A deterministic geometric representation of temporal rainfall: sensitivity analysis for a storm in Boston

In an earlier study, Puente and Obregón [Water Resour. Res. 32(1996)2825] reported on the usage of a deterministic fractal–multifractal (FM) methodology to faithfully describe an 8.3 h high-resolution rainfall time series in Boston, gathered every 15 s and made of 1990 points, as the derived distribution of a classical multifractal measure via a fractal interpolating function. This work further studies the robustness of the FM methodology via an exhaustive sensitivity analysis aimed at obtaining even better FM descriptions for the Boston storm. This is carried out by varying a host of pertinent attributes that include usage of: (a) alternative objective functions for the inverse problem based on cumulative distributions of the records and of their derivatives; (b) a genetic algorithm in order to find the best FM parameters; (c) fractal interpolating functions passing by 3, 4 and 5 points, considering all relevant parameter-combination cases separately; and (d) two scales of aggregation, i.e. records with 199 and 1990 bins. The analysis indicates that previous results may indeed be improved when cumulative distributions of the records, rather than the records themselves, are employed in the FM parameter search, especially for representations based on 4 and 5 interpolating points and at the highest data resolution.