Space–time multifractality of remotely sensed rainfall fields

Deidda, Roberto; Badas, Maria Grazia; Piga, Emanuela

doi:10.1016/j.jhydrol.2005.02.036

Cited by 54 publications

(41 citation statements)

References 19 publications

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“…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.…”

Section: Discrete Beta-logstable (Bls) Canonical Modelmentioning

confidence: 99%

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

Serinaldi

2010

Nonlin. Processes Geophys.

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Abstract. Discrete multiplicative random cascade (MRC) models were extensively studied and applied to disaggregate rainfall data, thanks to their formal simplicity and the small number of involved parameters. Focusing on temporal disaggregation, the rationale of these models is based on multiplying the value assumed by a physical attribute (e.g., rainfall intensity) at a given time scale L, by a suitable number b of random weights, to obtain b attribute values corresponding to statistically plausible observations at a smaller L/b time resolution. In the original formulation of the MRC models, the random weights were assumed to be independent and identically distributed. However, for several studies this hypothesis did not appear to be realistic for the observed rainfall series as the distribution of the weights was shown to depend on the space-time scale and rainfall intensity. Since these findings contrast with the scale invariance assumption behind the MRC models and impact on the applicability of these models, it is worth studying their nature. This study explores the possible presence of dependence of the parameters of two discrete MRC models on rainfall intensity and time scale, by analyzing point rainfall series with 5-min time resolution. Taking into account a discrete microcanonical (MC) model based on beta distribution and a discrete canonical beta-logstable (BLS), the analysis points out that the relations between the parameters and rainfall intensity across the time scales are detectable and can be modeled by a set of simple functions accounting for the parameterrainfall intensity relationship, and another set describing the link between the parameters and the time scale. Therefore, MC and BLS models were modified to explicitly account for these relationships and compared with the continuous in Correspondence to: F. Serinaldi (f.serinaldi@unitus.it) scale universal multifractal (CUM) model, which is used as a physically based benchmark model. Monte Carlo simulations point out that the dependence of MC and BLS parameters on rainfall intensity and cascade scales can be recognized also in CUM series, meaning that these relations cannot be considered as a definitive sign of departure from multifractality. Even though the modified MC model is not properly a scaling model (parameters depend on rainfall intensity and scale), it reproduces the empirical traces of the moments and moment exponent function as effective as the CUM model. Moreover, the MC model is able to reproduce some rainfall properties of hydrological interest, such as the distribution of event rainfall amount, wet/dry spell length, and the autocorrelation function, better than its competitors owing to its strong, albeit unrealistic, conservative nature. Therefore, even though the CUM model represents the most parsimonious and the only physically/theoretically consistent model, results provided by MC model motivate, to some extent, the interest recognized in the literature for this type of discrete models.

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Section: Discrete Beta-logstable (Bls) Canonical Modelmentioning

confidence: 99%

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

Serinaldi

2010

Nonlin. Processes Geophys.

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“…Accurate rainfall field 86 simulation requires knowledge of rainfall rate variability in both space and time domains. There is not enough research in the 87 area of space-time interpolation apart from a few works, such as (Deidda, 2006). Thus, an appropriate space-time interpolation 88 model that can preserve the underlying statistical properties at finer scales is needed.…”

Section: ) 70mentioning

confidence: 99%

A New Approach for Rainfall Rate Field Space-Time Interpolation for Western Europe

Yang

Ndzi

Paulson

et al. 2018

Preprint

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Abstract. The prediction of rainfall rate characteristics at small space-time scales is currently an important topic, particularly within the context 10 of the planning and design of satellite network systems. A new comprehensive interpolation approach is presented in this paper to deal with 11 such an issue. There are three novelties in the proposed approach: 1) the proposed interpolation approach is not directly applied to measured 12 rain precipitation (either radar or raingauge-derived data) but focuses on the coefficients of the fitted statistical distributions and/or computed 13 rain characteristics at each location; 2) the parameter databases are provided and the contour maps of coefficients spanning Western Europe 14 have been created. It conveniently and efficiently provides the rain parameter for any location within the studied map; 3) more speculatively, 15 the space-time interpolation approach can extrapolate to rain parameters at space-time resolutions shorter than those in the NIMROD 16 databases.

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“…The form of the Eq. (13) is the same of the one used to interpret the c behaviour for GATE, TOGA-COARE, and TRMM-LBA sequences (Deidda, 2000;Deidda et al, 2004Deidda et al, , 2006. Estimates of the c parameter obtained for these radar campaigns are displayed in Fig.…”

Section: Scale Invariant Properties On Rainfall Events Extracted On Amentioning

confidence: 99%

“…Analyzing a transect along the Southern Alps of New Zealand, Harris et al (1996) and Purdy et al (2001) found a dependence of scaling parameters on orography and rain features. More recently Deidda et al (2006) investigated the presence of rainfall spatial heterogeneity induced by orography on rainfall fields retrieved over Brazil by radars (TRMM-LBA, Tropical Rainfall Measurement Mission -Large Scale Biosphere Atmosphere Experiment). Nevertheless this analysis did not highlight the presence of any spatial heterogeneity, probably because of the absence of orographic barriers that could significantly force upward air movements.…”

Section: Introductionmentioning

confidence: 99%

Modulation of homogeneous space-time rainfall cascades to account for orographic influences

Badas

Deidda

Piga

2006

Nat. Hazards Earth Syst. Sci.

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Abstract. The development of efficient space-time rainfall downscaling procedures is highly important for the implementation of a meteo-hydrological forecasting chain operating over small watersheds. Multifractal models based on homogeneous cascade have been successfully applied in literature to reproduce space-time rainfall events retrieved over ocean, where the hypothesis of spatial homogeneity can be reasonably accepted. The feasibility to apply this kind of models to rainfall fields occurring over a mountainous region, where spatial homogeneity may not hold, is herein investigated. This issue is examined through the analysis of rainfall data retrieved by the high temporal resolution rain gage network of the Sardinian Hydrological Survey. The proposed procedure involves the introduction of a modulating function which is superimposed to homogeneous and isotropic synthetic fields to take into account the spatial heterogeneity detected in observed precipitation events. Specifically the modulating function, which reproduces the differences in local mean values of the precipitation intensity probability distribution, has been linearly related to the terrain elevation of the analysed spatial domain. Comparisons performed between observed and synthetic data show how the proposed procedure preserves the observed rainfall fields features and how the introduction of the modulating function improves the reproduction of spatial heterogeneity in rainfall probability distributions.

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Space–time multifractality of remotely sensed rainfall fields

Cited by 54 publications

References 19 publications

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

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

A New Approach for Rainfall Rate Field Space-Time Interpolation for Western Europe

Modulation of homogeneous space-time rainfall cascades to account for orographic influences

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