GenerateToyData {SpecsVerification}

Generate artificial data for ensemble verification using a signal-plus-noise model

Description

Generate artificial data for ensemble verification using a signal-plus-noise model

Usage

GenerateToyData(
  N = 20,
  mu.y = 0,
  s.s = 7,
  s.eps = 6,
  mu.x = 0,
  beta = 0.2,
  s.eta = 8,
  K = 10,
  mu.x.ref = NA,
  beta.ref = NA,
  s.eta.ref = NA,
  K.ref = NA
)

Arguments

N

number of forecasts and observations

mu.y

expectation value of the observations

s.s

standard deviation of the predictable signal

s.eps

standard deviation of the unpredictable noise

mu.x

expectation value of the ensemble

beta

weighting parameter of the signal in the ensemble forecasting system

s.eta

average spread of the ensemble

K

number of members of the ensemble

mu.x.ref

expectation value of the reference ensemble

beta.ref

weighting parameter of the signal in the reference ensemble forecasting system

s.eta.ref

average spread of the reference ensemble

K.ref

number of members of the reference ensemble

Details

The function simulates data from the latent variable model:

y_t = mu_y + s_t + eps_t

x_t,r = mu_x + beta * s_t + eta_t,r

where y_t is the observation at time t, and x_t,r is the r-th ensemble member at time t. The latent variable s_t is to be understood as the "predictable signal" that generates correlation between observations and ensemble members. If all arguments that end in ".ref" are specified, a reference ensemble is returned to also test comparative verification.

Value

A list with elements:

obs

N-vector of observations

ens

N*K matrix of ensemble members

ens.ref

N*K.ref matrix of reference ensemble members

Examples

 l <- GenerateToyData()
 with(l, EnsCrps(ens, obs))