Preliminary Multifractal Rainfall Analysis in the Tunis Region

This study investigates the scaling properties of rainfall in Tunis over temporal scales ranging from 5 min to 2.5 years using high-resolution rain gauge data from three recording stations. We employ the Universal Multifractal (UM) framework to characterize scaling properties across multiple temporal regimes. The UM model was selected over alternative multifractal approaches because of its parsimonious three-parameter formulation (C1, α, H). It explicitly accounts for non-conservative processes through the Fractionally Integrated Flux (FIF) extension and includes established bias correction methods for highly intermittent signals. This framework has demonstrated universality across diverse climatic conditions and enables direct comparison with existing rainfall studies in Mediterranean environments. Spectral analysis reveals three distinct scaling regimes: micro-scale (5 min–2 h 40 min), meso-scale (2 h 40 min–7 days), and synoptic scale (>7 days). The non-conservative nature of the micro-scale regime is addressed through a multifractal fractionally integrated flux model. A key challenge in applying UM analysis to rainfall data is the prevalence of low and zero rain rates (>98% zeros in our dataset). This extreme intermittency introduces significant bias in parameter estimation. Existing correction methods require either continuous rain sequences—scarce in semi-arid climates—or are limited to moderate intermittency levels. We propose an empirical correction method that extends the existing semi-empirical approach by explicitly linking the percentage of zero values to biased UM parameters through empirical relationships applicable to sequences with as few as 50% rainy observations. This advancement enables reliable parameter estimation from highly intermittent datasets. In such conditions, traditional event-by-event analysis yields insufficient samples (only five continuous events longer than 2 h 40 min over 2.5 years in Tunis). The corrected estimates (α = 1.63, C1 = 0.16 for micro-scales) demonstrate strong consistency with continuous rainfall events and align well with high-resolution studies, validating our approach for extreme intermittency conditions characteristic of Mediterranean semi-arid climates.