Precipitation clusters are contiguous raining regions characterized by a precipitation threshold, size, and the total rainfall contained within—termed the cluster power. Tropical observations suggest that the probability distributions of both cluster size and power contain a power-law range (with slope ~ −1.5) bounded by a large-event “cutoff.” Events with values beyond the cutoff signify large, powerful clusters and represent extreme events. A two-dimensional stochastic model is introduced to reproduce the observed cluster distributions, including the slope and the cutoff. The model is equipped with coupled moisture and weak temperature gradient (WTG) energy equations, empirically motivated precipitation parameterization, temporally persistent noise, and lateral mixing processes, all of which collectively shape the model cluster distributions. Moisture–radiative feedbacks aid clustering, but excessively strong feedbacks push the model into a self-aggregating regime. The power-law slope is stable in a realistic parameter range. The cutoff is sensitive to multiple model parameters including the stochastic forcing amplitude, the threshold moisture value that triggers precipitation, and the lateral mixing efficiency. Among the candidates for simple analogs of precipitation clustering, percolation models are ruled out as unsatisfactory, but the stochastic branching process proves useful in formulating a neighbor probability metric. This metric measures the average number of nearest neighbors that a precipitating entity can spawn per time interval and captures the cutoff parameter sensitivity for both cluster size and power. The results here suggest that the clustering tendency and the horizontal scale limiting large tropical precipitating systems arise from aggregate effects of multiple moist processes, which are encapsulated in the neighbor probability metric.
We propose a theoretical modelling framework for earthquake occurrence and clustering based on a family of invariant Galton–Watson (IGW) stochastic branching processes. The IGW process is a rigorously defined approximation to imprecisely observed or incorrectly estimated earthquake clusters modelled by Galton–Watson branching processes, including the Epidemic Type Aftershock Sequence (ETAS) model. The theory of IGW processes yields explicit distributions for multiple cluster attributes, including magnitude-dependent and magnitude-independent offspring number, cluster size and cluster combinatorial depth. Analysis of the observed seismicity in southern California demonstrates that the IGW model provides a close fit to the observed earthquake clusters. The estimated IGW parameters and derived statistics are robust with respect to the catalogue lower cut-off magnitude. The proposed model facilitates analyses of multiple quantities of seismicity based on self-similar tree attributes, and may be used to assess the proximity of seismicity to criticality.more » « less
- NSF-PAR ID:
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Geophysical Journal International
- Medium: X Size: p. 567-583
- ["p. 567-583"]
- Sponsoring Org:
- National Science Foundation
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