ensembleMOSgev0 {ensembleMOS}

Censored generalized extreme value distribution EMOS modeling

Description

Fits a Censored generalized extreme value distribution EMOS model to ensemble forecasts for specified dates.

Usage

ensembleMOSgev0(ensembleData, trainingDays, consecutive = FALSE,
                dates = NULL, control = controlMOSgev0(),
                warmStart = FALSE, exchangeable = NULL)

Arguments

ensembleData

An ensembleData object including ensemble forecasts with the corresponding verifying observations and their dates. Missing values (indicated by NA) are allowed.

trainingDays

An integer giving the number of time steps (e.g. days) in the training period. There is no default.

consecutive

If TRUE then the sequence of dates in the training set are treated as consecutive, i.e. date gaps are ignored.

dates

The dates for which EMOS forecasting models are desired. By default, this will be all dates in ensembleData for which modeling is allowed given the training rule.

control

A list of control values for the fitting functions specified via the function controlMOSgev0. For details and default values, see controlMOSgev0.

warmStart

If TRUE, then starting values for parameters in optimization are set to the estimates of the preceding date's fit.

exchangeable

A numeric or character vector or factor indicating groups of ensemble members that are exchangeable (indistinguishable). The modeling will have equal parameters within each group. The default determines exchangeability from ensembleData.

Details

Given an ensemble of size m: X_1, \ldots , X_m, the following generalized extreme value distribution EMOS model left-censored at 0 is fit by ensembleMOSgev0:

Y ~ GEV_0(\mu,\sigma,q)

where GEV_0 denotes the generalized extreme value distribution left-censored at zero, with location \mu, scale \sigma and shape q. The model is parametrized such that the mean m is a linear function a + b_1 X_1 + \ldots + b_m X_m + s p_0 of the ensemble forecats, where p_0 denotes the ratio of ensemble forecasts that are exactly 0, and the shape parameter \sigma is a linear function of the ensemble variance c + d MD(X_1,\ldots,X_m), where MD(X_1,\ldots,X_m) is Gini's mean difference. See ensembleMOSgev0 for details.

B is a vector of fitted regression coefficients: b_1, \ldots, b_m. Specifically, a, b_1,\ldots, b_m, s, c, d, q are fitted to optimize the mean CRPS over the specified training period using optim.

Value

A list with the following output components:

training

A list containing information on the training length and lag and the number of instances used for training for each modeling date.

a

A vector of fitted EMOS intercept parameters for each date.

B

A matrix of fitted EMOS coefficients for each date.

s

A vector of fitted EMOS coefficients for p_0 for each date, see details.

c, d

The fitted coefficients for the shape parameter, see details.

q

Fitted shape parameter, see details.

References

M. Scheuerer, Probabilistic quantitative precipitation forecasting using ensemble model output statistics. Quarterly Journal of the Royal Meteorological Society 140:1086–1096, 2014.

See Also

controlMOSgev0, fitMOSgev0

Examples

data("ensBMAtest", package = "ensembleBMA")

ensMemNames <- c("gfs","cmcg","eta","gasp","jma","ngps","tcwb","ukmo")

obs <- paste("PCP24","obs", sep = ".")
ens <- paste("PCP24", ensMemNames, sep = ".")
prcpTestData <- ensembleData(forecasts = ensBMAtest[,ens],
                             dates = ensBMAtest[,"vdate"],
                             observations = ensBMAtest[,obs],
                             station = ensBMAtest[,"station"],
                             forecastHour = 48,
                             initializationTime = "00")
                             
prcpTestFitGEV0 <- ensembleMOSgev0(prcpTestData, trainingDays = 25,
                                   dates = "2008010100")