Social-distancing to combat the COVID-19 pandemic has led to widespread reductions in air pollutant emissions. Quantifying these changes requires a business as usual counterfactual that accounts for the synoptic and seasonal variability of air pollutants. We use a machine learning algorithm driven by information from the NASA GEOS-CF model to assess changes in nitrogen dioxide (NO$_{2}$) and ozone (O$_{3}$) at 5,756 observation sites in 46 countries from January through June 2020. Reductions in NO$_{2}$ correlate with timing and intensity of COVID-19 restrictions, ranging from 60% in severely affected cities (e.g., Wuhan, Milan) to little change (e.g., Rio de Janeiro, Taipei). On average, NO$_{2}$ concentrations were 18% lower than business as usual from February 2020 onward. China experienced the earliest and steepest decline, but concentrations since April have mostly recovered and remained within 5% to the business as usual estimate. NO$_{2}$ reductions in Europe and the US have been more gradual with a halting recovery starting in late March. We estimate that the global NO$_{x}$ (NO+NO$_{2}$) emission reduction during the first 6 months of 2020 amounted to 2.9 TgN, equivalent to 5.1% of the annual anthropogenic total. The response of surface O$_{3}$ is complicated by competing influences of non-linear atmospheric chemistry. While surface O$_{3}$ increased by up to 50% in some locations, we find the overall net impact on daily average O$_{3}$ between February - June 2020 to be small. However, our analysis indicates a flattening of the O$_{3}$ diurnal cycle with an increase in night time ozone due to reduced titration and a decrease in daytime ozone, reflecting a reduction in photochemical production. The O$_{3}$ response is dependent on season, time scale, and environment, with declines in surface O$_{3}$ forecasted if NO$_{x}$ emission reductions continue.
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