ESA's CryoSat-2 has transformed the way we monitor Arctic sea ice, providing routine measurements of the ice thickness with near basin-wide coverage. Past studies have shown that uncertainties in the sea ice thickness retrievals can be introduced at several steps of the processing chain, for instance, in the estimation of snow depth, and snow and sea ice densities. Here, we apply a new physical model to CryoSat-2, which further reveals sea ice surface roughness as a key overlooked feature of the conventional retrieval process. High-resolution airborne observations demonstrate that snow and sea ice surface topography can be better characterized by a lognormal distribution, which varies based on the ice age and surface roughness within a CryoSat-2 footprint, than a Gaussian distribution. Based on these observations, we perform a set of simulations for the CryoSat-2 echo waveform over "virtual" sea ice surfaces with a range of roughness and radar backscattering configurations. By accounting for the variable roughness, our new lognormal retracker produces sea ice freeboards that compare well with those derived from NASA's Operation IceBridge airborne data and extends the capability of CryoSat-2 to profile the thinnest/smoothest sea ice and thickest/roughest ice. Our results indicate that the variable ice surface roughness contributes a systematic uncertainty in sea ice thickness of up to 20% over first-year ice and 30% over multiyear ice, representing one of the principal sources of pan-Arctic sea ice thickness uncertainty. Plain Language Summary We have developed a new way of measuring sea ice thickness in the Arctic, by comparing real and simulated data from the European Space Agency satellite: CryoSat-2. Our simulations are guided by aircraft observations that demonstrate sea ice has distinct patterns of surface roughness. Traditional methods ignore or misrepresent the surface roughness, which reduces our confidence in the measured ice thickness by around one third. If we account for the roughness, however, we can extend the capability of Cryosat-2 for measuring both the thinnest smoothest sea ice and thickest roughest ice. These improvements will boost our confidence in derived estimates of the Arctic Ocean's sea ice volume budget and freshwater fluxes, while enhancing the accuracy of sea ice forecasts primed with satellite data.