1. Clara Deser and Adam Phillips (2017) An overview of decadal-scale sea surface temperature variability in the observational record. Past Global Changes Magazine 25(1): 2 - 6 https://doi.org/10.22498/pages.25.1.2, Boston MA, USA, American Meteorological Society
2. Leela M. Frankcombe and Matthew H. England and Jules B. Kajtar and Michael E. Mann and Byron A. Steinman (2018) On the Choice of Ensemble Mean for Estimating the Forced Signal in the Presence of Internal Variability. Journal of Climate 31(14): 5681 - 5693 https://doi.org/10.1175/JCLI-D-17-0662.1, https://journals.ametsoc.org/view/journals/clim/31/14/jcli-d-17-0662.1.xml, Boston MA, USA, American Meteorological Society
3. Sergey Kravtsov (2017) Comment on “Comparison of Low-Frequency Internal Climate Variability in CMIP5 Models and Observations ”. Journal of Climate 30(23): 9763 - 9772 https://doi.org/10.1175/JCLI-D-17-0438.1, https://journals.ametsoc.org/view/journals/clim/30/23/jcli-d-17-0438.1.xml, Boston MA, USA, American Meteorological Society
4. Gavrilov, A. and Kravtsov, S. and Mukhin, D. (2020) {Analysis of 20th century surface air temperature using linear dynamical modes}. Chaos 30(12): 123110 https://doi.org/10.1063/5.0028246, American Institute of Physics Inc., 33380060, dec, 10897682, :home/andrey/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Gavrilov, Kravtsov, Mukhin - 2020 - Analysis of 20th century surface air temperature using linear dynamical modes.pdf:pdf, A Bayesian Linear Dynamical Mode (LDM) decomposition method is applied to isolate robust modes of climate variability in the observed surface air temperature (SAT) field. This decomposition finds the optimal number of internal modes characterized by their own time scales, which enter the cost function through a specific choice of prior probabilities. The forced climate response, with time dependence estimated from state-of-the-art climate-model simulations, is also incorporated in the present LDM decomposition and shown to increase its optimality from a Bayesian standpoint. On top of the forced signal, the decomposition identifies five distinct LDMs of internal climate variability. The first three modes exhibit multidecadal scales, while the remaining two modes are attributable to interannual-to-decadal variability associated with El Ni{\ {n}}o-Southern oscillation; all of these modes contribute to the secular climate signal - the so-called global stadium wave - missing in the climate-model simulations. One of the multidecadal LDMs is associated with Atlantic multidecadal oscillation. The two remaining slow modes have secular time scales and patterns exhibiting regional-to-global similarities to the forced-signal pattern. These patterns have a global scale and contribute significantly to SAT variability over the Southern and Pacific Oceans. In combination with low-frequency modulation of the fast LDMs, they explain the vast majority of the variability associated with interdecadal Pacific oscillation. The global teleconnectivity of the secular climate modes and their possible crucial role in shaping the forced climate response are the two key dynamical questions brought about by the present analysis.
5. Gavrilov, Andrey and Mukhin, Dmitry and Loskutov, Evgeny and Volodin, Evgeny and Feigin, Alexander and Kurths, Juergen (2016) {Method for reconstructing nonlinear modes with adaptive structure from multidimensional data}. Chaos 26(12): 123101 https://doi.org/10.1063/1.4968852, AIP Publishing LLC, dec, Bayes methods,chaos,nonlinear dynamical systems,time series, 10541500, We present a detailed description of a new approach for the extraction of principal nonlinear dynamical modes (NDMs) from high-dimensional data. The method of NDMs allows the joint reconstruction of hidden scalar time series underlying the observational variability together with a transformation mapping these time series to the physical space. Special Bayesian prior restrictions on the solution properties provide an efficient recognition of spatial patterns evolving in time and characterized by clearly separated time scales. In particular, we focus on adaptive properties of the NDMs and demonstrate for model examples of different complexities that, depending on the data properties, the obtained NDMs may have either substantially nonlinear or linear structures. It is shown that even linear NDMs give us more information about the internal system dynamics than the traditional empirical orthogonal function decomposition. The performance of the method is demonstrated on two examples. First, this approach is successfully tested on a low-dimensional problem to decode a chaotic signal from nonlinearly entangled time series with noise. Then, it is applied to the analysis of 250-year preindustrial control run of the INMCM4.0 global climate model. There, a set of principal modes of different nonlinearities is found capturing the internal model variability on the time scales from annual to multidecadal.