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

Abstract

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.