The mean frequency of recurrence of in-time-multidimensional events for drought analyses

Abstract. Droughts are related with prolonged periods when moisture is significantly below normal values. Drought indices attempt to scale the main drought features to facilitate comparisons. Numerous indices are found in the literature based on different drought features. Many of them were created for particular places and specific objectives, and therefore not suitable to generalize the results. However, there have been attempts to develop a general index, which would provide full characterization of drought events. Two of the most well known are the Palmer Drought Severity Index (PDSI) and the Standard Precipitation Index (SPI). Each one has particular advantages and disadvantages. Still neither of them or any other includes a full representation of droughts in a single value index, being useful for all general application. The fact that droughts have a random nature prescribes the statistical theory for the foundation of a complete and generic index, which would meet this goal.

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.