R: Create Example Forecast-Observation Pairs

toymodel {easyVerification} | R Documentation

## Create Example Forecast-Observation Pairs

### Description

This toy model lets you create forecast-observation pairs with specified ensemble and forecast size, correlation skill, and overconfidence (underdispersion) for application with the verification functionality provided as part of the easyVerification package.

### Usage

    toymodel(N = 35, nens = 51, alpha = 0.5, beta = 0)

    toyarray(dims = c(10, 5), ...)

### Arguments

`N` | number of forecast instances
`nens` | number of ensemble members
`alpha` | nominal correlation skill of forecasts
`beta` | overconfidence parameter (see details)
`dims` | independent (e.g. spatial) dimensions for the toy model
`...` | additional arguments passed to `toymodel`

### Details

The toy model is the TM2 model as introduced by Weigel and Bowler (2009) with a slight modification to allow for forecasts with negative correlation skill. In this toy model, the observations x and forecasts f_i are defined as follows:

x = μ_x + ε_x

f_i = α / |α| μ_x + ε_{β} + ε_i

where

μ_x ~ N(0, α^2)

ε_x ~ N(0, 1 - α^2)

ε_{β} ~ N(0, β^2)

ε_i ~ N(0, 1 - α^2 - β^2)

α^2 ≤ 1

0 ≤ β ≤ 1 - α^2

### Note

This toy model is intended to provide example forecast observation pairs and not to serve as a conceptual model to study real forecasts. For models to do the latter, please refer to Siegert et al. (2015).

### References

A. Weigel and N. Bowler (2009). Comment on 'Can multi-model combination really enhance the prediction skill of probabilistic ensemble forecasts?'. Quarterly Journal of the Royal Meteorological Society, 135, 535-539.

S. Siegert et al. (2015). A Bayesian framework for verification and recalibration of ensemble forecasts: How uncertain is NAO predictability? Preprint on ArXiv, http://arxiv.org/abs/1504.01933.

### Examples

    ## compute the correlation for a toy forecast with default parameters
    tm <- toyarray()
    f.corr <- veriApply("EnsCorr", fcst=tm$fcst, obs=tm$obs)

[Package easyVerification version 0.4.4 Index]