In this study, we investigate the use of a lognormal prior probability distribution in atmospheric inverse modelling. We present the formal implementation in a variational inversion framework and analyze how the choice of statistical optimization parameter (mean, median, or mode) affects the inversion outcome. Using a case study of inverse modelling of sulfur hexafluoride (SF₆) in Europe, we evaluate the performance of the lognormal implementation through both synthetic and real data experiments, and compare the results to inversions using a normal prior probability distribution. We estimate the posterior uncertainties using a Monte Carlo approach and examine their distribution.</p> <p>We find that optimizing for the mean or the mode can produce improved emission estimates under the condition of a strong observational constraint, however, this can lead to unstable and strongly biased inversion results under a weak constraint. In contrast, optimizing for the median consistently improves emission estimates and leads to physically plausible results across all tested cases, providing the most reliable option.</p> <p>We show that inversions using a lognormal prior distribution produce a similar posterior emission pattern as when using a normal prior distribution, however, avoid non-physical negative emission values and occasionally allow for stronger positive emission adjustments. Posterior uncertainties can be estimated using interpercentile ranges from an ensemble of inversions with prior emission errors following a lognormal distribution. Due to the strong asymmetry of posterior distributions with respect to the sign of the inversion increments, error reduction is better assessed in log space, where it provides a clearer measure of the constraints imposed by the observations.