Part II:   What is ensemble forecasting aiming for?

     In the current deterministic NWP practice, one wishes to use single model output (Xm) to represent true atmospheric state (X), i.e.

 X=Xm                                                      (1)

    Since IC state and model state used in a model actually represent a kind of mean state in a certain degree, a corresponding model forecast (Xm) is, therefore, depicting a mean state too and the equation (1) is never the case in reality. Instead,

X=Xm+x0                                                 (2)

is always observed, where x0 is a departure of model forecast from truth. Since exact value of x0 is something we really don’t know in prior, we hope to estimate a possible set of solutions Xm+X’ to include the truth X or an error distribution X’ to have x0 be within the estimated distribution via a certain approach, i.e.

X Є Xm+X’                                                (3)

Since the intrinsic unavoidable uncertainties introduced at each of forecast steps are probably random in nature, the error distribution X’ must not be a single value but a kind of probabilistic distribution associated with initial uncertainties, instability of flow and the degree of nonlinearity of a modeling system. To reliably estimate and accurately describe this flow-dependent error distribution or forecast uncertainty range X’ to have truth be encompassed within Xm+X’ is the primary Mission of Ensemble Forecasting. Here, to improve the capability of predicting the error distribution X’ needs to improve ensembling technique and strategy, while to improve the accuracy of predicting mean state Xm mainly depends on model and IC qualities. In other words, the ensemble technique is dealing with the random error of a forecast, while the model and IC are dealing with the systematic error of a forecast. A good model and a high quality IC are the basis of ensemble forecasting. Therefore, improving model, IC quality and ensembling technique should be viewed as a whole to advance NWP. By the definition of ensemble mission, one can imagine that ensemble forecasting is most valuable when large forecast uncertainty is around and forecasters don’t know what solution to choose from in mainly high-impact events and has minimal value when weather is quiescent and highly predictable (although one still needs ensemble to identify such occasions).

    It might be worth pointing out that although ensembling method is gaining popularity in research and operation nowadays, a commonly seen incomplete use or even misunderstanding of the technique is that ensemble is merely used as a tool to improve the accuracy of a single value forecast such as by ensemble averaging all members or constructing a performance-based consensus forecast while the ensemble spread or forecast variance are purposely or mistakenly regarded as meaningless noises to be filtered out. We often heard people are saying that “forecast error can be reduced such and such by using ensemble data”. Indeed, due to the nonlinear filtering process, an ensemble mean forecast is statistically or on average more robust and accurate than a single forecast and then an improved forecast, but ensembling technique is not only a tool to improve a single deterministic forecast but more importantly to quantify forecast uncertainty which is the ultimate goal and the core mission of ensemble forecasting as discussed above. Ensemble averaging or other approaches to construct a consensus forecast are only one of the three possible ensemble-based product types: consensus or a most probable solution (mean is the simplest one), spread or forecast variance/confidence, and probability or a distribution (see Part 4).

    After this forecast uncertainty issue was realized, the earlier attempt was using statistical approaches such as MOS (Model Output Statistics, Glahn and Lowry, 1972) to address the issue. For example, based on model performance over a long-time period in the past, statistical characteristic of forecast error is obtained for a particular model and the error distribution can then be applied to the model forecast to estimate a probabilistic forecast such as Probability of Precipitation (PoP) (the “Eq. 3” thinking by estimating X’); or, some linear regression equations can statistically be established by either using model outputs (MOS) or observations (Perfect Prog, PP) as predictors to have a best estimate of a variable one wishes to forecast (the “Eq. 2” approach by estimating x0). Apparently, MOS-, POP- and PP-like approach is an important positive development in NWP history to address or reduce forecast uncertainty. However, an intrinsic limitation of any statistical approach is that the estimated error characteristic or distribution represents only the historical performance of a model in general such as model systematic bias but not the error related to the current flow situation (so called “error of the day”). Statistical method also heavily depends on the length of historical data and suffers when model frequently changes (a situation happens all the time in reality). In contrast, ensemble forecasting is a dynamical approach to capture the flow-dependent error of the day since it’s derived directly from the current model forecasts of the same day but not from past forecasts and also automatically improves as soon as a base model is improved. Surely, it will be desirable to combine both statistical and dynamical approaches together to portray a best picture of future true state (see Part 5).

Contact  Jun Du