The ergodic hypothesis, introduced by Boltzmann, states that, given an infinite time period, the orbit of the representative point of the system in 1,-space will pass through all points of the energy surface (the so-called ’quasi-ergodic’ hypothesis, introduced later, states that the orbit will pass close to all points of the energy surface). It follows that if this is the case, an average value for the location of the representative point determined by following its successive positions through time will be the same as the average value calculated over an ensemble (i.e. collection with similar properties) of systems for a point in time.

As a geomorphological example, consider a region in which there is a wide variety of different types of river reach, of which 3 per cent have a sinuosity of 1.2. If ergodic conditions apply, it can be predicted that the average river in that region will have that sinuosity for 3 per cent of its lifetime.



At the broadest level, location-for time substitution models in geomorphology can be divided into two general categories: those which postulate some sort of equilibrium between landform, process and environmental controls, and then extrapolate through time; and those which model progressive change and/or ’relaxation’ in a system. Using the terminology of Brunsden and Thornes (1979) these will be termed ’characteristic form’ and ’relaxation time’ models respectively. Each has problems due to the particular geomorphological assumptions made.

Research themes for this session include:
1-space for time substitutions models in geomorphology.
2- Ergodic cases and non ergodic cases in geomorphology.
3-main indexes in an ergodic geomorphic case.
4. techniques and advances such as remote sensing, GIS, and computing that are specifically aimed at improving the techniques used in Ergodic modeling in geomorphology.