ABSTRACT
To date, two dozen differential equations have been suggested to describe slope behavior. A. Young recognizes four classes of slope evolution models: based upon direct recession, based upon creep and flow mechanisms, involving form interaction, and based on process measurements. Among the first two sets of models, there appears to be a convergence of approach yielding two basic equations. The first equation is applicable under any conditions in which the rate of denudation is proportional to slope. A second equation is capable of describing the form of accumulation slopes such as alluvial fans. These equations implicitly assume the ergodic principle, namely that one can substitute space for time. This chapter shows a method of extracting information from the landform in a fashion that lends itself readily to construction of useful models of landform behavior. Stated bluntly, the ergodic principle is: ‘time can be equated with space.’ More exactly, the statement should read: ‘time averages can be replaced by space averages.’
