Technical note: Complexity–uncertainty curve (c-u-curve) – a method to analyse, classify and compare dynamical systems
We propose and provide a proof of concept of a method to analyse, classify and compare dynamical systems of arbitrary dimensions by the two key features uncertainty and complexity. It starts by subdividing the system's time trajectory into a number of time slices. For all values in a time slice...
Gespeichert in:
Veröffentlicht in: | Hydrology and earth system sciences 2023-07, Vol.27 (14), p.2591-2605 |
---|---|
Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Zusammenfassung: | We propose and provide a proof of concept of a method to analyse, classify
and compare dynamical systems of arbitrary dimensions by the two key features
uncertainty and complexity. It starts by subdividing the system's time trajectory into a number of time slices. For all values in a time
slice, the Shannon information entropy is calculated, measuring within-slice
variability. System uncertainty is then expressed by the mean entropy of all time
slices. We define system complexity as “uncertainty about uncertainty” and express it by the entropy of the entropies of all time slices. Calculating and
plotting uncertainty “u” and complexity “c” for many different numbers of time
slices yields the c-u-curve. Systems can be analysed, compared and classified by the
c-u-curve in terms of (i) its overall shape, (ii) mean and maximum
uncertainty, (iii) mean and maximum complexity and (iv) characteristic
timescale expressed by the width of the time slice for which maximum
complexity occurs. We demonstrate the method with the example of both
synthetic and real-world time series (constant, random noise, Lorenz
attractor, precipitation and streamflow) and show that the shape and
properties of the respective c-u-curve clearly reflect the particular
characteristics of each time series. For the hydrological time series, we
also show that the c-u-curve characteristics are in accordance with
hydrological system understanding. We conclude that the c-u-curve method can
be used to analyse, classify and compare dynamical systems. In particular,
it can be used to classify hydrological systems into similar groups, a
pre-condition for regionalization, and it can be used as a diagnostic measure
and as an objective function in hydrological model calibration. Distinctive features of the method are (i) that it is based on
unit-free probabilities, thus permitting application to any kind of data,
(ii) that it is bounded, (iii) that it naturally expands from single-variate to
multivariate systems, and (iv) that it is applicable to both deterministic
and probabilistic value representations, permitting e.g. application to
ensemble model predictions. |
---|---|
ISSN: | 1607-7938 1027-5606 1607-7938 |
DOI: | 10.5194/hess-27-2591-2023 |