## 1 Introduction  
Precipitation is one of the pivotal driving factors of surface hydrological processes and serves as an essential parameter in land-atmospheric interactions. Given its fundamental importance, accurate estimation of precipitation is crucial across various fields, including climate change, weather forecasting, hydrologic applications, and societal activities [1, 2, 3, 4]. Generally, precipitation is obtained through ground monitoring networks (e.g., rain gauges and radars), meteorological and numerical weather prediction models [5, 6], and more recently, by satellite observations [7]. Ground-based observations are believed to be more accurate, yet are prone to limited spatial representativeness (e.g., for rain gauges) and reflectivity issues (e.g., for meteorological radars) [8]. Alternatively, precipitation in areas without reliable ground observations can be obtained by model simulation. However, these estimates are also prone to large uncertainties due to model imperfections, particularly in areas with scarce ground observations [9]. Satellite remote sensing has been widely employed to monitor precipitation over the last decades. It can produce gridded precipitation with different spatial resolutions and coverages, thus filling gaps regarding the spatial representativeness. The problem is that it indirectly estimates instantaneous precipitation through atmospheric signals [10] and thus may fail to reproduce the real surface precipitation, for instance, the \"top-down\" approach [11]. The soil moisture has a strong physical connection with precipitation, whereby the soil moisture exhibits a sudden increase after precipitation occurs, and gradually decreases with processes, such as evapotranspiration and drainage. Based on this, a \"bottom-up\" approach (i.e., the SM2 RAIN algorithm) has been proposed by [PERSON] et al. [11] recently. The basic assumption of this algorithm is to treat the soil as a naturally formed rain gauge to measure precipitation. It estimates accumulated rather than instantaneous precipitation using consecutive in situ or satellite soil moisture as input by inverting the soil water balance equation. Over the past decades, the SM2 RAIN algorithm has been successfully applied at regional and global scales to produce precipitation datasets [11; 12; 13; 14; 15; 16; 17; 18], offering good results, and those datasets have been employed in hydrological and water resources applications [4; 19; 20; 21; 22; 23]. Besides, it has been utilized as an indirect method to evaluate satellite-based soil moisture products [24]. Moreover, as an independent precipitation data source, SM2 RAIN-derived precipitation can act as complementary to conventional precipitation estimate methods and offer a unique opportunity for applying the Triple Collocation [25] analysis worldwide, especially in poorly gauged areas. Additionally, its integration with the \"top-down\" approach has been successfully examined (e.g., [12; 26; 27]). However, the accuracy of the bottom-up approach is strongly influenced by the quality of the input satellite soil moisture products as demonstrated by [PERSON] et al. [15]. Further, as to our knowledge, few studies have systematically investigated the error sources of the SM2 RAIN algorithm when using satellite soil moisture as input. The Tibetan Plateau (TP) plays an important role in regional and global climate. However, due to the harsh environment, ground observations have been extremely sparse over this region, especially over the western TP [28; 29]. Currently available precipitation products over TP are also subject to large uncertainties, such as significant systematic and random errors in satellite retrievals [30] and obvious wet bias in modeled precipitation [31]. Several studies have been conducted to assess the quality of SM2 RAIN-derived precipitation in the TP. For example, [PERSON] et al.