Models of atmospheric composition play an essential role in our scientific understanding of atmospheric processes and in providing policy strategies to deal with societally relevant problems such as climate change, air quality and ecosystem degradation. The fidelity of these models needs to be assessed against observations to ensure that errors in model formulations are found and that model limitations are understood. A range of approaches are necessary for these comparisons. Here, we apply a spectral analysis methodology for this comparison. We use the Lomb-Scargle Periodogram, a method similar to a Fourier transform, but better suited to dealing with the gapped datasets typical of observational data. We apply this methodology to long-term hourly ozone observations and the equivalent model (GEOS-Chem) output. We show that the spectrally transformed observational data shows a distinct power spectrum with regimes indicative of meteorological processes (weather, macroweather) and specific peaks observed at the daily and annual timescales together with corresponding harmonic peaks at half, third etc. of these frequencies. Model output shows corresponding features. A comparison between the amplitude and phase of these peaks introduces a new comparison methodology between model and measurements.We focus on the amplitude and phase of diurnal and seasonal cycles and present observational/model comparisons and discuss model performance. We find large biases notably for the seasonal cycle in the mid-latitude northern hemisphere where the amplitudes are generally overestimated by up to 16 ppb, and phases are too late on the order of 1–5 months. This spectral methodology can be applied to a range of model-measurement applications and is highly suitable for Multimodel Intercomparison Projects (MIPs).