What on earth is this? CAPE stands for convective available potential energy, the clue is in the word "potential". It is the energy an air parcel would have if it were lifted some distance vertically in the atmosphere. Note the phrase "if it were lifted", so this implies we need a source of lift for this potential energy to become useful in terms of convective development.

LI is the lifted index, which is another measure of instability. In detail, it is the temperature difference between the atmosphere at a given level (I think it's typically the 500mb level) and an air parcel if it were lifted to that height. Or in more mathematical terms:

LI = Temperature of lifted air parcel - Temperature of environment at the new level

If an air parcel is warmer than its surroundings, then through the difference in density it is liable to rise. As we can see, this would also provide a negative value of LI. In this case the atmosphere is unstable, with more negative values indicating greater instability. Conversely, if an air parcel is cooler than its surroundings, it will be more dense than the environment, so it is unlikely to rise and may even sink. This results in a positive LI and denotes a stable atmosphere - which would suppress any convective development.

However, both of these quantities don't really mean much if there is no source of lift, or a "trigger" mechanism. We need to give an air parcel and initial "nudge" in the vertical to make use of the unstable atmosphere. Without this initial vertical motion then instability in the atmosphere may not be realised.

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