Department of Mathematics and Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA.
Proc Natl Acad Sci U S A. 2011 Aug 2;108(31):12599-604. doi: 10.1073/pnas.1108132108. Epub 2011 Jul 18.
Understanding and improving the predictive skill of imperfect models for complex systems in their response to external forcing is a crucial issue in diverse applications such as for example climate change science. Equilibrium statistical fidelity of the imperfect model on suitable coarse-grained variables is a necessary but not sufficient condition for this predictive skill, and elementary examples are given here demonstrating this. Here, with equilibrium statistical fidelity of the imperfect model, a direct link is developed between the predictive fidelity of specific test problems in the training phase where the perfect natural system is observed and the predictive skill for the forced response of the imperfect model by combining appropriate concepts from information theory with other concepts based on the fluctuation dissipation theorem. Here a suite of mathematically tractable models with nontrivial eddy diffusivity, variance, and intermittent non-Gaussian statistics mimicking crucial features of atmospheric tracers together with stochastically forced standard eddy diffusivity approximation with model error are utilized to illustrate this link.
理解和提高复杂系统对外界强迫响应的不完善模型的预测能力，是气候变化科学等多种应用中的一个关键问题。不完善模型在合适的粗粒变量上的平衡统计保真度是具有这种预测能力的必要但非充分条件，这里给出了一些基本示例来证明这一点。在这里，通过结合信息论的概念和基于涨落耗散定理的其他概念，在不完善模型的平衡统计保真度的基础上，建立了在训练阶段观测到的完美自然系统中特定测试问题的预测保真度与受强迫的不完善模型响应的预测能力之间的直接联系。这里使用了一系列具有非平凡涡动扩散率、方差和间歇非高斯统计的数学上易于处理的模型，这些模型模拟了大气示踪剂的关键特征，以及带有模型误差的随机强迫标准涡动扩散率近似，以此来说明这种联系。
