Impact of integration time steps of rain drop size distribution on their structuring and their modelling: a case study in northern Benin

Abstract

This paper focused on modelling rain drop size distributions (DSDs) of various integration time steps using unimodal DSD models (gamma and lognormal). Rain DSD data considered are those collected from 2005 to 2007 near Djougou city in the north-western region of Benin Republic. The efficiency of these models was characterized by statistical criteria, mainly Nash and KGE. These criteria are used to assess the level of fitting of rain DSD spectra. Superimposed rain DSDs were then parameterized with the rainfall rate, using the scaling law formalism. Results show that there is an improvement in the structuring of the rain DSDs according to their measurement duration. Analysis of the occurrence statistics of the structuring of the spectra reveals that the Spectra ill adjusted by a unimodal DSD model represents 5 to 15% of the population of 1 min rain DSDs. This population decreases according to the measurement duration of the spectra. The optimal measurement time is found to be 10 min. Furthermore, parameters of the shape functions (gamma and lognormal) increase or decrease markedly according to the measurement duration of the rain DSD spectra. For applications using the relationships deduced from the rain DSDs, results suggested that the measurement time scale must be taken into account when choosing appropriate relationships.

Keywords

• Rain DSD
• Scaling law
• Unimodal DSD models
• Rainfall
• Parameterization
• Integration time steps
• West Africa