Investigation of the Linear Variance Calibration using an idealized stochastic ensemble

The accurate estimation of forecast uncertainty is of vital importance in the risk assessment of events attributable to or influenced by meteorology, including (but not limited to) hurricane landfall, wintertime roadway conditioning, and the transport of harmful airborne contaminants. It is this final class of hazard on which we focus our study, but may be applicable elsewhere.

One common method to estimate the uncertainly is through the use of meteorological ensembles. These ensembles provide an easily quantifiable measure of the uncertainty in the forecast, usually in the form of the ensemble variance. However, ensembles may not accurately reflect the actual uncertainty in the forecast, so any measure of uncertainty derived from the ensemble should be calibrated to provide a more reliable estimate of the actual uncertainty in the forecast. Past study has introduced the Linear Variance Calibration (LVC) as a simple method of calibration that performs well on historical low-level wind forecasts from the NCEP Short-Range Ensemble Forecast (SREF) system.

This study uses the LVC on an idealized stochastic ensemble to more thoroughly investigate the LVC in a controlled setting. The results show that when using an ensemble of fewer than several hundred (which is most or all operational ensembles), sampling error due to the finite ensemble size causes deviations in the LVC slope and y-intercept even in an otherwise ‘perfect' ensemble where the errors and ensemble members are chosen from the same distribution. This effect is insensitive to observation error modeled as normal white noise, which only increases the y-intercept by the variance of the noise. As the ensemble increases in size, the LVC slope and y-intercept approach their ideal values. We also investigate the formulation of an expression that will estimate the infinite-member equivalent of finite-member ensemble LVC parameters, which would provide a fair assessment of an ensemble's second-order moment performance.