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Scenarios avoiding global warming greater than 1.5 or 2 °C, as stipulated in the Paris Agreement, may require the combined mitigation of anthropogenic greenhouse gas emissions alongside enhancing negative emissions through approaches such as afforestation/reforestation (AR) and biomass energy with carbon capture and storage (BECCS). We use the JULES land-surface model coupled to an inverted form of the IMOGEN climate emulator to investigate mitigation scenarios that achieve the 1.5 or 2 °C warming targets of the Paris Agreement. Specifically, we characterise the global and regional effectiveness of land-based (BECCS and/or AR) and anthropogenic methane (CH4) emission mitigation, separately and in combination, on the anthropogenic fossil fuel carbon dioxide emission budgets (AFFEBs) to 2100, using consistent data and socio-economic assumptions from the IMAGE integrated assessment model. The analysis includes the effects of the methane and carbon-climate feedbacks from wetlands and permafrost thaw, which we have shown previously to be significant constraints on the AFFEBs. Globally, mitigation of anthropogenic CH4 emissions has large impacts on the anthropogenic fossil fuel emission budgets, potentially offsetting (i.e. allowing extra) carbon dioxide emissions of 188-212 GtC. Methane mitigation is beneficial everywhere, particularly for the major CH4-emitting regions of India, USA and China. Land-based mitigation has the potential to offset 51-100 GtC globally, but both the effectiveness and the preferred land-management strategy (i.e., AR or BECCS) have strong regional dependencies. Additional analysis shows extensive BECCS could adversely affect water security for several regions. Our results highlight the extra potential CO2 emissions that can occur, while still keeping global warming below key warming thresholds, by investment in regionally appropriate mitigation strategies. [ABSTRACT FROM AUTHOR]