| Type: | Package |
| Title: | Ensemble Model Output Statistics |
| Version: | 0.8.2 |
| Date: | 2018-03-21 |
| Author: | RA Yuen, Sandor Baran, Chris Fraley, Tilmann Gneiting, Sebastian Lerch, Michael Scheuerer, Thordis Thorarinsdottir |
| Maintainer: | Sandor Baran <baran.sandor@inf.unideb.hu> |
| Depends: | R (≥ 2.10.0), ensembleBMA, chron, evd |
| Suggests: | fields, maps |
| Description: | Ensemble Model Output Statistics to create probabilistic forecasts from ensemble forecasts and weather observations. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Packaged: | 2018-03-22 09:40:18 UTC; sebastian |
| NeedsCompilation: | no |
| Repository: | CRAN |
| Date/Publication: | 2018-03-22 09:50:57 UTC |
Brier Score
Description
Computes the Brier score for the probability of exceedance of precipitation threshold values for univariate ensemble forecasting models.
Usage
brierScore(fit, ensembleData, thresholds, dates=NULL, ...)
Arguments
fit |
A model fit to ensemble forecasting data, obtained using
|
ensembleData |
An |
thresholds |
Threshold values for which the probability of exceedance is evaluated, set to 0 to evaluate probability of precipitation forecasts. |
dates |
The dates for which the CRPS will be computed.
These dates must be consistent with |
... |
Included for generic function compatibility. |
Details
Note that the Brier scores are only available for EMOS models suitable for precipitation accumulation, i.e. the censored and shifted gamma, and the censored generalized extreme value distribution EMOS model.
Value
BScores is a vector giving the Brier scores for each instance in the
data.
References
T. Gneiting and A. E. Raftery, Strictly proper scoring rules, prediction and estimation, Journal of the American Statistical Association 102:359–378, 2007.
See Also
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")
prcpTestFitCSG0 <- ensembleMOScsg0(prcpTestData, trainingDays = 25,
dates = "2008010100")
brierScore(prcpTestFitCSG0, ensembleData = prcpTestData,
thresholds = 0)
Cummulative distribution function for ensemble forcasting models
Description
Computes the cumulative distribution function (CDF) of an ensemble forecasting model at observation locations.
Usage
cdf(fit, ensembleData, values, dates = NULL, ...)
Arguments
fit |
A model fit to ensemble forecasting data, obtained using
|
ensembleData |
An |
values |
The vector of desired values at which the CDF of the ensemble forecasting model is to be evaluated. |
dates |
The dates for which the CDF will be computed.
These dates must be consistent with |
... |
Included for generic function compatibility. |
Details
This method is generic, and can be applied to any ensemble forecasting
model obtained using fitMOS or ensembleMOS.
For the EMOS models that allow for point masses at 0, i.e. the censored and
shifted gamma, and the censored generalized extreme value distribution EMOS model,
the function contains an addition logical argument randomizeATzero that specifies
whether the value of the CDF at zero should be chosen randomly from the interval between
0 and the value of the CDF at zero. The default choice if FALSE, setting
randomizeATzero = TRUE is practical for computing randomized PIT values.
Value
A matrix of probabilities corresponding to the CDF at the desired values. Useful for determining propability of freezing, precipitation, etc.
References
T. Gneiting, A. E. Raftery, A. H. Westveld and T. Goldman, Calibrated probabilistic forecasting using ensemble model output statistics and minimum CRPS estimation. Monthly Weather Review 133:1098–1118, 2005.
See Also
ensembleMOS,
fitMOS,
quantileForecast
Examples
data("ensBMAtest", package = "ensembleBMA")
ensMemNames <- c("gfs","cmcg","eta","gasp","jma","ngps","tcwb","ukmo")
obs <- paste("T2", "obs", sep = ".")
ens <- paste("T2", ensMemNames, sep = ".")
tempTestData <- ensembleData(forecasts = ensBMAtest[,ens],
dates = ensBMAtest[,"vdate"],
observations = ensBMAtest[,obs],
station = ensBMAtest[,"station"],
forecastHour = 48,
initializationTime = "00")
tempTestFit <- ensembleMOS(tempTestData, trainingDays = 25,
model = "normal",
dates = "2008010100")
tempTestCDF <- cdf(tempTestFit, tempTestData,
values = seq(from=277, to=282, by = 1))
tempTestCDF
Control parameters for censored and shifted gamma EMOS models
Description
Specifies a list of values controling the censored and shifted gamma EMOS fit of ensemble forecasts.
Usage
controlMOScsg0(scoringRule = c("crps", "log"),
optimRule = c("Nelder-Mead", "BFGS", "L-BFGS-B"),
coefRule = c("square", "none", "positive"),
varRule = c("square", "none"),
start = list(a = NULL, B = NULL,
c = NULL, d = NULL, q = NULL),
maxIter = Inf)
Arguments
scoringRule |
The scoring rule to be used in optimum score estimation. Options are "crps" for the continuous ranked probability score and "log" for the logarithmic score. |
optimRule |
Numerical optimization method to be supplied to |
coefRule |
Method to control non-negativity of regression estimates. Options are:
|
varRule |
Method to control non-negativity of the scale parameters.
Options |
start |
A list of starting parameters, |
maxIter |
An integer specifying the upper limit of the number of iterations used to fit the model. |
Details
If no value is assigned to an argument, the first entry of
the list of possibly choices will be used by default.
Note that optimMethod options are only available for scoringRule = "log".
In case of scoringRule = "crps", the optimization method
is set to "L-BFGS-B" by default.
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 ensembleMOScsg0
for details.
Value
A list whose components are the input arguments and their assigned values.
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
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")
prcpTestFitCSG0 <- ensembleMOScsg0(prcpTestData, trainingDays = 25,
dates = "2008010100",
control = controlMOScsg0(maxIter = as.integer(100),
scoringRule = "log",
optimRule = "Nelder-Mead",
coefRule= "none",
varRule = "square"))
Control parameters for censored generalized extreme value distribution EMOS models
Description
Specifies a list of values controling the censored generalized extreme value distribution EMOS fit of ensemble forecasts.
Usage
controlMOSgev0(optimRule = c("Nelder-Mead", "L-BFGS-B", "BFGS"),
coefRule = c("square", "none", "positive"),
varRule = c("square", "none"),
start = list(a = NULL, B = NULL,
s = NULL, c = NULL,
d = NULL, q = NULL),
maxIter = Inf)
Arguments
optimRule |
Numerical optimization method to be supplied to |
coefRule |
Method to control non-negativity of regression estimates. Options are:
|
varRule |
Method to control non-negativity of the scale parameters.
Options |
start |
A list of starting parameters, |
maxIter |
An integer specifying the upper limit of the number of iterations used to fit the model. |
Details
Note that only minimum CRPS estimation is available and chosen by default.
If no value is assigned to an argument, the first entry of the list of possibly choices will be used by default.
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.
Value
A list whose components are the input arguments and their assigned values.
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
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",
control = controlMOSgev0(maxIter = as.integer(100),
optimRule = "Nelder-Mead",
coefRule= "none",
varRule = "square"))
Control parameters for log-normal EMOS models
Description
Specifies a list of values controling the log-normal EMOS fit of ensemble forecasts.
Usage
controlMOSlognormal(scoringRule = c("crps", "log"),
optimRule = c("BFGS","Nelder-Mead"),
coefRule = c("square", "none", "positive"),
varRule = c("square", "none"),
start = list(a = NULL, B = NULL,
c = NULL, d = NULL),
maxIter = Inf)
Arguments
scoringRule |
The scoring rule to be used in optimum score estimation. Options are "crps" for the continuous ranked probability score and "log" for the logarithmic score. |
optimRule |
Numerical optimization method to be supplied to |
coefRule |
Method to control non-negativity of regression estimates. Options are:
|
varRule |
Method to control non-negativity of the variance parameters.
Options |
start |
A list of starting parameters, |
maxIter |
An integer specifying the upper limit of the number of iterations used to fit the model. |
Details
If no value is assigned to an argument, the first entry of
the list of possibly choices will be used by default.
Given an ensemble of size m: X_1, \ldots , X_m, the
following log-normal model is fit by ensembleMOSlognormal:
Y ~ LN(\mu, \sigma)
where LN denotes the log-normal distrbution with meanlog
parameter \mu and scalelog parameter \sigma, see
Lognormal. The model is parametrized such that the mean value of
the log-normal distribution is a linear function a + b_1 X_1 + \ldots + b_m X_m
of the ensemble forecats, and the variance is a linear function
c + d S^2. For transformations between \mu, \sigma and mean
and variance of the log-normal distribution, see Baran and Lerch (2015).
See ensembleMOSlognormal for details.
Note that in case of scoringRule = "log", forecast cases in the
training period with observation values of 0 are ignored in the model
estimation as 0 is not included in the support of the log-normal
distribution.
Value
A list whose components are the input arguments and their assigned values.
References
S. Baran and S. Lerch, Log-normal distribution based Ensemble Model Output Statistics models for probabilistic wind-speed forecasting. Quarterly Journal of the Royal Meteorological Society 141:2289–2299, 2015.
See Also
ensembleMOSlognormal,
fitMOSlognormal
Examples
data("ensBMAtest", package = "ensembleBMA")
ensMemNames <- c("gfs","cmcg","eta","gasp","jma","ngps","tcwb","ukmo")
obs <- paste("MAXWSP10","obs", sep = ".")
ens <- paste("MAXWSP10", ensMemNames, sep = ".")
windTestData <- ensembleData(forecasts = ensBMAtest[,ens],
dates = ensBMAtest[,"vdate"],
observations = ensBMAtest[,obs],
station = ensBMAtest[,"station"],
forecastHour = 48,
initializationTime = "00")
windTestFitLN <- ensembleMOSlognormal(windTestData, trainingDays = 25,
dates = "2008010100",
control = controlMOSlognormal(maxIter = as.integer(100),
scoringRule = "log",
optimRule = "BFGS",
coefRule= "none",
varRule = "square"))
Control parameters for Gaussian (normal) EMOS models
Description
Specifies a list of values controling the Gaussian (normal) EMOS fit of ensemble forecasts.
Usage
controlMOSnormal(scoringRule = c("crps", "log"),
optimRule = c("BFGS","Nelder-Mead"),
coefRule = c("square", "none", "positive"),
varRule = c("square", "none"),
start = list(a = NULL, B = NULL,
c = NULL, d = NULL),
maxIter = Inf)
Arguments
scoringRule |
The scoring rule to be used in optimum score estimation. Options are "crps" for the continuous ranked probability score and "log" for the logarithmic score. |
optimRule |
Numerical optimization method to be supplied to |
coefRule |
Method to control non-negativity of regression estimates. Options are:
|
varRule |
Method to control non-negativity of the variance parameters.
Options |
start |
A list of starting parameters, |
maxIter |
An integer specifying the upper limit of the number of iterations used to fit the model. |
Details
If no value is assigned to an argument, the first entry of
the list of possibly choices will be used by default.
Given an ensemble of size m: X_1, \ldots , X_m, the
following Gaussian model is fit by ensembleMOSnormal:
Y ~ N(a + b_1 X_1 + ... + b_m X_m , c + dS^2).
B is the array of fitted regression coefficients b_1,
\ldots, b_m for each date. See ensembleMOSnormal for details.
Value
A list whose components are the input arguments and their assigned values.
References
T. Gneiting, A. E. Raftery, A. H. Westveld and T. Goldman, calibrated probabilistic forecasting using ensemble model output statistics and minimum CRPS estimation. Monthly Weather Review 133:1098–1118, 2005.
See Also
ensembleMOSnormal,
fitMOSnormal
Examples
data("ensBMAtest", package = "ensembleBMA")
ensMemNames <- c("gfs","cmcg","eta","gasp","jma","ngps","tcwb","ukmo")
obs <- paste("T2", "obs", sep = ".")
ens <- paste("T2", ensMemNames, sep = ".")
tempTestData <- ensembleData(forecasts = ensBMAtest[,ens],
dates = ensBMAtest[,"vdate"],
observations = ensBMAtest[,obs],
station = ensBMAtest[,"station"],
forecastHour = 48,
initializationTime = "00")
tempTestFit <- ensembleMOSnormal(tempTestData, trainingDays = 25,
dates = "2008010100",
control = controlMOSnormal(maxIter = as.integer(100),
scoringRule = "log",
optimRule = "BFGS",
coefRule= "none",
varRule = "square"))
Control parameters for truncated normal EMOS models
Description
Specifies a list of values controling the truncated normal EMOS fit of ensemble forecasts.
Usage
controlMOStruncnormal(scoringRule = c("crps", "log"),
optimRule = c("BFGS","Nelder-Mead"),
coefRule = c("square", "none", "positive"),
varRule = c("square", "none"),
start = list(a = NULL, B = NULL,
c = NULL, d = NULL),
maxIter = Inf)
Arguments
scoringRule |
The scoring rule to be used in optimum score estimation. Options are "crps" for the continuous ranked probability score and "log" for the logarithmic score. |
optimRule |
Numerical optimization method to be supplied to |
coefRule |
Method to control non-negativity of regression estimates. Options are:
|
varRule |
Method to control non-negativity of the scale parameters.
Options |
start |
A list of starting parameters, |
maxIter |
An integer specifying the upper limit of the number of iterations used to fit the model. |
Details
If no value is assigned to an argument, the first entry of the list of possibly choices will be used by default.
Given an ensemble of size m: X_1, \ldots , X_m, the
following truncated normal model is fit by ensembleMOStruncnormal:
Y ~ N_0(a + b_1 X_1 + ... + b_m X_m, c + dS^2),
where N_0 denotes the normal distribution truncated at zero,
with location a + b_1 X_1 + ... + b_m X_m and squared scale
c + dS^2.
B is a vector of fitted regression coefficients b_1,
\ldots, b_m. See ensembleMOStruncnormal for details.
Value
A list whose components are the input arguments and their assigned values.
References
T. L. Thorarinsdottir and T. Gneiting, Probabilistic forecasts of wind speed: Ensemble model output statistics by using heteroscedastic censored regression. Journal of the Royal Statistical Society Series A 173:371–388, 2010.
See Also
ensembleMOStruncnormal,
fitMOStruncnormal
Examples
data("ensBMAtest", package = "ensembleBMA")
ensMemNames <- c("gfs","cmcg","eta","gasp","jma","ngps","tcwb","ukmo")
obs <- paste("MAXWSP10","obs", sep = ".")
ens <- paste("MAXWSP10", ensMemNames, sep = ".")
windTestData <- ensembleData(forecasts = ensBMAtest[,ens],
dates = ensBMAtest[,"vdate"],
observations = ensBMAtest[,obs],
station = ensBMAtest[,"station"],
forecastHour = 48,
initializationTime = "00")
windTestFitTN <- ensembleMOStruncnormal(windTestData, trainingDays = 25,
dates = "2008010100",
control = controlMOStruncnormal(maxIter = as.integer(100),
scoringRule = "log",
optimRule = "BFGS",
coefRule= "none",
varRule = "square"))
Continuous Ranked Probability Score
Description
Computes the continuous ranked probability score (CRPS) for univariate ensemble forecasting models.
Usage
crps(fit, ensembleData, dates=NULL, ...)
Arguments
fit |
A model fit to ensemble forecasting data, obtained using
|
ensembleData |
An |
dates |
The dates for which the CRPS will be computed.
These dates must be consistent with |
... |
Included for generic function compatibility. |
Details
These methods are generic, and can be applied to all ensemble
forecasting models. Missing values in forecasts and/or observations
result in NA values in the CRPS vector.
Value
crps is a matrix giving the CRPS for each instance in the data for
both the raw ensemble and the probabilistic forecast.
References
T. Gneiting and A. E. Raftery, Strictly proper scoring rules, prediction and estimation, Journal of the American Statistical Association 102:359–378, 2007.
See Also
Examples
data("ensBMAtest", package = "ensembleBMA")
ensMemNames <- c("gfs","cmcg","eta","gasp","jma","ngps","tcwb","ukmo")
obs <- paste("T2", "obs", sep = ".")
ens <- paste("T2", ensMemNames, sep = ".")
tempTestData <- ensembleData(forecasts = ensBMAtest[,ens],
dates = ensBMAtest[,"vdate"],
observations = ensBMAtest[,obs],
station = ensBMAtest[,"station"],
forecastHour = 48,
initializationTime = "00")
tempTestFit <- ensembleMOS(tempTestData, trainingDays = 25,
dates = "2008010100",
model = "normal")
crpsValues <- crps(tempTestFit, tempTestData)
colMeans(crpsValues)
EMOS modeling
Description
Fits a EMOS model to ensemble forecasts. Allows specification of a model, training rule, and forecasting dates.
Usage
ensembleMOS(ensembleData, trainingDays, consecutive = FALSE,
dates = NULL, control = NULL, warmStart = FALSE,
model = NULL, exchangeable = NULL)
Arguments
ensembleData |
An |
trainingDays |
An integer giving the number of time steps (e.g. days) in the training period. There is no default. |
consecutive |
If |
dates |
The dates for which EMOS forecasting models are desired.
By default, this will be all dates in |
control |
A list of control values for the fitting functions. The corresponding
control function has to be chosen in accordance with the selected
|
warmStart |
If |
model |
A character string describing the EMOS model to be fit.
Current choices are |
exchangeable |
A numeric or character vector or factor indicating groups of
ensemble members that are exchangeable (indistinguishable).
The model fit will have equal weights and parameters within each
group.
The default determines exchangeability from |
Details
If dates are specified in dates that cannot be forecast
with the training rule, the corresponding EMOS model parameter
outputs will be missing (NA) but not NULL.
The training rule uses the number of days corresponding to its
length regardless of whether or not the dates are consecutive.
Value
A list containing information on the training (length, lag and the
number of instances used for training for each modeling date), the
exchangeability, and vectors and/or matrics containing the estimated
regression and variance coefficient values depending on the specified
model.
References
Gaussian (normal) EMOS model:
T. Gneiting, A. E. Raftery, A. H. Westveld and T. Goldman,
Calibrated probabilistic forecasting using ensemble model output
statistics and minimum CRPS estimation.
Monthly Weather Review 133:1098–1118, 2005.
Truncated normal EMOS model:
T. L. Thorarinsdottir and T. Gneiting,
Probabilistic forecasts of wind speed:
Ensemble model output statistics by using
heteroscedastic censored regression.
Journal of the Royal Statistical Society Series A
173:371–388, 2010.
Log-normal EMOS model:
S. Baran and S. Lerch, Log-normal distribution based Ensemble Model
Output Statistics models for probabilistic wind-speed forecasting.
Quarterly Journal of the Royal Meteorological Society 141:2289–2299,
2015.
Censored and shifted gamma EMOS model:
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.
Censored generalized extreme value distribution EMOS model:
M. Scheuerer, Probabilistic quantitative precipitation forecasting using ensemble
model output statistics. Quarterly Journal of the Royal Meteorological
Society 140:1086–1096, 2014.
See Also
trainingData,
ensembleMOSnormal,
ensembleMOStruncnormal,
ensembleMOSlognormal,
ensembleMOScsg0,
ensembleMOSgev0,
controlMOSnormal,
controlMOStruncnormal,
controlMOSlognormal,
controlMOScsg0,
controlMOSgev0,
Examples
data("ensBMAtest", package = "ensembleBMA")
ensMemNames <- c("gfs","cmcg","eta","gasp","jma","ngps","tcwb","ukmo")
obs <- paste("T2", "obs", sep = ".")
ens <- paste("T2", ensMemNames, sep = ".")
tempTestData <- ensembleData(forecasts = ensBMAtest[,ens],
dates = ensBMAtest[,"vdate"],
observations = ensBMAtest[,obs],
station = ensBMAtest[,"station"],
forecastHour = 48,
initializationTime = "00")
tempTestFit <- ensembleMOS(tempTestData, trainingDays = 25,
model = "normal")
## Same as
## tempTestFit <- ensembleMOSnormal(tempTestData, trainingDays = 25)
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 |
trainingDays |
An integer giving the number of time steps (e.g. days) in the training period. There is no default. |
consecutive |
If |
dates |
The dates for which EMOS forecasting models are desired.
By default, this will be all dates in |
control |
A list of control values for the fitting functions specified via the function controlMOScsg0. For details and default values, see controlMOScsg0. |
warmStart |
If |
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 |
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
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)
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 |
trainingDays |
An integer giving the number of time steps (e.g. days) in the training period. There is no default. |
consecutive |
If |
dates |
The dates for which EMOS forecasting models are desired.
By default, this will be all dates in |
control |
A list of control values for the fitting functions specified via the function controlMOSgev0. For details and default values, see controlMOSgev0. |
warmStart |
If |
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 |
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 |
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
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")
Log-normal EMOS modeling
Description
Fits a log-normal EMOS model to ensemble forecasts for specified dates.
Usage
ensembleMOSlognormal(ensembleData, trainingDays, consecutive = FALSE,
dates = NULL, control = controlMOSlognormal(),
warmStart = FALSE, exchangeable = NULL)
Arguments
ensembleData |
An |
trainingDays |
An integer giving the number of time steps (e.g. days) in the training period. There is no default. |
consecutive |
If |
dates |
The dates for which EMOS forecasting models are desired.
By default, this will be all dates in |
control |
A list of control values for the fitting functions specified via the function controlMOStruncnormal. For details and default values, see controlMOStruncnormal. |
warmStart |
If |
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 |
Details
Given an ensemble of size m: X_1, \ldots , X_m, the
following log-normal model is fit by ensembleMOSlognormal:
Y ~ LN(\mu, \sigma)
where LN denotes the log-normal distrbution with meanlog
parameter \mu and scalelog parameter \sigma, see
Lognormal. The model is parametrized such that the mean value of
the log-normal distribution is a linear function a + b_1 X_1 + \ldots + b_m X_m
of the ensemble forecats, and the variance is a linear function
c + d S^2. For transformations between \mu, \sigma and mean
and variance of the log-normal distribution, see Baran and Lerch (2015).
See ensembleMOSlognormal for details.
B is a vector of fitted regression coefficients: b_1,
\ldots, b_m. Specifically, a, b_1,\ldots, b_m, c, d 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. |
References
S. Baran and S. Lerch, Log-normal distribution based Ensemble Model Output Statistics models for probabilistic wind-speed forecasting. Quarterly Journal of the Royal Meteorological Society 141:2289–2299, 2015.
See Also
controlMOSlognormal,
fitMOSlognormal
Examples
data("ensBMAtest", package = "ensembleBMA")
ensMemNames <- c("gfs","cmcg","eta","gasp","jma","ngps","tcwb","ukmo")
obs <- paste("MAXWSP10","obs", sep = ".")
ens <- paste("MAXWSP10", ensMemNames, sep = ".")
windTestData <- ensembleData(forecasts = ensBMAtest[,ens],
dates = ensBMAtest[,"vdate"],
observations = ensBMAtest[,obs],
station = ensBMAtest[,"station"],
forecastHour = 48,
initializationTime = "00")
windTestFitLN <- ensembleMOSlognormal(windTestData, trainingDays = 25)
Gaussian (normal) EMOS modeling
Description
Fits a Gaussian (normal) EMOS model to ensemble forecasts for specified dates.
Usage
ensembleMOSnormal(ensembleData, trainingDays, consecutive = FALSE,
dates = NULL, control = controlMOSnormal(),
warmStart = FALSE, exchangeable = NULL)
Arguments
ensembleData |
An |
trainingDays |
An integer giving the number of time steps (e.g. days) in the training period. There is no default. |
consecutive |
If |
dates |
The dates for which EMOS forecasting models are desired.
By default, this will be all dates in |
control |
A list of control values for the fitting functions specified via the function controlMOSnormal. For details and default values, see controlMOSnormal. |
warmStart |
If |
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 |
Details
Given an ensemble of size m: X_1, \ldots , X_m, the
following Gaussian model is fit by ensembleMOSnormal:
Y ~ N(a + b_1 X_1 + ... + b_m X_m , c + dS^2).
B is a vector of fitted regression coefficients: b_1,
\ldots ,b_m. Specifically, a,b_1,\ldots , b_m, c, d 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 |
Vectors of the fitted variance parameters for each date, see details. |
References
T. Gneiting, A. E. Raftery, A. H. Westveld and T. Goldman, Calibrated probabilistic forecasting using ensemble model output statistics and minimum CRPS estimation. Monthly Weather Review 133:1098–1118, 2005.
See Also
controlMOSnormal,
fitMOSnormal
Examples
data("ensBMAtest", package = "ensembleBMA")
ensMemNames <- c("gfs","cmcg","eta","gasp","jma","ngps","tcwb","ukmo")
obs <- paste("T2", "obs", sep = ".")
ens <- paste("T2", ensMemNames, sep = ".")
tempTestData <- ensembleData(forecasts = ensBMAtest[,ens],
dates = ensBMAtest[,"vdate"],
observations = ensBMAtest[,obs],
station = ensBMAtest[,"station"],
forecastHour = 48,
initializationTime = "00")
tempTestFit <- ensembleMOSnormal(tempTestData, trainingDays = 25)
Truncated normal EMOS modeling
Description
Fits a truncated normal EMOS model to ensemble forecasts for specified dates.
Usage
ensembleMOStruncnormal(ensembleData, trainingDays, consecutive = FALSE,
dates = NULL, control = controlMOStruncnormal(),
warmStart = FALSE, exchangeable = NULL)
Arguments
ensembleData |
An |
trainingDays |
An integer giving the number of time steps (e.g. days) in the training period. There is no default. |
consecutive |
If |
dates |
The dates for which EMOS forecasting models are desired.
By default, this will be all dates in |
control |
A list of control values for the fitting functions specified via the function controlMOStruncnormal. For details and default values, see controlMOStruncnormal. |
warmStart |
If |
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 |
Details
Given an ensemble of size m: X_1, \ldots , X_m, the
following truncated normal model is fit by ensembleMOStruncnormal:
Y ~ N_0(a + b_1 X_1 + ... + b_m X_m, c + dS^2),
where N_0 denotes the normal distribution truncated at zero,
with location a + b_1 X_1 + ... + b_m X_m and squared scale
c + dS^2.
B is a vector of fitted regression coefficients: b_1,
\ldots, b_m. Specifically, a, b_1,\ldots, b_m, c, d 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 squared scale, see details. |
References
T. L. Thorarinsdottir and T. Gneiting, Probabilistic forecasts of wind speed: Ensemble model output statistics by using heteroscedastic censored regression. Journal of the Royal Statistical Society Series A 173:371–388, 2010.
See Also
controlMOStruncnormal,
fitMOStruncnormal
Examples
data("ensBMAtest", package = "ensembleBMA")
ensMemNames <- c("gfs","cmcg","eta","gasp","jma","ngps","tcwb","ukmo")
obs <- paste("MAXWSP10","obs", sep = ".")
ens <- paste("MAXWSP10", ensMemNames, sep = ".")
windTestData <- ensembleData(forecasts = ensBMAtest[,ens],
dates = ensBMAtest[,"vdate"],
observations = ensBMAtest[,obs],
station = ensBMAtest[,"station"],
forecastHour = 48,
initializationTime = "00")
windTestFitTN <- ensembleMOStruncnormal(windTestData, trainingDays = 25)
EMOS model fit to a training set
Description
Fits an EMOS model to a given training set.
Usage
fitMOS(ensembleData, control = NULL, model = NULL,
exchangeable = NULL)
Arguments
ensembleData |
An |
control |
A list of control values for the fitting functions. The corresponding
control function has to be chosen in accordance with the selected
|
model |
A character string describing the EMOS model to be fit.
Current choices are |
exchangeable |
A numeric or character vector or factor indicating groups of
ensemble members that are exchangeable (indistinguishable).
The model fit will have equal weights and parameters
within each group.
The default determines exchangeability from |
Value
A list with estimated coefficient values. The specific content depends on
the chosen model.
References
Gaussian (normal) EMOS model:
T. Gneiting, A. E. Raftery, A. H. Westveld and T. Goldman,
Calibrated probabilistic forecasting using ensemble model output
statistics and minimum CRPS estimation.
Monthly Weather Review 133:1098–1118, 2005.
Truncated (normal) EMOS model:
T. L. Thorarinsdottir and T. Gneiting,
Probabilistic forecasts of wind speed:
Ensemble model output statistics by using
heteroscedastic censored regression.
Journal of the Royal Statistical Society Series A
173:371–388, 2010.
Log-normal EMOS model:
S. Baran and S. Lerch, Log-normal distribution based Ensemble Model
Output Statistics models for probabilistic wind-speed forecasting.
Quarterly Journal of the Royal Meteorological Society 141:2289–2299,
2015.
Censored and shifted gamma EMOS model:
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.
Censored generalized extreme value distribution EMOS model:
M. Scheuerer, Probabilistic quantitative precipitation forecasting using ensemble
model output statistics. Quarterly Journal of the Royal Meteorological
Society 140:1086–1096, 2014.
See Also
fitMOSnormal fitMOStruncnormal fitMOSlognormal fitMOScsg0 fitMOSgev0 controlMOSnormal controlMOStruncnormal controlMOSlognormal controlMOScsg0 controlMOSgev0
Examples
data("ensBMAtest", package = "ensembleBMA")
ensMemNames <- c("gfs","cmcg","eta","gasp","jma","ngps","tcwb","ukmo")
obs <- paste("T2", "obs", sep = ".")
ens <- paste("T2", ensMemNames, sep = ".")
tempTestData <- ensembleData(forecasts = ensBMAtest[,ens],
dates = ensBMAtest[,"vdate"],
observations = ensBMAtest[,obs],
station = ensBMAtest[,"station"],
forecastHour = 48,
initializationTime = "00")
tempTrain <- trainingData(tempTestData, trainingDays = 30,
date = "2008010100")
tempTrainFit <- fitMOS(tempTrain, model = "normal")
## equivalent to
## tempTrainFit <- fitMOSnormal(tempTrain)
Censored and shifted gamma EMOS modeling
Description
Fits a censored and shifted gamma EMOS model to a given training set.
Usage
fitMOScsg0(ensembleData, control = controlMOScsg0(),
exchangeable = NULL)
Arguments
ensembleData |
An |
control |
A list of control values for the fitting functions specified via the function controlMOScsg0. For details and default values, see controlMOScsg0. |
exchangeable |
An optional numeric or character vector or factor indicating groups of
ensemble members that are exchangeable (indistinguishable).
The models have equal EMOS coefficients within each group.
If supplied, this argument will override any specification of
exchangeability in |
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 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,
ensembleMOScsg0,
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")
prcpTrain <- trainingData(prcpTestData, trainingDays = 30,
date = "2008010100")
prcpTestFit <- fitMOScsg0(prcpTrain)
Censored generalized extreme value distribution EMOS modeling
Description
Fits a censored generalized extreme value distribution EMOS model to a given training set.
Usage
fitMOSgev0(ensembleData, control = controlMOSgev0(),
exchangeable = NULL)
Arguments
ensembleData |
An |
control |
A list of control values for the fitting functions specified via the function controlMOSgev0. For details and default values, see controlMOSgev0. |
exchangeable |
An optional numeric or character vector or factor indicating groups of
ensemble members that are exchangeable (indistinguishable).
The models have equal EMOS coefficients within each group.
If supplied, this argument will override any specification of
exchangeability in |
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 |
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,
ensembleMOSgev0,
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")
prcpTrain <- trainingData(prcpTestData, trainingDays = 30,
date = "2008010100")
prcpTestFit <- fitMOSgev0(prcpTrain)
Log-normal EMOS model fit to a training set
Description
Fits a log-normal EMOS model to a given training set.
Usage
fitMOSlognormal(ensembleData, control = controlMOSlognormal(),
exchangeable = NULL)
Arguments
ensembleData |
An |
control |
A list of control values for the fitting functions specified via the function controlMOSlognormal. For details and default values, see controlMOSlognormal. |
exchangeable |
An optional numeric or character vector or factor indicating groups of
ensemble members that are exchangeable (indistinguishable).
The models have equal EMOS coefficients within each group.
If supplied, this argument will override any specification of
exchangeability in |
Details
Given an ensemble of size m: X_1, \ldots , X_m, the
following log-normal model is fit by ensembleMOSlognormal:
Y ~ LN(\mu, \sigma)
where LN denotes the log-normal distrbution with meanlog
parameter \mu and scalelog parameter \sigma, see
Lognormal. The model is parametrized such that the mean value of
the log-normal distribution is a linear function a + b_1 X_1 + \ldots + b_m X_m
of the ensemble forecats, and the variance is a linear function
c + d S^2. For transformations between \mu, \sigma and mean
and variance of the log-normal distribution, see Baran and Lerch (2015).
See ensembleMOSlognormal for details.
Value
A list with the following output components:
a |
The fitted intercept. |
B |
The fitted EMOS coefficients. |
c, d |
The fitted parameters for the variance, see details. |
References
S. Baran and S. Lerch, Log-normal distribution based Ensemble Model Output Statistics models for probabilistic wind-speed forecasting. Quarterly Journal of the Royal Meteorological Society 141:2289–2299, 2015.
See Also
controlMOSlognormal,
ensembleMOSlognormal,
Examples
data("ensBMAtest", package = "ensembleBMA")
ensMemNames <- c("gfs","cmcg","eta","gasp","jma","ngps","tcwb","ukmo")
obs <- paste("MAXWSP10","obs", sep = ".")
ens <- paste("MAXWSP10", ensMemNames, sep = ".")
windTestData <- ensembleData(forecasts = ensBMAtest[,ens],
dates = ensBMAtest[,"vdate"],
observations = ensBMAtest[,obs],
station = ensBMAtest[,"station"],
forecastHour = 48,
initializationTime = "00")
windTrain <- trainingData(windTestData, trainingDays = 30,
date = "2008010100")
windTestFit <- fitMOSlognormal(windTrain)
Gaussian (normal) EMOS model fit to a training set
Description
Fits a Gaussian (normal) EMOS model to a given training set.
Usage
fitMOSnormal(ensembleData, control = controlMOSnormal(),
exchangeable = NULL)
Arguments
ensembleData |
An |
control |
A list of control values for the fitting functions specified via the function controlMOSnormal. For details and default values, see controlMOSnormal. |
exchangeable |
An optional numeric or character vector or factor indicating groups of
ensemble members that are exchangeable (indistinguishable).
The models have equal EMOS coefficients within each group.
If supplied, this argument will override any specification of
exchangeability in |
Details
Given an ensemble of size m: X_1, \ldots , X_m, the
following Gaussian model is fit by ensembleMOSnormal:
Y ~ N(a + b_1 X_1 + ... + b_m X_m , c + dS^2).
B is a vector of fitted regression coefficients: b_1,
\ldots ,b_m. Specifically, a,b_1,\ldots , b_m, c, d 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:
a |
The fitted intercept. |
B |
The fitted EMOS coefficients. |
c, d |
The fitted variance parameters, see details. |
References
T. Gneiting, A. E. Raftery, A. H. Westveld and T. Goldman, Calibrated probabilistic forecasting using ensemble model output statistics and minimum CRPS estimation. Monthly Weather Review 133:1098–1118, 2005.
See Also
controlMOSnormal,
ensembleMOSnormal,
Examples
data("ensBMAtest", package = "ensembleBMA")
ensMemNames <- c("gfs","cmcg","eta","gasp","jma","ngps","tcwb","ukmo")
obs <- paste("T2", "obs", sep = ".")
ens <- paste("T2", ensMemNames, sep = ".")
tempTestData <- ensembleData(forecasts = ensBMAtest[,ens],
dates = ensBMAtest[,"vdate"],
observations = ensBMAtest[,obs],
station = ensBMAtest[,"station"],
forecastHour = 48,
initializationTime = "00")
tempTrain <- trainingData(tempTestData, trainingDays = 30,
date = "2008010100")
tempTrainFit <- fitMOSnormal(tempTrain)
Truncated normal EMOS model fit to a training set
Description
Fits a truncated normal EMOS model to a given training set.
Usage
fitMOStruncnormal(ensembleData, control = controlMOStruncnormal(),
exchangeable = NULL)
Arguments
ensembleData |
An |
control |
A list of control values for the fitting functions specified via the function controlMOStruncnormal. For details and default values, see controlMOStruncnormal. |
exchangeable |
An optional numeric or character vector or factor indicating groups of
ensemble members that are exchangeable (indistinguishable).
The models have equal EMOS coefficients within each group.
If supplied, this argument will override any specification of
exchangeability in |
Details
Given an ensemble of size m: X_1, \ldots , X_m, the
following truncated normal model is fit by ensembleMOStruncnormal:
Y ~ N_0(a + b_1 X_1 + ... + b_m X_m, c + dS^2),
where N_0 denotes the normal distribution truncated at zero,
with location a + b_1 X_1 + ... + b_m X_m and squared scale
c + dS^2.
B is a vector of fitted regression coefficients: b_1,
\ldots, b_m. Specifically, a, b_1,\ldots, b_m, c, d 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:
a |
The fitted intercept. |
B |
The fitted EMOS coefficients. |
c, d |
The fitted parameters for the squared scale, see details. |
References
T. L. Thorarinsdottir and T. Gneiting, Probabilistic forecasts of wind speed: Ensemble model output statistics by using heteroscedastic censored regression. Journal of the Royal Statistical Society Series A 173:371–388, 2010.
See Also
controlMOStruncnormal,
ensembleMOStruncnormal,
Examples
data("ensBMAtest", package = "ensembleBMA")
ensMemNames <- c("gfs","cmcg","eta","gasp","jma","ngps","tcwb","ukmo")
obs <- paste("MAXWSP10","obs", sep = ".")
ens <- paste("MAXWSP10", ensMemNames, sep = ".")
windTestData <- ensembleData(forecasts = ensBMAtest[,ens],
dates = ensBMAtest[,"vdate"],
observations = ensBMAtest[,obs],
station = ensBMAtest[,"station"],
forecastHour = 48,
initializationTime = "00")
windTrain <- trainingData(windTestData, trainingDays = 30,
date = "2008010100")
windTestFit <- fitMOStruncnormal(windTrain)
Forecast distribution parameters
Description
Computes the parameters of the forecast distribution resulting for univariate ensemble forecasting models.
Usage
pars(fit, ensembleData, dates=NULL, ...)
Arguments
fit |
A model fit to ensemble forecasting data, obtained using
|
ensembleData |
An |
dates |
The dates for which the parameters will be computed.
These dates must be consistent with |
... |
Included for generic function compatibility. |
Details
These methods are generic, and can be applied to all ensemble forecasting models.
Value
pars is a matrix giving the distribution parameter values
for each instance in the data. The returned parameters denoted in
the column names depend on the model used to generate the
fit object.
See Also
Examples
data("ensBMAtest", package = "ensembleBMA")
ensMemNames <- c("gfs","cmcg","eta","gasp","jma","ngps","tcwb","ukmo")
obs <- paste("T2", "obs", sep = ".")
ens <- paste("T2", ensMemNames, sep = ".")
tempTestData <- ensembleData(forecasts = ensBMAtest[,ens],
dates = ensBMAtest[,"vdate"],
observations = ensBMAtest[,obs],
station = ensBMAtest[,"station"],
forecastHour = 48,
initializationTime = "00")
tempTestFit <- ensembleMOS(tempTestData, trainingDays = 25,
dates = c("2008010100", "2008010200"),
model = "normal")
parValues <- pars(tempTestFit, tempTestData)
parValues
Quantile forecasts at observation locations
Description
Computes quantiles for the probability distribution function (PDF) for ensemble forecasting models.
Usage
quantileForecast(fit, ensembleData, quantiles = 0.5, dates = NULL, ...)
Arguments
fit |
A model fit to ensemble forecasting data. |
ensembleData |
An |
quantiles |
The vector of desired quantiles for the PDF of the EMOS model. |
dates |
The dates for which the quantile forecasts will be computed.
These dates must be consistent with |
... |
Included for generic function compatibility. |
Details
This method is generic, and can be applied to any ensemble forecasting model. This can be used to compute prediction intervals for the PDF.
Value
A matrix of forecasts corresponding to the desired quantiles.
References
T. Gneiting, A. E. Raftery, A. H. Westveld and T. Goldman, Calibrated probabilistic forecasting using ensemble model output statistics and minimum CRPS estimation. Monthly Weather Review 133:1098–1118, 2005.
See Also
Examples
data("ensBMAtest", package = "ensembleBMA")
ensMemNames <- c("gfs","cmcg","eta","gasp","jma","ngps","tcwb","ukmo")
obs <- paste("T2", "obs", sep = ".")
ens <- paste("T2", ensMemNames, sep = ".")
tempTestData <- ensembleData(forecasts = ensBMAtest[,ens],
dates = ensBMAtest[,"vdate"],
observations = ensBMAtest[,obs],
station = ensBMAtest[,"station"],
forecastHour = 48,
initializationTime = "00")
tempTestFit <- ensembleMOS(tempTestData, trainingDays = 25,
dates = c("2008010100", "2008010200"),
model = "normal")
tempTestForc <- quantileForecast(tempTestFit, tempTestData)
Extract Training Data
Description
Extracts a subset of an ensembleData object corresponding
to a given date and number of training days.
Usage
trainingData(ensembleData, trainingDays, consecutive = FALSE, date)
Arguments
ensembleData |
An |
trainingDays |
An integer specifying the number of days in the training period. |
consecutive |
If |
date |
The date for which the training data is desired. |
Value
An ensembleData object corresponding to the training data for
the given date relative to
ensembleData.
References
A. E. Raftery, T. Gneiting, F. Balabdaoui and M. Polakowski, Using Bayesian model averaging to calibrate forecast ensembles, Monthly Weather Review 133:1155-1174, 2005.
J. M. Sloughter, A. E. Raftery, T. Gneiting and C. Fraley, Probabilistic quantitative precipitation forecasting using Bayesian model averaging, Monthly Weather Review 135:3309–3320, 2007.
C. Fraley, A. E. Raftery, T. Gneiting and J. M. Sloughter,
ensembleBMA: An R Package for Probabilistic Forecasting
using Ensembles and Bayesian Model Averaging,
Technical Report No. 516R, Department of Statistics, University of
Washington, December 2008.
Available at: http://www.stat.washington.edu/research/reports/
C. Fraley, A. E. Raftery and T. Gneiting, Calibrating multi-model forecast ensembles with exchangeable and missing members using Bayesian model averaging, Monthly Weather Review 138:190-202, 2010.
See Also
ensembleMOSnormal,
fitMOSnormal
Examples
data("ensBMAtest", package = "ensembleBMA")
ensMemNames <- c("gfs","cmcg","eta","gasp","jma","ngps","tcwb","ukmo")
obs <- paste("T2", "obs", sep = ".")
ens <- paste("T2", ensMemNames, sep = ".")
tempTestData <- ensembleData(forecasts = ensBMAtest[,ens],
dates = ensBMAtest[,"vdate"],
observations = ensBMAtest[,obs],
station = ensBMAtest[,"station"],
forecastHour = 48,
initializationTime = "00")
tempTrain <- trainingData(tempTestData, trainingDays = 30,
date = "2008010100")
tempTrainFit <- fitMOSnormal(tempTrain)