A critical evaluation of the newly released precipitation data set is very important for both the end users and data developers. Meanwhile, the evaluation may provide a benchmark for the product’s continued development and future improvement. To these ends, the four precipitation estimates including IMERG (the Integrated Multi-satellitE Retrievals for the Global Precipitation Measurement) V04A, IMERG V03D, CMORPH (the Climate Prediction Center Morphing technique)-CRT and TRMM (the Tropical Rainfall Measuring Mission) 3B42 are systematically evaluated against the gauge precipitation estimates at multiple spatiotemporal scales from 1 June 2014 to 30 November 2015 over three different topographic and climatic watersheds in China. Meanwhile, the statistical methods are utilized to quantize the performance of the four satellite-based precipitation estimates. The results show that: (1) over the Tibetan Plateau cold region, among all products, IMERG V04A underestimates precipitation with the largest RB (−46.98%) during the study period and the similar results are seen at the seasonal scale. However, IMERG V03D demonstrates the best performance according to RB (7.46%), RMSE (0.44 mm/day) and RRMSE (28.37%). Except for in summer, TRMM 3B42 perform better than CMORPH according to RMSEs, RRMSEs and Rs; (2) within the semi-humid Huaihe River Basin, IMERG V04A has a slight advantage over the other three satellite-based precipitation products with the lowest RMSE (0.32 mm/day) during the evaluation period and followed by IMERG V03D, TRMM 3B42 and CMORPH orderly; (3) over the arid/semi-arid Weihe River Basin, in comparison with the other three products, TRMM 3B42 demonstrates the best performance with the lowest RMSE (0.1 mm/day), RRMSE (8.44%) and highest R (0.92) during the study period. Meanwhile, IMERG V03D perform better than IMERG V04A according all the statistical indicators; (4) in winter, IMERG V04A and IMERG V03D tend to underestimate the total precipitation with RBs (−70.62% vs. −6.47% over the Tibetan Plateau, −46.92% vs. −0.66% over the Weihe River Basin, respectively); and (5) overall, except for IMERG V04A in Tibetan Plateau, all satellite-based precipitation captured the gauge-based precipitation well over the three regions according to RRMSEs, Rs and Rbs during the study period. IMERG V03D performs better than its predecessors-TRMM 3B42 and CMORPH over the Tibetan Plateau region and the Huaihe River Basin, while IMERG V04A only does so over the latter. Between the two IMERG products, IMERG V04A does not show an advantage over IMERG V03D over the Tibetan Plateau region and the Weihe River Basin. In particular, over the former, IMERG V04A performs far worse than IMERG V03D. These findings provide valuable feedback for both IMERG algorithm developers and data users.

As the Global Precipitation Measurement (GPM) Core Observatory satellite continues its mission, the latest GPM-era satellite-based precipitation estimations, including Global Satellite Mapping of Precipitation (GSMaP) and Integrated Multi-satellitE Retrievals for the GPM (IMERG), have been released. However, few studies have systematically evaluated these products over mainland China, although this is very important for both the end users and data developers. To these ends, the final-run uncalibrated IMERG V05 (V05UC), gauge-calibrated IMERG V05 (V05C) and IMERG V04 (V04C), and latest gauge-calibrated GSMaP V7 (GSMaP) are systematically evaluated and mutually compared against a merged product obtained from the China Meteorological Data Service Center via continuous statistical indices and an error decomposition analysis technology suite over mainland China from April 2014 to December 2016 at a 3 hourly scale and 0.1° × 0.1° resolution. The results show that, irrespective of the slight overestimation in the southeast and underestimation in the northern Tibetan Plateau, all four GSPEs could generally capture the spatial patterns of precipitation over mainland China. Meanwhile, the overall quality of the GSMaP is slightly superior to the IMERG products in east and south China; however, it also suffers from an overestimation of light rain and an underestimation of heavy rain. Such overestimation and underestimation are primarily from a large false precipitation in light rain and a negative hit bias in heavy rain, respectively. The latest IMERG V05 products have not shown significant improvement over the earlier version (V04C) in east and south China, but the calibrated V05C can best reproduce the probability density function in terms of precipitation intensity. Furthermore, V04C shows remarkable underestimation over the Tibetan Plateau, while this shortcoming has been resolved significantly in V05C. Alternately, the effects of the gauge calibration algorithm (GCA) used in IMERG are examined by comparison of V05UC and V05C. The results indicate that GCA cannot reduce the missed precipitation, and even enlarges the false precipitation over some regions. This reveals that GCA cannot effectively alleviate the bias resulting from the rain areas’ delineation and raining or not-raining detection. In addition, all of the products’ performance can be improved, particularly in the dry climate and high-latitude regions. This is a systematic estimation for GSPEs, providing deep insight into the characteristics and sources of error, and it could be valuable as a reference for both algorithm developers and data users, as well as for associated global products and various applications.

In this paper, we establish sufficient conditions for the mean square and quasi-sure exponential stability of stochastic differential equations driven by the $ G $-Lévy process under discrete-time feedback control in the drift term. Departing from the conventional Lyapunov-based approach, we propose a comparative method to analyze the stabilization effect of the designed control. An example validates the effectiveness of the proposed control strategy.