*4.2. Uncertainties from Rain Gauge Data*

We employed rain gauge data as a reference to validate the 12 precipitation products in detecting precipitation trends at different time scales across MC. It should be noted that the inherent uncertainties within the gauge data, which are related to flaws in calibration, wind-related under-catch, and wetting and evaporation losses, could bias the gauge measurements from the real values and weaken the robustness of the validation results (e.g., [106–109]). For example, Shedekar et al. [109] found that relative to the actual rainfall depths, the precipitation measurements from three calibrated tipping-bucket rain gauges were underestimations, particularly for heavy rainfall, and they highlighted that the biases were closely associated with the gauge calibrations. When it is windy, gauge observations are often impacted by wind-related under-catch effects through deflecting the flow and inducing eddies and turbulence around the gauges [108–111]. In general, wind can cause some raindrops, especially smaller ones, to miss the funnel or fall at an inclination, and finally impact the catch efficiency of the gauges. To what extent wind influences the accuracy of the gauge measurements is dependent on ambient wind speed, raindrop size distribution, and gauge design [110]. Sieck et al. [110] reported that, compared to rainfall from collocated buried gauges, wind-exposed aboveground gauges would likely observe about 2–10% less precipitation. Due to water adhering to the inside walls of the gauge and then evaporating, the gauge-recorded precipitation is generally lower than the true value, and the biases vary among gauge configurations (e.g., frequency of emptying) and precipitation types [106,112,113]. A Russian study revealed that, for each record of rainfall measurement, the mean average wetting loss was 0.2 mm, but for both snow and mixed precipitation the value was 0.15 mm [112]. Due to being exposed to the atmosphere, water within rain gauges is usually evaporated (i.e., evaporation losses; [114–117]). It is reported that evaporation losses for gauged precipitation generally range from 0.1 to 0.8 mm/day or from 0 to 1%; however, the magnitudes differ among gauge types, climate backgrounds, and seasons [114]. The combined effects induced by the aforementioned factors on rain gauge measurements are likely to underestimate the recorded precipitation [118], e.g., the bias-corrected annual precipitation (removing the uncertainties within raw observations) being 30–330 mm or 10–65% higher than the raw observations over Siberia.

Usually, the quality of precipitation observations is accompanied by an issue of standardization, or lack of, which is mainly due to changes in gauge instruments, station relocation and environment, etc. [119–122]. Moreover, these factors result in negative impacts on data quality, in particular for climate researches using long-term time series (e.g., linear trend evaluation in this study). Before using the gauged precipitation measurements, it is necessary to reduce and even remove the associated uncertainties, e.g., adjust the raw records using metadata about gauges, and at least eliminating sites with non-homogeneous measurements identified by some statistic methods. The Pettitt test has been used to remove sites with non-homogenous measurements due to a lack of metadata for the selected sites, but there is no guarantee that the remaining sites have no issues, which can weaken the confidence level of the results. Besides, mismatches between representatives of gauge precipitation (i.e., a point of space in time accumulation) and selected products (i.e., a snapshot of time in space aggregation) are likely to have an effect on the accuracy and precision of qualitative and quantitative assessments of various precipitation products [123–125]. For instance, the spatial resolution of all the 12 products is generally lower than 0.25◦ × 0.25◦ (except for PERSIANN-CCS), across which the estimated precipitation was averaged, while the spatial representation of a gauge is much smaller than the coverage of the pixel of the 12 products. Considering the variability of precipitation over a small spatial extent, a sparse gauge network may not identify meso-/micro-scale weather system-associated precipitation (e.g., convective precipitation; [126–129]); thus, gauge precipitation measurements may be smaller in magnitude and frequency than the ground-truthed values for a given pixel.

#### **5. Conclusions**

As important surrogate for precipitation estimates, various satellite-based and reanalysis precipitation products need to be validated from different perspectives. Especially, the information about the capacity of the satellite-based and reanalysis precipitation is scarce on a sub-daily scale, especially for China. However, the assessments regarding precipitation trends are fundamental for selecting the reliable products to explore precipitation changes, particularly for regions with limited or even no observations. Thus, with a motivation to explore twelve popular precipitation products (i.e., six satellite-based and six reanalysis products) in detecting precipitation linear trends across MC, we collected daytime and nighttime observations from a dense rain gauge network during 2003–2017, and examined LTwd, LTd, and LTn across mainland China. We found that annual and seasonal LTwd, LTd, and LTn for MC and most WRRs were positive but with regional differences. In terms of magnitude and sign (i.e., decreasing and increasing), LTd and LTn in a certain region showed evident differences, confirming the necessity to evaluate precipitation products at a sub-daily scale. Then, several statistical metrics (i.e., CC, B, RMSE, AS, and JAS) were employed to identify the differences and agreements of LTs for MC and ten WRRs between twelve precipitation products and gauge observations on sub-daily scale. In general, values of a given metric for annual and seasonal LTwd, LTd, or LTn differed among products. Meanwhile, performances for single product varied among seasons and between daytime and nighttime. At last, the metric-based OPs were identified for MC and each WRR. The metric-based OPs varied among regions and seasons, and between daytime and nighttime, but the most frequent OPs were TRMM3B42, ERA-Interim, and MERRA-2.

The comparison of satellite-based and reanalysis products in ability to detect precipitation linear trends in this study provides suggestions for developers and the potential users of these products across mainland China. For a given product, varying performance for different validation metrics at different timescales (between daytime and nighttime) suggests that the product's group can try to develop specific algorithms/models during a certain season (at a sub-daily scale) and correction procedures to improve its capacity to reproduce precipitation trends. For the potential users who focus on long-term precipitation changes across MC, this study provides necessary and detailed information about the existing popular precipitation products' performances in detecting linear trends, which is fundamental to obtaining robust conclusions.

**Author Contributions:** Conceptualization, S.S. and W.S.; methodology, W.S. and H.C.; software, S.Z.; validation, S.S., W.S. and Y.Z.; formal analysis, S.S., R.C. and W.S.; investigation, S.S.; resources, S.S. and H.S.; data curation, W.S. and R.C.; writing—original draft preparation, S.S., W.S. and S.Z.; writing—review and editing, S.S., G.W. and H.C.; visualization, S.S and W.S.; supervision, S.S., G.W. and H.C.; project administration, S.S., G.W. and H.C.; funding acquisition, S.S., G.W. and H.C. All authors discussed the results and revised the manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was jointly supported by the National Key Research and Development Program of China (Grant No. 2018YFC1507101), Natural Science Foundation of China (Grant Nos. 41875094), and Qinglan Project of Jiangsu Province of China.

**Acknowledgments:** We thank all data (i.e., satellite-based and reanalysis precipitation products) developers, and their managers and funding agencies, whose work and support were essential for obtaining the datasets, without which the analyses conducted in this study would have been impossible. Notably, precipitation data at more than 2000 gauges are not available to the public, but they can be obtained and used through cooperation with the CMA. Source code used to conduct this study is available from the authors upon request (sun.s@nuist.edu.cn or ppsunsanlei@126.com).

**Conflicts of Interest:** The authors declare no conflict of interest.
