Probabilistic mesoscale forecast error prediction using short-range ensembles
One measure of the utility of ensemble prediction systems is the relationship between ensemble spread and forecast error. Unfortunately, this relationship is often characterized by an inadequate measure (the spread-error correlation) that makes two critical assumptions: (1) a linear dependency between ensemble spread and forecast error and (2) an end user that has a continuous sensitivity to forecast error. The validity of these assumptions is investigated with a simple, stochastic model that estimates the upper bound in expected performance of real ensembles. The linear dependence assumption is shown to be invalid under a variety of spread and error metrics.A more complete understanding is achieved by considering the spread-skill relationship in a probabilistic context. A perfect spread-skill relationship can be interpreted as a higher-order statistical consistency, where ensemble variance equals ensemble-mean error variance for all individual classes of ensemble spread. This interpretation allows for a new approach to forecast error prediction, where error climatologies conditioned on the ensemble spread are used as probabilistic forecasts of error. The ensemble spread-skill relationship is evaluated by the skill of such probabilistic error forecasts relative to the skill of the overall error climatology.For ideal ensembles based on a stochastic model, the skill of spread-based conditional error climatology forecasts is nearly equal to the skill of forecasts taken directly from the ensemble probability density function. The skill of spread-based, conditional error climatology forecasts is highest for cases with extreme spread and lowest for cases with near-normal spread, which reinforces earlier results. Additionally, it is concluded that end users should choose a spread metric consistent with their own cost function to form appropriate error climatologies.A 361-case archive of mesoscale, short-range ensemble forecasts developed at the University of Washington is used to analyze the spread-skill relationship for real ensembles. Probabilistic error forecasts of near-surface winds and temperatures from spread-based, conditional error climatologies are more skillful than forecasts taken directly from the ensemble probability density function. This performance advantage is achieved because the direct ensemble forecasts are biased and uncalibrated. As direct ensemble probability forecasts improve, the advantage gained by using spread-based, conditional error climatologies diminishes.
- Atmospheric sciences