A Hybrid Power Law Approach for Spatial and Temporal Pattern Analysis of Salt Marsh Evolution

A striking feature in salt marshes is vegetation distribution, which can self-organize in patterns over time and space. Self-organized patchiness of vegetation can often give rise to power law relationships in the frequency distribution of vegetation patch sizes. In cases where the whole distribution does not follow a power law, the variance of scale in its tail may often be disregarded. The deviation from power laws represents stochastic effect that can be hybridized on the basis of a Fuzzy Bayesian (FB) generative algorithm, to emphasize the influence of different physical and climatic variables on the patch size distribution to detect tipping point of the ephemeral life of a salt marsh under frequent disturbance events. Using remote sensing observations, we investigate the statistical distribution of spatial vegetation patterns controlled by changes in environmental variables acting on salt marshes, and we speculate the conditions under which a shift from a scale-invariant (power law) distribution to patterns characterized by a dominant patch size could be expected using channel sinuosity as a parameter. Our results show that the hybrid model without considering channel sinuosity can only detect the pure power law exponent, while considering channel sinuosity detects the exponent in the tail of the patch size distribution. Thus the evolution of vegetation patches (under power law) detected by the hybrid model considering channel sinuosity can then be used to forecast potential deviation from steady states in intertidal systems, taking into account the climatic and hydrological regimes. The research shows how numerical thresholds can describe the influence of changes in the non-linearity of patch size frequency distribution and how these thresholds can be reflected as attributes for the resilience capacity measurements in estuarine salt marshes.