^{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 **mutually exclusive** and
**exhaustive**.

^{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 is 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.