Quantitative Precipitation Estimates (QPE) from merged rain gauge and radar measurements have become widely available in the last two decades. The errors associated with these products are yet to be fully understood, especially in complex terrain where ground clutter and overshooting artifacts are significant and vary in space and time depending on the storm and underlying synoptic conditions. The location and timing of precipitation in addition to rainfall intensity and duration are critical to the simulation of flood response in headwater basins. This work proposes a generalizable Physics-guided Artificial Intelligence (PAI) framework for QPE error modeling. First, QPE error climatology derived from the hydrologic Inverse Rainfall Correction (Liao & Barros, 2022) to historical floods in selected headwater basins is analyzed to identify dominant precipitation regimes. Second, for each precipitation regime, a Multilayer Perceptron (MLP) error prediction model is trained using event-specific precipitation metrics at hourly scale as input, and subsequently used to predict estimation errors for various QPE products. The corrected QPE can then be used for hydrologic simulations and flood nowcasting. The PAI framework is demonstrated in the Southern Appalachian Mountains using the 57 largest floods over 2008-2017. The Probability Distribution Function of predicted precipitation errors follows a Gaussian-like distribution but varies significantly between cold and warm season events, while the spatial distribution is inextricably connected to basin geomorphology. On average, large improvements on hourly KGE from -0.5 to 0.4 are achieved, and the peak flood error is reduced by 70%, with distinctively better results for cold season events.