The aim of Israel in pursuing a ground operation in Southern Lebanon is such:

By deeply penetrating southern Lebanon and occupying the territory, Israel creates a buffer zone which lengthens the distance that Hizballah rockets must travel in order to successfully strike targets. After all, if Hizballah cannot operate in the Southern portion, it will be forced to operate from entral and northern areas of Lebanon. There is further benefit to this because the population of central and northern Lebanon is less sympathetic to Hizballah.

The difficulty comes in the actual occupation, wherein an insurgency akin to Iraq is inevitable. Despite this unpalatable situation, Israel would rather its soldiers face danger than its civilians. Israel can sustain an indefinite occupation while sustaining occupation casulaties with little disruption to its economy. This is politically undesirable, but something that Israeli politicians currently view as a necessity.

Of course, Israel can further gain if the people and government of Lebanon fail to support Hizballah. This is impossible if Hizballah operates from its southern stronghold, but far more likely in Central and Northern Lebanon. Christian elements will not be thrilled to see Shiite Muslims launching rockets from their neighborhoods.