Abstract
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 statistics are obtained using closed form analytical expressions for statistics of the orders 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 the optimal model fitting of RBL1 and RBL2. The first issue 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 past papers. The second issue 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.
Highlights
Rainfall is the main input to a range of models in geophysics such as hydrological catchment models, sewerage discharge models and erosion models
Models randomised Bartlett–Lewis model version 1 (RBL1) and randomised Bartlett–Lewis model version 2 (RBL2) are fitted using the original equations for these models
These equations are not shown in this paper, they are contained in the new sets of equations given above: for each statistic, the first equation given is that found in the past papers, with its domain of validity for α
Summary
Rainfall is the main input to a range of models in geophysics such as hydrological catchment models, sewerage discharge models and erosion models. A second homogeneous Poisson process defines the cell arrival times over a duration of storm activity that defines a random variable (see Onof and Wheater, 1993; Khaliq and Cunnane, 1996; Verhoest et al, 1997; Kossieris et al, 2018) For both Poisson cluster processes, the SMSAs are represented by rectangular pulses corresponding to a random constant rainfall intensity over a random duration. The most promising ways forward in this respect come from combining the Poisson cluster model with a coarse-scale model that captures much of the longerterm variability (Park et al, 2019) or from letting climatological information guide the weighting to be assigned to different months in the data in calibrating the model (Kaczmarska et al, 2015; Cross et al, 2020) For the purpose of the numerical investigation of estimators, Greenwich (14.5 years of 5 min data from February 1987 to July 2001) data are used
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