A Nudge to the\nTruth: Atom Conservation as a Hard\nConstraint in Models of Atmospheric Composition Using a Species-Weighted\nCorrection

Computational models\nof atmospheric composition are not always\nphysically consistent. For example, not all models respect fundamental\nconservation laws such as conservation of atoms in an interconnected\nchemical system. In well performing models, these unphysical deviations\nare often ignored because they are frequently minor, and thus only\nneed a small nudge to perfectly conserve mass. Here we introduce a\nmethod that anchors a prediction from any numerical model to physically\nconsistent hard constraints, nudging concentrations to the nearest\nsolution that respects the conservation laws. This closed-form model-agnostic\ncorrection uses a single matrix operation to minimally perturb the\npredicted concentrations to ensure that atoms are conserved to machine\nprecision. To demonstrate this approach, we train a gradient boosting\ndecision tree ensemble to emulate a small reference model of ozone\nphotochemistry and test the effect of the correction on accurate but\nnonconservative predictions. The nudging approach minimally perturbs\nthe already well-predicted results for most species, but decreases\nthe accuracy of important oxidants, including radicals. We develop\na weighted extension of this nudging approach that considers the uncertainty\nand magnitude of each species in the correction. This species-level\nweighting approach is essential to accurately predict important low\nconcentration species such as radicals. We find that applying the\nspecies-weighted correction slightly improves overall accuracy by\nnudging unphysical predictions to a more likely mass-conserving solution.