# Weekly ECV Subseasonal Hindcast Verification

This is a practical case to compute monthly skill scores for the ECMWF/S2S-ENSForhc subseasonal hindcast using as a reference dataset ERA5. The ECV is air temperature at surface level (tas). 
Note that since this case is practical, it is heavy and takes much time to finish running.

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 (this is the *$sdate$*).
However, we will analyze the 20 previous years (this is the *$syear$*) of those initializations.

The figure to see details on the subeasonal hindcasts storage:

<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 $var$, $sdate$ and $syear$:

```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 following the scheme in this figure:

<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)
```

Now, we define the obs dates to load the reference dataset:

_(NOTE: The time attributes of exp returned by Start() cannot be used for defining
the obs dates because the time values saved in exp data are with 1-week lag. E.g., file for 19600104 has time values 1960-01-11, 1960-01-18, 1960-01-25, 1960-02-01.)_

```r
# Corresponding ERA5 
## Generate the syears from the sdates.seq
syears <- t(sapply(sdates.seq, function(x) {
                   year <- as.numeric(substr(x, 1, 4))
                   syears <- paste0((year-20):(year-1), substr(x, 5, 8))
       }))
names(dim(syears)) <- c('sdate', 'syear')

## Generate the times from the syears
Sys.setenv(TZ='UTC') # this helps to get UTC times
times <- lapply(syears, function(x) {
                x <- as.Date(x, format = "%Y%m%d", tz = "UTC")
                x <- seq(x, x + 25, by = 'week')
               format(x, "%Y%m%d")
              })
times <- Reduce(c, times)
dim(times) <- c(time = 4, sdate = 103, syear = 20)
times <- s2dv::Reorder(times, c(2,3,1))

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 = times,
             latitude = indices(1:121),
             longitude = indices(1:240),
             split_multiselected_dims = TRUE,
             return_vars = list(latitude = NULL,
                                longitude = NULL,
                                time = 'file_date'),
             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(hindcast, reference, sdates.seq, scores = 'all') {
  
  # Anomaly computation
  reference <- s2dv::InsertDim(reference, pos = 3, len = 1, name = 'ensemble')
  clim <- s2dv:::.Clim(hindcast, reference, time_dim = 'syear',
                       memb_dim = 'ensemble', memb = FALSE)
  hindcast <- s2dv::Ano(hindcast, clim$clim_exp)
  reference <- s2dv::Ano(reference, clim$clim_obs)
      
  # 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)
    hindcast_month <- ClimProjDiags::Subset(hindcast, 'sdate', 
                                            list(startdates))
    reference_month <- ClimProjDiags::Subset(reference, 'sdate',
                                             list(startdates))
    # reshape dimension to be [sdate, ensemble]
    dim(hindcast_month) <- c(sdate = prod(dim(hindcast_month)[c('sdate', 'syear')]),
                             dim(hindcast_month)['ensemble'])
    dim(reference_month) <- c(sdate = prod(dim(reference_month)[c('sdate', 'syear')]),
                              dim(reference_month)['ensemble'])

    if (any(c('fairrpss', 'frpss', 'all') %in% tolower(scores))) {
      Scores <- c(Scores, 
                  unlist(easyVerification::veriApply("FairRpss",
                    fcst = hindcast_month, obs = reference_month,
                    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 = hindcast_month, obs = reference_month,
                    tdim = 1, ensdim = 2)))
    } 
    if (any(c('enscorr', 'corr', 'all') %in% tolower(scores))) {
      fcst_mean <- rowMeans(hindcast_month)
      Scores <- c(Scores,
                  cor = cor(fcst_mean, reference_month,
                            use = "complete.obs"),
                  cor.pv = cor.test(fcst_mean, reference_month,
                           use = "complete.obs")$p.value)
    }
    if (any(c('bss10', 'fbss10', 'all') %in% scores)) {
      Scores <- c(Scores,
                  unlist(easyVerification::veriApply("FairRpss",
                    fcst = hindcast_month, obs = reference_month, 
                    prob = (1/10), tdim = 1, ensdim = 2)))
    }
    if (any(c('bss90', 'fbss90', 'all') %in% scores)) {
      Scores <- c(Scores, 
                  unlist(easyVerification::veriApply("FairRpss",
                    fcst = hindcast_month, 
                    obs = reference_month,
                    prob = (9/10), tdim = 1, ensdim = 2)))
    }
    Skill_Scores <- cbind(Skill_Scores, Scores)
    Scores <- NULL
  }
  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(hindcast = c('sdate','syear','ensemble'),
                                reference = c('sdate', 'syear')),
             output_dims = list(c('scores', 'month')),
             use_libraries = c('easyVerification',
                               'SpecsVerification',
                               's2dv', 'ClimProjDiags'))
# 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---------
  queue_host = 'nord4'   #your own host name for Nord3v2
  temp_dir =  '/gpfs/scratch/bsc32/bsc32339/startR_hpc/'
  ecflow_suite_dir = '/home/Earth/nperez/startR_local/'  #your own local directory
#------------------------------------------------------------
result <- Compute(wf,
               chunks = list(time = 4, longitude = 2, latitude = 2),
               threads_load = 2,
               threads_compute = 12,
               cluster = list(queue_host = queue_host,
                              queue_type = 'slurm',
                              cores_per_job = 12,
                              temp_dir = temp_dir,
                              polling_period = 10,
                              job_wallclock = '03:00:00',
                              max_jobs = 16,
                              bidirectional = FALSE),
               ecflow_suite_dir = ecflow_suite_dir,
               wait = TRUE)
```
*Notice that the execution of `Compute` may last for ~2 hours each chunk. Consider set `wait` as false (see [practical guide](https://earth.bsc.es/gitlab/es/startR/-/blob/master/inst/doc/practical_guide.md#collect-and-the-ec-flow-gui)).*

If 'all' scores are requested the order in the 'scores' dimension of the output will be:
  - FairRpss_skillscore (1), FairRpss_sd (2), 
  - FairCrpss_skillscore (3), FairCrpss_sd (4), 
  - EnsCorr (5), EnsCorr_pv (6)
  - FairBSS10 (7), FairBSS10_pv (8)
  - FairBSS90 (9), FairBSS90_pv (10)

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:


```r
dim(result$output1)
library(multiApply) # to use Apply and calculate significance
library(ClimProjDiags) # to use ArrayToList facilitating the use of PlotLayout
library(s2dv) # to use PlotLayout combined with PlotEquiMap
FRPSS.pv <- Apply(result$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


sig <- ArrayToList(FRPSS.pv[,1,1,1,,], 1, names = 'dots',
                    level = 'sublist')
vars <- ArrayToList(result$output1[1,,1,1,1,,], 1, names = '')
PlotLayout(fun = PlotEquiMap, 
           plot_dims = c('latitude', 'longitude'),
           var = vars,
           lon = attributes(exp)$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 the first 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.

*References*

Wilks, D. S. (2011). Statistical methods in the atmospheric sciences. Elsevier/Academic Press.

Vitart, F., Buizza, R., Alonso Balmaseda, M., Balsamo, G., Bidlot, J.-R., Bonet, A., Fuentes, M., Hofstadler, A., Molteni, F., & Palmer, T. N. (2008). The new VarEPS-monthly forecasting system: A first step towards seamless prediction. Quarterly Journal of the Royal Meteorological Society, 134(636), 1789–1799. https://doi.org/10.1002/qj.322

*Credits to*
  - *Original code: Andrea Manrique*
  - *Adaptation: Núria Pérez-Zanón*