Considerations in multifractal downscaling of rainfall: canonical vs. microcanonical cascades

Disaggregation of rainfall time series focuses on preserving the statistical properties of those small-scale intensities, which are being downscaled from measured large-scale values. Multifractal scaling properties have offered, for a few decades already, a parsimonious framework for simulating the joint statistics observed in the small-scale values, and recent work emphasizes the use of more sophisticated cascading processes, in order to better capture all statistical requirements imposed (Cappelli et al., Stoch Environ Res Risk Assess 2024, https://doi.org/10.1007/s00477-024-02827-8). Comparisons between downscaling models based on canonical vs. microcanonical cascades have been presented already more than two decades ago (see e.g. Molnar and Burlando, Atmos Res 77, 2005, https://doi.org/10.1016/j.atmosres.2004.10.024), but recent theoretical results (Aguilar-Flores and Carsteanu, Fractals 32, 2024, https://doi.org/10.1142/S0218348X24500725) have prompted us to consider the importance of taking into account the asymptotic properties of the measures generated by canonical and microcanonical cascades, respectively, for downscaling purposes. The reflection of such properties in real-life rainfall data is being analyzed in the work communicated herein.