^{1} Uncertainty is **not** just a matter of
meteorological ignorance. The new ideas of chaos and nonlinear
dynamic imply predictability limits even with **perfect**
knowledge of the physics. That perfect knowledge would yield perfect
forecasts only in the case where we have infinitely accurate
measurements of every relevant quantity everywhere all the time. Our
current observational system is rather short of that ideal.

^{2} Under these conditions, the *m* categories
*y _{i}* are said to be

^{3} A thunderstorm's probability is conditional on the
simultaneous presence of moisture, instability, and lift.

^{4} There are other viewpoints. This will be explained as
we consider verification.

^{5} This leads to the question of how to *interpret*
the values inside the contours. It's possible to assume that all the
pseudo-points that are touched by the contour have the value assigned
to the contour, but what about *in between* contours? One
possibility is to interpolate values to all the interior
pseudo-points. Another is to assign the contour value to everything
inside a given contour up to the next interior contour. The latter
means that only a limited set of probability values are allowed. Yet
another interpretation is that probabilities are binned, such that
everything inside one contour and exterior to another falls in a
particular assigned bin range. The choice among these and any other
possible interpretations is somewhat arbitrary and depends on the
verification being done.

^{6} That is, it contains the totals for the
*ensemble* of forecasts, which might cover many days and many
forecast periods. To examine the time-dependendent information, you
must reconsider the individual forecasts.