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Technical note: An improved Grassberger–Procaccia algorithm for analysis of climate system complexity

Abstract. Understanding the complexity of natural systems, such as climate
systems, is critical for various research and application purposes. A range
of techniques have been developed to quantify system complexity, among which
the Grassberger–Procaccia (G-P) algorithm has been used the most. However,
the use of this method is still not adaptive and the choice of scaling
regions relies heavily on subjective criteria. To this end, an improved G-P
algorithm was proposed, which integrated the normal-based K-means
clustering technique and random sample consensus (RANSAC) algorithm for
computing correlation dimensions. To test its effectiveness for computing
correlation dimensions, the proposed algorithm was compared with traditional
methods using the classical Lorenz and Henon chaotic systems. The results
revealed that the new method outperformed traditional algorithms in computing
correlation dimensions for both chaotic systems, demonstrating the
improvement made by the new method. Based on the new algorithm, the
complexity of precipitation, and air temperature in the Hai River
basin (HRB) in
northeastern China was further evaluated. The results showed that there
existed considerable regional differences in the complexity of both climatic
variables across the HRB. Specifically, precipitation was shown to become
progressively more complex from the mountainous area in the northwest to the
plain area in the southeast, whereas the complexity of air temperature
exhibited an opposite trend, with less complexity in the plain area. Overall,
the spatial patterns of the complexity of precipitation and air temperature
reflected the influence of the dominant climate system in the region.
