Evidence of Low-dimensional Determinism in Short Time Series of Solute Transport

Abstract

Investigating the vadose zone, the physics behind the temporal and spatial instabilities of flow (in unsaturated media) is still of question. Although chaotic approaches have been widely employed for identifying different surface hydrology processes, such as rainfall, runoff, lake volume, etc., they were not applied for subsurface systems as much. On this ground, the present study attempts to investigate nonlinear determinism in solute transport processes in vadose zone. Previously, a few studies have investigated/examined solute transport processes from the view point of nonlinear chaos. However, this is the first study that is directly analyzing solute transport time series from field experiments. Also, it is analyzing short time series (68 data points) from a soil profile (62 measurement probes). For this purpose, Correlation Dimension Method is used as the most celebrated nonlinear chaotic technique in the hydrological studies. In general, the results of correlation dimension analysis provide the minimum number of ordinary differential equations needed to map a given dynamics. This study placed its main focus on the evolution of Correlation Exponent (CE) vs. Embedding Dimension (EM). The oscillation of correlation exponents between different values (2-4) which is referred to as Instable Saturation (IS) has been observed. Plausible explanations for this instability is discussed. The values of correlation dimensions for stable saturation are 2 and 3 among which CD=3 is the most frequent CD for SS is 3; for the rest of SS, CD is 2. In case of instable saturation, however, CD values are varying between 2 and 4 where IS-2, 3 is the most frequent one. Although the results are not as ‘accurate’ as other hydro-chaotic studies which dealt with longer time series, the consistent pattern and the order of magnitude in the results are in good agreement with previous findings. On a large scheme, the results encouragingly indicate a promising avenue from the presuppositional perspective of stochasticism towards nonlinear determinism for hydrological studies especially subsurface processes.

• author: Khatami, Sina
• organization: Division of Water Resources Engineering
• publishing date: 2013
• type: Book/Report
• publication status: published
• subject: Water Engineering
• keywords: Nonlinear time series analysis, Chaos Theory, Correlation Dimension Method, Solute transport, short time series, unsaturated zone, vadose zone
• pages: 63 pages
• publisher: Department of Water Resources Engineering, Lund Institute of Technology, Lund University
• language: English
• LU publication?: yes
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