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In a prior study, GOES-R Geostationary Lightning Mapper (GLM) flash extent density (FED) data were assimilated using ensemble Kalman filter into a convection-allowing model for a mesoscale convective system (MCS) and a supercell storm. The FED observation operator based on a linear relation with column graupel mass was tuned by multiplying a factor to avoid large FED forecast bias. In this study, new observation operators are developed by fitting a third-order polynomial to GLM FED observations and the corresponding FED forecasts of graupel mass of the MCS and/or supercell cases. The new operators are used to assimilate the FED data for both cases, in three sets of experiments called MCSFit, SupercellFit, and CombinedFit, and their performances are compared with the prior results using the linear operator and with a reference simulation assimilating no FED data. The new nonlinear operators reduce the frequency biases (root-mean-square innovations) in the 0–4-h forecasts of the FED (radar reflectivity) relative to the results using the linear operator for both storm cases. The operator obtained by fitting data from the same case performs slightly better than fitting to data from the other case, while the operator obtained by fitting forecasts of both cases produce intermediate but still very similar results, and the latter is considered more general. In practice, a more general operator can be developed by fitting data from more cases. Significance Statement: Prior studies found that assimilation of satellite lightning observation can benefit storm forecasts for up to 4 h. A linear lightning observation operator originally developed for assimilating pseudo-satellite lightning observations was tuned earlier through sensitivity experiments when assimilating real lightning data. However, the linear relation does not fit the model and observational data well and significant bias can exist. This study develops new lightning observation operators by fitting a high-order polynomial to satellite lightning observations and model-predicted quantities that directly relate to lightning. The new operator was found to reduce the frequency biases and root-mean-square innovations for lightning and radar reflectivity forecasts, respectively, up to several hours relative to the linear operator. The methodology can be applied to larger data samples to obtain a more general operator for use in operational data assimilation systems. [ABSTRACT FROM AUTHOR]