ASSESSING DEPENDENCE AMONG WEIGHTS IN A MULTIPLICATIVE CASCADE MODEL OF TEMPORAL RAINFALL

''Classical'' multifractal analysis shows, with a good degree of confi dence, that the fit of multiplicative cascades to rainfall time series is appropriate, at least from the point of view of preserving the f(a lpha) spectrum of scaling exponents. However, basing the analysis only on the f(alpha) curve allows only limited discrimination between diff erent types of cascade models; thus other descriptors with more discri minating power are needed. Also, the question of whether cascades with independent weights are appropriate for rainfall remains unanswered a nd needs to be addressed. In the present work we address this question and provide an assessment of the dependence structure among weights i n a multiplicative cascade model of temporal rainfall. We introduce a quantity based on oscillation coefficients (describing how many of the total n-tuples of the series are obeying a certain pattern up-down-up etc.), and find that this quantity is invariant under aggregation for a multiplicative cascade model and has the ability to depict the pres ence and type of correlation in the weights of the cascade generator. Application of this development to high-resolution temporal rainfall s eries consistently suggests the need for negative correlation in weigh ts of a binary multiplicative cascade in order-to match the oscillatio n coefficient structure of rainfall. This is interpreted as an indicat ion of dependence in the splitting mechanisms of intensities cascading over successive scales and might have important implications for rain fall modeling and process understanding.