Radiation damage to space-based Charge-Coupled Device (CCD) detectors creates defects which result in an increasing Charge Transfer Inefficiency (CTI) that causes spurious image trailing. Most of the trailing can be corrected during post-processing, by modelling the charge trapping and moving electrons back to where they belong. However, such correction is not perfect -- and damage is continuing to accumulate in orbit. To aid future development, we quantify the limitations of current approaches, and determine where imperfect knowledge of model parameters most degrade measurements of photometry and morphology. As a concrete application, we simulate $1.5times10^{9}$ worst case galaxy and $1.5times10^{8}$ star images to test the performance of the Euclid visual instrument detectors. There are two separable challenges: If the model used to correct CTI is perfectly the same as that used to add CTI, $99.68$ % of spurious ellipticity is corrected in our setup. This is because readout noise is not subject to CTI, but gets over-corrected during correction. Second, if we assume the first issue to be solved, knowledge of the charge trap density within $Deltarho/rho!=!(0.0272pm0.0005)$ %, and the characteristic release time of the dominant species to be known within $Deltatau/tau!=!(0.0400pm0.0004)$ % will be required. This work presents the next level of definition of in-orbit CTI calibration procedures for Euclid.
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