel committed
681
682
683
684
685
    pars.init <- IDF.init(int.vec,durs,n.y,method)  
    mu.init <- pars.init$mu
    sigma.init <- pars.init$sigma
    xi.init <- pars.init$xi
    eta.init <- pars.init$eta
Christoph Ritschel's avatar
Christoph Ritschel committed
686
    
Christoph Ritschel's avatar
Christoph Ritschel committed
687
  }
Christoph Ritschel's avatar
Christoph Ritschel committed
688
689
690
  ######################################################
  ### Estimate parameters for duration-dependent GEV ###
  ######################################################
Christoph Ritschel's avatar
Christoph Ritschel committed
691
692
  if(!is.na(mu.init) | !is.na(sigma.init) | !is.na(xi.init) | !is.na(eta.init)) {
    fit <- fit.fun(obs=int.vec,dur=durs,mu=mu.init,sigma=sigma.init,xi=xi.init,theta=theta.init,eta=eta.init,use.log=use.log,
693
                   DEBUG=DEBUG,method=method,upper=upper,lower=lower,...)
Christoph Ritschel's avatar
Christoph Ritschel committed
694
695
696
  }else {
    cat("Warning: Optimization not carried out due to invalid initial values. \n")
    fit.min <- NA
Rust Henning's avatar
Rust Henning committed
697
  }
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
  ######################################################
  ### success? Than plot!                            ###
  ######################################################
  
  if(plot&& !is.na(fit$min)) {
    ds <- sort(rep(d.all,length(int.vec)/length(d.all)))
    IDF.plot(pars=fit$par,probs,st.name=station.name,dt.name=data.name,ints=int.vec,ds=durs)
  }
  
  
  if(!plot && is.na(fit$min)) {
    cat("Warning: optimization did not converge and no parameters were estimated. \n")
  }
  
  if(plot && is.na(fit$min)) {
    cat("Warning: optimization did not converge and no parameters were estimated. Plot not possible. \n")
  }
  
  return(list("ints"=int.vec,"durs"=durs,"min"=fit$min,"par"=fit$par))
  
718
719
}
## End of function IDF.fit
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764


#' @title Fitting IDF model parameters to annual maximum intensity time series
#' @description The function \code{IDF.short} fits the IDF model parameters \code{mu,sigma,xi,eta,theta}
#' to vectors of annnual maximum intensities \code{int.vec} at different durations \code{durs}.
#' The starting values of the IDF model parameters can be determined by the user as well as specific options to use
#' during optimization. Logartihmic transformation, debugging, the optimization method, and an option to plot the
#' IDF curves.
#' @param ints.vec a \code{vector} of yearly maxima of intensity sorted by year and aggregatin level
#' @param durs a vector of aggregation levels used to fit the IDF curves. One value for each year. Has to have same lenght as \code{int.vec}
#' @param n.y \code{integer} value specifying the number of years of data
#' @param mu.init initial estimation of location parameter, default is NA. Initial value estimated by fitting individual gev parameters
#' @param sigma.init initial estimation of scale parameter,default is NA. Initial value estimated by fitting individual gev parameters
#' @param xi.init inital estimation of shape parameter, default is NA. Initial value estimated by fitting individual gev parameters
#' @param eta.init intial estimation of slope parameter for sigma-power law, default is NA. Initial value estimated by fitting individual gev parameters
#' @param theta.init inital value defining the curvature of the IDF, default is zero, it is not recommended to change it
#' @param use.log \code{logical} value for usage of logarithmic values, default is \code{FALSE}
#' @param DEBUG \code{logical} value for usage of debugging, if \code{TRUE} the input parameters and the value of negative
# 'log-likelihood are printed on console for each iteration during optimization.
#' @param method \code{character} defining the method to be used in \code{optim}, preferences are: "Nelder-Mead", "BFGS", "L-BFGS-B"e
#' @param lower \code{vector} specifying the lower boundary of parameters for "L-BFGS-B" method
#' @param upper \code{vector} specifying the upper boundary of parameters for "L-BFGS-B" method
#' @param plot \code{logical} option of creating a plot of IDF curves with estimated parameters.
#' @param probs a vector of probabilities for which the IDF curves are calculated
#' @param cols a vector of colors for the seperate IDF curves, needs same length as \code{probs}
#' @param station.name \code{character} overall naming of the IDF plot, e.g. name of location or model name
#' @param data.name \code{character} naming the data points, e.g. obs or model name
#' @return $ints vector of sorted intensities for selected aggregation levels
#' @return $durs vector of sorted aggregation levels
#' @return $min minimum value of negative log-likelihood during optimization
#' @return $par vector of estimated IDF model parameters mu,sigma,xi,theta,eta at minimum value of negative log-likelihood.
#' @examples 
#' RR <- rgamma(10*30*24,shape=1)
#' year <- sort(rep(1:(10),30*24))
#' data <- data.frame(RR,year)
#' data.agg <- IDF.agg(data,agg.lev=c(2,3,6,12,24))
#' int.vec <- data.agg$int.vec
#' durs <- data.agg$durs
#' n.y <- data.agg$n.y
#' fit <- IDF.short(int.vec,durs,n.y)
#' pars <- fit$par 
#' @author Christoph Ritschel \email{christoph.ritschel@@met.fu-berlin.de}

IDF.short <- function(int.vec,durs,n.y,mu.init=NA,sigma.init=NA,xi.init=NA,theta.init=0,eta.init=NA,
                      use.log=FALSE,DEBUG=FALSE,method="Nelder-Mead",upper=Inf,lower=-Inf,plot=FALSE,
765
766
                      probs=c(0.5,0.9,0.99),cols=c(rgb(1,0,0,1),rgb(0,1,0,1),rgb(0,0,1,1)),
                      station.name="Station",data.name="obs",...) {
767
768
769
770
771
  
  ###################################################################################
  ### Estimate Parameters for single duration if not given initial values by user ###
  ###################################################################################
  if(is.na(mu.init) | is.na(sigma.init) | is.na(xi.init) | is.na(eta.init)) {
Christoph Ritschel's avatar
Christoph Ritschel committed
772
    
773
774
775
776
777
    pars.init <- IDF.init(int.vec,durs,n.y,method)  
    mu.init <- pars.init$mu
    sigma.init <- pars.init$sigma
    xi.init <- pars.init$xi
    eta.init <- pars.init$eta
Christoph Ritschel's avatar
Christoph Ritschel committed
778
    
779
780
781
782
  }
  ######################################################
  ### Estimate parameters for duration-dependent GEV ###
  ######################################################
783
    if(!is.na(mu.init) | !is.na(sigma.init) | !is.na(xi.init) | !is.na(eta.init)) {
784
    fit <- fit.fun(obs=int.vec,dur=durs,mu=mu.init,sigma=sigma.init,xi=xi.init,theta=theta.init,eta=eta.init,use.log=use.log,
785
                   DEBUG=DEBUG,method=method,upper=upper,lower=lower,...)
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
  }else {
    cat("Warning: Optimization not carried out due to invalid initial values. \n")
    fit.min <- NA
  }
  ######################################################
  ### success? Than plot!                            ###
  ######################################################
  
  if(plot&& !is.na(fit$min)) {
    d.all <- unique(durs)
    ds <- sort(rep(d.all,length(int.vec)/length(d.all)))
    IDF.plot(pars=fit$par,probs,st.name=station.name,dt.name=data.name,ints=int.vec,ds=durs)
  }
  
  
  if(!plot && is.na(fit$min)) {
    cat("Warning: optimization did not converge and no parameters were estimated. \n")
  }
  
  if(plot && is.na(fit$min)) {
    cat("Warning: optimization did not converge and no parameters were estimated. Plot not possible. \n")
  }
  
  return(list("ints"=int.vec,"durs"=durs,"min"=fit$min,"par"=fit$par))
  
} ## End of function IDF.fit
######################################################################################################################


########################################################################################################
#' @title Plotting IDF curves
#' @description The function \code{IDF.plot} plots a set of IDF curves with given IDF model parameters \code{pars} for
#' several probability levels \code{probs} at given durations \code{dur}. The colors of the curves can be defined with
#' parameter \code{cols} (need to have same length as \code{probs}). The \code{station.name} will be printed in the legend.
#' @param pars a vector of IDF model parameters mu,sigma,xi,eta,theta
#' @param probs a vector of probabilities for which the IDF curves are calculated
#' @param dur a vector of durations at which the IDF curves are calculated
#' @param cols a vector of colors for the seperate IDF curves, needs same length as \code{probs}
#' @param st.name \code{character} overall naming of the IDF plot, e.g. name of location or model name
#' @param dt.name \code{character} naming the data points, e.g. obs or model name
#' @param ints \code{vector} of observational intensities (surted by durations)
#' @param ds \code{vector} of durations (same length as intensities)
#' @examples 
#' RR <- rgamma(10*30*24,shape=1)
#' year <- sort(rep(1:(10),30*24))
#' data <- data.frame(RR,year)
#' fit <- IDF.fit(data)
#' param <- fit$par
#' IDF.plot(pars=param,st.name="example",dt.name="rgamma")
#' @author Christoph Ritschel \email{christoph.ritschel@@met.fu-berlin.de}

837
838
839
840
IDF.plot <- function(pars,probs=c(0.5,0.9,0.99),
                     dur=c(0.5,1,2,3,6,12,24,48,72,96),
                     cols=rainbow(length(probs)),lty=1,
                     st.name="Station",dt.name="obs",ints=NA,ds=NA,ylim=NA,add=FALSE,...) {
841
842
843
844
845
846
  
  ## initialize array for IDF values at different durations and for different probabilities
  idf.array <- array(NA,dim=c(length(dur),length(probs)))
  
  ## loop over probabilities
  for(i in 1:length(probs)) {
Christoph Ritschel's avatar
Christoph Ritschel committed
847
    
848
849
    ## calculate IDF values for given probability at all durations
    idf.array[,i] <- qgev.d(probs[i],mu=pars[1],sigma=pars[2],xi=pars[3],theta=pars[4],eta=pars[5],d=dur)
Christoph Ritschel's avatar
Christoph Ritschel committed
850
    
851
  } ## end of loop over probs
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
    if(!add){
        ## initiialize plot window with limits of IDF values
        y.range <- ifelse(is.na(ylim), c(min(idf.array[,1],na.rm=T),max(idf.array[,3],na.rm=T)),ylim)
        plot(NA,axes=F,xlim=c(min(dur,na.rm=T),max(dur,na.rm=T)),ylim=y.range,xlab="duration [h]",ylab="intensity [mm/h]",log="xy",...)
        axis(1,at=dur,labels=dur)
        axis(2)  
        points(ds,ints,pch=16,col=rgb(0,0,0,0.5))
        ## loop over probabilities
        ## plot IDF curve
        
        legend.text.2 <- "quantile"
        
        ## plot legend
        legend(x="topright",legend=c(st.name,dt.name,paste(probs,legend.text.2,sep=" ")),
               col=c(1,rgb(0,0,0,0.5),cols),lty=c(NA,NA,rep(1,length(cols))),pch=c(NA,16,rep(NA,length(cols))))
    }
    
    for(i in 1:length(probs)) 
        lines(dur,idf.array[,i],col=cols[i],lwd=1.5,lty=lty)
        
872
873
874
875
} ## end of function IDF.plot
###################################################################################


876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
ydat = NULL
mul = NULL
sigl = NULL
shl = NULL
thetal = NULL
etal = NULL
mulink = identity
siglink = identity
shlink = identity
thetalink = identity
etalink = identity 
muinit = NULL
siginit = NULL
shinit = NULL
thetainit = NULL
etainit = NULL
show = TRUE
method = "Nelder-Mead"
maxit = 10000