Abstract. The CALIOPE air quality modelling system, namely WRF-ARW/HERMES-EMEP/CMAQ/BSC-DREAM8b, has been used to perform the simulation of ground level O₃ concentration for the year 2004, over the Iberian Peninsula. We use this system to study the daily ground-level O₃ maximum. We investigate the use of a post-processing such as the Kalman Filter bias-adjustment technique to improve the simulated O₃ maximum. The Kalman Filter bias-adjustment technique is a recursive algorithm to optimally estimate bias-adjustment terms from previous measurements and model results. The bias-adjustment technique is found to improve the simulated O₃ maximum for the entire year and the whole domain. The corrected simulation presents improvements in statistical indicators such as correlation, root mean square error, mean bias, standard deviation, and gross error. After the post-processing the exceedances of O₃ concentration limits, as established by the European Directive 2008/50/CE, are better reproduced and the uncertainty of the modelling system is reduced from 20% to 7.5%. Such uncertainty in the model results is under the established EU limit of the 50%. Significant improvements in the O₃ average daily cycle and in its amplitude are also observed after the post-processing. The systematic improvements in the O₃ maximum simulations suggest that the Kalman Filter post-processing method is a suitable technique to reproduce accurate estimate of ground-level O₃ concentration.