Journal of Geographical Sciences >
Analyses of geographical observations in the Heihe River Basin: Perspectives from complexity theory
Gao Jianbo, Professor, specialized in complexity theory. Email: jbgao.pmb@aliyun.com 
Received date: 20181030
Accepted date: 20190320
Online published: 20191211
Supported by
National Natural Science Foundation of China(No.71661002)
National Natural Science Foundation of China(No.41671532)
National Key R&D Program of China(No.2017YFB0504102)
The Fundamental Research Funds for the Central Universities
Copyright
Since 2005, dozens of geographical observational stations have been established in the Heihe River Basin (HRB), and by now a large amount of meteorological, hydrological, and ecological observations as well as data pertaining to water resources, soil and vegetation have been collected. To adequately analyze these available data and data to be further collected in future, we present a perspective from complexity theory. The concrete materials covered include a presentation of adaptive multiscale filter, which can readily determine arbi trary trends, maximally reduce noise, and reliably perform fractal and multifractal analysis, and a presentation of scaledependent Lyapunov exponent (SDLE), which can reliably dis tinguish deterministic chaos from random processes, determine the error doubling time for prediction, and obtain the defining parameters of the process examined. The adaptive filter is illustrated by applying it to obtain the global warming trend and the Atlantic multidecadal os cillation from sea surface temperature data, and by applying it to some variables collected at the HRB to determine diurnal cycle and fractal properties. The SDLE is illustrated to deter mine intermittent chaos from river flow data.
GAO Jianbo , FANG Peng , YUAN Lihua . Analyses of geographical observations in the Heihe River Basin: Perspectives from complexity theory[J]. Journal of Geographical Sciences, 2019 , 29(9) : 1441 1461 . DOI: 10.1007/s1144201916706
Figure 1 Adaptive algorithm used to capture the trend signals for the global annual sea surface temperature (SST): (a) original data and trends determined by global linear trend and AFA with two window sizes; (b) the residuals related to the three trends. The residuals designated as the blue and the red curves had been shifted upward and downward by 0.5, respectively. 
Figure 2 Adaptive algorithm used to capture the trend signals for Atlantic Multidecadal Oscillation (AMO): the detrended North Atlantic sea surface temperature anomalies data (grey) and the blue multideccadal signal are obtained from the NOAA°s website, http://www.cdc.noaa.gov/data/climateindices/List, the red and green signals are obtained by the adaptive algorithm. Clearly, the red curve is better than the blue one in tracing out the variations in the original signal, while the green curve is the best in only capturing the multidecadal oscillation. 
Figure 3 Adaptive algorithm used to capture the trend signals of the soil moisture at 4 cm of A’rou station in the Heihe River Basin in different seasons 
Figure 4 Adaptive algorithm used to capture the detrended data of the raw soil moisture at 4 cm of A’rou station in the Heihe River Basin in different seasons 
Figure 5 Power spectral density (PSD) curves for the detrended soil moisture at 4 cm of A’rou station in the Heihe River Basin in different seasons (corresponding to Figure 4) 
Figure 6 A schematic of the three super stations at the Heihe River Basin: A’rou station, Daman station, and Sidaoqiao station 
Figure 7 AFA of wind speed data at the A’rou station (a1c1), the Daman station (a2c2), and the Sidaoqiao station (a3c3) at 5 m, 10 m and 15 m from January 2015 to July 2015, respectively. The slopes denoted by H_{1} and H_{2} are the Hurst parameters. 
Figure 8 Variation of the Hurst parameter for wind speed with heights for the three stations: (a) short time scale H_{1} and (b) long time scale H_{2}. 
Figure 9 Detecting chaos in the Colorado River flow data: (a): error growth curves; (b): SDLE curves. The blue (solid) and red (dashed) curves are for the original and denoised data, respectively. Here, embedding parameters are m=6, L=3, and different curves are based on a few different shells described by Eq. (16). Except at the initial stage in the error growth curves, they collapse on each other. 
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