Assessing the Iterative Finite Difference Mass Balance and 4D‐Var Methods to Derive Ammonia Emissions Over North America Using Synthetic Observations

We evaluate two inverse modeling methods by conducting inversion experiments using the GEOS‐Chem chemical transport model and its adjoint. We simulate synthetic NH 3 column density as observed by the Cross‐track Infrared Sounder over North America to test the ability of the iterative finite difference mass balance (IFDMB) and the four‐dimensional variational assimilation (4D‐Var) methods to recover known NH 3 emissions. Comparing to the more rigorous 4D‐Var method, the IFDMB approach requires 3–4 times lower computational cost and yields similar or smaller errors (12–17% vs 17–26%) in the top‐down inventories at 2° × 2.5° resolution. These errors in IFDMB‐derived emission estimates are amplified (53–62%) if compared to the assumed true emissions at 0.25° × 0.3125° resolution. When directly conducting inversions at 0.25° × 0.3125°, the IFDMB consistently exhibits larger errors (44–69% vs 30–45%) than the 4D‐Var approach. Analysis of simulated differences in NH 3 columns and in NH 3 emissions suggests stronger misalignments at the finer resolution, since the local column is more strongly influenced by spatial smearing from neighboring grids. Adjoint calculations indicate that the number of adjacent grids needed to account for most (>65%) of the emission contributions to the local columnar NH 3 abundance over an NH 3 source site increases from ~1 at 2° × 2.5° to ~10 at 0.25° × 0.3125°, leading to increased errors especially in IFDMB. Applying inversion results at 2° × 2.5° to update the a priori emissions at 0.25° × 0.3125° could improve the accuracy of IFDMB inversions and reduce the computational cost of 4D‐Var.