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Correlation dimension analysis of complex hydrological systems; what information can the method provide?

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Authors:Ma, Miaomiao
Source:106p. Institution: Freie Universität Berlin, Berlin, Germany
Publication Date:2013
Note:In English. 110 refs. Doctoral dissertation
Summary:A variety of different methods have been suggested to classify catchment runoff or groundwater dynamics, to relate these to catchment or aquifer properties and thus to utilize inherent information of data. To that end, the correlation dimension method, a powerful nonlinear time series analysis method based on the chaos theory, has been suggested to assess the intrinsic dimensionality of time series according to Takens (1981). It can provide an assessment of the minimum number of processes that is required to map the observed dynamics. In the first study, the correlation dimension method was applied to the observed hydrographs of 35 catchments in the Federal State of Brandenburg, Germany. The intrinsic dimensionality of these catchments ranged from 2.2 to 5.8. It was uncorrelated with the results of standard time series analysis methods, such as autocorrelation, the slope of the power spectrum and the Hurst coefficient, revealing that the correlation dimension method captured information independent from these measures. The correlation dimension values did not exhibit any clear spatial patterns, but showed significant correlations with the spatial heterogeneity within the catchments. In addition, the correlation dimension method was applied to groundwater head and lake level data in the biosphere reserve Schorfheide-Chorin region. The intrinsic dimensionality of groundwater level ranged from 0.9 to 5, while lake level exhibited small variations, around 1.57 to 2. The correlation dimension values of groundwater level exhibited no correlation with the screening depth of groundwater wells, but displayed spatial patterns due to the different aquifer conditions (confined or unconfined). It seems that high correlation dimension values indicate partly confined conditions. Most of the available hydrological models are highly over-parameterized concerning available data and encounter the equifinality problem: different model parameterizations and even different models yield the same best results, which has severe consequences with respect to model uncertainty. However, if these models are used for process identification or as a basis for the modeling of reactive solute transport, they exhibit substantial variety. The same problem exists for model applications to different boundary conditions. Thus, model validation by comparing measured with simulated time series only is not sufficient. In the second study, we proposed a different approach based on the correlation dimension method. Simulated hydrographs from three hydrological models with increasing complexities were investigated using the correlation dimension method and the relationship between correlation dimension values and Nash-Sutcliffe efficiency values was explored. The correlation dimension method imposes additional constraints to the models and is more powerful to reduce the equifinality problem compared with the traditional Nash-Sutcliffe efficiency criteria. Therefore, the combination of the Nash-Sutcliffe efficiency criterion and the correlation dimension method detects the intrinsic property underlying the system dynamics, but also improves the prediction accuracy, serving as a promising approach for model performance evaluation. In addition, the correlation dimension analyses of model rainfall, evapotranspiration and discharge time series suggested that the hydrological models likely acted as intrinsic dimensionality reducing filters for the high-dimensional model inputs to outputs. The model reduced more intrinsic dimensionalities of simulations, if the higher model complexity was.
Subjects:Correlation; Ground water; Hydrodynamics; Hydrology; Lateral heterogeneity; Methods; Potentiometric surface; Quantitative analysis; Statistical analysis; Time series analysis; Wellhead protection; Asia; Brandenburg Germany; Central Europe; China; Europe; Far East; Germany; Dissertation; River discharge
Coordinates:N512300 N533500 E0144800 E0111500
Record ID:802829-1
Copyright Information:GeoRef, Copyright 2021 American Geosciences Institute. Reference includes data from Geoline, Bundesanstalt fur Geowissenschaften und Rohstoffe, Hanover, Germany
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