## 1. Introduction

Most agricultural, hydrological and ecological models require long sequences of daily rainfall as a major meteorological input. However, at many sites, such data series are often too short to allow a good estimation of the probability of extreme events or such data are simply unavailable. This has led to the development of mathematical models, known as stochastic weather generators, frequently used to produce long synthetic weather series that are statistically similar to historical records (e.g., Wilks and Wilby, 1999). Numerous approaches for the generation of daily rainfall data at single point are available in the hydrological and climatological literature (e.g., Richardson, 1981; Srikanthan and McMahon, 1985; Woolhiser, 1992; Sharma and Lall, 1999; Hayhoe, 2000; Wan *et al.*, 2005; Srikanthan *et al.*, 2005; Zheng and Katz, 2008; Liu *et al.*, 2009). These models are widely used because they are easy to formulate and fast to implement (Wilks, 1999). Nevertheless, an important limitation of commonly used single site daily rainfall models is their inability to represent the monthly characteristics of historical rainfall. Therefore, the resultant daily series, when aggregated into monthly totals, will not adequately represent important statistical characteristics of monthly series.

Because rainfall data at the daily scale form the basic data set for the monthly precipitation series, a proper daily model should preserve monthly characteristics in addition to preserving the daily characteristics (Srikanthan and McMahon, 2001). Wang and Nathan (2007) pointed out the importance of preserving the statistical characteristics of rainfall at different time scales for many applications such as the assessment of water supply systems. In order to address this outstanding problem, in their investigation of rainfall generation Wang and Nathan (2002) developed a daily and monthly mixed model for the simulation of precipitation at a single site. The model first generates two rainfall series, reproducing daily and monthly statistics. Next, the monthly series are used to modify the generated daily rainfall values, after incorporating the serial correlation (Srikanthan and McMahon, 2001). Srikanthan and Chiew (2003) and Siriwardena *et al.* (2002) implemented a simplified approach for the Wang and Nathan model by generating only one sequence of daily rainfall amounts, but whereby the daily rainfall is adjusted to match the monthly characteristics.

This study attempts to extend our previous work on a single-site daily precipitation model (Mhanna and Bauwens, 2009) to a daily and monthly mixed model. The stochastic rainfall model is developed mainly for running a simulation model used to evaluate the performance of small-scale rainwater harvesting systems in arid and semi-arid areas in the Middle East. These areas are generally characterized by very high temporal variability of the rainfall. Therefore, a sufficiently long rainfall record is potentially important in order to ensure that the pattern of dry and wet periods is well represented within the rainfall time series. The paper is structured as follows. In Section 2, the study area and data variability are described. The daily model and the adjustment procedure are presented in Section 3. In Section 4, criteria used to evaluate the performance of the model are given. Section 5 compares the statistics of the generated series with the observations. Finally, conclusions drawn from the results end the paper in Section 6.