The temporal fractality of precipitation in mainland Spain and the Balearic Islands and its relation to other precipitation variability indices

Recent years have seen a rise in research into the behaviour of precipitation variability on account of the application of new statistical techniques with a longstanding tradition in other fields. Fractal is a word used to refer to regular objects or processes that cannot be defined by the classical Euclidian mathematics. The fractal dimension of the temporal distribution of precipitation (D) is an indicator of the property of self-similarity in rainfall distribution at different time intervals. While its spatial meaning has previously been developed extensively and is well defined, the interpretation of the concept of fractality applied to the temporal distribution is abstract. The overarching goal of this article is to give climatic significance to this indicator. To this end, data logged at 10-min intervals from 44 weather stations in mainland Spain and the Balearic Islands for the period from 1997 to 2010 has been employed. The D values obtained ranged between 1.4499 for the observatory in Ibiza and 1.6039 for the observatory in Jaca. The fractal dimension presents a significant and good negative correlation (−0.55) with the concentration index (CI), and a significant and good positive correlation (0.67) with entropy. The correlation of D with other traditionally used indices, such as the coefficient of variation or the consecutive disparity index is very limited, as this indicator is more focused on the distribution of precipitation intervals than on the total accumulated rainfall over a given period. In an endeavour to develop multivariate models that explain the behaviour of D, only two-variable models can be obtained, which account for most of the variability and that involve the CI or entropy. Self-similarity is therefore associated with the regular recurrence of precipitation intervals, which is more evident in those observatories with higher D values.