TIME LAGS AND EMERGENT STABILITY IN MORPHOGENIC PEDOGENIC SYSTEM MODELS

The balance between pedogenic forces operating normal to and morphogen ic forces operating tangent to the land surface is critical to landsca pe stability and evolution. A simple nonlinear first-order difference model of the slope mass balance for a unit area along a hillslope show s chaotic behavior when morphogenesis and pedogenesis are in phase, su ch that there is no lag between debris production and its availability for removal. However, when morphogenesis and pedogenesis are out of p hase, the model is stable and nonchaotic. The lagged, out-of-phase ver sion of the model produces a stable equilibrium thickness of soil/rego lith cover, no matter what parameter values are used to describe rates of morphogenic and pedogenic processes or the feedbacks between pedog enic processes and regolith thickness. This model shows that inclusion of a simple one-increment lag with no other changes in model structur e can produce qualitatively different results, which are especially st riking in the spatial domain. Whereas lags in geomorphic and pedologic systems (and in nonlinear dynamical systems in general) have generall y been viewed as sources of instability and chaos, in this case the in clusion of a lag leads to stability. The emergence of stability at bro ader spatial scales may thus be linked to lag effects, rather than to spatial averaging.