Statistical linguistic characterization of variability in observed and synthetic daily precipitation series

This paper deals with an application of Zipf law in climatology. This analysis allows the extraction of information not available by standard methods. In particular, rainfall temporal aggregation patterns associated with different climates are characterized by means of exponents derived from the resulting scaling laws. The analogy with linguistic analysis is obtained using a particular coding of precipitation as a discrete variable with four states (corresponding to four standard precipitation thresholds); each weekly symbolic sequence of observed precipitation is considered as a “word”, and each local station defines a “language” characterized by the observed words in a period representative of the climatology. To characterize these precipitation languages, we obtained characteristic exponents derived from the Zipf law for a set of representative stations of the main Köppenʹs climates and subclimates. We found different scaling behaviors for different subclimates, given by a single exponent in the range 0.6 (humid tropical climates) to 1.4 (polar climates); some humid middle-latitude subclimates exhibit a crossover with two different characteristic exponents corresponding to high and low frequency aggregation patterns (no explanation for this behavior is provided). As an application of the proposed methodology, the same analysis was applied to stochastic time series obtained from standard weather generators. We found that the language defined by a first-order Markov process agrees with the observed language of the observed series.