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Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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Discussion papers
https://doi.org/10.5194/hess-2019-406
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-2019-406
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: research article 12 Aug 2019

Submitted as: research article | 12 Aug 2019

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Hydrology and Earth System Sciences (HESS).

Modelling rainfall with a Bartlett–Lewis process: New developments

Christian Onof and Li-Pen Wang Christian Onof and Li-Pen Wang
  • Department of Civil and Environmental Engineering, Imperial College London, SW7 2AZ, UK

Abstract. The use of Poisson-cluster processes to model rainfall time series at a range of scales now has a history of more than 30 years. Among them, the Randomised (also called modified) Bartlett–Lewis model (RBL1) is particularly popular, while a refinement of this model was proposed recently (RBL2) (Kaczmarska et al., 2014). Fitting such models essentially relies upon minimising the difference between theoretical statistics of the rainfall signal and their observed estimates. The first are obtained using closed form analytical expressions for statistics of order 1 to 3 of the rainfall depths, as well as useful approximations of the wet-dry structure properties. The second are standard estimates of these statistics for each month of the data. This paper discusses two issues that are important for optimal model fitting of the RBL1 and RBL2. The first is that, when revisiting the derivation of the analytical expressions for the rainfall depth moments, it appears that the space of possible parameters is wider than has been assumed in the past papers. The second is that care must be exerted in the way monthly statistics are estimated from the data. The impact of these two issues upon both models, in particular upon the estimation of extreme rainfall depths at hourly and sub-hourly timescales is examined using 69 years of 5-min and 105 years of 10-min rainfall data from Bochum (Germany) and Uccle (Belgium), respectively.

Christian Onof and Li-Pen Wang
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Status: open (until 07 Oct 2019)
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Christian Onof and Li-Pen Wang
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Short summary
The randomised Bartlett–Lewis (RBL) model is widely-used to synthesise rainfall time series with realistic statistical features. However, it tends to underestimate rainfall extremes at sub-hourly and hourly timescales. In this paper, we revisit the derivation of equations that represent rainfall properties and compare statistical estimation methods that impact model calibration. These changes largely improved RBL model's capacity to reproduce sub-hourly and hourly rainfall extremes.
The randomised Bartlett–Lewis (RBL) model is widely-used to synthesise rainfall time series with...
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