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Satellite observations are indispensable for weather forecasting, climate change monitoring, and environmental studies. Understanding and quantifying errors and uncertainties associated with satellite observations are essential for hardware calibration, data assimilation, and developing environmental and climate data records. Satellite observation errors can be classified into four categories: measurement, observation operator, representativeness, and preprocessing errors. Current methods for diagnosing observation errors still yield large uncertainties due to these complex errors. When simulating satellite errors, empirical errors are usually used, which do not always accurately represent the truth. We address these challenges by developing an error inventory simulator, the Satellite Error Representation and Realization (SatERR). SatERR can simulate a wide range of observation errors, from instrument measurement errors to model assimilation errors. Most of these errors are based on physical models, including existing and newly-developed algorithms. SatERR takes a bottom-up approach: Errors are generated from root sources and forward propagate through radiance and science products. This is different from, but complementary to, the top-down approach of current diagnostics, which inversely solves unknown errors. The impact of different errors can be quantified and partitioned, and a ground-truth testbed can be produced to test and refine diagnostic methods. SatERR is a community error inventory, open-source on GitHub, which can be expanded and refined with input from engineers, scientists, and modelers. This debut version of SatERR is centered on microwave sensors, covering traditional large satellites and small satellites operated by NOAA, NASA, and EUMETSAT.