Hilbert problems for the geosciences in the 21st century – 20 years later

Abstract

<jats:p>Abstract. The scientific problems posed by the Earth's atmosphere, oceans, cryosphere – along with the land surface and biota that interact with them – are central to major socio-economic and political concerns in the 21st century. It is natural, therefore, that a certain impatience should prevail in attempting to solve these problems. The point of a review paper published in this journal in 2001 was that one should proceed with all diligence, but not excessive haste: festina lente, i.e. hurry in a measured way. The earlier paper traced the necessary progress through the solutions of ten problems, starting with What can we predict beyond one week, for how long, and by what methods? and ending with Can we achieve enlightened climate control of our planet by the end of the century? A unified framework was proposed to deal with these problems in succession, from the shortest to the longest time scale, i.e. from weeks to centuries and millennia. The framework is that of dynamical systems theory, with an emphasis on successive bifurcations and the ergodic theory of nonlinear systems, on the one hand, and on pursuing this approach across a hierarchy of climate models, from the simplest, highly idealized ones, to the most detailed ones. Here, we revisit some of these problems, 20 years later, and extend the framework to coupled climate-economics modeling. </jats:p>