## 5 Discussion  
The proposed FS-ConvLSTM framework effectively merges hourly precipitation data from rain gauge and GPM observations, resulting in improved accuracy and reduced uncertainty when estimating spatial precipitation. The framework's ability to capture the precipitation variation process and its superior performance compared to alternative models highlight its potential for practical application in precipitation estimation. The comparison results presented in Table 3 and Figure 6 demonstrate that the proposed FS-ConvLSTM outperforms LSTM in terms of accuracy and stability. While traditional LSTM models only consider time-series dependencies, ConvLSTM combines the strengths of LSTM and convolutional neural networks (CNN), allowing it to effectively capture spatiotemporal dependencies and model both temporal and spatial dimensions [27]. Additionally, traditional LSTM primarily relies on matrix multiplication and element-wise operations [28], which limits its capacity to model data nonlinearly. In contrast, by utilizing multiple filters and the local connectivity of the convolution kernel, ConvLSTM can learn richer feature representations and extract more complex spatiotemporal patterns in the data. These characteristics contribute to the improved accuracy and stability of FS-ConvLSTM observed in the comparison results. Comparing the fusion results of FS-ConvLSTM for different magnitudes of rainfall data (Table 4, Figures 6 and 7), it can be observed that the fusion results for heavy rainfall are better. Heavy rains exhibit stronger spatial and temporal correlation and spatial expansion, whereas small rains tend to be more localized and discrete. The convolution operation in ConvLSTM utilizes shared weights across different spatial locations [29], enabling it to effectively capture the spatial characteristics of heavy rainfall. Furthermore, heavy rainfall events have longer durations, and past rainfall conditions can influence future rainfall. The gating mechanism and memory units in ConvLSTM aid the model in retaining and updating key spatiotemporal information [30], facilitating the capture of long-term dependencies associated with heavy rainfall. These capabilities of ConvLSTM contribute to its superior performance in understanding and fusing heavy rainfall data. From the spatial distribution of the rainfall data before and after fusion presented in Figures 8 and 9, it is evident that the fusion process retains the distribution features of both data sources while achieving higher accuracy. The introduction of multiple input channels in the ConvLSTM model enables the simultaneous processing of inputs from multiple data sources [31]. This allows the model to leverage the strengths of each data source, capture their spatial features, and retain the expression of these features in the fusion results. Moreover, the ConvLSTM model exhibits a large capacity and nonlinear modeling capability, enabling it to effectively handle the heterogeneity and nonlinear correlation between different data sources during the fusion process [32]. The model learns adaptively and adjusts the weights based on the importance and contribution of each data source. This ability enables the model to identify and reduce the impact of data with large deviations on the accuracy of fusion results, resulting in more accurate outcomes. While the proposed framework successfully merges precipitation data from satellites and rain gauges, it has certain limitations. The ConvLSTM method was chosen for this study due to its ability to capture spatial and temporal dependencies in rainfall data, but alternative deep learning models such as Transformer-based models may also have advantages in processing spatiotemporal structured data. Exploring and comparing the performance of different architectures for precipitation data fusion would be a valuable direction for future research.