Scale invariant behavior of cropping area losses

This paper shows how crop losses, display Self-Organized Critical Behavior, which implies that under a wide range of circumstances, these losses exhibit a power-law dependence on frequency in the affected area whose order of magnitude approximates those reported for extreme climate events. Self-Organized Critical Behavior has been observed in many extreme climate events, as well as in the density and distribution of pests linked to crop production. Empirical proof is provided by showing that the frequency-size distribution of the cropland loss fits the Pareto and the Weibull models with scaling exponents that are statistically similar to the expected value. In addition, the test included comparisons of the expected value and the predicted value of the scaling exponents among different subsystems and among systems of the same universality class. Results show that the Pareto model fits the heavy-tailed distribution of losses mostly caused by extreme climate events, while the Weibull model fits the whole distribution, including small events. The analyses show that crop losses adopt Self-Organized Critical Behavior regardless of the growing season and the water provision method (irrigated or rainfed). Irrigated systems show more stable behavior than rainfed systems, which display higher variability. The estimation is robust not only for calculating model parameters but also for testing the proximity to a power-law-like relationship.A long-term risk index by growing season and water provision method is derived as an application of this power-law behavior. The index is flexible, comparable between geographical units regardless of their size and provides an indirect measure of the probability of losing a cropping area of a given size.