Fluctuation-Dissipation, Stochasticity, and Climate-Dependent Subgrid-Scale Parameterizations for Efficient Climate Models
Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
Theoretical Chemistry: Molecules, Materials, Surfaces
Final Report Abstract
For several applications in climate modeling, e.g. paleoclimatology or climate sensitivity studies, there is need for an especially efficient representation of the atmosphere. Low-order models, based on optimized basis function, and using an empirically determined linear subgridscale (SGS) parameterization of small-scale processes, compare well with general circulation models, so that they could be an interesting tool in this regard. A remaining problem is the climate sensitivity of the empirical SGS parameterization. This is an issue of broader relevance: The parameterization is trained using reference data from present-day climate, either from a more complex model or from real nature, but it is intended to be applied to quite different conditions, such as past paleo climates, or future climates changed by anthropogenic effects. Studies indicate that it is not permissible to just apply the unmodified parameterization. They thus point to serious issues that SGS parameterizations, abundantly in use in climate models, e.g. representing clouds, localized heavy weather, turbulence, etc., might face that have been obtained via Deep Learning, or Artificial Intelligence (AI), from available climate data. What is needed is understanding of the atmosphere to the degree that the response of SGS parameterizations to external perturbations can be predicted based on theory. Within the framework of low-order climate models, two closely interrelated approaches have been investigated to address this issue: (1) The fluctuation-dissipation theorem has been applied to predict the response of the climate statistics of an atmospheric model, realistically representing extratropical weather and its dynamics, to externally imposed heat perturbations. This response has then been used to predict the response in an SGS parameterization to be used by very efficient low-order models of the atmosphere. It has been shown that this approach can help the low-order models in performing well under perturbed conditions, provided that the anomalous heating is sufficiently weak and the low-order model sufficiently complex. This could be considered to be applied as well to SGS parameterizations based on AI. (2) The second approach that has been investigated is stochastic mode reduction (SMR), a theoretical framework that allows calculating an SGS parameterization directly from the basic atmospheric equations. This is possible if the atmospheric motions can be separated into fast and slow processes, i.e. they can be separated into two classes with a clear time-scale separation, e.g. slow larger-scale weather systems and rapidly variable turbulence. In applications of the approach to the same low-order approximations of the same atmosphere model as in (1), it is found that the climate dependence of this approach is not sufficiently reliable. This can be attributed to the fact that there is no clear time-scale separation in the atmosphere, but processes actually act on a broad range of time scales. Hence, semi-empirical methods combined with the FDT as investigated in (1) might be a more promising approach for obtaining reliable SGS parameterizations for climate models. Further tests with low-order models of a few hundred degrees of freedom should, however, be done before final conclusions are drawn. Beyond this the project has contributed to the further development of the potential of the SMR to yield reliable locally based SGS parameterizations that are more focused on rapid SGS processes, and also to the successful implementation and validation of a new fundamental approach for the representation of the largest-scale and slowest motions in the climate system.
Publications
- 2016: Parametrization of stochastic multiscale triads. Nonlin. Processes Geophys., 23, 435–445
Wouters, J., Dolaptchiev, S.I., Lucarini. V., and U. Achatz
(See online at https://doi.org/10.5194/npg-2016-37) - 2018: Climate-Dependence in Empirical Parameters of Subgrid-Scale Parameterizations using the Fluctuation-Dissipation Theorem. J. Atmos. Sci., 75, 3843 – 3860
Pieroth, M., Dolaptchiev, S.I., Zacharuk, M., Heppelmann, T., Gritsun, A. und U. Achatz
(See online at https://doi.org/10.1175/JAS-D-18-0022.1) - 2018: Stochastic subgrid-scale parameterization for one-dimensional shallow water dynamics using stochastic mode reduction. Quart. J. Roy. Met. Soc., 1–16
Zacharuk, M., Dolaptchiev, S.I., Achatz, U. und I.Timofeyev
(See online at https://doi.org/10.1002/qj.3396) - 2019: Planetary geostrophic Boussinesq dynamics: barotropic flow, baroclinic instability and forced stationary waves. Quart. J. Roy. Met. Soc.
Dolaptchiev, S.I., Achatz, U. und Th. Reitz
(See online at https://doi.org/10.1002/qj.3655)
