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  • 1
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    Climate Dependence in Empirical Parameters of Subgrid-Scale Parameterizations using the Fluctuation–Dissipation Theorem (2018)
    American Meteorological Society
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    Publication Date: 2018-10-10
    Description: Many subgrid-scale (SGS) parameterizations in climate models contain empirical parameters and are thus data dependent. In particular, it is not guaranteed that the SGS parameterization still helps the model to produce the correct climate projection in the presence of an external perturbation (e.g., because of climate change). Therefore, a climate dependence of tuning parameters is proposed, using the fluctuation–dissipation theorem (FDT). The FDT provides an estimation of the changes in the statistics of a system, caused by a small external forcing. These estimations are then used to update the SGS parameterization. This procedure is tested for a toy atmosphere given by a quasigeostrophic three-layer model (QG3LM). We construct a low-order climate model for this toy atmosphere, based on a reduced number of its empirical orthogonal functions (EOFs), equipped with either an empirical deterministic or an empirical stochastic SGS parameterization. External forcings are considered that are either a local anomalous heat source in the extratropics or a global dynamical forcing represented by individual EOF patterns. A quasi-Gaussian variant of the FDT is able to successfully update the SGS parameterization leading to an improvement in both amplitude and correlation between the low-order climate model and the QG3LM, in case of a perturbed system. The stochastic closure exhibits nearly no improvement compared to the deterministic parameterization. The application of a more sophisticated non-Gaussian FDT algorithm (i.e., the blended short-time/quasi-Gaussian FDT) yields only marginal improvement over the simple quasi-Gaussian FDT.
    Print ISSN: 0022-4928
    Electronic ISSN: 1520-0469
    Topics: Geography , Geosciences , Physics
    Published by American Meteorological Society
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  • 2
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    Fluctuations, response, and resonances in a simple atmospheric model (2017)
    Elsevier
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    Publication Date: 2017-06-01
    Print ISSN: 0167-2789
    Electronic ISSN: 1872-8022
    Topics: Physics
    Published by Elsevier
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  • 3
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    Climate Response Using a Three-Dimensional Operator Based on the Fluctuation–Dissipation Theorem (2007)
    American Meteorological Society
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    Publication Date: 2007-07-01
    Description: The fluctuation–dissipation theorem (FDT) states that for systems with certain properties it is possible to generate a linear operator that gives the response of the system to weak external forcing simply by using covariances and lag-covariances of fluctuations of the undisturbed system. This paper points out that the theorem can be shown to hold for systems with properties very close to the properties of the earth’s atmosphere. As a test of the theorem’s applicability to the atmosphere, a three-dimensional operator for steady responses to external forcing is constructed for data from an atmospheric general circulation model (AGCM). The response of this operator is then compared to the response of the AGCM for various heating functions. In most cases, the FDT-based operator gives three-dimensional responses that are very similar in structure and amplitude to the corresponding GCM responses. The operator is also able to give accurate estimates for the inverse problem in which one derives the forcing that will produce a given response in the AGCM. In the few cases where the operator is not accurate, it appears that the fact that the operator was constructed in a reduced space is at least partly responsible. As an example of the potential utility of a response operator with the accuracy found here, the FDT-based operator is applied to a problem that is difficult to solve with an AGCM. It is used to generate an influence function that shows how well heating at each point on the globe excites the AGCM’s Northern Hemisphere annular mode (NAM). Most of the regions highlighted by this influence function, including the Arctic and tropical Indian Ocean, are verified by AGCM solutions as being effective locations for stimulating the NAM.
    Print ISSN: 0022-4928
    Electronic ISSN: 1520-0469
    Topics: Geography , Geosciences , Physics
    Published by American Meteorological Society
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  • 4
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    Climate Response of Linear and Quadratic Functionals Using the Fluctuation–Dissipation Theorem (2008)
    American Meteorological Society
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    Publication Date: 2008-09-01
    Description: A generalization of the fluctuation–dissipation theorem (FDT) that allows generation of linear response operators that estimate the response of functionals of system state variables is tested for a system defined by an atmospheric general circulation model (AGCM). A sketch of the proof of this generalization is provided, followed by comparison of response estimates based on the theory and actual responses of the AGCM for various idealized anomalous equatorial heat sources. Tested response quantities include precipitation, variances of bandpass and low-pass streamfunction, and momentum and heat fluxes. The solutions from the FDT operators are very similar to the AGCM solutions in terms of structure while overestimating response amplitudes by about 20%. As an example of an application of such response operators, the FDT operator that estimates the response of bandpass upper-tropospheric streamfunction variance is used to find the most efficient means of disturbing the Atlantic storm tracks by tropical heating. The results of the study suggest that the generalized FDT is an attractive method for systematically studying response attributes of the climate system that are of interest to climate scientists and society.
    Print ISSN: 0022-4928
    Electronic ISSN: 1520-0469
    Topics: Geography , Geosciences , Physics
    Published by American Meteorological Society
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  • 5
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    Fluctuation–Dissipation Supplemented by Nonlinearity: A Climate-Dependent Subgrid-Scale Parameterization in Low-Order Climate Models (2013)
    American Meteorological Society
    Details
    Publication Date: 2013-05-29
    Description: Climate-system models use a multitude of parameterization schemes for small-scale processes. These should respond to externally forced climate variability in an appropriate manner so as to reflect the response of the parameterized process to a changing climate. The most attractive route to achieve such a behavior would certainly be provided by theoretical understanding sufficiently deep to enable the a priori design of climate-sensitive parameterization schemes. An alternative path might, however, be helpful when the parameter tuning involved in the development of a scheme is objective enough so that these parameters can be described as functions of the statistics of the climate system. Provided that the dynamics of the process in question is sufficiently stochastic, and that the external forcing is not too strong, the fluctuation–dissipation theorem (FDT) might be a tool to predict from the statistics of a system (e.g., the atmosphere) how an objectively tuned parameterization should respond to external forcing (e.g., by anomalous sea surface temperatures). This problem is addressed within the framework of low-order (reduced) models for barotropic flow on the sphere, based on a few optimal basis functions and using an empirical linear subgrid-scale (SGS) closure. A reduced variant of quasi-Gaussian FDT (rqG-FDT) is used to predict the response of the SGS closure to anomalous local vorticity forcing. At sufficiently weak forcing, use of the rqG-FDT is found to systematically improve the agreement between the response of a reduced model and that of a classic spectral code for the solution of the barotropic vorticity equation.
    Print ISSN: 0022-4928
    Electronic ISSN: 1520-0469
    Topics: Geography , Geosciences , Physics
    Published by American Meteorological Society
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  • 6
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    Simulation of observed climate changes in 1850–2014 with climate model INM-CM5 (2018)
    Copernicus
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    Publication Date: 2018-05-08
    Description: Climate changes observed in 1850-2014 are modeled and studied on the basis of seven historical runs with the climate model INM-CM5 under the scenario proposed for Coupled Model Intercomparison Project, Phase 6 (CMIP6). In all runs global mean surface temperature rises by 0.8K at the end of the experiment (2014) in agreement with the observations. Periods of fast warming in 1920–1940 and 1980–2000 as well as its slowdown in 1950–1975 and 2000–2014 are correctly reproduced by the ensemble mean. The notable change here with respect to the CMIP5 results is correct reproduction of the slowdown of global warming in 2000–2014 that we attribute to more accurate description of the Solar constant in CMIP6 protocol. The model is able to reproduce correct behavior of global mean temperature in 1980–2014 despite incorrect phases of the Atlantic Multidecadal Oscillation and Pacific Decadal Oscillation indices in the majority of experiments. The Arctic sea ice loss in recent decades is reasonably close to the observations just in one model run; the model underestimates Arctic sea ice loss by the factor 2.5. Spatial pattern of model mean surface temperature trend during the last 30 years looks close the one for the ERA Interim reanalysis. Model correctly estimates the magnitude of stratospheric cooling.
    Electronic ISSN: 2190-4995
    Topics: Geosciences
    Published by Copernicus on behalf of European Geosciences Union.
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  • 7
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    Simulation of observed climate changes in 1850–2014 with climate model INM-CM5 (2018)
    Copernicus
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    Publication Date: 2018-10-25
    Description: Climate changes observed in 1850–2014 are modeled and studied on the basis of seven historical runs with the climate model INM-CM5 under the scenario proposed for the Coupled Model Intercomparison Project Phase 6 (CMIP6). In all runs global mean surface temperature rises by 0.8 K at the end of the experiment (2014) in agreement with the observations. Periods of fast warming in 1920–1940 and 1980–2000 as well as its slowdown in 1950–1975 and 2000–2014 are correctly reproduced by the ensemble mean. The notable change here with respect to the CMIP5 results is the correct reproduction of the slowdown in global warming in 2000–2014 that we attribute to a change in ocean heat uptake and a more accurate description of the total solar irradiance in the CMIP6 protocol. The model is able to reproduce the correct behavior of global mean temperature in 1980–2014 despite incorrect phases of the Atlantic Multidecadal Oscillation and Pacific Decadal Oscillation indices in the majority of experiments. The Arctic sea ice loss in recent decades is reasonably close to the observations in just one model run; the model underestimates Arctic sea ice loss by a factor of 2.5. The spatial pattern of the model mean surface temperature trend during the last 30 years looks close to the one for the ERA-Interim reanalysis. The model correctly estimates the magnitude of stratospheric cooling.
    Print ISSN: 2190-4979
    Electronic ISSN: 2190-4987
    Topics: Geosciences
    Published by Copernicus on behalf of European Geosciences Union.
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  • 8
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    A new mathematical framework for atmospheric blocking events (2019)
    Springer
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    Publication Date: 2019-11-01
    Description: We use a simple yet Earth-like hemispheric atmospheric model to propose a new framework for the mathematical properties of blocking events. Using finite-time Lyapunov exponents, we show that the occurrence of blockings is associated with conditions featuring anomalously high instability. Longer-lived blockings are very rare and have typically higher instability. In the case of Atlantic blockings, predictability is especially reduced at the onset and decay of the blocking event, while a relative increase of predictability is found in the mature phase. The opposite holds for Pacific blockings, for which predictability is lowest in the mature phase. Blockings are realised when the trajectory of the system is in the neighbourhood of a specific class of unstable periodic orbits (UPOs), natural modes of variability that cover the attractor the system. UPOs corresponding to blockings have, indeed, a higher degree of instability compared to UPOs associated with zonal flow. Our results provide a rigorous justification for the classical Markov chains-based analysis of transitions between weather regimes. The analysis of UPOs elucidates that the model features a very severe violation of hyperbolicity, due to the presence of a substantial variability in the number of unstable dimensions, which explains why atmospheric states can differ a lot in term of their predictability. Additionally, such a variability explains the need for performing data assimilation in a state space that includes not only the unstable and neutral subspaces, but also some stable modes. The lack of robustness associated with the violation of hyperbolicity might be a basic cause contributing to the difficulty in representing blockings in numerical models and in predicting how their statistics will change as a result of climate change. This corresponds to fundamental issues limiting our ability to construct very accurate numerical models of the atmosphere, in term of predictability of the both the first and of the second kind in the sense of Lorenz.
    Print ISSN: 0930-7575
    Electronic ISSN: 1432-0894
    Topics: Geosciences , Physics
    Published by Springer
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