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Similarly, a negative wave height EFI would indicate relatively calm seas.

Time sequence of cumulative density functions and probability density functions

A convenient and powerful way to show the temporal evolution of successive ENS forecasts for a given day is to overlay the CDFs corresponding to each of those runs.  

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 Fig8.1.4.2.6: A schematic illustration of the CDF (left) and PDF (right) for forecasts of 12hr accumulated precipitation showing the ENS T+48hr forecast (light green),  ENS T+96hr forecast (dark green) and ENS T+144hr (blue), together with the M-climate (black) verifying at the same time in the future. Note how the  The CDFs and PDFs both give, in different ways, a visual indication of mean, spread and asymmetry.

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A convenient and powerful way to depict the temporal evolution of successive ENS forecasts for a given day (akin also to a "lagged ensemble") is to overlay the CDFs corresponding to each of those runs, as in Figs 8.1.4.2.6 (for e.g. rainfall) and 8.1.4.2.7 (for e.g. 2m temperature).  In the first example, for rainfall (In Fig 8.1.4.2.6 ) the area between the CDF lines and M-climate, and hence the EFI, is becoming greater as the verifying time approaches, suggesting .  This suggests increasing probability of an unusual rainfall event. Indeed the EFI is approaching  EFI approaches +1 on the T+48 forecast suggesting very unusual rainfall compared to climatology.  The steepness of the CDF and hence the peaked shape of the PDF charts at T+48 indicate that many of the ENS members are showing similar results and thus an extreme event of the magnitude indicated (on the x-axis) can be considered quite likely (assuming of course that the forecasts are not systematically biased).

Fig8.1.4.2.7: Schematic set of idealised CDFs from a series of ENS runs (cyan earliest, red latest), for a variable for which the climatological distribution is approximately Gaussian (e.g. 2m temperature). If  If the M-Climate (or forecast) CDF curve resembles a "skewed S-shape" then that distribution is approximately Gaussian. 

As well as illustrating CDF structures for distributions that are approximately Gaussian Fig8.1.4.2.7 also shows how , typically, one can may expect successive forecasts to behave as the valid date approaches:

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In practice there is often some non-uniformity of progress through this idealised sequence of events, particularly for maximum wind gust and rainfall parameters. The forecaster  The user needs to identify patterns in the series of CDFs as forecast lead-time shortens and investigate any departures from the expected changes.

One could define a substantial "ensemble forecast jump" (for a given parameter) to be when If the median of a new forecast (half way point on the y-axis) lies outside the range of the previous forecast then a substantial "ensemble forecast . This jump" (for a given parameter) has occurred.  This would usually also be denoted by shown as a big change in the EFI.  Such jumps are very uncommon, although probably they occur slightly more often than they should on purely probabilistic grounds.  They can be very disconcerting for forecasters.  Accordingly, forecasters need to be cognisant  Examples of meteorological scenarios when such behaviour is more likely .  Two such examples are are organised convective rainfall and and extreme cyclonic windstorms.

_{Updated/Amended 06/11/20 - Added and improved diagrams}

_{Updated/Amended 21/12/20 - Added ppn diagrams}