Downscaling of rain gauge time series by multiplicative beta cascade

Paulson, Kevin; Baxter, Paul D.

doi:10.1029/2006jd007333

Cited by 31 publications

(31 citation statements)

References 25 publications

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“…In order to correct this bias, Veneziano et al (2006) have applied an iterative estimation procedure that adjusts the parameters estimated on the dressed process so that the K(q) function of the simulated (disaggregated) series reproduces that of the observed series. Paulson and Baxter (2007) have used a similar approach, wherein, the objective function of an optimization process is the sum of the absolute differences between the second and third moments of the measured rainfall time series across the considered scales. In this study, to point out the impact of the model structure (canonical and microcanonical) on the bias of the estimates, any bias correction is applied.…”

Section: Discrete Beta-logstable (Bls) Canonical Modelmentioning

confidence: 99%

“…As the bare process R b,k is not really observed, weights W can only be estimated by the reverse dressed process R k . In general, the statistics of the bare rainfall provide biased estimates of the dressed rainfall, and vice versa (e.g., Lovejoy and Schertzer, 1995;Veneziano et al, 2006;Paulson and Baxter, 2007). In order to correct this bias, Veneziano et al (2006) have applied an iterative estimation procedure that adjusts the parameters estimated on the dressed process so that the K(q) function of the simulated (disaggregated) series reproduces that of the observed series.…”

Section: Discrete Beta-logstable (Bls) Canonical Modelmentioning

confidence: 99%

“…The interest in discrete MRC models is related to their simplicity compared to more complex approaches, as well as to their link to the energy transfer processes in turbulent flows (Kolmogorov, 1941(Kolmogorov, , 1991Schertzer and Lovejoy, 1987;Veneziano et al, 2006;Paulson and Baxter, 2007). However, these models can be considered as the "first generation" of MRC models (Lovejoy and Schertzer, 2010a), while more realistic results are provided by the "second generation" of continuous in scale multifractal processes based on Lévy stable random variables (e.g., Lovejoy, 1987, 1997;Lovejoy and Schertzer, 1995;Lovejoy et al, 2008).…”

Section: Introductionmentioning

confidence: 99%

“…However, as discussed by Veneziano et al (2006), even though the multiplicative combination of the weights W is generally supported by empirical evidence Veneziano et al, 2006), commonly the iid assumption does not seem to be realistic. Cascade weights have been found to be dependent on scale (Veneziano et al, 1996;Menabde et al, 1997;Menabde and Sivapalan, 2000;Molnar and Burlando, 2005;Paulson and Baxter, 2007), on covariates such as large-scale rainfall intensity (Over andGupta, 1994, 1996;Deidda, 2000;Molnar and Burlando, 2005), and on the interval class, i.e. intervals at the beginning, middle, or end of a rainfall event (Olsson, 1998;Olsson and Berndtsson, 1998;Güntner et al, 2001;Veneziano and Iacobellis, 2002).…”

Section: Introductionmentioning

confidence: 99%

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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%

Section: Discrete Beta-logstable (Bls) Canonical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…Empirical investigation of the scaling behaviour does indeed show that not all rainfall fields obey the basic assumption that the increments of ε between scales are i.i.d. Divergences from this behaviour were described by various authors who observed that the increments were dependent on factors such as large-scale rainfall intensity (Deidda, 2000;Over and Gupta, 1994) and pixel size (Menabde et al, 1997;Over and Gupta, 1994;Paulson and Baxter, 2007). Additionally, scaling behaviour was found to differ with the intensity of storms (Venugopal et al, 2006) and thus the nonraining intervals do not scale (Olsson, 1998).…”

Section: Introductionmentioning

confidence: 94%

Imperfect scaling in distributions of radar-derived rainfall fields

Berg

Delobbe

Verhoest

2014

Hydrol. Earth Syst. Sci.

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Abstract. Fine-scale rainfall observations for modelling exercises are often not available, but rather coarser data derived from a variety of sources are used. Effectively using these data sources in models often requires the probability distribution of the data at the applicable scale. Although numerous models for scaling distributions exist, these are often based on theoretical developments, rather than on data. In this study, we develop a model based on the α-stable distribution of rainfall fields, and tested on 5 min radar data from a Belgian weather radar. We use these data to estimate functions that describe parameters of the distribution over various scales. Moreover, we study how the mean of the distribution and the intermittency change with scale, and validate and design functions to describe the shape parameter of the distribution. This information was combined into an effective model of the distribution.

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Statistical framework to simulate daily rainfall series conditional on upper-air predictor variables

Langousis

Kaleris

2014

Water Resour. Res.

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We propose a statistical framework to generate synthetic rainfall time series at daily resolution, conditional on predictor variables indicative of the atmospheric circulation at the mesoscale. We do so by first introducing a dimensionless measure to assess the relative influence of upper-air variables at different pressure levels on ground-level rainfall statistics, and then simulating rainfall occurrence and amount by proper conditioning on the selected atmospheric predictors. The proposed scheme for conditional rainfall simulation operates at a daily time step (avoiding discrete approaches for identification of weather states), can incorporate any possible number and combination of predictor variables, while it is capable of reproducing rainfall seasonality directly from the variation of upper-air variables, without any type of seasonal analysis or modeling. The suggested downscaling approach is tested using atmospheric data from the ERAInterim archive and daily rainfall measurements from western Greece. The model is found to accurately reproduce several statistics of actual rainfall time series, at both annual and seasonal levels, including wet day fractions, the alternation of wet and dry intervals, the distributions of dry and wet spell lengths, the distribution of rainfall intensities in wet days, short-range dependencies present in historical rainfall records, the distribution of yearly rainfall maxima, dependencies of rainfall statistics on the observation scale, and long-term climatic features present in historical rainfall records. The suggested approach is expected to serve as a useful tool for stochastic rainfall simulation conditional on climate model outputs at a regional level, where climate change impacts and risks are assessed.

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Downscaling of rain gauge time series by multiplicative beta cascade

Cited by 31 publications

References 25 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

Imperfect scaling in distributions of radar-derived rainfall fields

Statistical framework to simulate daily rainfall series conditional on upper-air predictor variables

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