ensembleMOScsg0 {ensembleMOS}

Censored and shifted gamma EMOS modeling

Description

Fits a censored and shifted gamma EMOS model to ensemble forecasts for specified dates.

Usage

ensembleMOScsg0(ensembleData, trainingDays, consecutive = FALSE,
                dates = NULL, control = controlMOScsg0(),
                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 controlMOScsg0. For details and default values, see controlMOScsg0.

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 shifted gamma model left-censored at 0 is fit by ensembleMOScsg0:

Y ~ Gamma_0(\kappa,\theta,q)

where Gamma_0 denotes the shifted gamma distribution left-censored at zero, with shape \kappa, scale \theta and shift q. The model is parametrized such that the mean \kappa\theta is a linear function a + b_1 X_1 + \ldots + b_m X_m of the ensemble forecats, and the variance \kappa\theta^2 is a linear function of the ensemble mean c+d \overline{f}, see Baran and Nemoda (2016) for details.

B is a vector of fitted regression coefficients: b_1, \ldots, b_m. Specifically, a, b_1,\ldots, b_m, c, d, q are fitted to optimize control$scoringRule over the specified training period using optim with method = control$optimRule.

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.

c, d

The fitted parameters for the variance, see details.

q

Fitted shift parameter, see details.

References

M. Scheuerer and T. M. Hamill, Statistical post-processing of ensemble precipitation forecasts by fitting censored, shifted gamma distributions. Monthly Weather Review 143:4578–4596, 2015.

S. Baran and D. Nemoda, Censored and shifted gamma distribution based EMOS model for probabilistic quantitative precipitation forecasting. Environmetrics 27:280–292, 2016.

See Also

controlMOScsg0, fitMOScsg0

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")

fitDates <- c("2008010100", "2008010200")
prcpTestFitGEV0 <- ensembleMOSgev0(prcpTestData, trainingDays = 25,
                                   dates = fitDates)