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An analytical examination of mathematical models for the rainfall rate distribution function

Étude analytique de modèles mathématiques pour la fonction de distribution des intensités de précipitation

Abstract

A large, digitized data base is employed in a detailed examination of the mathematical form of the point rainfall-rate distribution function. The optimum form is found to depend on both the data sampling rate and the rain rate limits considered. In general, the lognormal function appears to provide a very good approximation to the distribution. It is found, however, that a better fit is provided by piecewise power-law approximations to different portions of the distribution. As the sampling interval is reduced to the ultimate limit imposed by the tipping bucket itself, a single power relationship is found to provide the best fit over the range of rainfall rates from several mm/h to the observed upper limit.

Analyse

Un grand nombre de données numériques sont utilisées pour l’étude précise de l’expression mathématique de la distribution des intensités de pluie locales. La forme optimale dépend de la fréquence d’échantillonnage et des valeurs limites des intensités de précipitation. En général, la fonction log-normale semble donner une très bonne approximation de la distribution. On obtient cependant une meilleure représentation par la superposition d’approximations de loi de puissance à différentes parties de la distribution. Lorsque la période d’échantillonnage est réduite à la limite ultime imposée par l’élément basculant du pluviomètre, une seule loi de puissance fournit une bonne approximation pour les précipitations dont l’intensité va de quelques mm/h jusqu’aux limites supérieures observées.

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Segal, B. An analytical examination of mathematical models for the rainfall rate distribution function. Ann. Télécommunic. 35, 434–438 (1980). https://doi.org/10.1007/BF03003524

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Key words

  • Wave attenuation
  • Microwaves
  • Rain
  • Pluviometry
  • Statistical model

Mots clés

  • Affaiblissement onde
  • Hyperfréquence
  • Pluie
  • Pluviosité
  • Modèle statistique