Maximum Certainty Principle applied to rainfall modelling and regionalisation in Ecuador

Abstract. This study introduces the Maximum Certainty Principle (PCM, from the Spanish “Principio de Certeza Máxima”) as a variational framework for the probabilistic modelling of storm events and its application to the regionalisation of extreme rainfall. First, the PCM is developed and applied in the Metropolitan District of Quito through the Storm Information Model (MIT-Q), which represents the intra-event temporal structure using a truncated exponential formulation derived from the PCM variational functional. Within MIT-Q, event maximum precipitation (PRE) and event duration (DT) are modelled using Weibull and truncated exponential distributions, respectively. Stochastic simulations equivalent to 500 years of rainfall were performed, calibrated against Intensity–Duration–Frequency (IDF) curves from the Quito-Observatory station and validated at four additional stations within an area of approximately 2500 km². Results indicate that extreme rainfall intensities with durations shorter than 2 h are statistically independent of daily intensities, and that the structural separation between PRE and DT improves the representation of short-duration extremes. Second, the structural insights obtained at the local scale are extended to the existing national rainfall regionalisation framework of Ecuador. A scaling factor (𝜑) associated with the potential number of rainfall bursts, representing the dynamics of local winds and the growth of storm cells, is introduced, enabling the derivation of Potential Intensity–Duration–Frequency (IDFP) curves that remain useful under sparse observation network conditions, such as those of the Ecuadorian network. The proposed approach integrates theoretical development, local validation, and regional scaling within a structural probabilistic framework for the analysis of extreme rainfall.