Mathematical Problems in Prediction and Controlling of Climate and Environmental Systems
气候与环境预测和调控中的数学问题

This paper was presented as a keynote lecture at the 148th Xiangshan Scientific Symposium with the title 'Modern Sciences and Mathematics" held in October 19-21, 2000. The interaction between the modern sciences and mathematics promotes both their bright and sound development. A problem without solid and precise mathematical expression and analysis can not be considered as belonging to the modern sciences and can not be well solved. Mathematics are everywhere. This paper discusses some important and fundamental mathematical problems related with the prediction and controlling of climate and natural environmental systems. In the category of prediction problems, the followings are discussed: the well-posedness; the relation between predictability and the nonlinear behaviour such as chaos, bifurcation and abrupt change; 4D data assimilation; nesting of models with different resolutions and the numerical methods. In the category of problems related with the controlling of natural environment-the natural cybernetics, the following examples are discussed: artificial weather modification; man-made improvement of local-regional climate regime; controlling of silt sedimentation and optimal engineering of navigation channel, and the planning of regulation of ecosystems.