Estimating rainfall distributions at high temporal resolutions using a multifractal model

Abstract

Rainfall data from 18 stations in the vicinity of Tokyo city, measured to a precision of 1 mm, were analysed for multifractal properties. A multifractal model based on the scaling properties of temporal distribution of rainfall intensities was formulated to investigate the intensity distribution relationships in the available scaling regime. Although conventional analysis did not provide encouraging results with these measurements, an alternative approach that could be applied to rainfall data of widely variable quality and duration was used to establish a scaling relationship between daily and hourly rainfall intensities. Using a discrete cascade algorithm based on the log-Lèvy generator, synthetic hourly rainfall series were generated from the multifractal statistics of daily-accumulated rainfall. Several properties of rainfall time series that are relevant to the use of rainfall data in surface hydrological studies were used to determine, statistically, the degree of agreement between the synthetic hourly series and observed hourly rainfall.

Multifractality, imperfect scaling and hydrological properties of rainfall time series simulated by continuous universal multifractal and discrete random cascade models

“…As these inter-arrival times 710 F. Serinaldi: Modeling scaling and imperfect scaling in rainfall time series were longer than the typical evolution time of the storms for the specific climatic region (≈5-6 h on an average), a value of seven hours was adopted. This value is equal to or coherent with that applied by Salvadori and De Michele (2001) for a similar climate, and by Koutsoyiannis and Pachakis (1996) and Pathirana et al (2003) for different climates.…”

“…The probability p 0 describes the lacunarity and is related to the fractal dimension of the series, whereas the distribution G of the positive weights is often assumed to be lognormal (e.g., Gupta and Waymire, 1993;Molnar and Burlando, 2005), log-Poisson (e.g., Deidda et al, 1999Deidda et al, , 2006Deidda, 2000;Onof et al, 2005;Sivakumar and Sharma, 2008;Mascaro et al, 2010) or logstable (e.g., Schertzer and Lovejoy, 1987;Olsson, 1995;Pathirana et al, 2003;Veneziano et al, 2006). It should be noted that the hypothesis of existence of a fractal support is alternative to the assumption of a low threshold for the measurable rainfall intensity, allowing for a cross-check of the two hypotheses.…”

Analysis and modelling of rainfall fields at different resolutions in southern Italy

“…This approach is a standard tool for rainfall downscaling and has been applied by several authors. In particular, for rainfall time series, Güntner et al (2001) reproduced hourly rainfall from daily data sets concerning Brazil and the UK; Pathirana et al (2003) obtained hourly rainfall data from daily measurements for 18 stations close to Tokyo city, in Japan; Hingray and Ben Haha (2005) tested several disaggregation models, including random cascades, for the generation of 10-min rainfall time series from hourly rainfall heights observed at Pully, in Switzerland; Molnar and Burlando (2005) generated 10-min rainfall data referring to a raingauge located in Zurich, Switzerland; Paulson and Baxter (2007) generated a 10-s rainfall time series from lowerresolution data observed in the UK; Sivakumar and Sharma (2008) disaggregated daily time series into a 3-h data set; Rupp et al (2009) obtained hourly data from a daily set observed at the Christchurch Airport gauge in New Zealand; Licznar et al (2011) disaggregated quasi-daily rainfall data into 5-min time series for the raingauge located at Wroclaw, in Poland. An extensive theoretical review of the random cascade model is provided by Veneziano et al (2006b).…”

Multifractal analysis as a tool for validating a rainfall model

“…Thus, an area can be classified depending on the amount of precipitation it receives (Strahler and Strahler, 1978). Rainfall intensities increase in magnitude as the temporal accumulation length (time scale) decreases (Pathirana et al, 2003). This relation can be easily observed with the intensity-duration-frequency (IDF) curves, which are very useful for hydrology risk analysis and design (Eagleson, 1970;Chow et al, 1988;Veneziano and Furcolo, 2002;Veneziano et al, 2006b).…”