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

Di, Chongli; Wang, Tiejun; Yang, Xiaohua; Li, Siliang

doi:10.5194/hess-22-5069-2018

Cited by 13 publications

(4 citation statements)

References 51 publications

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“…However, the water level data and wave, noise, and rainfall-runoff components have stochastic characteristics as it showed a diverging pattern. Di et al (2018) confirmed that correlation dimension of rainfall data at a specific rainfall station is diverging even though the dimension increases [36]. Through the above study, we can estimate that the water level time series shows stochastic characteristics because the correlation dimension diverged without converging to a specific value.…”

Section: Estimation Of Correlation Dimensionsupporting

confidence: 58%

Chaotic Features of Decomposed Time Series from Tidal River Water Level

et al. 2021

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This study assessed the characteristics of water-level time series of a tidal river by decomposing it into tide, wave, rainfall-runoff, and noise components. Especially, the analysis for chaotic behavior of each component was done by estimating the correlation dimension with phase-space reconstruction of time series and by using a close returns plot (CRP). Among the time series, the tide component showed chaotic characteristics to have a correlation dimension of 1.3. It was found out that the water level has stochastic characteristics showing the increasing trend of the correlation exponent in the embedding dimension. Other components also showed the stochastic characteristics. Then, the CRP was used to examine the characteristics of each component. The tide component showed the chaotic characteristics in its CRP. The CRP of water level showed an aperiodic characteristic which slightly strayed away from its periodicity, and this might be related to the tide component. This study showed that a low water level is mainly affected by a chaotic tide component through entropy information. Even though the water level did not show chaotic characteristics in the correlation dimension, it showed stochastic chaos characteristics in the CRP. Other components showed stochastic characteristics in the CRP. It was confirmed that the water level showed chaotic characteristics when it was not affected by rainfall and stochastic characteristics deviating from the bounded trajectory when water level rises due to rainfall. Therefore, we have shown that the water level related to the chaotic tide component can also have chaotic properties because water level is influenced by chaotic tide and rainfall shock, thus it showed stochastic chaos characteristics.

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Section: Estimation Of Correlation Dimensionsupporting

confidence: 58%

Chaotic Features of Decomposed Time Series from Tidal River Water Level

et al. 2021

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“…Note that selection of scaling regions is critical for calculating CDs. The automated algorithm proposed by Di et al (2018) was utilized to select scaling regions. If D 2 (m) reaches a certain value (usually called a saturation value) after a value of m, the saturation value is defined as the CD of the time series X i (i = 1, 2, …, N).…”

Section: Correlation Dimensionmentioning

confidence: 99%

“…Conceptually, a chaotic system is controlled by few independent variables that are sensitive to initial conditions, which results in random‐looking processes (May, 1976; Sivakumar, 2004). Chaotic behaviors have been reported in rainfall (Di et al., 2018; Fuwape et al., 2017), streamflow (Ghorbani et al., 2018), and soil moisture (Di et al., 2019). Those studies suggested that the underlying systems regulating those hydrological processes are mainly controlled by few independent variables, the number of which is determined by the stochasticity of those processes; thus, it can provide useful information for various application purposes such as model parameterizations and hydrological simulation (Sivakumar, 2017).…”

Section: Introductionmentioning

confidence: 99%

Complexity and Predictability of Daily Actual Evapotranspiration Across Climate Regimes

Wang

Mai

et al. 2023

Water Resources Research

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Actual evapotranspiration (ET a ) is a key terrestrial ecosystem process that links hydrosphere with atmosphere and biosphere through modulating a range of land surface and ecohydrological processes (Fisher et al., 2017;Wang & Dickinson, 2012). Despite the rapid developments of sensing and modeling technologies in recent decades (Hansen & Wei, 2021;Zhao et al., 2019), it still remains challenging to accurately estimate ET a due to its complex spatiotemporal ET a patterns across scales (Han et al., 2021;Hu et al., 2018). To improve the predictability of ET a , it requires a thorough evaluation of the complexity of ET a dynamics along with its influencing factors across diverse climate regimes and ecosystems (Sang et al., 2015).In general, the predictability of hydrometeorological variables decreases with increasing system complexity, which in turn is tightly related to the degree of system stochasticity (Koutsoyiannis, 2010;Rajagopalan et al., 2019). It is worth noting that the predictability investigated here is different from the one frequently used for hydrological models (Haughton et al., 2018), the latter of which is commonly defined as the prediction skills that can be compromised by uncertainties in initial value, boundary value, and parameter estimation problems (Kumar, 2011). Instead, the predictability is specifically defined here as the estimation of the deterministic (predictable) versus the stochastic (unpredictable) nature of ET a dynamics (Westerhold et al., 2020).The complexity and predictability of system variables can be investigated with the aid of the chaos theory. Previous studies have revealed that hydrological systems exhibit chaotic features, which display both deterministic patterns that are dictated by physical laws and stochastic behaviors that determine the complexity of hydrological systems and subsequently the predictability of hydrological variables (Sivakumar & Singh, 2012). Conceptually, a chaotic system is controlled by few independent variables that are sensitive to initial conditions, which results in random-looking processes (

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“…The calibration and verification of the SWAT model, using flow data collected at the An Khe hydrological station and the Cung Son hydrological station, was divided into two phases: calibration (1981)(1982)(1983)(1984)(1985)(1986)(1987)(1988)(1989)(1990)(1991) (Figure 6a,b) and verification (1992-2002) (Figure 6c,d). The parameter optimization techniques have been analyzed and applied in recent studies, such as Wang et al (2019) [83] and Di et al (2018) [84]. However, the automatic calibration process uses the SWAT Calibration Uncertainties Program (SWAT-CUP) software, with automatic algorithms that match the instability values.…”

Section: Calibration and Validation Of The Swat Modelmentioning

confidence: 99%

Application of Meteorological and Hydrological Drought Indices to Establish Drought Classification Maps of the Ba River Basin in Vietnam

2019

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The objective of this study was to establish drought classification maps to simulate and calculate the lack of discharge in the Ba River basin in Vietnam. The maps were established using three meteorological drought indices (the Standardized Precipitation Index (SPI), the Drought Index (J), and the Ped Index (Ped)), the Soil and Water Assessment Tool (SWAT) model, and the hydrological drought index (KDrought). The results from the calculation of the SPI, Aridity Index (AI), and Ped at three stations (An Khe, Ayunpa, and MDrak) showed that the J index was suitable for the study area. Based on the J index, an extreme drought was predicted to occur at the Ayunpa, An Khe, and MDrak stations. During the calibration process, the SWAT Calibration Uncertainties Program (SWAT-CUP) model, with automatic algorithms, was used to select the parameters to optimize the SWAT model. For the calibration and validation, the observed discharge at two hydrology stations, An Khe and Cung Son, from the periods 1981–1991 and 1992–2002, respectively, were used. The simulated discharge was found to be acceptable, with the Nash–Sutcliffe efficiency (NSE), Percent bias (PBIAS), and R2 reaching good levels in both calibration and validation. The results from the calculation of the drought index (KDrought), and the established drought classification maps in 2016, showed that the most affected areas were the communes of the Gia Lai and Dak Lak provinces. The results from the simulation and calculations were found to be consistent with the situation that occurred in practice. The application of meteorological and hydrological drought indices, as well as the hydrological model, to support impact assessments of drought classification in space and time, as well as the establishment of forecasting and warning maps, will help managers to effectively plan policy responses to drought.

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

Cited by 13 publications

References 51 publications

Chaotic Features of Decomposed Time Series from Tidal River Water Level

Chaotic Features of Decomposed Time Series from Tidal River Water Level

Complexity and Predictability of Daily Actual Evapotranspiration Across Climate Regimes

Application of Meteorological and Hydrological Drought Indices to Establish Drought Classification Maps of the Ba River Basin in Vietnam

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