Short- and long-term forecast for chaotic and random systems (50 years after Lorenz's paper)

We briefly review a history of the impact of the famous 1963 paper by E Lorenz on hydrodynamics, physics and mathematics communities on both sides of the iron curtain. This paper was an attempt to apply the ideas and methods of dynamical systems theory to the problem of weather forecast. Its major discovery was the phenomenon of chaos in dissipative dynamical systems which makes such forecasts rather problematic, if at all possible. In this connection we present some recent results which demonstrate that both a short-term and a long-term forecast are actually possible for the most chaotic dynamical (as well as for the most random, like IID and Markov chain) systems. Moreover, there is a sharp transition between the time interval where one may use a short-term forecast and the times where a long-term forecast is applicable. Finally we discuss how these findings could be incorporated into the forecast strategy outlined in the Lorenz's paper.