MSSS | R Documentation |

Compute the mean square error skill score (MSSS) between an array of forecast
'exp' and an array of observation 'obs'. The two arrays should have the same
dimensions except along 'dat_dim' and 'memb_dim'. The MSSSs are computed along
'time_dim', the dimension which corresponds to the start date dimension.
MSSS computes the mean square error skill score of each exp in 1:nexp
against each obs in 1:nobs which gives nexp * nobs MSSS for each grid point
of the array.

The p-value and significance test are optionally provided by an one-sided
Fisher test or Random Walk test.

```
MSSS(
exp,
obs,
ref = NULL,
time_dim = "sdate",
dat_dim = NULL,
memb_dim = NULL,
pval = TRUE,
sign = FALSE,
alpha = 0.05,
sig_method = "one-sided Fisher",
sig_method.type = NULL,
ncores = NULL
)
```

`exp` |
A named numeric array of experimental data which contains at least time dimension (time_dim). It can also be a vector with the same length as 'obs', then the vector will automatically be 'time_dim'. |

`obs` |
A named numeric array of observational data which contains at least time dimension (time_dim). The dimensions should be the same as parameter 'exp' except the length of 'dat_dim' and 'memb_dim' dimension. It can also be a vector with the same length as 'exp', then the vector will automatically be 'time_dim'. |

`ref` |
A named numerical array of the reference forecast data with at least time dimension, or 0 (typical climatological forecast) or 1 (normalized climatological forecast). If it is an array, the dimensions must be the same as 'exp' except 'memb_dim' and 'dat_dim'. If there is only one reference dataset, it should not have dataset dimension. If there is corresponding reference for each experiment, the dataset dimension must have the same length as in 'exp'. If 'ref' is NULL, the typical climatological forecast is used as reference forecast (equivalent to 0.) The default value is NULL. |

`time_dim` |
A character string indicating the name of dimension along which the MSSS are computed. The default value is 'sdate'. |

`dat_dim` |
A character string indicating the name of dataset (nobs/nexp) dimension. The default value is NULL. |

`memb_dim` |
A character string indicating the name of the member dimension to compute the ensemble mean; it should be set to NULL if the data are already the ensemble mean. The default value is NULL. |

`pval` |
A logical value indicating whether to compute or not the p-value of the test Ho: MSSS = 0. The default value is TRUE. |

`sign` |
A logical value indicating whether to compute or not the statistical significance of the test Ho: MSSS = 0. The default value is FALSE. |

`alpha` |
A numeric of the significance level to be used in the statistical significance test. The default value is 0.05. |

`sig_method` |
A character string indicating the significance method. The options are "one-sided Fisher" (default) and "Random Walk". |

`sig_method.type` |
A character string indicating the test type of the
significance method. Check |

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

A list containing the numeric arrays with dimension:

c(nexp, nobs, all other dimensions of exp except time_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.

`$msss` |
A numerical array of the mean square error skill score. |

`$p.val` |
A numerical array of the p-value with the same dimensions as $msss.
Only present if |

`sign` |
A logical array of the statistical significance of the MSSS with the same
dimensions as $msss. Only present if |

```
# Load sample data as in Load() example:
example(Load)
clim <- Clim(sampleData$mod, sampleData$obs)
ano_exp <- Ano(sampleData$mod, clim$clim_exp)
ano_obs <- Ano(sampleData$obs, clim$clim_obs)
rmsss <- MSSS(ano_exp, ano_obs, dat_dim = 'dataset', memb_dim = 'member')
# Synthetic data:
exp <- array(rnorm(30), dim = c(dataset = 2, time = 3, memb = 5))
obs <- array(rnorm(15), dim = c(time = 3, dataset = 1))
res <- MSSS(exp, obs, time_dim = 'time', dat_dim = 'dataset', memb_dim = 'memb')
```

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