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A Cox process with State-Dependent exponential pulses to model rainfall

A Cox process with State-Dependent exponential pulses to model rainfall

Ramesh, Nadarajah ORCID: 0000-0001-6373-2557, Rode, Gayatri and Onof, Christian (2022) A Cox process with State-Dependent exponential pulses to model rainfall. Water Resources Management, 36:378. pp. 297-313. ISSN 0920-4741 (Print), 1573-1650 (Online) (doi:

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A point process model based on a class of Cox processes is developed to analyse precipitation data at a point location. The model is constructed using state-dependent exponential pulses that are governed by an unobserved underlying Markov chain. The mathematical formulation of the model where both the arrival rate of the rain cells and the initial pulse depth are determined by the Markov chain is presented. Second-order properties of the rainfall depth process are derived and utilised in model assessment. A method of moment estimation is employed in model fitting. The proposed model is used to analyse 69 years of sub-hourly rainfall data from Germany and 15 years of English rainfall data. The results of the analysis using variants of the proposed model with fixed pulse lifetime and variable pulse duration are presented. The performance of the proposed model, in reproducing second-moment characteristics of the rainfall, is compared with that of two stochastic models where one has exponential pulses and the other has rectangular pulses. The proposed model is found to capture most of the empirical rainfall properties well and outperform the two alternative models considered in our analysis.

Item Type: Article
Uncontrolled Keywords: Cox process model; exponential pulse; rainfall; second-order properties
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Faculty / School / Research Centre / Research Group: Faculty of Engineering & Science
Faculty of Engineering & Science > Mathematical Modelling for Engineering Research Theme
Faculty of Engineering & Science > School of Computing & Mathematical Sciences (CMS)
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Last Modified: 10 Feb 2022 11:01

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