Page History

...

The CDF for the ensemble values is constructed from the temperature or precipitation forecast by each ensemble member (red line in the examples below) together with the CDF of the temperature or rainfall M-climate (black line) for that location for the date in question.

...

• Some values are positive (i.e. warmer than the M-climate), some in the tails of the plot can be extremely positive; some are negative (i.e. colder than the M-climate), some in the tails of the plot can be extremely negative.  The x-axis on the diagrams starts from the overall minimum encountered within all the displayed CDFs (M-climate and ensemble forecasts). 

...

• Some values are positive (i.e. wetter than the M-climate), some in the upper tail of the plot can be extremely positive.  For the vast majority of the world the lower tail of the M-climate this will  will equate to zero precipitation for the day and it is impossible to get less than zero precipitation. 
• The x-axis on the diagrams starts from zero.

...

Fig8.1.9.1-2(right): The probability density function (PDF) is defined as the first derivative of the CDF.  The graphs correspond to the example CDF curves in Fig8.1.9.1-2 with the temperature M-climate (blue) and the forecast distribution (red). 

Dotted lines show the median for the M-Climate and forecast.

The median and any other percentile is given by reading the point on the x-axis where a horizontal probability line intersects the curve.  The most likely values are associated with those where the CDF is steepest.  Similarly, the PDF shows peaks in the curve at the highest probability intervals.  The EFI can be understood and interpreted with both the CDF and PDF in mind; the former relates to the EFI value, the latter clarifies the connection to probabilities.  A steep slope of the CDF, or equivalently a narrow peak of the PDF, implies a high confidence in the forecast.

...