Nonlinear spatial series analysis from unidirectional transects of soil physical properties

Soil is usually presented as a complex dynamical system. Nevertheless, evidences based on the theoretical background of complex system physics are still scarce. The main objective of this work was to search for chaotic parameters using some basic concepts of nonlinear dynamical system theory with spatial series of soil properties. Three spatial series consisting of 1000 data point transects were used. We selected horizontal and vertical electrical conductivity (EC_h and EC_v, respectively) and gravimetric water content from a Vertisol (Typic Hapludert) under rice cropping. Each spatial transect was oriented from South to North with 1-m spacing. It was used the TISEAN Software Package (a public domain software available at http://www.mpipks-dresdren.mpg.de/~tisean) for deriving nonlinear parameters from spatial series. We found interesting evidences of chaotic behaviour as maximal Lyapunov exponents were all positive. They ranged from λ_m = 0.129 for water content to λ_m = 0.219 for EC_v (filtered series in each case). Original (unfiltered), filtered, and surrogate spatial series confirmed these findings as they also showed positive Lyapunov exponents. All the spatial series showed a higher deterministic component (|κ|> 0.9 in most cases). The Lyapunov range of correlation (ρ) was within the limits 4.56 m (EC_v) to 7.75 m (gravimetric water content) as usually reported from geostatistical investigations. Future works based on dynamical system theory will advance our knowledge on spatial variability of important soil properties and the emergence of deterministic and/or stochastic components.