The mean frequency of recurrence of in-time-multidimensional events for drought analyses
Résumé
In this work, a procedure that allows a complete statistical characterization of drought events is presented. Droughts are characterized, from a statistical point of view, based both on the deviation from a normal regime and persistence. The events are represented as multivariate ones, whose dimensionality depends on the duration. Equal duration events are discriminated through their deviations from normality. The mean frequency of recurrence (MFR) is theoretically derived for such multivariate events, and it is used to scale such deviations. Therefore, events with different dimensionalities can be compared on a common dimension of interest, the MFR. This may be used as a drought index for drought characterization, both for analyzing historical events and monitoring current conditions. It may also be applied to analyze precipitation, streamflows and other hydroclimatic records. Its statistical nature and its general conception support its universality. Results may be applied not only to drought analysis, but also to analyze other random natural hazards. Applications of the procedure for drought analysis in Texas (USA) and in Gibraltar (Iberian Peninsula) are made and compared with PDSI and SPI results. The MFR applied over drought analysis allows the representation of the main drought characteristics in a single value, based on the statistical feature of the phenomenon, and scaled on the mean frequency of recurrence.