Differential Geometry of Diffeomorphism Groups

In 1963 E. N. Lorenz stated that a two-week forecast would be the theoretical bound for predicting the future state of the atmosphere using large-scale numerical models [Lor]. Modern meteorology has currently reached a good correlation of the observed versus predicted for roughly seven days in the northern hemisphere, whereas this period is shortened by half in the southern hemisphere and by two-thirds in the tropics for the same level of correlation [Kri]. These differences are due to a very simple factor: the available data density.