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| Titel |
Multifractality, imperfect scaling and hydrological properties of rainfall time series simulated by continuous universal multifractal and discrete random cascade models |
| VerfasserIn |
F. Serinaldi |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 17, no. 6 ; Nr. 17, no. 6 (2010-12-08), S.697-714 |
| Datensatznummer |
250013759
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| Publikation (Nr.) |
 copernicus.org/npg-17-697-2010.pdf |
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| Zusammenfassung |
| 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 parameter-rainfall 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 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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