*3.1. Data*

3.1.1. Integrated Multi-satellitE Retrievals for Global Precipitation Measurement (GPM) (IMERG) Satellite Precipitation Products

The Global Precipitation Measurement (GPM) mission is a satellite precipitation measurement project initiated by the National Aeronautics and Space Administration (NASA) and the Japan Aerospace Exploration Agency (JAXA). The goal of the GPM mission is to provide new-generation global satellite precipitation products with high precision and resolution. The GPM mission has an extended TRMM sensing load and an enhanced capacity for precipitation detection. The dual-frequency radar carried by the GPM Core Observatory (GPMCO) operates in the Ku and Ka bands. In particular, in the Ka band, it can operate in the high-sensitivity interleaved sampling mode. Meanwhile, the microwave radiometer of the GPMCO operates in four bands with higher frequencies than that of the TRMM Microwave Imager, which increases the observation capacity for light and solid precipitation. A comparison between the Integrated Multisatellite Retrievals for GPM (IMERG) products and other commonly used satellite precipitation datasets in Xinjiang has shown that IMERG exhibits the best performance [26–28]. Therefore, the IMERG monthly precipitation data were utilized as the initial data in this study.

IMERG can provide quasi-global precipitation data with a temporal resolution of 30 min and a spatial resolution of 0.1◦ × 0.1◦. According to the calibration methods and data sources used for these precipitation data, the IMERG products can be divided into three types, namely, "Early-run", "Late-run", and "Final-run" products. Among them, the "Early-run" and "Late-run" products are quasi-real-time data in the sense that they are released 4 and 12 h after the observations, respectively, while the "Final-run" products are post-real-time data with a time lag of 3.5 months. These products are available at the Precipitation Measurement Missions (PMM) website (https://pmm.nasa.gov/dataaccess/downloads/gpm). Specifically, the V06B IMERG "Final-run" product was selected for use in this study because this product is subjected to gauge adjustment using monthly observation data from the Global Precipitation Climatology Centre (GPCC) and offers higher precision than the "Early-run" or "Late-run" products. There are only 9 Global Telecommunication System (GTS) stations used by the GPCC in the Tianshan Mountains; these stations account for a very small proportion (<1%) of the total AWSs in the region (1074) and were excluded in this study to ensure the independence of the precipitation evaluation. Because the AWSs in the study area cannot measure snowfall during the cold season, the study period was restricted to the warm seasons (May to September) from 2014 to 2018.

#### 3.1.2. Observed Precipitation

Daily precipitation data were collected from 1065 AWSs in the Tianshan region and accumulated to the monthly scale. The distribution of the stations is shown in Figure 1. The time range of these precipitation observations was consistent with that of the IMERG precipitation data. To ensure the independence of model training and validation, the 9 GTS stations in the study area were excluded (Figure 1). The observed data were collected by the Information Center of the Xinjiang Meteorological Bureau, and the quality control procedures included a climatic extreme value test, a single-station extreme value test, and a data consistency test. The data from September 2018 were excluded due to missing records for a large number of regional stations. In addition, since retrospective IMERG data are available from June 2000 to the present, a longer period of data was used to validate the effectiveness of the OI-GWR method in Section 5.2.

**Figure 1.** Digital elevation model (DEM) and distribution of the observation stations on a map of the Tianshan Mountains. The black dots and red flags represent automatic weather stations (AWSs) and Global Telecommunication System (GTS) stations, respectively.
