Instability, intermittency, and multiscaling in discrete growth models of kinetic roughening

We show by numerical simulations that discretized versions of commonly studied continuum nonlinear growth equations (such as the Kardar-Parisi-Zhangequation and the Lai-Das Sarma-Villain equation) and related atomistic models of epitaxial growth have a generic instability in which isolated pillars (or grooves) on an otherwise flat interface grow in time when their height (or depth) exceeds a critical value. Depending on the details of the model, the instability found in the discretized version may or may not be present in the truly continuum growth equation, indicating that the behavior of discretized nonlinear growth equations may be very different from that of their continuum counterparts. This instability can be controlled either by the introduction of higher-order nonlinear terms with appropriate coefficients or by restricting the growth of pillars (or grooves) by other means. A number of such ''controlled instability'' models are studied by simulation. For appropriate choice of the parameters used for controlling the instability, these models exhibit intermittent behavior, characterized by multiexponent scaling of height fluctuations, over the time interval during which the instability is active. The behavior found in this regime is very similar to the ''turbulent'' behavior observed in recent simulations of several one- and two-dimensional atomistic models of epitaxial growth.

Parameter estimation of a two-horizon soil profile by combining crop canopy and surface soil moisture observations using GLUE

Estimation of soil parameters by inverse modeling using observations on either surface soil moisture or crop variables has been successfully attempted in many studies, but difficulties to estimate root zone properties arise when heterogeneous layered soils are considered. The objective of this study was to explore the potential of combining observations on surface soil moisture and crop variables - leaf area index (LAI) and above-ground biomass for estimating soil parameters (water holding capacity and soil depth) in a two-layered soil system using inversion of the crop model STICS. This was performed using GLUE method on a synthetic data set on varying soil types and on a data set from a field experiment carried out in two maize plots in South India. The main results were (i) combination of surface soil moisture and above-ground biomass provided consistently good estimates with small uncertainity of soil properties for the two soil layers, for a wide range of soil paramater values, both in the synthetic and the field experiment, (ii) above-ground biomass was found to give relatively better estimates and lower uncertainty than LAI when combined with surface soil moisture, especially for estimation of soil depth, (iii) surface soil moisture data, either alone or combined with crop variables, provided a very good estimate of the water holding capacity of the upper soil layer with very small uncertainty whereas using the surface soil moisture alone gave very poor estimates of the soil properties of the deeper layer, and (iv) using crop variables alone (else above-ground biomass or LAI) provided reasonable estimates of the deeper layer properties depending on the soil type but provided poor estimates of the first layer properties. The robustness of combining observations of the surface soil moisture and the above-ground biomass for estimating two layer soil properties, which was demonstrated using both synthetic and field experiments in this study, needs now to be tested for a broader range of climatic conditions and crop types, to assess its potential for spatial applications. (C) 2012 Elsevier B.V. All rights reserved.