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• The Multiple-point geostatistics (MPS) method is further developed to downscale heavy rainfall fields. • It can be applied in places with limited availability of high-resolution data. • Both rainfall intensity and spatial structure are accurately downscaled. • The method is tested to downscale rainfall fields in Beijing. • Hourly heavy rainfall is adequately downscaled from 8 km to 1 km. High-resolution gridded rainfall products at sub-daily and 100 km scales are required for hydrological applications in mountainous and urban catchments. As most catchments are ungauged, gridded rainfall data are often obtained through remote sensing. However, their spatial resolution is often too coarse (at 101 km) and requires to be downscaled to a finer resolution. The challenge is not only to downscale the rainfall intensity to a finer scale by considering areal reduction factors, but also the spatial structure of the storm, as both elements are equally important to the assessment of the surface hydrological response. As a result of the lack of training data, the latter is difficult to obtain. Further development of the stochastic multiple-point geostatistics (MPS) framework is presented to downscale long-term satellite-derived gridded rainfall series using only a few years of high-resolution rainfall observations. We demonstrate how the MPS framework can be used to downscale the satellite-derived CMORPH rainfall from 8 to 1 km resolution for 1998–2019, taking the city of Beijing as a case study, with a specific focus on extreme rainfall events. The high-resolution multisource-merged CMPAS dataset (1 km, hourly), available for 2015–2020, is used as the source of the training images. We show that the downscaling framework preserves the observed mean areal rainfall (with a bias of 2 %), reproduces the spatial coefficient of variance (with a similar bias), and also retains extreme rainfall at the 99th percentile (with a bias of 6 %). Furthermore, it adequately reproduces the rainfall spatial structure, preserving the variograms of the rainfall fields. Similarities were also observed comparing the 2- to 30-year return period maps of the downscaled rainfall extreme with ground observations, with half of the stations (10 out of 19) agreeing on the location and intensity of the extreme rainfall for all return periods. The results indicate that our framework downscales rainfall intensities and preserves the spatial structure well, especially for heavy rainfall, even if limited data is available. The proposed approach can be applied to other rainfall datasets and regions. [ABSTRACT FROM AUTHOR]