@misc{marwan2019lodz,
title = {Recurrence based entropies},
author = {Norbert Marwan and Kai Hauke Kraemer and Karolin Wiesner and Sebastian F. M. Breitenbach and Jens Leonhardt},
editor = {Fourth International Conference on Recent Advances in Nonlinear Mechanics, Łódz (Poland)},
year = {2019},
date = {2019-05-07},
abstract = {Many dynamical processes are considered to be of complex nature. To get a quantitative idea of the complexity, often the Shannon entropy of the value distribution of a measurement is used. Alternative entropy measures have been suggested using the recurrence plot (RP) approach. A RP is a matrix that represents the recurrences of states in the d-dimensional phase space. The RP can consist of small-scale structures, such as single points, diagonal and vertical lines, which characterize important dynamical properties of the system. Various entropy measures have been defined using different features of the RP or can be related to certain properties of the RP. Because of the different features that are used, some entropy measures represent different aspects of the analysed system and, thus, behave differently. This fact can lead to misunderstandings and difficulties in interpreting and understanding those measures. We discuss definitions, motivation and interpretation of some of those entropy measures, compare their differences and discuss some of the pitfalls when using them. },
note = {Fourth International Conference on Recent Advances in Nonlinear Mechanics, Łódz (Poland)},
keywords = {},
pubstate = {published},
tppubtype = {presentation}
}
Many dynamical processes are considered to be of complex nature. To get a quantitative idea of the complexity, often the Shannon entropy of the value distribution of a measurement is used. Alternative entropy measures have been suggested using the recurrence plot (RP) approach. A RP is a matrix that represents the recurrences of states in the d-dimensional phase space. The RP can consist of small-scale structures, such as single points, diagonal and vertical lines, which characterize important dynamical properties of the system. Various entropy measures have been defined using different features of the RP or can be related to certain properties of the RP. Because of the different features that are used, some entropy measures represent different aspects of the analysed system and, thus, behave differently. This fact can lead to misunderstandings and difficulties in interpreting and understanding those measures. We discuss definitions, motivation and interpretation of some of those entropy measures, compare their differences and discuss some of the pitfalls when using them.
@inproceedings{marwan2019,
title = {Recurrence based entropies},
author = {Norbert Marwan and Kai Hauke Kraemer and Karolin Wiesner and Sebastian F. M. Breitenbach and Jens Leonhardt},
url = {https://bbh.pik-potsdam.de/wp-content/uploads/2021/04/EGU2019-2817.pdf},
year = {2019},
date = {2019-04-08},
booktitle = {Geophysical Research Abstracts},
volume = {21},
pages = {EGU2019-2817},
abstract = {Dynamical processes in Earth sciences are often considered to be of complex nature. The term complexity is often used for processes that are either unpredictable (e.g. nonlinear dynamics), consist of many different components, or exhibit regime transitions (e.g. tipping points). To measure complexity, the Shannon entropy is often used.
Here we present various entropy measures that have been defined on the base of the recurrence plot. Because of the different features that are used, these entropy measures represent different aspects of the analysed system and, thus, behave differently. In the past, this fact has lead to difficulties in interpreting and understanding those measures. We summarize the definitions, the motivation and interpretation of these entropy measures, compare their differences and discuss some of the pitfalls when using them.
Finally, we illustrate their potential in an application on palaeoclimate time series. Using entropy measures, changes and transitions in the climate dynamics in the past can be identified and interpreted.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
Dynamical processes in Earth sciences are often considered to be of complex nature. The term complexity is often used for processes that are either unpredictable (e.g. nonlinear dynamics), consist of many different components, or exhibit regime transitions (e.g. tipping points). To measure complexity, the Shannon entropy is often used.
Here we present various entropy measures that have been defined on the base of the recurrence plot. Because of the different features that are used, these entropy measures represent different aspects of the analysed system and, thus, behave differently. In the past, this fact has lead to difficulties in interpreting and understanding those measures. We summarize the definitions, the motivation and interpretation of these entropy measures, compare their differences and discuss some of the pitfalls when using them.
Finally, we illustrate their potential in an application on palaeoclimate time series. Using entropy measures, changes and transitions in the climate dynamics in the past can be identified and interpreted.
At PIK, among other things, new methods are being developed that, on the one hand, can be used to investigate new aspects in palaeoclimate data, but on the other hand can also cope with the difficulties usually associated with palaeoclimate analyses – such as gaps in data series, uncertainties in the dating, or irregularities in the data sampling. Although this is basic research, it is also immediately applied to interesting questions.
In this example, a method was developed to determine the regularity of certain recurring pattern in the data. The technical terms here are “recurrence” and “entropy” (a measure of disorder). Methods that look for recurring patterns are used in various disciplines, not only in the geosciences, but also in medicine, mechanical engineering, finance, and so on. Besides finding abrupt changes, they are also used for comparing different data sets or for classification (e.g. for machine learning).
The newly developed method was applied to the carbon isotopeIsotopChemische Elemente können aus verschieden aufgebauten Atomen gebildet sein. Die Anzahl Protonen im Atomkern ist zwar dabei gleich, aber die Anzahl der Neutronen kann variieren. Man spricht dann von Isotopen, deren Massen kleine, aber messbare Unterschiede aufweisen. Der Atomkern des Sauerstoffs besteht z. B. aus 8 Protonen und in der Regel aus 8 Neutronen. Es gibt aber auch Sauerstoff, dessen Kerne aus 8 Protonen und 9 oder 10 Neutronen bestehen (neben selteneren, instabilen Sauerstoffisotopen). Um das zu kennzeichnen, gibt man zusätzlich zum chemischen Symbol noch die Massenzahl (Summe aus Protonen und Neutronen) an, also 16O, 17O oder 18O. Die unterschiedlichen Isotope verhalten sich zwar chemisch identisch, physikalisch aber - aufgrund ihres unterschiedlichen Gewichtes - leicht unterschiedlich. Damit stellen sie äusserst wertvolle Marker dar, die uns wichtige Hinweise zur Änderung des Klimas, der Umgebungsvegetation, Bodenaktivität und vielem mehr geben. data from BB-1 and BB-3 (for this purpose, the data from both stalagmites were combined into one long data series using a special procedure). Interestingly, there are regular differences during the influence of the maritime climate (Atlantic influence) and during the influence of the continental climate. During the Atlantic influence, the climate seems to have changed more regularly than during the dominant continental climate (this may be related to the regular change of cold events in the North Atlantic, so-called “Bond events”, or to the North Atlantic Oscillation). This could be used to extend our knowledge about the migration of the climate zone boundary, as known for the last 4,000 years (see Climate Zone Shift in central Europe), further into the past. Whenever the new measure indicates that there were more regular climate dynamics, the climate zone boundary was further east of the Bleßberg Cave.
