Nonlinear Dynamics of Soil Moisture at Climate Scales: 2. Chaotic Analysis

Abstract

The soil moisture balance equation over large spatial territories is analyzed at seasonal time scales.Local recycling of precipitation and dynamic effects of soil moisture in the generation and modification of mesoscale circulations are explicitly included in the parameterization which also incorporates time delays in the above effects. It is shown that the dynamics of the equation is quite complex, being capable of exhibiting fixed point, limit cycle, and chaotic type of behavior. The implications of this dynamics are important for the interpretation and modeling of hydrologic phenomena.

A non-linear and stochastic response surface method for Bayesian estimation of uncertainty in soil moisture simulation from a land surface model

“…Wiener (1938) has shown that if deterministic dynamical model is highly nonlinear (with a tendency to exhibit chaotic behavior), then it is possible to approximate both inputs and outputs (treated here as random processes) of the uncertain model through series expansion of standard random variables using Hermite Polynomials. Although the presence of chaotic behavior in the hydrologic system under study is not addressed herein, recent literature supports the wisdom of choosing the "Theory of Homogeneous Chaos" as a basis for formulation of the interpolator (Sivakumar, 2000;Sivakumar et al, 2001a, b;Rodriguez-Iturbe et al, 1991). Rodriguez-Iturbe et al (1991) has demonstrated chaotic behavior of soil moisture dynamics at seasonal time scales.…”

“…Although the presence of chaotic behavior in the hydrologic system under study is not addressed herein, recent literature supports the wisdom of choosing the "Theory of Homogeneous Chaos" as a basis for formulation of the interpolator (Sivakumar, 2000;Sivakumar et al, 2001a, b;Rodriguez-Iturbe et al, 1991). Rodriguez-Iturbe et al (1991) has demonstrated chaotic behavior of soil moisture dynamics at seasonal time scales. Since our effective study period was seasonal (from March to November 1998), this observation by Rodriguez-Iturbe et al (1991) therefore justifies the use of a chaotic approach for our methodology.…”

“…Rodriguez-Iturbe et al (1991) has demonstrated chaotic behavior of soil moisture dynamics at seasonal time scales. Since our effective study period was seasonal (from March to November 1998), this observation by Rodriguez-Iturbe et al (1991) therefore justifies the use of a chaotic approach for our methodology. Furthermore, the requirement of multiple ordinary non-linear differential equations as the necessary condition for chaotic behavior in soil moisture dynamics has also been noted by Rodriguez-Iturbe Table 1) to intuitively expect a chaotic behavior relationship (between soil moisture prediction the hydraulic parameters).…”

“…We do not demonstrate the presence or absence of chaotic behavior of simulations in this study. However, we are encouraged by the recent well-documented discovery of chaos in hydrologic systems (Sivakumar et al, 2001a and2001b;Sivakumar, 2000;Jayawardena and Lai, 1994;Rodriguez-Iturbe et al, 1991). Essential concepts of the interpolator are inferred from an uncertainty estimation tool originally developed by Isukapalli et al (2000).…”

An analysis of mean transition time between flood and drought in the large river basin

“…The model has physically based components, and it introduces a parameterization scheme for the local recycling of precipitation. They have analyzed the model using a stochastic analysis (Rodriguez-Iturbe et al, 1991a) and a chaotic analysis (Rodriguez-Iturbe et al, 1991b). Their analysis shows that stochastic¯uctuations in the soil moisture balance equation may give rise to separate and distinct statistical modes and transitions between these modes.…”