Adjoint measurement and calibration of Manning roughness in E3SM's river dynamical core

We present a transient discrete adjoint of RDycore, the river dynamical core of the Energy Exascale Earth System Model (E3SM), and use it to measure how much of a flood model's error its roughness parameter can remove. We differentiate the production solver in place rather than port it to a differentiable-programming framework: one exact, assembled shallow-water Jacobian serves the implicit integrator, the adjoint, and the calibration. An objective and its gradient cost about two forward solves for any number of parameters, every derivative passes a finite-difference gate on the full nonlinear solve, and it all runs on GPUs: four NVIDIA A100s run a calibration iteration on a dense-gauge twin 19x faster than a 64-core CPU socket. For Hurricane Harvey on a 30 m Houston mesh, our best roughness calibration removes about 15% of the model's error against the surveyed high-water marks it was fit to. Forward runs scanning one global roughness scale put the reachable amount at 11% (4% inside the prior), before any optimizer runs. The calibration problem's eigenvalues at the published land-cover table show why so little is reachable: if that table is trusted to +/-30%, the marks outweigh it on only about three combinations of its fifteen classes. Two of those three land in the same place under every prior we ran, below the table's own range for developed ground; the third goes where the prior lets it. The stream gauges cannot arbitrate between survey and table: most sit in channels the mesh does not resolve, and calibrating on the few it does leaves the model worse at the marks than no calibration. Roughness is absorbing whichever error each observable sees. Pointed at the initial state, the same measurement finds a larger effect: the model holds too much water when the window opens. The error lives in the water balance and the mesh, not the friction.