Model projections of future CO2 and CH4 exchange in Arctic tundra diverge widely. Here we used ecosys to examine how climate change will affect CO2 and CH4 exchange in troughs, rims, and centers of a coastal polygonal tundra landscape at Barrow, AK. The model was shown to simulate diurnal and seasonal variation in CO2 and CH4 fluxes associated with those in air and soil temperatures (Ta and Ts) and soil water contents (θ) under current climate in 2014 and 2015. During RCP 8.5 climate change from 2015 to 2085, rising Ta, atmospheric CO2 concentrations (Ca), and precipitation (P) increased net primary productivity (NPP) from 50–150 g C m-2 y-1, consistent with current biometric estimates, to 200–250 g C m−2 y−1. Concurrent increases in heterotrophic respiration (Rh) were slightly smaller, so that net CO2 exchange rose from values of −25 (net emission) to +50 (net uptake) g C m−2 y−1 to ones of −10 to +65 g C m−2 y−1. Increases in net CO2 uptake were largely offset by increases in CH4 emissions from 0–6 to 1–20 g C m−2 y−1, reducing gains in net ecosystem productivity. These increases in net CO2 uptake and CH4 emissions were modeled with hydrological boundary conditions that were assumed not to change with climate. Both these increases were smaller if boundary conditions were gradually altered to increase landscape drainage during model runs with climate change.