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Radar inference of the bulk properties of glacier beds, most notably identifying basal melting, is, in general, derived from the basal reflection coefficient. On the scale of an ice sheet, unambiguous determination of basal reflection is primarily limited by uncertainty in the englacial attenuation of the radio wave, which is an Arrhenius function of temperature. Existing bed-returned power algorithms for deriving attenuation assume that the attenuation rate is regionally constant, which is not feasible at an ice-sheet-wide scale. Here we introduce a new semi-empirical framework for deriving englacial attenuation, and, to demonstrate its efficacy, we apply it to the Greenland Ice Sheet. A central feature is the use of a prior Arrhenius temperature model to estimate the spatial variation in englacial attenuation as a first guess input for the radar algorithm. We demonstrate regions of solution convergence for two input temperature fields and for independently analysed field campaigns. The coverage achieved is a trade-off with uncertainty and we propose that the algorithm can be "tuned" for discrimination of basal melt (attenuation loss uncertainty ∼ 5 dB). This is supported by our physically realistic ( ∼20 dB) range for the basal reflection coefficient. Finally, we show that the attenuation solution can be used to predict the temperature bias of thermomechanical ice sheet models and is in agreement with known model temperature biases at the Dye 3 ice core.