Part I:   Why is ensemble forecast needed?

    The ultimate goal of science is to predict future. A prediction process has four basic components: data collection (observation), assimilation of observed data into initial conditions to be used by a numerical forecasting model, model integration to project the initial state into future, and the application of the forecasts to real world situations. Intrinsic uncertainties are introduced at each of those steps during a forecast process, for example, instrumental and human error introduced during the process of collecting data; errors introduced during data assimilation process due to mathematical assumptions; imperfect model physics (approximation of real world such as parameterization of sub-grid effects) and numeric (e.g., discontinuity or truncation); and differences in human (both forecasters and end-users)’s interpretation and decision to a same forecast depending on situations (who, what, when and where). All these kind of errors are intrinsic, unavoidable and sometimes even unknown to us in a real world operation.

    Due to its highly nonlinear nature, a numerical prediction model of weather, climate and water is chaotic i.e. a tiny difference in initial states could possibly be amplified into significantly large difference in future states in unstable condition (Lorenz, 1963, 1965, 1993; Thompson, 1957). The difference could be as large as that being randomly picked from model climatology. Therefore, such forecasts become meaningless, which indicates that prediction of weather, climate and water events has uncertainty and limit (predictability). Figures 1-2 depict two such examples of many from the U.S. National Weather Service’s daily real-time operational model guidance. Figure 1 shows that two NCEP (National Centers for Environmental Prediction) operational GFS (Global Forecasting System) model’s medium-range (16 days) forecasts which were initialized at only 6-hour apart in time predicting two completely opposite large-scale flow at 500 hpa level: one places a strong trough over the East Coast and another over the West Coast of U.S. (more than 3000 km apart)! Similar situation happens at short range too: two NCEP operational regional Eta model’s short-range (2.5 days) forecasts which had slight difference only in their initial atmospheric conditions predicted two distinct scenarios: one predicts a deep low pressure system (<976 hpa) while another a high pressure ridge (around 1008 hpa) over a same area (Fig. 2). Situations like these occur not uncommon in real-time operation especially during major high-impact weather events which are often associated with highly unstable atmospheric conditions.

    Therefore, uncertainty and predictability is a very real and important aspect of a forecast such as weather forecasting. Besides the prediction to an event itself, the uncertainty and predictability of the event also needs to be predicted, i.e. how small initial differences (uncertainties) evolve with time in a model. Without uncertainty quantified, a forecast is incomplete. Ensemble forecasting is a dynamical and flow-dependent approach to quantify such forecast uncertainty (error of the day) and provides a basis to communicate forecast uncertainty and forecast confidence to end-users who can then be best prepared. If reader is interested in observing how small initial differences evolving under various weather situations in a real-time ensemble forecasting system, one could go to the NCEP Short-Range Ensemble Forecasting (SREF) system web page as an example: http://www.emc.ncep.noaa.gov/mmb/SREF/SREF.html.

Figure 1

Figure 2

Contact  Jun Du