## 1 Introduction  
Precipitation is a critical meteorological variable with significant implications for many applications, including flood forecasting [1], agriculture [2], water resource management [3], and climate change studies [4]. Due to its large spatiotemporal variability, the accurate estimation of precipitation remains challenging, especially in areas with complex terrains and limited observational networks [5, 6]. Traditional approaches to precipitation estimation rely on observations from rain gauges. These are simple devices that collect and measure the amount of precipitation. The observation data are usually considered reliable and accurate but have limited spatial coverage and are prone to errors due to gauge under-catch and exposure issues [7]. To overcome these limitations, many alternative approaches have been developed to estimate precipitation, including remote sensing technologies such as radar and satellite [8]. Radar waves provide information on precipitation location, intensity, and distribution with a high temporal and spatial resolution. In contrast, satellite observations provide a large-scale view of precipitation with a relatively high spatial resolution but lower temporal resolution than radar waves [9]. Both offer improved spatial and temporal coverage, but the data may not be as accurate as that obtained from rain gauges. Therefore, combining data from multiple sources, also known as multi-source precipitation fusion, has become a promising way to overcome these limitations and provide more accurate estimates of precipitation. In recent years, numerous statistical methods have been introduced for integrating precipitation data from rain gauges and satellites, including bias correction [10], Kriging-based methods [11], linear regression model [12], geographical difference analysis method [13], Bayesian combination method [14], Kalman filter calibration method [15], and geographically weighted regression method [16]. [PERSON] et al. [17] merged the precipitation data observed at ground stations with the TRMM 3B42 satellite precipitation data by separately employing linear regression, geographically weighted regression, Kalman filer fusion, and the optimal interpolation method. The comparison results show that linear regression shows the best merging effect across the daily scale, while at the monthly scale, the precipitation data processed using the Kalman filter presented the highest accuracy. However, the aforementioned methodologies rely heavily on mathematical equations and strong assumptions, which can result in various limitations. Given the rapid advancement of machine learning (ML) technology, it possesses the potential to surmount certain limitations intrinsic to the aforementioned methods [18]. Unlike traditional approaches, ML exhibits more robust learning and generalization abilities, allowing it to effectively manage complex nonlinear relationships without requiring explicit statistical models. Additionally, ML demonstrates superior efficiency in processing vast amounts of data, thus enhancing its computational performance. [PERSON] et al. [19] used five ML algorithms (extreme gradient boosting, gradient boosting decision tree, random forest, LightGBM, and multiple linear regression) together with auxiliary geographic parameters to merge hourly data from meteorological stations, Radar, and satellites. The results show that the random forest-based hourly precipitation merging model is suitable for analyzing monsoon rainstorm events, while the extreme gradient boosting-based hourly precipitation merging model is suitable for analyzing typhoon events. [PERSON] et al. [20] applied four ML approaches, including a support vector machine, a random forest algorithm, an artificial neural network, and extreme gradient boosting, to construct the estimation models in which cloud properties are taken as additional predictors to improve the early run of the Integrated Multi-satellite Retrievals for GPM (IMERG).