A stochastic cluster model of daily rainfall sequences

Abstract

A two‐level point stochastic model for the rainfall occurrences at a given rainfall station is constructed in the time dimension. The model is a cluster process of the Neyman‐Scott type. The model has the rainfall‐generating mechanisms as its primary level and the rainfalls that are generated by these mechanisms as the secondary level. It uses infinite superposition of rainfalls and has a very flexible dependence structure. The model is fitted to daily rainfall sequences in Indiana after these are stationarized by a transformation. The fit of the model is then tested in terms of its correlation and marginal probability characteristics. The present form of the Neyman‐Scott cluster model is time homogeneous. Therefore the Neyman‐Scott process, as presented in this paper, may be of practical use only for modeling the stationary rainfall occurrences.

A continuous rainfall model based on vine copulas

“…Therefore, several rainfall modelling approaches have been proposed during the last decades (e.g. Kavvas and Delleur, 1981;Rodriguez-Iturbe et al, 1987a, b;Katz and Parlange, 1998;Menabde and Sivapalan, 2000;Willems, 2001;Evin and Favre, 2008;Gyasi-Agyei, 2011;Viglione et al, 2012), which can be subdivided into models that generate design storms and models that allow for the simulation of continuous time series at a point or spatially distributed. Design storms are generally developed for a given return period and storm duration.…”

Bayesian Inference for Non-Markovian Point Processes

“…Observing this from a fixed point in space (e.g., a rain gauge), we see varying amounts of rainfall over time, with precipitation tending to come in clusters. Mathematically, Le Cam (1960) was first to suggest modeling rainfall at a location by a cluster point process, while Kavvas and Delleur (1981) proposed a Neyman-Scott Poisson cluster process, in which the primary process is a non-homogeneous Poisson process, and were the first to fit it to observed data. In a sequence of papers in the 1980's, a variety of cluster process approaches were developed (a review is provided in Guttorp, 1996;Salim and Pawitan, 2003, discusses more recent work), usually made stationary by considering only a short time period each year, such as a month.…”

Rainfall nowcasting by at site stochastic model P.R.A.I.S.E.

“…Models of the former type, that include AutoRegressive Stochastic Models (Box and Jenkins, 1976;Salas et al, 1980;Brockwell and Davis, 1987;Burlando et al, 1993;Hipel and McLeod, 1994;Burlando et al, 1996;Toth et al, 2000), describe the rainfall process at discrete time steps, are not intermittent and therefore can be applied for describing the "within storm" rainfall. Models of the latter type (Lewis, 1964;Kavvas and Delleur, 1981;Smith and Karr, 1983;Rodriguez-Iturbe et al, 1984Rodriguez-Iturbe, 1986;Cowpertwait et al, 1996;Sirangelo and Iiritano, 1997;Calenda and Napolitano, 1999;Montanari and Brath, 1999;Cowpertwait, 2004) are continuous time series models, are intermittent and therefore can simulate interstorm periods also.…”