ACC: Compute the spatial anomaly correlation coefficient between...

In s2dv: A Set of Common Tools for Seasonal to Decadal Verification

Compute the spatial anomaly correlation coefficient between the forecast and corresponding observation

Description

Calculate the spatial anomaly correlation coefficient (ACC) for the ensemble mean of each model and the corresponding references over a spatial domain. It can return a forecast time series if the data contain forest time dimension, and also the ACC mean over one dimension, e.g., start date dimension. The domain of interest can be specified by providing the list of longitudes/ latitudes of the data together with the corners of the domain: lonlatbox = c(lonmin, lonmax, latmin, latmax). The data will be adjusted to have a spatial mean of zero, then area weighting is applied. The formula is referenced from Wilks (2011; section 7.6.4; https://doi.org/10.1016/B978-0-12-385022-5.00008-7).

Usage

ACC(
  exp,
  obs,
  dat_dim = NULL,
  lat_dim = "lat",
  lon_dim = "lon",
  avg_dim = "sdate",
  memb_dim = "member",
  lat = NULL,
  lon = NULL,
  lonlatbox = NULL,
  alpha = 0.05,
  pval = TRUE,
  sign = FALSE,
  conf = TRUE,
  conftype = "parametric",
  ncores = NULL
)

Arguments

exp	A numeric array of experimental anomalies with named dimensions. The dimension must have at least 'lat_dim' and 'lon_dim'.
obs	A numeric array of observational anomalies with named dimensions. The dimension should be the same as 'exp' except the length of 'dat_dim' and 'memb_dim'.
dat_dim	A character string indicating the name of dataset (nobs/nexp) dimension. The default value is NULL (no dataset).
lat_dim	A character string indicating the name of the latitude dimension of 'exp' and 'obs' along which ACC is computed. The default value is 'lat'.
lon_dim	A character string indicating the name of the longitude dimension of 'exp' and 'obs' along which ACC is computed. The default value is 'lon'.
avg_dim	A character string indicating the name of the dimension to be averaged, which is usually the time dimension. If no need to calculate mean ACC, set as NULL. The default value is 'sdate'.
memb_dim	A character string indicating the name of the member dimension. If the data are not ensemble ones, set as NULL. The default value is 'member'.
lat	A vector of the latitudes of the exp/obs grids. It is used for area weighting and when the domain of interested 'lonlatbox' is specified.
lon	A vector of the longitudes of the exp/obs grids. Only required when the domain of interested 'lonlatbox' is specified. The default value is NULL.
lonlatbox	A numeric vector of 4 indicating the corners of the domain of interested: c(lonmin, lonmax, latmin, latmax). The default value is NULL and the whole data will be used.
alpha	A numeric indicating the significance level for the statistical significance test. The default value is 0.05.
pval	A logical value indicating whether to compute the p-value or not. The default value is TRUE.
sign	A logical value indicating whether to retrieve the statistical significance of the test Ho: ACC = 0 based on 'alpha'. The default value is FALSE.
conf	A logical value indicating whether to retrieve the confidence intervals or not. The default value is TRUE.
conftype	A charater string of "parametric" or "bootstrap". "parametric" provides a confidence interval for the ACC computed by a Fisher transformation and a significance level for the ACC from a one-sided student-T distribution. "bootstrap" provides a confidence interval for the ACC and MACC computed from bootstrapping on the members with 100 drawings with replacement. To guarantee the statistical robustness of the result, make sure that your experiment and observation always have the same number of members. "bootstrap" requires 'memb_dim' has value. The default value is 'parametric'.
ncores	An integer indicating the number of cores to use for parallel computation. The default value is NULL.

Value

A list containing the numeric arrays:

acc	The ACC with the dimensions c(nexp, nobs, the rest of the dimension except lat_dim, lon_dim and memb_dim). nexp is the number of experiment (i.e., dat_dim in exp), and nobs is the number of observation (i.e., dat_dim in obs). If dat_dim is NULL, nexp and nobs are omitted.
macc	The mean anomaly correlation coefficient with dimensions c(nexp, nobs, the rest of the dimension except lat_dim, lon_dim, memb_dim, and avg_dim). Only present if 'avg_dim' is not NULL. If dat_dim is NULL, nexp and nobs are omitted.
conf.lower (if conftype = "parametric") or acc_conf.lower (if conftype = "bootstrap")	The lower confidence interval of ACC with the same dimensions as ACC. Only present if conf = TRUE.
conf.upper (if conftype = "parametric") or acc_conf.upper (if conftype = "bootstrap")	The upper confidence interval of ACC with the same dimensions as ACC. Only present if conf = TRUE.
p.val	The p-value with the same dimensions as ACC. Only present if pval = TRUE and conftype = "parametric".
$sign	The statistical significance. Only present if sign = TRUE.
macc_conf.lower	The lower confidence interval of MACC with the same dimensions as MACC. Only present if conftype = "bootstrap".
macc_conf.upper	The upper confidence interval of MACC with the same dimensions as MACC. Only present if conftype = "bootstrap".

References

Joliffe and Stephenson (2012). Forecast Verification: A Practitioner's Guide in Atmospheric Science. Wiley-Blackwell.; Wilks (2011; section 7.6.4; https://doi.org/10.1016/B978-0-12-385022-5.00008-7).

Examples

 
sampleData$mod <- Season(sampleData$mod, monini = 11, moninf = 12, monsup = 2)
sampleData$obs <- Season(sampleData$obs, monini = 11, moninf = 12, monsup = 2) 
clim <- Clim(sampleData$mod, sampleData$obs)
ano_exp <- Ano(sampleData$mod, clim$clim_exp)
ano_obs <- Ano(sampleData$obs, clim$clim_obs)
acc <- ACC(ano_exp, ano_obs, lat = sampleData$lat, dat_dim = 'dataset')
acc_bootstrap <- ACC(ano_exp, ano_obs, conftype = 'bootstrap', 
                    lat = sampleData$lat, dat_dim = 'dataset')
# Combine acc results for PlotACC
res <- array(c(acc$conf.lower, acc$acc, acc$conf.upper, acc$p.val), 
            dim = c(dim(acc$acc), 4))
res_bootstrap <- array(c(acc$acc_conf.lower, acc$acc, acc$acc_conf.upper, acc$p.val),
                      dim = c(dim(acc$acc), 4))
 
PlotACC(res, startDates)
PlotACC(res_bootstrap, startDates)
 

s2dv documentation built on Oct. 13, 2024, 9:07 a.m.