A Simple Method for Calibrating Ensemble Variability to Represent Meteorological Model Uncertainty

Having an accurate representation of the uncertainty is valuable in a wide variety of meteorological applications, from the representation of uncertainty in Atmospheric Transport & Dispersion (AT&D) models following a dangerous chemical release, to providing confidence intervals for day-to-day numerical weather prediction (NWP). One way to estimate the uncertainty of the meteorological fields is to compute the ensemble spread, i.e., the variance/covariance within an ensemble of meteorological model forecasts. These ensemble variances/covariances must then be calibrated to accurately represent the actual error variance/covariance.

This study examines such a calibration by using single-point ensemble variance/covariance as a predictor of actual error variance/covariance via a simple linear relationship. Results show a good agreement to this simple linear model for several meteorological variables, with slopes that are strongly dependent on model integration time and other factors. A simple slope-intercept relationship is useful for defining scaling factors to calibrate ensemble variances from operational centers' NWP systems to better represent the actual error variances. We also examine the usefulness of calculating two-point ensemble covariance as a function of distance as a means of estimating an error correlation length scale. Here data shows a strong correlation between the distance and the ensemble spread or covariance between two points, which varies for different variable fields in a logical manner.