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This is a practical case to compute monthly skill scores for the ECMWF/S2S-ENSForhc subseasonal forecast using as a reference dataset ERA5. The ECV is air temperature at surface level (tas).
Here, we aim to calculate the skill scores of the corresponding hindcast of 2016.
Note that to do this, we will detect the Mondays and Thursdays, which are the days of the week in which this model is initialized) during the year 2016. However, we will work with the previous year of initialization.
<kbd><img src="inst/doc/figures/subseasonal_1.png" width="600" /></kbd>
After loading startR package, the paths to the hindcast should be defined, including labels for $var$ and others:
```{r}
library(startR)
ecmwf_path <- paste0('/esarchive/exp/ecmwf/s2s-monthly_ensforhc/',
'weekly_mean/$var$_f24h/$sdate$/$var$_$syear$.nc')
```
Now, create the sequence of start dates in 2016 that is explaind in the figure too:
<kbd><img src="inst/doc/figures/subseasonal_2.png" width="600" /></kbd>
```{r}
forecast.year <- 2016
# Mondays
sdates.seq.mon <- format(seq(as.Date(paste(forecast.year, 01, 04, sep = '-')),
as.Date(paste(forecast.year, 12, 31, sep='-')),
by = 'weeks'), format = '%Y%m%d')
# Thursdays (Monday+3days)
sdates.seq.thu <- format(seq(as.Date(paste(forecast.year, 01, 04, sep = '-')) + 3,
as.Date(paste(forecast.year, 12, 31, sep = '-')),
by = 'weeks'), format = '%Y%m%d')
# Joint dates in order
sdates.seq <- c(sdates.seq.mon, sdates.seq.thu)
ind <- order(as.Date(sdates.seq, format = '%Y%m%d')) # dates in order
sdates.seq <- sdates.seq[ind]
# Leap years, remove 29th of February:
pos.bis <- which(sdates.seq == paste0(forecast.year,"0229"))
if(length(pos.bis) != 0) sdates.seq <- sdates.seq[-pos.bis]
exp <- Start(dat = ecmwf_path,
var = 'tas',
sdate = sdates.seq,
syear = 'all', # before hdate
time = 'all',
ensemble = "all",
latitude = indices(1:121),
longitude = indices(1:240),
syear_depends = 'sdate',
return_vars = list(latitude = NULL,
longitude = NULL,
time = c('sdate', 'syear')),
retrieve = FALSE)
```
The time attributes returned by Start() are then used to define the corresponding dates to load the reference dataset:
# Corresponding ERA5
dates <- attr(exp, 'Variables')$common$time #20*4*103=8240 middle day of weekly averages
file_date <- sapply(dates, format, '%Y%m%d')
dim(file_date) <- c(length(sdates.seq), 20, 4)
names(dim(file_date)) <- c('sdate', 'syear', 'time')
obs_path <- paste0("/esarchive/recon/ecmwf/era5/weekly_mean/",
"$var$_f1h-240x121/$var$_$file_date$.nc")
obs <- Start(dat = obs_path,
var = 'tas',
file_date = file_date, # sdate syear time
# 103 20 4
latitude = indices(1:121),
longitude = indices(1:240),
split_multiselected_dims = TRUE,
retrieve = FALSE)
```
The next step is to define our function to calculate scores:
<kbd><img src="inst/doc/figures/subseasonal_3.png" width="600" /></kbd>
```{r}
score_calc <- function(forecast, reference, sdates.seq,
scores = 'all') {
library(easyVerification)
anomaly_crossval <- function(data) {
avg <- NA * dim(data)['syear'] # one avg per year
for (t in 1:dim(data)['syear']) {
avg[t]<- mean(data[,-t,])
}
data <- Apply(data, c('syear'), function(x) x - avg)[[1]]
return(data)
}
reference <- s2dv::InsertDim(reference, pos = 3, len = 1, name = 'ensemble')
forecast <- anomaly_crossval(forecast)
reference <- anomaly_crossval(reference)
# create objects to store the outputs
Scores <- NULL
Skill_Scores <- NULL
for(month in 1:12) {
# take only data of 1 month (indices of each month in start_dates)
startdates <- which(as.integer(substr(sdates.seq, 5,6)) == month)
forecast_month <- s2dverification::Subset(forecast, 'sdate',
list(startdates))
reference_month <- s2dverification::Subset(reference, 'sdate',
list(startdates))
forecast_month_reshaped <- array(forecast_month,
c(dim(forecast_month)['sdate'] * dim(forecast_month)['syear'],
dim(forecast_month)['ensemble']))
reference_month_reshaped <- array(reference_month,
c(dim(reference_month)['sdate'] *
dim(reference_month)['syear'],
dim(reference_month)['ensemble']))
if (any(c('fairrpss', 'frpss', 'all') %in% tolower(scores))) {
Scores <- c(Scores, unlist(easyVerification::veriApply("FairRpss",
fcst = forecast_month_reshaped, obs = reference_month_reshaped,
prob = c(1/3, 2/3), tdim = 1, ensdim = 2)))
}
if (any(c('faircrpss', 'fcrpss', 'all') %in% tolower(scores))) {
Scores <- c(Scores, unlist(easyVerification::veriApply("FairCrpss",
fcst = forecast_month_reshaped, obs = reference_month_reshaped,
tdim = 1, ensdim = 2)))
}
if (any(c('enscorr', 'corr', 'all') %in% tolower(scores))) {
fcst_mean <- Apply(forecast_month_reshaped, 'ensemble', mean)[[1]]
Scores <- c(Scores,
cor = cor(fcst_mean, reference_month_reshaped,
use = "complete.obs"),
cor.pv = cor.test(fcst_mean, reference_month_reshaped,
use = "complete.obs")$p.value)
}
if (any(c('bss10', 'fbss10', 'all') %in% scores)) {
Scores <- c(Scores, unlist(easyVerification::veriApply("FairRpss",
fcst = forecast_month_reshaped, obs = reference_month_reshaped,
prob = (1/10), tdim = 1, ensdim = 2)))
}
if (any(c('bss90', 'fbss90', 'all') %in% scores)) {
Scores <- c(Scores, unlist(easyVerification::veriApply("FairRpss",
fcst = forecast_month_reshaped,
obs = reference_month_reshaped,
prob = (9/10), tdim = 1, ensdim = 2)))
}
return(Skill_Scores)
}
```
The workflow is created with Step() and AddStep()
<kbd><img src="inst/doc/figures/subseasonal_4.png" width="600" /></kbd>
```{r}
step <- Step(fun = score_calc,
target_dims = list(forecast = c('sdate','syear','ensemble'),
reference = c('sdate', 'syear')),
output_dims = list(c('scores', 'month')),
use_libraries = c('easyVerification',
'SpecsVerification',
's2dverification'))
# Workflow:
wf <- AddStep(list(exp,obs), step, sdates.seq = sdates.seq, scores = 'all')
```
Finally, execute the analysis, for instance, in Nord3:
```{r}
#-----------modify according to your personal info---------
temp_dir = '/gpfs/scratch/bsc32/bsc32339/startR_hpc/'
ecflow_suite_dir = '/home/Earth/nperez/startR_local/' #your own local directory
#------------------------------------------------------------
chunks = list(time = 4, longitude = 2, latitude = 2),
threads_load = 1,
threads_compute = 12,
cluster = list(queue_host = queue_host,
queue_type = 'lsf',
extra_queue_params = list('#BSUB -q bsc_es'),
cores_per_job = 12,
temp_dir = temp_dir,
polling_period = 10,
job_wallclock = '03:00',
max_jobs = 16,
bidirectional = FALSE),
ecflow_suite_dir = ecflow_suite_dir,
wait = TRUE)
```
If 'all' scores are requested the order in the 'scores' dimension of the output will be:
- FairRpss_skillscore, FairRpss_sd,
- FairCrpss_skillscore, FairCrpss_sd,
- EnsCorr, EnsCorr_pv
- FairBSS10, FairBSS10_pv
- FairBSS90, FairBSS90_pv
If you choose a subset of 'scores', it will follow the same order omitting the non-declared scores. It is useful to display the dimension names to understand the order of the output to create the plots. The significance can be also calculated using the standard deviation. Here, it is shown a simplified method:
dim(result$output1)
library(multiApply)
FRPSS.pv <- Apply(result$output1, target_dims = c('scores'),
fun = function(x, my.pvalue) {
(x[1] > 0) & (x[1] > x[2] * qnorm(1 - my.pvalue))},
my.pvalue = 0.05, ncores = 4)$output1
ArrayToList <- function(data, MARGINS, names = NULL, level = 'list') {
data <- asplit(data, MARGINS)
attributes(data) <- NULL
if (level == 'sublist') {
data <- lapply(data, function(x) {
res <- list(x)
names(res) <- names
return(res)})
} else {
names(data) <- names
}
return(data)
}
sig <- ArrayToList(FRPSS.pv[,1,1,1,,], 1, names = 'dots',
level = 'sublist')
vars <- ArrayToList(result$output1[1,,1,1,1,,], 1)
PlotLayout(fun = PlotEquiMap,
plot_dims = c('latitude', 'longitude'),
var = vars,
lon = attributes(exp)$Variables$common$longitude,
lat = attributes(exp)$Variables$common$latitude,
brks = seq(-1, 1, 0.2),
filled.continents = FALSE, sizetit = NULL, dot_symbol = '/',
special_args = sig,
toptitle = 'S2S FairRPSS - Hindcast 2016 - sweek 1',
title_scale = 0.7,
titles = month.name, bar_scale = 0.8,
fileout = 'startR/inst/doc/figures/subseasonal_5.png')
<kbd><img src="inst/doc/figures/subseasonal_5.png" width="600" /></kbd>
This multipanel plot shows the monthly skill score FairRPSS corresponding to thefirst lead time (i.e. first week of each month) of the 20 years hindcast of 2016. Blue (red) grid points correspond to low (high) values of the Fair RPSS in which the predictability is low (high). The highest values are found in tropical regions. However, the predictability is different for each month.
Given the high number of significant gridpoints, an alternative to display this information could be to filter the data for the non-significant points.