Nitrogen dioxide (NO$_2$) is a primary constituent of traffic-related air pollution and has well established harmful environmental and human-health impacts. Knowledge of the spatiotemporal distribution of NO$_2$ is critical for exposure and risk assessment. A common approach for assessing air pollution exposure is linear regression involving spatially referenced covariates, known as land-use regression (LUR). We develop a scalable approach for simultaneous variable selection and estimation of LUR models with spatiotemporally correlated errors, by combining a general-Vecchia Gaussian process approximation with a penalty on the LUR coefficients. In comparisons to existing methods using simulated data, our approach resulted in higher model-selection specificity and sensitivity and in better prediction in terms of calibration and sharpness, for a wide range of relevant settings. In our spatiotemporal analysis of daily, US-wide, ground-level NO$_2$ data, our approach was more accurate, and produced a sparser and more interpretable model. Our daily predictions elucidate spatiotemporal patterns of NO$_2$ concentrations across the United States, including significant variations between cities and intra-urban variation. Thus, our predictions will be useful for epidemiological and risk-assessment studies seeking daily, national-scale predictions, and they can be used in acute-outcome health-risk assessments.
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