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The forecast uncertainty, particularly for precipitation, serves as a crucial indicator of the reliability of deterministic forecasts. Traditionally, forecast uncertainty is estimated by ensemble forecasting, which is computationally expensive since the forecast model is run multiple times with perturbations. Recently, deep learning methods have been explored to learn the statistical properties of ensemble prediction systems due to their low computational costs. However, accurately and effectively capturing the uncertainty information in precipitation forecasts remains challenging. In this study, we present a novel spatiotemporal transformer network (ST-TransNet) as an alternative approach to estimate uncertainty with ensemble spread and probabilistic forecasts, by learning from historical ensemble forecasts. ST-TransNet features a hierarchical structure for extracting multiscale features and incorporates a spatiotemporal transformer module with window-based attention to capture correlations in both spatial and temporal dimensions. Additionally, window-based attention can not only extract local precipitation patterns but also reduce computational costs. The proposed ST-TransNet is evaluated on the TIGGE ensemble forecast dataset and Global Precipitation Measurement (GPM) precipitation products. Results show that ST-TransNet outperforms both traditional and deep learning methods across various metrics. Case studies further demonstrate its ability to generate reasonable and accurate spread and probability forecasts from a single deterministic precipitation forecast. It demonstrates the capacity and efficiency of neural networks in estimating precipitation forecast uncertainty. [ABSTRACT FROM AUTHOR]