Data-driven prediction of thresholded time series of rainfall and self-organized criticality models

Abstract

We study the occurrence of events, subject to threshold, in a representative SOC sandpile model and in high-resolution rainfall data. The predictability in both systems is analyzed by means of a decision variable sensitive to event clustering, and the quality of the predictions is evaluated by the receiver operating characteristics (ROC) method. In the case of the SOC sandpile model, the scaling of quiet-time distributions with increasing threshold leads to increased predictability of extreme events. A scaling theory allows us to understand all the details of the prediction procedure and to extrapolate the shape of the ROC curves for the most extreme events. For rainfall data, the quiet-time distributions do not scale for high thresholds, which means that the corresponding ROC curves cannot be straightforwardly related to those for lower thresholds. In this way, ROC curves are useful for highlighting differences in predictability of extreme events between toy models and real-world phenomena.

Probability estimation of a Carrington-like geomagnetic storm

“…It is noteworthy that many natural hazards share this property of self-similarity 53 , which is not linked to the particular model of the inter-occurrence times (i.e., not linked to the Weibull assumption). In the case of point events this has been observed for earthquakes 35,36 and forest fires 54 , whereas for time series (the case under consideration here) this behavior is present in rainfall events 49 , annual climate records (temperature, rives floods, etc. 50 ), and (of particular interest for its relation with geomagnetic storms) solar flares 23,24 .…”

“…Thus, the estimated probability of occurrence of a Carrington event in the first decade after 1859 is 3.33%, which is 3.6 times greater than the estimated probability for the current decade. This property in which hazard decreases over time is not only counter-intuitive but fundamental for hazard assessment, and seems to be present in the occurrence of many geological and astronomical extreme events 23,24,35,49–51 . The origin can be attributed to long-range correlations in the Dst time series, as several authors 50,52 have argued that in such a case the inter-occurrence time statistics is of the decreasing-hazard-rate type.…”

Increasing power-law range in avalanche amplitude and energy distributions

“…Note that the thresholding we perform turns out to be of the same kind as that in Refs. [26,27]. as the standard deviation for each bin [5].…”

Universal avalanche statistics and triggering close to failure in a mean-field model of rheological fracture

“…For example, correlations have been observed in stick-slip models with dissipation [76,80], yet they were shown not to be a consequence of event-event triggering but a consequence of slow temporal variations in the Poisson intensity or synchronization [81]. Power-law waiting times can also be artificially constructed by a non-quasistatic driving and a thresholding of the activity [82][83][84], without requiring the involvement of any triggering or aftershock process. Event-event triggering or aftershock sequences and the associated temporal correlations are commonly reproduced by introducing additional temporal scales affecting the propagation of the avalanches, without requiring to break the quasistatic condition.…”