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Precipitation nowcasting is mainly achieved by the radar echo extrapolation method. Due to the timing characteristics of radar echo extrapolation, convolutional recurrent neural networks (ConvRNNs) have been used to solve the task. Most ConvRNNs have been proven to perform far better than traditional optical flow methods, but they still have fatal problems. These models lack differentiation in the prediction of echoes of different intensities, which leads to the omission of responses from regions with high intensities. Moreover, because it is difficult for these models to capture long-term feature dependencies among multiple echo maps, the extrapolation effect declines sharply over time. This paper proposes an embedded multi-layer attention module (MLAM) to address the shortcomings of ConvRNNs. Specifically, an MLAM mainly enhances attention to critical regions in echo images and the processing of long-term spatiotemporal features through the interaction between input and memory features in the current moment. Comprehensive experiments were conducted on the radar dataset HKO-7 provided by the Hong Kong Observatory and the radar dataset HMB provided by the Hunan Meteorological Bureau. Experiments show that ConvRNNs embedded with MLAMs achieve more advanced results than standard ConvRNNs.