The need of understanding and modeling the high space-time variability of rainfall fields produced a large amount of literature in the last thirty years. A parameter parsimonious approach to this problem is based on the empirical detection of some regularities in hydrological observations, such as the scale-invariance properties of rainfall (e.g. Lovejoy and Schertzer, 1985). Models following this approach are based upon the assumption of a power law dependence of all statistical moments on the scale of aggregation. That means scaling properties can provide simple relationships to link the statistical distribution of the rainfall process at different spatial and temporal scales, in the ranges of which the power-law assumption can be verified (Marani, 2005). This work focuses on the analysis of the scaling properties of rainfall time series from a high density rain gauge network covering the urban area of Rome. The network consists of 24 sites, and the gauge record at each site has 10-minute time resolution and about 16-year length (1992-2007). In the hypotheses of stationary monthly rainfall series and spatial homogeneity of the rainfall fields over the study area, the scale-invariance properties in the time domain of the studied rainfall are investigated within some specific scale intervals (temporal scaling regimes) by using different methods: q-moments, PDMS, autocovariance structure. Furthermore, a multiplicative random cascade model (Rupp et al., 2009) is calibrated on each scaling regime and then the statistical properties of the simulated time series are validated with the observations.
Volpi, E., Napolitano, F., Lombardo, F. (2010). Investigating the scaling regimes of rainfall time series from a dense rain gauge network. In International Workshop on Advances in Statistical Hydrology.