A semi-phenomenological approach to explain the event-size distribution of the Drossel-Schwabl forest-fire model

Hergarten, Stefan; Krenn, Roland

doi:10.5194/npg-18-381-2011

Cited by 9 publications

(13 citation statements)

References 23 publications

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“…In this regime, retinal wave, or forest fire, sizes are characterized by a power-law distribution with scaling exponent of approximately (simulation based [32] , theoretical based [33] , [34] ). Parameters which have the largest and most direct impact on and are the per cell spontaneous firing rate , and the slow refractory variable (refer to Fig.…”

Section: Resultsmentioning

confidence: 99%

A Reaction-Diffusion Model of Cholinergic Retinal Waves

2014

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Prior to receiving visual stimuli, spontaneous, correlated activity in the retina, called retinal waves, drives activity-dependent developmental programs. Early-stage waves mediated by acetylcholine (ACh) manifest as slow, spreading bursts of action potentials. They are believed to be initiated by the spontaneous firing of Starburst Amacrine Cells (SACs), whose dense, recurrent connectivity then propagates this activity laterally. Their inter-wave interval and shifting wave boundaries are the result of the slow after-hyperpolarization of the SACs creating an evolving mosaic of recruitable and refractory cells, which can and cannot participate in waves, respectively. Recent evidence suggests that cholinergic waves may be modulated by the extracellular concentration of ACh. Here, we construct a simplified, biophysically consistent, reaction-diffusion model of cholinergic retinal waves capable of recapitulating wave dynamics observed in mice retina recordings. The dense, recurrent connectivity of SACs is modeled through local, excitatory coupling occurring via the volume release and diffusion of ACh. In addition to simulation, we are thus able to use non-linear wave theory to connect wave features to underlying physiological parameters, making the model useful in determining appropriate pharmacological manipulations to experimentally produce waves of a prescribed spatiotemporal character. The model is used to determine how ACh mediated connectivity may modulate wave activity, and how parameters such as the spontaneous activation rate and sAHP refractory period contribute to critical wave size variability.

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Section: Resultsmentioning

confidence: 99%

A Reaction-Diffusion Model of Cholinergic Retinal Waves

2014

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“…In any case, very big fire events are prevented through fire suppression by fire-fighters, this may results in a deviation from the power law fit in the tail of the distribution (Fig. 3), often referred as a finite-size effect (Corral et al, 2010;Hergarten, 2002). These results support that Northern Europe ecosystem show a more natural fire regime, since the influence of humans is located mainly in the upper tail of the distribution, and fire ignition and spreading is more likely be dictated by climate and fuel availability.…”

Section: Discussionmentioning

confidence: 99%

“…Regarding the latter category of models, Bak et al (1990) proposed an interpretation of the spatial distribution of wildfires involving the theory of Self-Organized Criticality (SOC). This theory was first formalized by Bak et al (1987) 1/f noise, using the analogy of the "sand pile" model, and then widely applied in various fields (Hergarten and Krenn, 2011;Hergarten, 2002;Jørgensen et al, 1998;Malamud et al, 2005b;Newman, 1996;Pueyo, 2007;Turcotte and Malamud, 2004). In this framework, a simple dynamical system accumulates energy (and mass) for a certain period of time and then energy is dissipated as a fractal (Bak et al, 1990) generating scale invariance in events magnitude (i.e.…”

Section: Introductionmentioning

confidence: 99%

Power law distributions of wildfires across Europe: benchmarking a land surface model with observed data

Mauro

Fava

Frattini

et al. 2015

Preprint

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Monthly wildfire burned area frequency is here modeled with a power law distribution and scaling exponent across dierent European biomes are estimated. Data sets, spanning from 2000 to 2009, comprehend the inventory of monthly burned areas from 5 the European Forest Fire Information System (EFFIS) and simulated monthly burned areas from a recent parameterization of a Land Surface Model (LSM), that is the Community Land Model (CLM). Power law exponents are estimated with a Maximum Likelihood Estimation (MLE) for dierent European biomes. The characteristic fire size (CFS), i.e. the area that most contributes to the total burned area, was also calcu10 lated both from EFFIS and CLM data set. We used the power law fitting and the CFS analysis to benchmark CLM model against the EFFIS observational wildfires data set available for Europe. Results for the EFFIS data showed that power law fittings holds for 2–3 orders of magnitude in the Boreal and Continental ecoregions, whereas the distribution of the 15 Alpine, Atlantic are fitted only in the upper tail. Power law instead is not a suitable model for fitting CLM simulations. CLM benchmarking analysis showed that the model strongly overestimates burned areas and fails in reproducing size-frequency distribution of observed EFFIS wildfires. This benchmarking analysis showed that some refinements in CLM structure (in par20 ticular regarding the anthropogenic influence) are needed for predicting future wildfires scenarios, since the low spatial resolution of the model and dierences in relative frequency of small and large fires can aect the reliability of the predictions

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“…The idea is in its spirit identical to the hierarchical clustering approach recently suggested by Hergarten and Krenn (2011) to explain the dynamics of the Drossel-Schwabl forest-fire model (Drossel and Schwabl, 1992).…”

Section: The Scaling Exponent Of the Event-size Distributionmentioning

confidence: 94%

Synchronization and desynchronization in the Olami-Feder-Christensen earthquake model and potential implications for real seismicity

Hergarten

Krenn

2011

Nonlin. Processes Geophys.

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Abstract. The Olami-Feder-Christensen model is probably the most studied model in the context of self-organized criticality and reproduces several statistical properties of real earthquakes. We investigate and explain synchronization and desynchronization of earthquakes in this model in the nonconservative regime and its relevance for the power-law distribution of the event sizes (Gutenberg-Richter law) and for temporal clustering of earthquakes. The power-law distribution emerges from synchronization, and its scaling exponent can be derived as τ = 1.775 from the scaling properties of the rupture areas' perimeter. In contrast, the occurrence of foreshocks and aftershocks according to Omori's law is closely related to desynchronization. This mechanism of foreshock and aftershock generation differs strongly from the widespread idea of spontaneous triggering and gives an idea why some even large earthquakes are not preceded by any foreshocks in nature.

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A semi-phenomenological approach to explain the event-size distribution of the Drossel-Schwabl forest-fire model

Cited by 9 publications

References 23 publications

A Reaction-Diffusion Model of Cholinergic Retinal Waves

A Reaction-Diffusion Model of Cholinergic Retinal Waves

Power law distributions of wildfires across Europe: benchmarking a land surface model with observed data

Synchronization and desynchronization in the Olami-Feder-Christensen earthquake model and potential implications for real seismicity

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