Abstract
Climate is a special spatiotemporal dynamical system. Its time scale can be extended indefinitely, but its space scale can never exceed that of the size of the system. We call this a “mismatching” in space and time domains. With the help of a simplified system of primitive equations, this exploratory paper shows that these scale characteristics may have a significant impact on the mathematical and physical structure of the system. The results show that the mismatching of space–time scales will lead to a decrease of the system’s dimension, degenerating the system from an infinite dimensional to a finite one. Also they show that “mismatched” domains can lead to a greater consistency of the system’s structure in space, as they form a system of uniform structures which are described as “patches”. This may lead to an alternative way of representing climate and its variability as a pattern system defined by the collective behavior of interacting patches or subsystems.
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Acknowledgements
This research was partially supported by the National Key R&D Program of China (2017YFC1501804) and the National Natural Science Foundation of China (42075054, 91737102 and 41575058). Useful discussions with Dr. Tianjun Zhou and Dr. Cheng-Zhi Zou are gratefully acknowledged. The authors are grateful to the three anonymous referees and Dr. Tamas Bodai for their useful comments that helped to improve the quality of the manuscript.
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Yang, P., Wang, G., Xiao, Z. et al. Climate: a dynamical system with mismatched space and time domains. Clim Dyn 56, 3305–3311 (2021). https://doi.org/10.1007/s00382-021-05646-7
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DOI: https://doi.org/10.1007/s00382-021-05646-7