Fluctuation-Dissipation, Stochasticity, and Climate-Dependent Subgrid-Scale Parameterizations for Efficient Climate Models

在气候模拟的一些应用中，例如古气候学或气候敏感性研究，需要一个特别有效的大气分量。基于经验正交函数（EOFs）并使用经验确定性线性亚电网尺度（SGS）参数化的低阶模型与一般环流模型具有很好的比较，因此它们可能是这方面的一个有趣工具。剩下的问题是经验SGS参数化的气候敏感性。需要研究两种密切相关的方法来解决这个问题：(1)最近的工作表明，波动耗散定理（FDT）有可能预测经验SGS参数化对外部扰动的响应，特别是当它应用的系统具有足够快的分量时。该研究中使用的正压涡度方程只允许正压行星波。因此，可以预期，在更现实的情况下，FDT战略将更加富有成效。因此，在不断增加真实感的道路上，计划将FDT方法扩展到准地转三层（QG3L）动力学的低阶模型，允许天气尺度斜压波，具有经验线性-随机（Ornstein-Uhlenbeck， OU）参数化。(2)与经验OU参数化方法相比，更基于第一性原理的方法是随机模态约简（SMR）。SMR中有效快模影响的显式推导，加上乘法噪声和非线性确定性项补充了OU参数化的强迫和加性噪声，有望在扰动气候中产生比直接的、纯粹数据驱动的SGS OU参数化更鲁棒的模型行为。然而，由于这种方法开发的模型往往具有气候偏差，并且鉴于上述经验方法的成功，本文旨在通过经验修改其确定性强迫和线性动力学来尝试和改善SMR低阶模型的性能。再次在QG3L上下文中，FDT应使用用于预测修正SMR模型中所有经验元素对外部扰动的响应。这些努力的最终目的是建立一个有效的大气模型，在目前的技术水平上尽可能多地基于第一原理，并使用FDT来控制剩余经验要素对气候的依赖。

For several applications in climate modeling, e.g. paleoclimatology or climate sensitivity studies, there is need for an especially efficient atmosphere component. Low-order models, based on empirical orthogonal functions (EOFs) and using an empirical deterministic linear subgrid-scale (SGS) parameterization, compare well with general circulation models, so that they could be an interesting tool in this regard. A remaining problem has been the climate sensitivity of the empirical SGS parameterization. Two closely interrelated approaches shall be investigated to address this: (1) Recent work indicates that the fluctuation-dissipation theorem (FDT) has a potential for predicting the response of an empirical SGS parameterization to external perturbations, especially if the system which it is applied to has enough fast components. The barotropic vorticity equation used in that study allows only barotropic planetary waves. It is to therefore to be expected that in a more realistic setting the FDT strategy will be even more fruitful. Hence, and also on the path to successively increasing realism, it is planned to extend the FDT approach to low-order models of quasigeostrophic three-layer (QG3L) dynamics, allowing synoptic-scale baroclinic waves, with an empirical linear-stochastic (Ornstein-Uhlenbeck, OU) parameterization.(2) Even more based on first principles than the approach with an empirical OU parameterization is stochastic mode reduction (SMR). The explicit derivation of the effective fast-mode impact in SMR, with multiplicative noise and nonlinear deterministic terms supplementing the forcing and additive noise of an OU parameterization, is expected to yield more robust a model behavior in a perturbed climate than a direct, purely data-driven, OU parameterization of the SGS. As models developed by such methods tend to have a climate bias, however, and given the success of the empirical methods described above, it is intended to try and improve the performance of SMR low-order models by empirically modifying their deterministic forcing and linear dynamics. Once more in the QG3L context, the FDT shall be used for predicting the response of all empirical elements in the modified SMR models to external perturbations.The ultimate purpose of these efforts is an efficient atmospheric model, based on first principles as much as presumably possible at the present state of the art, and using the FDT for controlling the climate dependence of the remaining empirical elements.