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Discussion papers
https://doi.org/10.5194/esd-2019-63
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/esd-2019-63
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: research article 04 Nov 2019

Submitted as: research article | 04 Nov 2019

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Earth System Dynamics (ESD).

Reconstructing coupled time series in climate systems by machine learning

Yu Huang, Lichao Yang, and Zuntao Fu Yu Huang et al.
  • Lab for Climate and Ocean-Atmosphere Studies, Dept. of Atmospheric and Oceanic Sciences, School of Physics, Peking University, Beijing, 100871, China

Abstract. Despite the great success of machine learning, its applications in climate dynamics have not been well developed. One concern might be how well the trained neural networks could learn a dynamical system and what can be the potential applications of this kind of learning. Detailed studies show that the coupling relations or dynamics among variables in linear or nonlinear systems can be well learnt by reservoir computer (RC) and long short-term memory (LSTM) machine learning, and these learnt coupling relations can be further applied to reconstruct one series from the other dominated by common coupling dynamics. In order to validate the above conclusions, toy models are applied to address the following three questions: (i) what can be learnt from different dynamical time series by machine learning; (ii) what factors significantly influence machine learning reconstruction; and (iii) how to select suitable explanatory or input variables for the reconstructed variable for machine learning. The results from these toy models show that both of RC and LSTM can indeed learn coupling relations among variables, and the learnt implicit coupling relation can be applied to accurately reconstruct one series from the other. Both of linear and nonlinear coupling relations between variables can influence the quality of the reconstructed series. If there is a strong linear coupling between variables, all of variables can be taken as explanatory variables for the reconstructed variable, and the reconstruction can be bi-directional. However, when the linear coupling among variables is much weaker, but with stronger nonlinear causality among variables, the reconstruction quality is direction-dependent and it may be only uni-directional. We propose using convergent cross mapping causality (CCM) index ρab to determine which variable can be taken as the reconstructed one and which can be taken as the explanatory variable. For example, the Pearson correlation between the average Tropical Surface Air Temperature (TSAT) and the average Northern Hemispheric SAT (NHSAT) is as weak as 0.08, but the CCM index of that NHSAT cross maps TSAT is ρNT = 0.70, it means that NHSAT could be taken as the explanatory variable. Then we find that TSAT can be well reconstructed from NHSAT by means of RC. However, the reconstruction quality in the opposite direction is poor, because the CCM index of that TSAT cross maps NHSAT is only ρTN = 0.24. These results also provide insights on machine learning approaches for paleoclimate reconstruction, parameterization scheme, and prediction in related climate studies.

Yu Huang et al.
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Yu Huang et al.
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Short summary
The variable-to-variable reconstruction in climate system is demonstrated variable- and direction-dependent, such as in reconstructing temperature series. We study how to better apply machine learning to reconstruct climate series under different coupling dynamics. Then the CCM causality coefficient is proposed to select explanatory variable, which is more effective than the Pearson correlation. It might offter some understanding for the application of machine learning to climate dynamics.
The variable-to-variable reconstruction in climate system is demonstrated variable- and...
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