Multifractality, imperfect scaling and hydrological properties of rainfall time series simulated by continuous universal multifractal and discrete random cascade models
Notice bibliographique
Résumé
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 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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Comment cette classification a été obtenuedéplier
Prédiction machine sur la base complète
Imitation des enseignantsNi prévalence calibrée, ni vérité terrain. Validation humaine à venir. Le volet Gemma est une étiquette directe du modèle pour chaque travail de la base, lue sur la notice réduite au titre. Le volet Codex est un classifieur appris des 10 348 étiquettes directes de Codex et calibré sur les taux pondérés de l'échantillon; les champs sans appui suffisant ne portent aucun appel Codex. Le mode candidate est l'union des deux volets; le consensus est leur intersection. Ces sorties portent le statut machine_predicted_unvalidated et ne sont pas des étiquettes humaines.
Scores du classifieur distillé par catégorie (deux têtes)
| Catégorie | Codex | Gemma |
|---|---|---|
| Métarecherche | 0,001 | 0,004 |
| Méta-épidémiologie (sens strict) | 0,000 | 0,000 |
| Méta-épidémiologie (sens large) | 0,000 | 0,001 |
| Bibliométrie | 0,001 | 0,000 |
| Études des sciences et des technologies | 0,000 | 0,001 |
| Communication savante | 0,001 | 0,001 |
| Science ouverte | 0,001 | 0,000 |
| Intégrité de la recherche | 0,001 | 0,000 |
| Charge utile insuffisante (le modèle a refusé de juger) | 0,001 | 0,000 |
Scores machine (provisoires)
Les deux têtes enseignantes du modèle étudiant, lues sur ce travail. Un score ordonne la base pour la relecture; il n'affirme jamais une catégorie, et le statut de validation accompagne chaque rangée tel quel.
Scores de référence d'un modèle non mature (critères de maturité non atteints, 7 itérations). Un score ordonne; il n'affirme jamais une catégorie.
score_only:v0-immature-baseline · tel quel depuis la passe de notation : score_only signifie que le nombre peut ordonner les travaux, et qu'aucune étiquette de catégorie n'en découleClassification
machine, non validéePrédiction automatique; un appel candidat d’une seule source (Gemma direct ou Codex distillé), pas un consensus.
Le détail, modèle par modèle et score par score, se trouve en fin de page sous « Comment cette classification a été obtenue ».