## 1. Introduction

[2] Weather sequences generated by stochastic models are often used in process simulations because historical weather data may be inadequate in terms of length, spatial coverage, and completeness. Moreover, weather sequences generated from stochastic models provide a mechanism for investigating the implications of weather uncertainty in process models.

[3] Because of its important role in a broad range of land surface processes, rainfall has been one of the most actively investigated elements in weather generator models. Over the past four decades, stochastic rainfall models have evolved through several generations; see review articles by, for example, *Wilks and Wilby* [1999], *Onof et al.* [2000], and *Wheater et al.* [2005]. Among the more popular types are alternating renewal models [*Green*, 1964; *Roldan and Woolhiser*, 1982], Markov chain models [*Chin*, 1977; *Katz*, 1977; *Richardson*, 1981; *Chandler and Wheater*, 2002], clustered point process models [*Kavvas and Delleur*, 1981; *Smith and Karr*, 1983; *Waymire et al.*, 1984; *Rodriguez-Iturbe et al.*, 1987; *Cox and Isham*, 1988; *Cowpertwait*, 1995; *Northrop*, 1998], and downscaling models [*Wilby et al.*, 1998; *Ferraris et al.*, 2003]. Many of the early models, such as those in the Markovian process framework, are “observation-based” in the sense that they make statistical assumptions on certain properties of rainfall, then construct the model and estimate parameters based directly on statistical analysis of observed data. Some more recent approaches, exemplified by clustered point process models, may be called “event-based” as they describe and simulate rainfall starting from a simplified prescription of how the storm event actually occurs and develops.

[4] These two types of modeling approaches differ in two basic respects: discreteness and spatial coverage. Observation-based models naturally arose from analysis of daily or hourly rainfall records at a single station. When extended to spatial models, they concern rainfall at multiple discrete locations as opposed to operating in a continuous spatial domain. In order to express the intercorrelation of rainfall between locations, a complex covariance structure and a large number of parameters are often needed [*Smith*, 1994; *Wilks*, 1998]. In contrast, event-based models can be intuitively played out in a continuous spatial domain, evolving seamlessly in time without artificial aggregation with regard to clock time intervals. This major advantage is possible because at the heart of these models is a quasi-physical picture of the rainfall process. Prescription of this simplified rainfall mechanism is where much effort is devoted in developing these models.

[5] In this paper we propose an event-based regional model along the line of point process models. At the center of the idea is a Boolean model [*Matheron*, 1975; *Serra*, 1982; *Stoyan et al.*, 1995; *Molchanov*, 1997], which consists of a spatial Poisson point process and additional properties attached to the points. The points are the center of rain patches, within which rainfall intensity varies according to a prescribed profile. This model has a clear spatiotemporal structure, works in continuous spatial and temporal scales, and can be estimated with widely available long-term historical data. To estimate the model parameters, stereological relations of the Boolean field are used. The proposed estimation strategy is well suited to the way rainfall is observed and recorded at rain gauges.

[6] We first describe the formulation of the model, then give a full account of the model fitting procedure. To validate the model against historical data, we use simulations and analytic derivations to examine several statistical properties of rainfall that such stochastic models are expected to capture. The presentation is illustrated throughout using a historical hourly rainfall data set, which we introduce now, before turning to the model itself.