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• if using climatological probability in the absence of other information (horizontal green line).
• if at long lead-times the event is forecast by very few ENS ensemble members.  The event probability commonly (though not always) reduces to zero with time (descending orange dotted line).
• if day by day the event is forecast with increasing frequency by ENS ensemble members.  The event probability commonly (though not always) increases with time (turquoise line).  However, at any lead-time, such an increase may stop, with event probabilities in subsequent forecasts falling back to lower levels or to zero (dashed orange lines). 

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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 Fig7.1.2).  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 ENS ensemble data.

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

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For hydrological applications there are two particularly important considerations related to areal probabilities:

• Firstly, since heavy Heavy rainfall can have hydrological consequences far away from its immediate location, there are practical advantages in calculating .  Calculate the probabilities of rain somewhere within specific groups of grid points that together define individual catchment areas.
• Secondly, one may be particularly interested in the probabilities of For rainfall volume integrated over a catchment, in which it would be helpful to sum .  Sum the rainfall totals across all the groups groups of grid points that together define individual catchment areas, and then compute probabilities for those totals.

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Probabilities of combined events

As with probabilities over longer time intervals or larger areas, probabilities Probabilities for combined events such as “cloud cover <6/8 and temperatures >20°C” or blizzards (combination of heavy snowfall and with strong windswind) cannot be made from the separate probabilities but .  They can, however, be calculated from the ENS dataensemble data.  ecCharts now includes the capacity to compute several types of combined probabilities. (type Input "combined" in the Add layers Filter box on ecCharts).

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Event probabilities are calculated from the proportion of ENS ensemble members exceeding a certain threshold (e.g. if 34% of ENS ensemble members forecast 2mm/12hr or more, then the probability for this event is considered to be 34%).  Since the The number of ENS ensemble members is limited, so the probability of an event is not necessarily 0% just because no member has forecast it, nor is it necessarily 100% because all members have forecast the event.  Depending on the underlying mathematical-statistical assumptions and the size of the ensemble, probabilities such as 1-2% and 98-99% could be assigned to situations when no or all members forecast an event, with intermediate probabilities adjusted slightly upwards or downwards accordingly.  

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Forecast probabilities often show systematic deviations from the observed frequencies.  Low probabilities are often too low, high probabilities are often too high.  Calibration of probabilities or statistical post-processing (MOS) can improve the reliability of the probability forecasts.  This might affect the internal consistency between parameters.  If an over-prediction of rain is coupled to an over-prediction of cloud and perhaps under-prediction of temperature, then ideally all the parameters would have to should be calibrated jointly, in order to maintain a physical consistency.

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