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Scaling properties of rainfall records in some Mexican zones

Angulo-Fernández F., Reyes-Ramírez I., Flores-Márquez E. L.

Acta Geophysica

2018

Vol. 66, no. 3

361--367

Since the 1990 decade, it has been suggested that atmospheric processes associated with rainfall could be a self-organized critical (SOC) phenomenon similar, for example, to seismicity. In this sense, the rain events taken as the output of the complex atmospheric system (sun’s radiation, water evaporation, clouds, etc.) are analogous to earthquakes, as the output of a relaxation process of the earth crust. A clue on this possible SOC behavior of rain phenomenon has been the ubiquitous presence of power laws in rain statistics. In the present article, we report the scaling properties of rain precipitation data taken from meteorological stations located at six zones of Mexico. Our results are consistent with those that assert that rainfall is a SOC phenomenon. We also analyze the Hurst exponent, which is appropriate to measure long-term memory of time series.

Advances in Symmetric Sandpiles

Formenti E., Masson B., Pisokas T.

Fundamenta Informaticae

2007

Vol. 76, nr 1-2

91-112

A symmetric version of the well-known SPM model for sandpiles is introduced. We prove that the new model has fixed-point dynamics. Although there might be several fixed points, a precise description of the fixed points is given. Moreover, we provide a simple closed formula for counting the number of fixed points originated by initial conditions made of a single column of grains. Bounds for the transient length are also given.