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

对于气候建模中的一些应用，例如古气候学或气候敏感性研究，需要特别有效的大气成分。低阶模式，根据经验正交函数（EOFs）和使用经验确定性线性亚网格尺度（SGS）参数化，比较一般环流模式，因此，他们可以在这方面的一个有趣的工具。一个遗留的问题是SGS经验参数化的气候敏感性。两个密切相关的方法应调查，以解决这个问题：（1）最近的工作表明，波动耗散定理（FDT）有一个潜在的预测响应的经验SGS参数化的外部扰动，特别是如果它被应用到系统有足够的快速组件。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，在更现实的环境中，FDT战略将取得更大的成果。因此，也在不断增加的现实主义的道路上，它计划扩展FDT的方法，准地转三层（QG 3L）动力学的低阶模式，允许天气尺度斜压波，经验线性随机（Ornstein-Uhlenbeck，ESTA）参数化。(2)随机模态缩减（SMR）比经验模态参数化方法更基于第一原理。SMR中有效快模态影响的显式推导，加上乘性噪声和非线性确定性项，补充强迫和加性噪声的SGS参数化，预计在扰动气候中产生比直接的、纯粹数据驱动的SGS参数化更稳健的模式行为。然而，由于这种方法开发的模式往往有气候偏差，并鉴于上述经验方法的成功，它的目的是尝试和改善SMR低阶模式的性能，通过经验修改其确定性强迫和线性动力学。再次在QG 3L的背景下，FDT将用于预测修改后的SMR模式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式，尽可能地基于现有技术水平的第一性原理，并使用FDT控制剩余经验元素的气候依赖性。

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.