  Ensemble forecasts of weather and climate are subject to systematic biases in
the ensemble mean and variance, leading to inaccurate estimates of the forecast
mean and variance. To address these biases, ensemble forecasts are
post-processed using statistical recalibration frameworks. These frameworks
often specify parametric probability distributions for the verifying
observations. A common choice is the Normal distribution with mean and variance
specified by linear functions of the ensemble mean and variance. The parameters
of the recalibration framework are estimated from historical archives of
forecasts and verifying observations. Often there are relatively few forecasts
and observations available for parameter estimation, and so the fitted
parameters are also subject to uncertainty. This artefact is usually ignored.
This study reviews analytic results that account for parameter uncertainty in
the widely used Model Output Statistics recalibration framework. The predictive
bootstrap is used to approximate the parameter uncertainty by resampling in
more general frameworks such as Non-homogeneous Gaussian Regression. Forecasts
on daily, seasonal and annual time scales are used to demonstrate that
accounting for parameter uncertainty in the recalibrated predictive
distributions leads to probability forecasts that are more skilful and reliable
than those in which parameter uncertainty is ignored. The improvements are
attributed to more reliable tail probabilities of the recalibrated forecast
distributions.
