Setting the length and time scales of a cellular automaton dune model from the analysis of superimposed bed forms

Abstract

[1] We present a new 3-D cellular automaton model for bed form dynamics in which individual physical processes such as erosion, deposition, and transport are implemented by nearest neighbor interactions and a time-dependent stochastic process. Simultaneously, a lattice gas cellular automaton model is used to compute the flow and quantify the bed shear stress on the topography. Local erosion rates are assumed to be proportional to the shear stress in such a way that there is a complete feedback mechanism between flow and bed form dynamics. In the numerical simulations of dune fields, we observe the formation and the evolution of superimposed bed forms on barchan and transverse dunes. Using the same model under different initial conditions, we perform the linear stability analysis of a flat sand bed disturbed by a small sinusoidal perturbation. Comparing the most unstable wavelength in the model with the characteristic size of secondary bed forms in nature, we determine the length and time scales of our cellular automaton model. Thus, we establish a link between discrete and continuous approaches and open new perspectives for modeling and quantification of complex patterns in dune fields.

Creative computing with Landlab: an open-source toolkit for building, coupling, and exploring two-dimensional numerical models of Earth-surface dynamics

“…This data structure also lends itself to the implementation of some cellular automata. For instance, pairwise transition automata (Narteau et al, 2001(Narteau et al, , 2009) represent the states of cells on a grid as paired "doublets", with rules prescribed to govern the rates of transition between each doublet type. These are readily implemented in Landlab by mapping the pair states onto the links of a Landlab grid, and representing the corresponding automaton cell states at grid nodes .…”

“…Although standardized frameworks for model interoperability are now in place (such as the framework designed and maintained by the Community Surface Dynamics Modelling System, CSDMS, group; Overeem et al, 2013;Peckham et al, 2013), many models are not compatible with these standards. We hypothesize this is largely due to the effort required by the original programmer to modify legacy codewhich in many cases was written before the standards were established -to meet these new interoperability criteria.…”

“…However, scientists who want to use an Earth-surface model often build their own unique model from the ground up, re-coding the basic building blocks of their model rather than taking advantage of codes that have already been written (Adams et al, 2014;Katz et al, 2015;Overeem et al, 2013). This undoubtedly does produce novel software capable of fulfilling its designer's needs, and can have advantages in helping the programmer to acquire a total understanding of the code base, but this approach also has many associated problems: many person hours are lost rewriting existing code, and the resulting software is often idiosyncratic, ad hoc, undocumented, and unable to interact with other software programs both in the same scientific community and beyond.…”

“…The design principles for Landlab have been guided both by our observations of current software design practices in the surface-system modelling community and by white papers issued by existing organizations both within this community (Adams et al, 2014;Overeem et al, 2013;Peckham et al, 2013) and in the scientific software design community more widely (Becker et al, 2015;Chue Hong, 2014;Katz et al, 2015;NSF, 2012). Our key observations are as follows:…”

A lattice grain model of hillslope evolution

“…Here we present only a brief overview of the Lattice Grain model's rules and behavior. The framework is based on the pairwise ("doublet") method developed by Narteau and colleagues (Rozier and Narteau, 2014), which has been applied to problems as diverse as eolian dune dynamics (Narteau et al, 2009;Zhang et al, 2010Zhang et al, , 2012 and the core-mantle interface (Narteau et al, 2001). …”