During the past 20 years, a controversy, or at least a difference of opinion, has developed over the relative merits of deterministic and random models in fluvial geomorphology. A survey of the literature indicates that there are actually two distinct approaches that make use of stochastic concepts. As all three groups draw upon physical principles to a considerable extent, the origin and development of deterministic and stochastic disciplines in physics are reviewed and illustrated with some simple examples. The information obtained is then used to examine the scientific content of the claims put forward by the three groups and to make some judgment of their validity.
Fluvial geomorphology involves the study of several complex and interrelated processes, such as chemical weathering, erosion, soil creep, sediment transport and deposition, development and maintenance of stream networks, and channel hydraulics. It is clearly very difficult to obtain detailed quantitative explanations of such processes. Consequently, a number of authors, beginning with Leopold and Langbein , have proposed that stochastic methods could be used to advantage in many instances. During the past 20 years, a controversy, or at least a difference of opinion, has developed over the relative merits of deterministic and stochastic models in fluvial geomorphology.