Page History

...

Probability forecasts cannot be linearly extrapolated into the future.  If an event was assigned a 10% probability in the forecast two days ago, 20% in yesterday’s forecast and 30% in today’s, there is no reason that it will necessarily further increase in tomorrow’s forecast; it could equally well remain at its current level or decrease (Fig7Fig71.1.1A).

Fig7Fig71.1.1A: A schematic illustration of what might be considered some "typical" event probability developments for a specific location over ten days.  The lines represent probability of the event:

...

It is very important to recognise that an apparent trend in probabilities is unreliable (e.g. turquoise line in Fig7Fig71.1.1A); a trend should not be extrapolated forwards.  In real scenarios probabilities may reduce, increase or remain the same, and indeed they may also go up and down as the event approaches.  In the turquoise line scenario, 6 days before the potential event there is ~40% chance that event will occur.  Equally there is ~60% chance that the event will not occur and equivalently a 60% chance that the probabilities in subsequent forecasts will decrease to zero (solid orange line).  

...

Probabilities cannot easily be combined: if the probability for an event in one time interval is 40% and for the next time interval 20%, there is normally no straightforward way to find out the probability over both time intervals together, except when the events are uncorrelated.  Depending on the correlation between the two time intervals, the combined probability that it will rain in either period might be anything between 40% and 60% and the probability that both periods will have rain can vary between 0% and 20% (see Fig7Fig71.1.2B).  The only way to get a correct probability for combined time intervals is to count the proportion of members having rain in either or bothof the time intervals in the original ensemble data.

Note: current graphical ECMWF products, including ecCharts, do not incorporate this "time windowing" approach to calculation of probabilities.  This may be something that ECMWF considers in future.  Meantime, tailored local processing of ECMWF output fields could be performed by specific users to achieve this goal.

 Fig7Fig71.1.2B:  If the events in the two adjacent time intervals are correlated, so that rain in the first interval is followed by rain in the second, the probability for rain at any time during the whole period is 40% (far left figure).  If they are anti-correlated (e.g. because of differing speeds of frontal passage), so that rain in the first period is followed by dry conditions in the second, and dry in the first period is followed by rain in the second, then the total probability is 60% (centre figure).  If the events in the two adjacent time intervals are non-correlated, the combined probability is (1 - (1 - 0.4) x (1 - 0.2)) =52% (far right figure).

...