-
Notifications
You must be signed in to change notification settings - Fork 0
/
myEVfunctions.r
365 lines (293 loc) · 12.6 KB
/
myEVfunctions.r
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
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
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
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
#----------------------------------------------------------------------------------------------------------
# Name: myEVfunctions.r
# Purpose: External functions called by the EV_RL.r & EV_RP.r scripts
# Author: Francesco Tonini
# Email: f_tonini@hotmail.com
# Created: 11/1/2009
# Copyright: (c) 2009 by Francesco Tonini
# License: GNU General Public License (GPL)
# Software: Tested successfully using R-2.14.0 64-bit version(http://www.r-project.org/)
#-------------------------------------------------------------------------------------------
##CALL PACKAGES MODULE
##This module is used to call all required packages
load.packages <- function()
{
#setRepositories(ind=1:2)
pkg <- c("ismev","stats","tcltk2","RANN","maptools","evd")
w <- which(pkg %in% row.names(installed.packages()) == FALSE)
if (length(w) > 0) install.packages(pkg)[w]
#install.packages(c("ismev","stats","tcltk2","RANN","maptools","evd")) alternatively
#Load (call) specific packages from the existing library collection into the current R session
require(ismev) #An Introduction to Statistical Modeling of Extreme Values
require(stats) #R statistical functions
require(tcltk2) #Tkinter objects and classes
require(RANN) #spatial functions (e.g. NN interpolation)
require(maptools) #reading and writing shapefiles
require(evd) #Functions for extreme value distributions
#require(raster) #functions for raster data type
#require(extRemes) #only for automatic return-values calculation
cat('\nAll libraries have been loaded successfully!\n')
}
##GRADIENT FUNCTION MODULE
##This module is used within the return level module to compute the confidence intervals
##with delta method
gevrlgradient<-function (z, p)
{
scale <- z$mle[2]
shape <- z$mle[3]
if (shape < 0)
zero.p <- p == 0
else zero.p <- logical(length(p))
out <- matrix(NA, nrow = 3, ncol = length(p))
out[1, ] <- 1
if (any(zero.p)) {
out[2, zero.p & !is.na(zero.p)] <- rep(-shape^(-1), sum(zero.p,
na.rm = TRUE))
out[3, zero.p & !is.na(zero.p)] <- rep(scale * (shape^(-2)),
sum(zero.p, na.rm = TRUE))
}
if (any(!zero.p)) {
yp <- -log(1 - p[!zero.p])
out[2, !zero.p] <- -shape^(-1) * (1 - yp^(-shape))
out[3, !zero.p] <- scale * (shape^(-2)) * (1 - yp^(-shape)) -
scale * shape^(-1) * yp^(-shape) * log(yp)
}
return(out)
}
##RETURN LEVEL CALCULATION MODULE
##This module computes return levels based on the distibution used (GEV, gumbel, GPD)
return.levels <- function (z, conf = 0.05, rperiods = c(10, 100, 210, 510, 810, 980), make.plot = TRUE)
{
out <- list()
out$conf.level <- conf
eps <- 1e-06
a <- z$mle
#prova
#a1<-z$mle[1] + z$mle[2]*rperiods
std <- z$se
mat <- z$cov
dat <- z$data
kappa <- qnorm(conf/2, lower.tail = FALSE)
nx <- length(rperiods)
cl <- 1 - conf
if (class(z) == "gev.fit") {
if (is.null(rperiods)) rperiods <- seq(1.1, 1000, , 200)
if (any(rperiods <= 1))
stop("return.level: this function presently only supports return periods >= 1")
yp <- -log(1 - 1/rperiods)
if (a[3] < 0)
zero.p <- yp == 0
else zero.p <- logical(length(rperiods))
zero.p[is.na(zero.p)] <- FALSE
q <- numeric(length(rperiods))
if (any(zero.p))
q[zero.p] <- a[1] - a[2]/a[3]
if (any(!zero.p)) {
if (a[3] != 0)
q[!zero.p] <- a[1] - (a[2]/a[3]) * (1 - (yp[!zero.p])^(-a[3]))
else if (a[3] == 0)
q[!zero.p] <- a[1] - a[2] * log(yp[!zero.p])
}
d <- gevrlgradient(z = z, p = 1/rperiods)
v <- apply(d, 2, q.form, m = mat)
yl <- c(min(dat, q, na.rm = TRUE), max(dat, q, na.rm = TRUE))
if (make.plot) {
xp <- 1/yp
plot(xp, q, log = "x", type = "n", xlim = c(0.1,
1000), ylim = yl, xlab = "Return Period", ylab = "Return Level",
xaxt = "n")
axis(1, at = c(0.1, 1, 10, 100, 1000), labels = c("0.1",
"1", "10", "100", "1000"))
lines(xp, q)
lines(xp, (q + kappa * sqrt(v)), col = "blue")
lines(xp, (q - kappa * sqrt(v)), col = "blue")
points(-1/log((1:length(dat))/(length(dat) + 1)),
sort(dat))
}
out$return.level <- q
out$return.period <- rperiods
conf3 <- cbind(q - kappa * sqrt(v), q + kappa * sqrt(v))
colnames(conf3) <- c("lower", "upper")
out$confidence.delta <- conf3
}
if (class(z) == "gum.fit") {
if (is.null(rperiods))
rperiods <- seq(1.1, 1000, length=200)
if (any(rperiods <= 1))
stop("return.level: this function presently only supports return periods >= 1")
yp <- -log(1 - 1/rperiods)
q <- a[1] - a[2] * log(yp)
vq <- std[1]^2 + ((-log(yp))^2 * std[2]^2)
sq <- sqrt(vq)
yl <- c(min(dat, q, na.rm = TRUE), max(dat, q, na.rm = TRUE))
if (make.plot) {
xp <- 1/yp
plot(xp, q, log = "x", type = "n", xlim = c(0.1,
1000), ylim = yl, xlab = "Return Period", ylab = "Return Level",
xaxt = "n")
axis(1, at = c(0.1, 1, 10, 100, 1000), labels = c("0.1",
"1", "10", "100", "1000"))
lines(xp, q)
lines(xp, (q + kappa * sq), col = "blue")
lines(xp, (q - kappa * sq), col = "blue")
points(-1/log((1:length(dat))/(length(dat) + 1)),
sort(dat))
}
out$return.level <- q
out$return.period <- rperiods
conf3 <- cbind(q - kappa * sq, q + kappa * sq)
colnames(conf3) <- c("lower", "upper")
out$confidence.delta <- conf3
}
if (class(z) == "gpd.fit") {
u <- z$threshold
la <- z$rate
a <- c(la, a)
n <- z$n
npy <- z$npy
xdat <- z$xdata
if (is.null(rperiods)) {
rperiods <- seq(0.1, 1000, , 200)
}
m <- rperiods * npy
if (a[3] == 0)
q <- u + a[2] * log(m * la)
else q <- u + a[2]/a[3] * ((m * la)^(a[3]) - 1)
d <- gpdrlgradient(z, m)
mat <- matrix(c((la * (1 - la))/n, 0, 0, 0, mat[1, 1],
mat[1, 2], 0, mat[2, 1], mat[2, 2]), nc = 3)
v <- apply(d, 2, q.form, m = mat)
yl <- c(u, max(xdat, q[q > u - 1] + kappa * sqrt(v)[q >
u - 1], na.rm = TRUE))
if (make.plot) {
if (any(is.na(yl)))
yl <- range(q, na.rm = TRUE)
plot(m/npy, q, log = "x", type = "n", xlim = c(0.1,
max(m)/npy), ylim = yl, xlab = "Return period (years)",
ylab = "Return level", xaxt = "n")
axis(1, at = c(0.1, 1, 10, 100, 1000), labels = c("0.1",
"1", "10", "100", "1000"))
lines(m[q > u - 1]/npy, q[q > u - 1])
lines((m[q > u - 1]/npy), (q[q > u - 1] + kappa *
sqrt(v)[q > u - 1]), col = "blue")
lines((m[q > u - 1]/npy), (q[q > u - 1] - kappa *
sqrt(v)[q > u - 1]), col = "blue")
nl <- n - length(dat) + 1
sdat <- sort(xdat)
points((1/(1 - (1:n)/(n + 1))/npy)[sdat > u], sdat[sdat >
u])
}
out$return.level <- q
out$return.period <- m/npy
conf3 <- cbind(q[q > u - 1] - kappa * sqrt(v)[q > u -
1], q[q > u - 1] + kappa * sqrt(v)[q > u - 1])
colnames(conf3) <- c("lower", "upper")
out$confidence.delta <- conf3
}
invisible(out)
}
##NN INTERPOLATION FOR WARNINGS MODULE (FOR RETURN LEVELS)
##This module serves the purpose of replacing pixels, flagged as warning in the main script
##because of convergence issues, with the median of the nearest 4 or 8 neighbors
##NOTE: this works better if the raster resolution is not too coarse and the terrain is
##quite uniform to that of the central pixel. This is not recommended if that is not the case, or
##if you are using a very coarse resolution raster (e.g. 10 Km or more).
median.interp_RL <- function()
{
Matr_coord <- cbind(dataset[1:npixels,]$x, dataset[1:npixels,]$y)
for (px in px.idWarning){
#Rook's neighborhood (using the 'spdep' package)
NN4 <- knearneigh(Matr_coord,4)
Matr_NN4 <- NN4$nn
#Queen's neighborhood (using the 'spdep' package)
#NN8 <- knearneigh(Matr_coord,8)
#Matr_NN8 <- NN8$nn
#take a subset of the NN matrix only for the pixels flagged with a warning
Sub4 <- Matr_NN4[px,]
#Sub8 <- Matr_NN8[px,]
Mat_param <- tab.parameters[Sub4,]
Mat_rlevels <- tab.rlevels[Sub4,]
tab.parameters[px,3:length(tab.parameters)] <- round(sapply(Mat_param[,-c(1:2)],median),2)
tab.rlevels[px,2:length(tab.rlevels)] <- round(sapply(Mat_rlevels[,-1],median),2)
}
}
##NN INTERPOLATION FOR WARNINGS MODULE (FOR PROBABILITY EXCEEDANCES)
##This module serves the purpose of replacing pixels, flagged as warning in the main script
##because of convergence issues, with the median of the nearest 4 or 8 neighbors
##NOTE: this works better if the raster resolution is not too coarse and the terrain is
##quite uniform to that of the central pixel. This is not recommended if that is not the case, or
##if you are using a very coarse resolution raster (e.g. 10 Km or more).
median.interp_RP <- function()
{
Matr_coord <- cbind(dataset[1:npixels,]$x, dataset[1:npixels,]$y)
for (px in px.idWarning){
#Rook's neighborhood (using the 'spdep' package)
NN4 <- knearneigh(Matr_coord,4)
Matr_NN4 <- NN4$nn
#Queen's neighborhood (using the 'spdep' package)
#NN8 <- knearneigh(Matr_coord,8)
#Matr_NN8 <- NN8$nn
#take a subset of the NN matrix only for the pixels flagged with a warning
Sub4 <- Matr_NN4[px,]
#Sub8 <- Matr_NN8[px,]
Mat_param <- tab.parameters[Sub4,]
Mat_prob <- tab.prob[Sub4,]
tab.parameters[px,3:length(tab.parameters)] <- round(sapply(Mat_param[,-c(1:2)],median),2)
tab.prob[px,2:length(tab.prob)] <- round(sapply(Mat_prob[,-1],median),2)
}
}
##SAVE SHAPEFILE MODULE (FOR RETURN LEVELS)
##This module is used to save a point dataset to a shapefile (.shp)
save_files_RL <- function()
{
Matr_coord <- cbind(dataset[1:npixels,]$x, dataset[1:npixels,]$y)
tab.parameters$X <- Matr_coord[,1]
tab.parameters$Y <- Matr_coord[,2]
tab.rlevels$X <- Matr_coord[,1]
tab.rlevels$Y <- Matr_coord[,2]
##Turn input point dataset into a SpatialPointsDataFrame
coordinates(tab.parameters) <- ~X+Y
coordinates(tab.rlevels) <- ~X+Y
##Path to folder
path <- file.path(mainDir, subDir)
##Write .csv tables
write.table(tab.parameters, paste(path,'/MLE_Parameters.csv',sep=''), row.names=F, sep=',')
write.table(tab.rlevels, paste(path,'/ReturnLevels.csv',sep=''), row.names=F, sep=',')
##Write/Save the shapefile (library 'maptools')
writeSpatialShape( tab.parameters, paste(path,'/MLE_Parameters',sep='') )
writeSpatialShape( tab.rlevels, paste(path,'/ReturnLevels',sep='') )
##Write/Save rasters (library 'raster')
}
##SAVE SHAPEFILE MODULE (FOR PROBABILITY EXCEEDANCES)
##This module is used to save a point dataset to a shapefile (.shp)
save_files_RP <- function()
{
Matr_coord <- cbind(dataset[1:npixels,]$x, dataset[1:npixels,]$y)
tab.parameters$X <- Matr_coord[,1]
tab.parameters$Y <- Matr_coord[,2]
tab.prob$X <- Matr_coord[,1]
tab.prob$Y <- Matr_coord[,2]
##Turn input point dataset into a SpatialPointsDataFrame
coordinates(tab.parameters) <- ~X+Y
coordinates(tab.prob) <- ~X+Y
##Path to folder
path <- file.path(mainDir, subDir)
##Write .csv tables
write.table(tab.parameters, paste(path,'/MLE_Parameters.csv',sep=''), row.names=F, sep=',')
write.table(tab.prob, paste(path,'/ProbExceedance.csv',sep=''), row.names=F, sep=',')
##Write/Save the shapefile (library 'maptools')
writeSpatialShape( tab.parameters, paste(path,'/MLE_Parameters',sep='') )
writeSpatialShape( tab.prob, paste(path,'/ProbExceedance',sep='') )
##Write/Save rasters (library 'raster')
}
##PROBABILITY OF EXCEEDANCE MODULE
##This module is used to calculate the probability that the event will be exceeded in any one month
##(or year, or season, depending on what is your maxima/minima time series unit).
##The return period is the inverse of the probability of exceedance
prob_fun <- function(dataset,value,tab.extreme,nome,n=3){
px.prob <- round(1 - pgev(-return_levels, loc=mu, scale=sig, shape=shp), 3)
#Use the following line, and not the previous, if you are working with MAXIMA instead of MINIMA
#px.prob <- round(1 - pgev(-return_levels, loc=mu, scale=sig, shape=shp), 3)
#NOTE: the return period will then simply be 1/prob (in the time unit used, e.g. months)
return(px.prob)
}