| 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. |