Original paper
Entropy of landscapes
Lechthaler Zdenkovic, M.; Scheidegger, A. E.
Zeitschrift für Geomorphologie Volume 33 Issue 3 (1989), p. 361 - 371
19 references
published: Oct 5, 1989
ArtNo. ESP022003303007, Price: 29.00 €
Abstract
“Entropy” has been defined in connection with landscapes on the one hand by setting up a complete analogy between relief altitude in a landscape and temperature in an isobaric system. On the other hand, landscape entropy has been defined by setting up an analogy with information systems and calculating the statistical probability of the presence of various relief heights, based on the Boltzmann probability formula. This paper investigates the relation between the two definitions of landscape entropy. It is shown that the two definitions are entirely equivalent within their respective contexts: they differ solely in that the thermodynamic analogy refers to an open isobaric system, whilst the statistical definition assumes a closed equipartitioned system. According to general thermodynamic principles, systems evolve so that their entropy increases. Both entropy definitions of landscapes show that smooth reliefs have a higher entropy than rugged ones. A smooth plain, thus, is the end result of landscape evolution. In the thermodynamic analogy corresponding to open system, this plain is the base level of erosion: mountains decay; the material from them is “lost” into infinity. In the statistical analogy corresponding to a closed system, the final plain can be formed at any elevation: the material from protuberances is transferred into the hollows since, because of the closedness, nothing can be “lost”. The pattern of landscape evolution is thus shown to conform entirely to that predicted by general systems theory.
Keywords
entropy • landscape • isobaric • thermodynamic • relief • erosion • Boltzmann probability formula