The relative geomorphic work effected by four processes in rainstorms: a conceptual approach to magnitude and frequency

Abstract

According to Wolman and Miller (1960) the high geomorphic power of extreme events is compensated by its low frequency, because the product of a power function (cause-effect relationship) by a negative exponential (frequency distribution of the causes) tends to zero for high values. This result is adequate for extreme values, but the difference between the most frequent (modal) events and those which produce the maximum of relative work depends on: (1) the exponent of the power function; and (2) the dispersion (standard deviation) of the frequency distribution. On the other hand, other kind of functions describing the cause-effect relationship, when multiplied by the frequency distribution can yield a maximum for trigger values whose frequency is very low. Most of the recent data about processes triggered by extreme rains in mountains show the chief role of rapid mass movements, the number of which increases very quickly with increasing rain fall. A general model which describes the increase of landsliding as afunction of event rainfall depth is here presented. It is able to describe the differences among diverse climatic and geomorphic scenarios, fits very well to two data sets, allows congruent extrapolations for higher rainfall values, and overcomes the problem of thresholds. Unfortunately, in its present form, it is unable to handle different rainfall intensities. A four hillslope process model built up with the same assumptions of the model from Wolman and Miller shows that, after a maximum of work made by chemical weathering, creep and wash, a new and higher maximum can appear for infrequent slide-triggering rains if they are not too rare and the slopes are steep enough. This model, though in a probabilistic-conceptual frame, is able to simulate most of the main characteristics of the magnitude-frequency relationships described elsewhere, tolerates a wide range of process combinations, and admits the analysis of the consequence of a change of the frequency of extreme rainfall events.