Abstract. The stratospheric contribution to tropospheric ozone (O3) has been a subject of much debate in recent decades but is known to have an important influence. Recent improvements in diagnostic and modelling tools provide new evidence that the stratosphere has a much larger influence than previously thought. This study aims to characterise the seasonal and geographical distribution of tropospheric ozone, its variability, and its changes and provide quantification of the stratospheric influence on these measures. To this end, we evaluate hindcast specified-dynamics chemistry–climate model (CCM) simulations from the European Centre for Medium-Range Weather Forecasts – Hamburg (ECHAM)/Modular Earth Submodel System (MESSy) Atmospheric Chemistry (EMAC) model and the Canadian Middle Atmosphere Model (CMAM), as contributed to the International Global Atmospheric Chemistry – Stratosphere-troposphere Processes And their Role in Climate (IGAC-SPARC) (IGAC–SPARC) Chemistry Climate Model Initiative (CCMI) activity, together with satellite observations from the Ozone Monitoring Instrument (OMI) and ozone-sonde profile measurements from the World Ozone and Ultraviolet Radiation Data Centre (WOUDC) over a period of concurrent data availability (2005–2010). An overall positive, seasonally dependent bias in 1000–450 hPa (∼0–5.5 km) sub-column ozone is found for EMAC, ranging from 2 to 8 Dobson units (DU), whereas CMAM is found to be in closer agreement with the observations, although with substantial seasonal and regional variation in the sign and magnitude of the bias (∼±4 DU). Although the application of OMI averaging kernels (AKs) improves agreement with model estimates from both EMAC and CMAM as expected, comparisons with ozone-sondes indicate a positive ozone bias in the lower stratosphere in CMAM, together with a negative bias in the troposphere resulting from a likely underestimation of photochemical ozone production. This has ramifications for diagnosing the level of model–measurement agreement. Model variability is found to be more similar in magnitude to that implied from ozone-sondes in comparison with OMI, which has significantly larger variability. Noting the overall consistency of the CCMs, the influence of the model chemistry schemes and internal dynamics is discussed in relation to the inter-model differences found. In particular, it is inferred that CMAM simulates a faster and shallower Brewer–Dobson circulation (BDC) compared to both EMAC and observational estimates, which has implications for the distribution and magnitude of the downward flux of stratospheric ozone over the most recent climatological period (1980–2010). Nonetheless, it is shown that the stratospheric influence on tropospheric ozone is significant and is estimated to exceed 50 % in the wintertime extratropics, even in the lower troposphere. Finally, long-term changes in the CCM ozone tracers are calculated for different seasons. An overall statistically significant increase in tropospheric ozone is found across much of the world but particularly in the Northern Hemisphere and in the middle to upper troposphere, where the increase is on the order of 4–6 ppbv (5 %–10 %) between 1980–1989 and 2001–2010. Our model study implies that attribution from stratosphere–troposphere exchange (STE) to such ozone changes ranges from 25 % to 30 % at the surface to as much as 50 %–80 % in the upper troposphere–lower stratosphere (UTLS) across some regions of the world, including western Eurasia, eastern North America, the South Pacific and the southern Indian Ocean. These findings highlight the importance of a well-resolved stratosphere in simulations of tropospheric ozone and its implications for the radiative forcing, air quality and oxidation capacity of the troposphere.