Comparative parametrization of the Bernoulli-lognormal cascade generator through binary breakdown coefficients and using its autocorrelation function

The multifractal Bernoulli-lognormal (BLN, traditionally known as beta-lognormal) cascade has been effectively used to model the intermittence and scale invariance found in precipitation intensities, particularly under extreme hydro-meteorological events that generate hydrologic and geomorphological hazards such as floods, landslides, and debris flows. However, the parametrization of its generator based on a single realization has been a challenge due to the inherent non-ergodic nature of the process, and it is relevant for understanding vulnerability, risk mitigation and societal response to weather-induced extremes. In this work, we compare two recently proposed advances in parametrisation: (i) an approximation for the distribution of the BLN breakdown coefficients (BDCs) and (ii) the explicit expression of the dressed-cascade autocorrelation function in terms of the moments of its generator. Based on these two statistics, we derive an equation system that directly links the parameters ($C_b$, $C_{ln}$) with the observable quantities: the BDCs' distributional moments and the decay rate of the autocorrelation. We use these two parametrisation methods on multiscale precipitation data obtained from Google Earth Engine, enabling the analysis of weather–precipitation relationships, socio-hydrological interactions, and their implications for preparedness, impact-based forecasting, and even insurance and reinsurance applications.