Newer
Older
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
#'Compute the ratio between the ensemble spread and RMSE
#'
#'Compute the ratio between the standard deviation of the members around the
#'ensemble mean in experimental data and the RMSE between the ensemble mean of
#'experimental and observational data. The p-value is provided by a one-sided
#'Fischer test.
#'
#'@param exp A named numeric array of experimental data with at least two
#' dimensions 'memb_dim' and 'time_dim'.
#'@param obs A named numeric array of observational data with at least two
#' dimensions 'memb_dim' and 'time_dim'. It should have the same dimensions as
#' parameter 'exp' except along 'dat_dim' and 'memb_dim'.
#'@param dat_dim A character string indicating the name of dataset (nobs/nexp)
#' dimension. If there is no dataset dimension, set as NULL. The default value
#' is 'dataset'.
#'@param memb_dim A character string indicating the name of the member
#' dimension. It must be one dimension in 'exp' and 'obs'. The default value
#' is 'member'.
#'@param time_dim A character string indicating the name of dimension along
#' which the ratio is computed. The default value is 'sdate'.
#'@param pval A logical value indicating whether to compute or not the p-value
#' of the test Ho : SD/RMSE = 1 or not. The default value is TRUE.
#'@param ncores An integer indicating the number of cores to use for parallel
#' computation. The default value is NULL.
#'
#'@return A list of two arrays with dimensions c(nexp, nobs, the rest of
#' dimensions of 'exp' and 'obs' except memb_dim and time_dim), which nexp is
#' the length of dat_dim of 'exp' and nobs is the length of dat_dim of 'obs'.
#' (only present if \code{pval = TRUE}) of the one-sided Fisher test with
#'Ho: SD/RMSE = 1.\cr\cr
#'\item{$ratio}{
#' The ratio of the ensemble spread and RMSE.
#'}
#'\item{$p_val}{
#' The p-value of the one-sided Fisher test with Ho: SD/RMSE = 1. Only present
#' if \code{pval = TRUE}.
#'}
#'
#'@examples
#'# Load sample data as in Load() example:
#'example(Load)
#'rsdrms <- RatioSDRMS(sampleData$mod, sampleData$obs)
#'rsdrms_plot <- array(dim = c(dim(rsdrms$ratio)[1:2], 4, dim(rsdrms$ratio)[3]))
#'rsdrms_plot[, , 2, ] <- rsdrms$ratio
#'rsdrms_plot[, , 4, ] <- rsdrms$p.val
#'\donttest{
#'PlotVsLTime(rsdrms_plot, toptitle = "Ratio ensemble spread / RMSE", ytitle = "",
#' monini = 11, limits = c(-1, 1.3), listexp = c('CMIP5 IC3'),
#' listobs = c('ERSST'), biglab = FALSE, siglev = TRUE,
#' fileout = 'tos_rsdrms.eps')
#'}
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
#'
#'@import multiApply
#'@export
RatioSDRMS <- function(exp, obs, dat_dim = 'dataset', memb_dim = 'member',
time_dim = 'sdate', pval = TRUE, ncores = NULL) {
# Check inputs
## exp and obs (1)
if (is.null(exp) | is.null(obs)) {
stop("Parameter 'exp' and 'obs' cannot be NULL.")
}
if (!is.numeric(exp) | !is.numeric(obs)) {
stop("Parameter 'exp' and 'obs' must be a numeric array.")
}
if (is.null(dim(exp)) | is.null(dim(obs))) {
stop(paste0("Parameter 'exp' and 'obs' must be array with as least two ",
"dimensions memb_dim and time_dim."))
}
if(any(is.null(names(dim(exp))))| any(nchar(names(dim(exp))) == 0) |
any(is.null(names(dim(obs))))| any(nchar(names(dim(obs))) == 0)) {
stop("Parameter 'exp' and 'obs' must have dimension names.")
}
if(!all(names(dim(exp)) %in% names(dim(obs))) |
!all(names(dim(obs)) %in% names(dim(exp)))) {
stop("Parameter 'exp' and 'obs' must have the same dimension names.")
}
## dat_dim
if (!is.null(dat_dim)) {
if (!is.character(dat_dim) | length(dat_dim) > 1) {
stop("Parameter 'dat_dim' must be a character string.")
}
if (!dat_dim %in% names(dim(exp)) | !dat_dim %in% names(dim(obs))) {
stop("Parameter 'dat_dim' is not found in 'exp' or 'obs' dimension.")
}
}
## memb_dim
if (!is.character(memb_dim) | length(memb_dim) > 1) {
stop("Parameter 'memb_dim' must be a character string.")
}
if (!memb_dim %in% names(dim(exp)) | !memb_dim %in% names(dim(obs))) {
stop("Parameter 'memb_dim' is not found in 'exp' or 'obs' dimension.")
}
## time_dim
if (!is.character(time_dim) | length(time_dim) > 1) {
stop("Parameter 'time_dim' must be a character string.")
}
if (!time_dim %in% names(dim(exp)) | !time_dim %in% names(dim(obs))) {
stop("Parameter 'time_dim' is not found in 'exp' or 'obs' dimension.")
}
## exp and obs (2)
name_exp <- sort(names(dim(exp)))
name_obs <- sort(names(dim(obs)))
if (!is.null(dat_dim)) {
name_exp <- name_exp[-which(name_exp == dat_dim)]
name_obs <- name_obs[-which(name_obs == dat_dim)]
}
name_exp <- name_exp[-which(name_exp == memb_dim)]
name_obs <- name_obs[-which(name_obs == memb_dim)]
if(!all(dim(exp)[name_exp] == dim(obs)[name_obs])) {
stop(paste0("Parameter 'exp' and 'obs' must have same length of ",
"all the dimensions expect 'dat_dim' and 'memb_dim'."))
}
## pval
if (!is.logical(pval) | length(pval) > 1) {
stop("Parameter 'pval' must be one logical value.")
}
## ncores
if (!is.null(ncores)) {
if (!is.numeric(ncores) | ncores %% 1 != 0 | ncores <= 0 |
length(ncores) > 1) {
stop("Parameter 'ncores' must be a positive integer.")
}
}
###############################
# Calculate RatioSDRMS
# If dat_dim = NULL, insert dat dim
remove_dat_dim <- FALSE
if (is.null(dat_dim)) {
dat_dim <- 'dataset'
exp <- InsertDim(exp, posdim = 1, lendim = 1, name = 'dataset')
obs <- InsertDim(obs, posdim = 1, lendim = 1, name = 'dataset')
remove_dat_dim <- TRUE
}
res <- Apply(list(exp, obs),
target_dims = list(c(dat_dim, memb_dim, time_dim),
c(dat_dim, memb_dim, time_dim)),
pval = pval,
fun = .RatioSDRMS,
ncores = ncores)
if (remove_dat_dim) {
if (length(dim(res[[1]])) > 2) {
res <- lapply(res, Subset, c('nexp', 'nobs'), list(1, 1), drop = 'selected')
} else {
res <- lapply(res, as.numeric)
}
}
return(res)
}
.RatioSDRMS <- function(exp, obs, pval = TRUE) {
# exp: [dat_exp, member, sdate]
# obs: [dat_obs, member, sdate]
nexp <- dim(exp)[1]
nobs <- dim(obs)[1]
# ensemble mean
ens_exp <- MeanDims(exp, 2, na.rm = TRUE) # [dat, sdate]
ens_obs <- MeanDims(obs, 2, na.rm = TRUE)
dif <- exp - InsertDim(ens_exp, 2, dim(exp)[2]) # [nexp, member, sdate]
std <- apply(dif, 1, sd, na.rm = TRUE) # [nexp]
enosd <- apply(Eno(dif, names(dim(exp))[3]), 1, sum, na.rm = TRUE)
# Create empty arrays
ratiosdrms <- array(dim = c(nexp = as.numeric(nexp), nobs = as.numeric(nobs))) # [nexp, nobs]
p.val <- array(dim = c(nexp = as.numeric(nexp), nobs = as.numeric(nobs))) # [nexp, nobs]
for (jexp in 1:nexp) {
for (jobs in 1:nobs) {
dif <- ens_exp[jexp, ] - ens_obs[jobs, ]
rms <- mean(dif^2, na.rm = TRUE)^0.5
enorms <- Eno(dif)
ratiosdrms[jexp, jobs] <- std[jexp]/rms
if (pval) {
F <- (enosd[jexp] * std[jexp]^2 / (enosd[jexp] - 1)) / (enorms * rms^2 / (enorms - 1))
if (!is.na(F) & !is.na(enosd) & !is.na(enorms) & enosd > 2 && enorms > 2) {
p.val[jexp, jobs] <- 1 - pf(F, enosd[jexp] - 1, enorms - 1)
} else {
ratiosdrms[jexp, jobs] <- NA
}
}
}
}
if (pval) {
return(invisible(list(ratio = ratiosdrms, p.val = p.val)))
} else {
return(invisible(list(ratio = ratiosdrms)))
}
}