Refine the Uncertainty of GPM IMERG Precipitation Product Accounting for the Inherent Error from Rain Gauges Estimations

Satellite precipitation retrieval accuracy assessment requires reliable ground validation, yet conventional approaches using rain gauges as "truth" neglect representativeness errors inherent in point-to-area approximations. This study quantifies these errors using 7,253 rain  gauges from the China Meteorological Administration's high-density gauge network during 2020-2024 in Jianghuai monsoon region, enabling a fundamental reassessment of the Integrated Multi-satellite Retrievals for GPM (IMERG) precipitation data performance. We established that ≥16 gauges per 0.2° grid (~4/100 km²) are required for reliable area-averaged precipitation estimates, with optimal sampling protocols minimizing random errors. Analysis reveals dual dependence of gauge errors on density (n) and intensity (RR): standard deviation decays exponentially with increasing n (Root Mean Square Error, RMSE ∝ ae⁻^bn), while rising with RR for fixed n. Parameterized relationships enable error quantification across density gradients. Direct IMERG-gauge comparisons show seasonal mean differences of 1.65, 3.35, 1.84, and 1.26 mm h⁻¹ (spring–winter), exhibiting significant negative spatial correlation with gauge density (r = -0.33, p = 3.88×10⁻⁴⁴), confirming network scarcity as primary discrepancy driver—not inherent retrieval deficiencies. Error decomposition using gauge uncertainties yielded bounded IMERG retrieval errors (RMSEᴮ_min/max). Applying the same framework to Kling-Gupta efficiency (KGE) revealed similarly improved skill after removing gauge-induced uncertainties, reinforcing the internal consistency of our analysis. Summer RMSEᴮ_min was substantially lower than RMSEᴮ_max and conventional RMSE, demonstrating that opposing signs of representativeness and retrieval errors cause severe IMERG performance underestimation—particularly in Shandong/Dabie mountains. Crucially, incorporating gauge errors reduced significant discrepancy frequency by 16%/6%/16%/17% across seasons, proving that traditional methods overestimate IMERG-gauge deviation occurrence by 6-17%. This establishes gauge density as critical accuracy determinant, provides robust error-quantification framework, and reveals that terrain-complexity misinterpretations arise when disregarding representativeness errors, with implications for global satellite precipitation validation.