Chaos game characterization of temporal precipitation variability:: Application to regionalization

We present an application of the fractal chaos game representation method in climatology for characterizing temporal precipitation aggregation patterns. To this aim, we establish an analogy with linguistic analysis considering precipitation as a discrete variable (e.g. rain, no rain). Each weekly, or monthly, symbolic sequence of observed precipitation is then considered a word and the climatological time series observed at a particular gauge defines a language. The distribution of different words within the language characterizes the particular precipitation aggregation scheme. In this paper we show that the chaos game representation method provides a graphical representation (a fractal pattern, or fingerprint) of the distribution of words and also gives a quantitative characterization in terms of parameters such as the box-counting dimension and the entropy. We show that different climates exhibit characteristic patterns with different fractal exponents and entropies. As an illustrative application, the method is used for automatic regionalization of a set of gauges in the Iberian peninsula, showing that these new indices outperform standard averaged statistics (monthly means, etc.).