A point process model for rainfall: further developments

Abstract

A stochastic model for rainfall at a single site is studied in which storms arrive in a Poisson process, each storm consisting of a cluster of a random number of rain cells, each cell having random duration and depth. A model studied in an earlier paper is extended to provide a better fit to empirical experience, the extension being based on the attachment of a single random variable to each storm to achieve in particular some correlation between the durations of the cells within a single storm. The properties of the new model are developed, its fitting to two sets of empirical data is described and the examination of adequacy of fit is studied in some detail via properties not used in the fitting procedure. Finally a theoretical study is made of short-term prediction from the model.

Estimating functions and the generalized method of moments

“…Typically, therefore, the only way that model realizations can be made to resemble observed rainfall in detail is by having an unrealistically high cell arrival rate and very short cells. This is an example of a model simplification that potentially renders likelihood-based analysis undesirable: maximum-likelihood parameter estimates might be expected to reflect the temporal resolution of the data rather than the underlying physical structures [19].…”

“…To account for seasonality in rainfall data, these models are usually fitted separately to data for each calendar month [18,19]: data from different years are considered to provide independent replicates of the rainfall process. Each of our simulations represents 20 years' worth of data for a single calendar month: specifically, m ¼ 20 independent sets of 30 days' worth of hourly values are generated, each from a model with parameter vector u 0 ¼ (23.5 0 0 1.1) 0 .…”

Evaluación del modelo de Neyman-Scott para simulación de lluvia en un punto geográfico

“…En la década del 80 los trabajos Kavvas y Delleur (1981), Waymire y Gupta (1981), Rodriguez-Iturbe et al (1984) y Valdes et al (1985), entre otros, abordaron el modelado temporal de lluvias mediante el uso de teoría de procesos puntuales (Cox e Isham, 1980). Avances posteriores fueron presentados por Marien y Vandewiele (1986), Rodriguez-Iturbe (1986), Rodriguez-Iturbe et al (1987a y b), Rodriguez-Iturbe et al (1988), Cowpertwait, (1991, Onof y Wheater (1993), Salsón y Garcia-Bartual (1998), Calenda y Napolitano (1999), Willems (1999Willems ( y 2001, Salsón (2001) y García-Bartual (2002). Dado que la información de lluvias está disponible a determinadas escalas de agregación, como lámina de lluvia en un determinado intervalo de tiempo (minutos, horas, días), los parámetros de los modelos continuos deben ser estimados a partir de datos agregados.…”

Application of the Poisson Cluster Rainfall Generation Model to the Urban Flood Analysis

“…Shin et al (2005) Kim et al, 2013a)이 활용된다. 추계학적강우생성모형은크게자기상관성의모사에초점 을맞춘Markov-Chain 기반의기법 (Lovejoy and Schertzer, 1990), 주어진강우를통계적특성에근거하여점차작은해상 도로 쪼개나가는 캐스케이드 기반의 기법 (Lall and Sharma, 1996;Tarboton et al, 1998;Westra et al, 2012), 강우세 포를 포함한 폭풍우가 포아송 프로세스에 의해 도착한다는 가정에 따른 포아송 클러스터 기법 (Rodriguez-Iturbe et al 1987, 1988 (Moretti and Montanari 2004;Brath et al, 2006;Dawson et al, 2006), 농약의 확산 (Nolan et al, 2008), 산사태 (Bathurst et al, 2005), 사막화 (Bathurst and Bovolo, 2004), 수자원 평가 (Fowler et al, 2005), 홍 수위험도 평가 (Kilsby et al, 2000) (Nix, 1994) XP-SWMM 유출 모 형에 불투수 면적비율은 고려되어야 한다. 남가좌 1분구 의 토지피복도 (Fig.…”