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1. Introduction
Diurnal rainfall variation plays an important role in the characterization of regional climate. It can help to detect weather and climate extremes, provide valuable clues for mechanism studies of local rain formation, and can also be used as a powerful tool to verify numerical forecast models (Trenberth et al. 2003; Lu et al. 2015, 2017; Ryu et al. 2016). As it is driven by solar radiation and affected by factors such as a heterogeneous underlying surface, multiscale atmospheric circulations, and water vapor path, diurnal rainfall variation shows remarkable regional differences (Carbone et al. 2002; Levizzani et al. 2010; Bao et al. 2011; Chen et al. 2015).
Existing studies usually adopted a top-down approach to studying the regional differences of diurnal rainfall variation, which needs predefined region boundaries. These region boundaries were often defined by natural geographic districts or just by rectangles (Jin et al. 2013; Wilson and Barros 2015; Yu et al. 2007a; Singh and Nakamura 2010). For example, in the former case, Jin et al. (2013) analyzed the nocturnal rainfall of the Sichuan Basin in southwest China, and Wilson and Barros (2015) studied the diurnal cycle of orographic rainfall in the southern Appalachians. In the latter case, Yu et al. (2007a) analyzed the diurnal variation of summer rainfall in five rectangular regions over China, and Singh and Nakamura (2010) studied the diurnal rainfall variation in two rectangular regions over central India and the southern Himalayan foothills.
The process of defining region boundaries depends on experiential knowledge and is somewhat subjective. In recent years, with the abundance of site-observed and satellite-based precipitation data, spatially continuous gridded precipitation fields can be obtained (Xie and Xiong 2011; Yong et al. 2016), which makes it possible to use a bottom-up approach to divide regions for the study of diurnal rainfall variation. By using the bottom-up approach, basic spatial units (e.g., grid cells in this study) can be divided into different groups according to their characteristics of diurnal rainfall variation. The spatial units within each group have similar diurnal rainfall variation, and their extents form the spatial distribution for one type of diurnal variation. In this way, the spatial distribution of diurnal rainfall variation can be objectively determined by gridded precipitation data, which is useful in analyzing...