Multifractal analysis as a tool for validating a rainfall model

García‐Marín, A. P.; Jiménez‐Hornero, Francisco J.; Ayuso-Muñoz, J. L.

doi:10.1002/hyp.6864

Cited by 19 publications

(10 citation statements)

References 46 publications

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“…The universal parameters estimated were similar to those obtained from previous analyses of local rainfall measured at the observation stations (Labat et al 2002, Tessier et al 1996, García-Marin et al 2008). The changes produced in both non-overlapping periods are shown in Table 2.…”

Section: Comparison Between 1957-1979 and 1980-2002supporting

confidence: 81%

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A universal multifractal description applied to precipitation patterns of the Ebro River Basin, Spain

Valencia¹,

Saá-Requejo²,

Gascó³

et al. 2010

Clim. Res.

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Water supplies in the Ebro River Basin are increasingly stressed, especially during the summer season. The year-to-year fluctuations in rainfall over this area exert vital influence on the regional hydrology, agriculture and several related industries in the region. Repeated anomalous rainfall in recent decades has had a devastating impact on this region, both socially and economically. We characterised the change in the rainfall variability pattern in the Ebro River Basin using universal multifractal (UM) analysis, which estimates the concentration of the data around the precipitation average (C 1 , codimension average), the degree of multiscaling behaviour in time (α index) and the maximum probable singularity in the rainfall distribution (γ s ). Fourteen meteorological stations were selected based on the length of rainfall series and the climatic classification to obtain a representative untreated data set from the river basin. Daily rainfall series from 1957 to 2002 were obtained from each meteorological station and subdivided (1957-1980 and 1981-2002) to analyse the difference between the 2 periods. The general scenario observed in this study, through the UM parameters, can be summarised as follows: the range of variation of precipitation amounts was spatially more homogenous in 1980-2002 than in 1957-1979; at the same time, there is higher frequency of dry periods at different scales in 1980-2002; and in almost all of the stations, the range of precipitation over the years has been decreasing at a lower rate than the rainfall average. We then analysed the evolution of the UM parameters from 1957 to 2002. Continuous variations in C 1 and α were found for 2 of the stations, indicating that a precipitation regime change has begun in the last few decades and should be considered in the agricultural development of the region.

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Section: Comparison Between 1957-1979 and 1980-2002supporting

confidence: 81%

“…The statistical multifractal nature of rain has been studied intensively (Tessier et al 1996, Harris et al 1997, Labat et al 2002, García-Marin et al 2008. One of the most important characteristics of multifractality is the self-similarity or invariance with the observation scale (λ).…”

Section: Multifractal Analysismentioning

confidence: 99%

A universal multifractal description applied to precipitation patterns of the Ebro River Basin, Spain

Valencia¹,

Saá-Requejo²,

Gascó³

et al. 2010

Clim. Res.

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“…The model has also been applied to hydraulic conductivity (Tennekoon et al, 2003) and log hydraulic conductivity (Liu and Molz, 1997a) data, space-time infiltration (Meng et al, 2006), river runoff (Koscielny-Bunde et al, 2006), rain-drop sizes and positions (Lilley et al, 2006) and soil properties (Zeleke and Si, 2006). Analyses which do not fit any specific model to q or K q include those of DeBartolo et al (2006) on river networks and braided channels, Roy and Padhi (2007) on earthquakes in Iran, García-Marín et al (2008) on validating a rainfall model, and Movahed and Hermanis (2008) and Zhang et al (2008Zhang et al ( , 2009) on streamflows. Modelfree analyses using wavelets have been described in the context of rainfall (Venugopal et al, 2006;Gan et al, 2007), soil water retention (Zeleke and Si, 2007), the area and width functions of river networks (Lashermes and Foufoula-Georgiou, 2007), and sediment transport (Singh et al, 2009).…”

Section: Multifractalitymentioning

confidence: 99%

Apparent/spurious multifractality of data sampled from fractional Brownian/Lévy motions

Neuman

2010

Hydrological Processes

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Abstract:Many earth and environmental variables appear to be self-affine (monofractal) or multifractal with spatial (or temporal) increments having exceedance probability tails that decay as powers of ˛where 1 <˛Ä 2. The literature considers selfaffine and multifractal modes of scaling to be fundamentally different, the first arising from additive and the second from multiplicative random fields or processes. We demonstrate theoretically that data having finite support, sampled across a finite domain from one or several realizations of an additive Gaussian field constituting fractional Brownian motion (fBm) characterized by˛D 2, give rise to positive square (or absolute) increments which behave as if the field was multifractal when in fact it is monofractal. Sampling such data from additive fractional Lévy motions (fLm) with 1 <˛< 2 causes them to exhibit spurious multifractality. Deviations from apparent multifractal behaviour at small and large lags are due to nonzero data support and finite domain size, unrelated to noise or undersampling (the causes cited for such deviations in the literature). Our analysis is based on a formal decomposition of anisotropic fLm (fBm when˛D 2) into a continuous hierarchy of statistically independent and homogeneous random fields, or modes, which captures the above behaviour in terms of only E C 3 parameters where E is Euclidean dimension. Although the decomposition is consistent with a hydrologic rationale proposed by Neuman (2003), its mathematical validity is independent of such a rationale. Our results suggest that it may be worth checking how closely would variables considered in the literature to be multifractal (e.g. experimental and simulated turbulent velocities, some simulated porous flow velocities, landscape elevations, rain intensities, river network area and width functions, river flow series, soil water storage and physical properties) fit the simpler monofractal model considered in this paper (such an effort would require paying close attention to the support and sampling window scales of the data). Parsimony would suggest associating variables found to fit both models equally well with the latter.

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“…() on river networks and braided channels, Roy and Padhi () on earthquakes in Iran, García‐Marín et al . () on validating a rainfall model, and Movahed and Hermanis () and Zhang et al . () on streamflows.…”

Section: Introductionmentioning

confidence: 98%

“…Their multiplicative cascade model, termed universal by the authors, has been applied (among others) to hydraulic conductivity (Tennekoon et al, 2003) and log hydraulic conductivity (Liu and Molz, 1997a) data, space-time infiltration (Meng et al, 2006), river runoff (Koscielny-Bunde et al, 2006), raindrop sizes and positions (Lilley et al, 2006) and soil properties (Zeleke and Si, 2006). Other multifractal studies include those of DeBartolo et al (2006) on river networks and braided channels, Roy and Padhi (2007) on earthquakes in Iran, García-Marín et al (2008) on validating a rainfall model, and Movahed and Hermanis (2008) and Zhang et al (2008Zhang et al ( , 2009) on streamflows. Multifractal analyses based on wavelets have been applied to rainfall (Venugopal et al, 2006;Gan et al, 2007), soil water retention (Zeleke and Si, 2007), the area and width functions of river networks (Lashermes and Foufoula-Georgiou, 2007), and sediment transport .…”

Section: Introductionmentioning

confidence: 99%

Numerical investigation of apparent multifractality of samples from processes subordinated to truncated fBm

Guadagnini

Neuman

Riva

2011

Hydrological Processes

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Abstract:We investigate numerically apparent multi-fractal behavior of samples from synthetically generated processes subordinated to truncated fractional Brownian motion (tfBm) on finite domains. We are motivated by the recognition that many earth and environmental (including hydrological) variables appear to be self-affine (monofractal) or multifractal with Gaussian or heavy-tailed distributions. The literature considers self-affine and multifractal types of scaling to be fundamentally different, the first arising from additive and the second from multiplicative random fields or processes. It has been demonstrated theoretically by one of us that square or absolute increments of samples from Gaussian/Lévy processes subordinated to tfBm exhibit apparent/ spurious multifractality at intermediate ranges of separation lags, with breakdown in power-law scaling at small and large lags as is commonly exhibited by real data. A preliminary numerical demonstration of apparent multifractality by the same author was limited to Gaussian fields having nearest neighbor autocorrelations and led to rather noisy results. Here, we adopt a new generation scheme that allows us to investigate apparent multifractal behaviors of samples taken from a broad range of processes including Gaussian with and without symmetric Lévy and log-normal (as well as potentially other) subordinators. Our results shed new light on the nature of apparent multifractality, which has wide implications vis-a-vis the scaling of many hydrological as well as other earth and environmental variables.

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Multifractal analysis as a tool for validating a rainfall model

Cited by 19 publications

References 46 publications

A universal multifractal description applied to precipitation patterns of the Ebro River Basin, Spain

A universal multifractal description applied to precipitation patterns of the Ebro River Basin, Spain

Apparent/spurious multifractality of data sampled from fractional Brownian/Lévy motions

Numerical investigation of apparent multifractality of samples from processes subordinated to truncated fBm

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