This study quantifies future changes in tropospheric ozone (O<sub>3</sub>) using a simple parameterisation of source-receptor relationships based on simulations from a range of models participating in the Task Force on Hemispheric Transport of Air Pollutants (TF-HTAP) experiments. Surface and tropospheric O<sub>3</sub> changes are calculated globally and across 16 regions from perturbations in precursor emissions (NO<sub>x</sub>, CO, VOCs) and methane (CH<sub>4</sub>) abundance. A source attribution is provided for each source region along with an estimate of uncertainty based on the spread of the results from the models. Tests against model simulations using HadGEM2-ES confirm that the approaches used within the parameterisation are valid. The O<sub>3</sub> response to changes in CH<sub>4</sub> abundance is slightly larger in TF-HTAP Phase 2 than in the TF-HTAP Phase 1 assessment (2010) and provides further evidence that controlling CH<sub>4</sub> is important for limiting future O<sub>3</sub> concentrations. Different treatments of chemistry and meteorology in models remains one of the largest uncertainties in calculating the O<sub>3</sub> response to perturbations in CH<sub>4</sub> abundance and precursor emissions, particularly over the Middle East and South Asian regions. Emission changes for the future ECLIPSE scenarios and a subset of preliminary Shared Socio-economic Pathways (SSPs) indicate that surface O<sub>3</sub> concentrations will increase by 1 to 8 ppbv in 2050 across different regions. Source attribution analysis highlights the growing importance of CH<sub>4</sub> in the future under current legislation. A global tropospheric O<sub>3</sub> radiative forcing of +0.07 W m<sup>−2</sup> from 2010 to 2050 is predicted using the ECLIPSE scenarios and SSPs, based solely on changes in CH<sub>4</sub> abundance and tropospheric O<sub>3</sub> precursor emissions and neglecting any influence of climate change. Current legislation is shown to be inadequate in limiting the future degradation of surface ozone air quality and enhancement of near-term climate warming. More stringent future emission controls provide a large reduction in both surface O<sub>3</sub> concentrations and O<sub>3</sub> radiative forcing. The parameterisation provides a simple tool to highlight the different impacts and associated uncertainties of local and hemispheric emission control strategies on both surface air quality and the near-term climate forcing by tropospheric O<sub>3</sub>.