DiffCorr {s2dv}

Compute the correlation difference and its significance

Description

Compute the correlation difference between two deterministic forecasts. Positive values of the correlation difference indicate that the forecast is more skillful than the reference forecast, while negative values mean that the reference forecast is more skillful. The statistical significance of the correlation differences is computed with a one-sided or two-sided test for equality of dependent correlation coefficients (Steiger, 1980; Siegert et al., 2017) using effective degrees of freedom to account for the autocorrelation of the time series (Zwiers and von Storch, 1995).

Usage

DiffCorr(
  exp,
  obs,
  ref,
  N.eff = NA,
  time_dim = "sdate",
  memb_dim = NULL,
  method = "pearson",
  alpha = 0.05,
  handle.na = "return.na",
  test.type = "two-sided",
  pval = TRUE,
  sign = FALSE,
  ncores = NULL
)

Arguments

exp

A named numerical array of the forecast data with at least time dimension.

obs

A named numerical array with the observations with at least time dimension. The dimensions must be the same as "exp" except 'memb_dim'.

ref

A named numerical array of the reference forecast data with at least time dimension. The dimensions must be the same as "exp" except 'memb_dim'.

N.eff

Effective sample size to be used in the statistical significance test. It can be NA (and it will be computed with the s2dv:::.Eno), a numeric (which is used for all cases), or an array with the same dimensions as "obs" except "time_dim" (for a particular N.eff to be used for each case) . The default value is NA.

time_dim

A character string indicating the name of the time dimension. The default value is 'sdate'.

memb_dim

A character string indicating the name of the member dimension to compute the ensemble mean of the forecast and reference forecast. If it is NULL (default), the ensemble mean should be provided directly to the function.

method

A character string indicating the correlation coefficient to be computed ("pearson" or "spearman"). The default value is "pearson".

alpha

A numeric of the significance level to be used in the statistical significance test (output "sign"). The default value is 0.05.

handle.na

A charcater string indicating how to handle missing values. If "return.na", NAs will be returned for the cases that contain at least one NA in "exp", "ref", or "obs". If "only.complete.triplets", only the time steps with no missing values in all "exp", "ref", and "obs" will be used. If "na.fail", an error will arise if any of "exp", "ref", or "obs" contains any NA. The default value is "return.na".

test.type

A character string indicating the type of significance test. It can be "two-sided" (to assess whether the skill of "exp" and "ref" are significantly different) or "one-sided" (to assess whether the skill of "exp" is significantly higher than that of "ref") following Steiger (1980). The default value is "two-sided".

pval

A logical value indicating whether to return the p-value of the significance test Ho: DiffCorr = 0. The default value is TRUE.

sign

A logical value indicating whether to return the statistical significance of the test Ho: DiffCorr = 0 based on 'alpha'. The default value is FALSE.

ncores

An integer indicating the number of cores to use for parallel computation. The default value is NULL.

Value

A list with:

$diff.corr

A numerical array of the correlation differences with the same dimensions as the input arrays except "time_dim" (and "memb_dim" if provided).

$sign

A logical array of the statistical significance of the correlation differences with the same dimensions as the input arrays except "time_dim" (and "memb_dim" if provided). Returned only if "sign" is TRUE.

$p.val

A numeric array of the p-values with the same dimensions as the input arrays except "time_dim" (and "memb_dim" if provided). Returned only if "pval" is TRUE.

References

Steiger, 1980; https://content.apa.org/doi/10.1037/0033-2909.87.2.245 Siegert et al., 2017; https://doi.org/10.1175/MWR-D-16-0037.1 Zwiers and von Storch, 1995; https://doi.org/10.1175/1520-0442(1995)008<0336:TSCIAI>2.0.CO;2

Examples

exp <- array(rnorm(1000), dim = c(lat = 3, lon = 2, member = 10, sdate = 50))
obs <- array(rnorm(1000), dim = c(lat = 3, lon = 2, sdate = 50))
ref <- array(rnorm(1000), dim = c(lat = 3, lon = 2, member = 10, sdate = 50))
res_two.sided_sign <- DiffCorr(exp, obs, ref, memb_dim = 'member', 
                               test.type = 'two-sided', alpha = 0.05)
res_one.sided_pval <- DiffCorr(exp, obs, ref, memb_dim = 'member', 
                               test.type = 'one-sided', alpha = NULL)