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Doubly stochastic Poisson pulse model for fine-scale rainfall

Doubly stochastic Poisson pulse model for fine-scale rainfall

Thayakaran, R. and Ramesh, N.I. (2016) Doubly stochastic Poisson pulse model for fine-scale rainfall. Stochastic Environmental Research and Risk Assessment, 31 (3). pp. 705-724. ISSN 1436-3240 (Print), 1436-3259 (Online) (doi:https://doi.org/10.1007/s00477-016-1270-2)

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Abstract

Stochastic rainfall models are widely used in hydrological studies because they provide a framework not only for deriving information about the characteristics of rainfall but also for generating precipitation inputs to simulation models whenever data are not available. A stochastic point process model based on a class of doubly stochastic Poisson processes is proposed to analyse finescale point rainfall time series. In this model, rain cells arrive according to a doubly stochastic Poisson process whose arrival rate is determined by a finite-state Markov chain. Each rain cell has a random lifetime. During the lifetime of each rain cell, instantaneous random depths of rainfall bursts (pulses) occur according to a Poisson process. The covariance structure of the point process of pulse occurrences is studied. Moment properties of the time series of accumulated rainfall in discrete time intervals are derived to model 5-min rainfall data, over a period of 69 years, from Germany. Second-moment as well as third-moment properties of the rainfall are considered. The results show that the proposed model is capable of reproducing rainfall properties well at various sub-hourly resolutions. Incorporation of third-order moment properties in estimation showed a clear improvement in fitting. A good fit to the extremes is found at larger resolutions, both at 12-h and 24-h levels, despite underestimation at 5-min aggregation. The proportion of dry intervals is studied by comparing the proportion of time intervals, from the observed and simulated data, with rainfall depth below small thresholds. A good agreement was found at 5-min aggregation and for larger aggregation levels a closer fit was obtained when the threshold was increased. A simulation study is presented to assess the performance of the estimation method.

Item Type: Article
Additional Information: © The Author(s) 2016. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Uncontrolled Keywords: Moment properties; Point process; Precipitation; Rainfall generator; Stochastic models; Sub-hourly rainfall
Subjects: G Geography. Anthropology. Recreation > GE Environmental Sciences
Faculty / Department / Research Group: Faculty of Architecture, Computing & Humanities
Faculty of Architecture, Computing & Humanities > Department of Mathematical Sciences
Last Modified: 23 Apr 2019 13:28
Selected for GREAT 2016: None
Selected for GREAT 2017: GREAT b
Selected for GREAT 2018: None
Selected for GREAT 2019: GREAT 3
URI: http://gala.gre.ac.uk/id/eprint/15783

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