Many Earth system models, including the Energy Exascale Earth System Model (E3SM), use explicit flux coupling to transfer conserved quantities (energy, mass, and momentum) between the atmosphere and surface components. In E3SM, this means that fluxes are calculated once per atmosphere coupling time step based on the current model state (in either the coupler code or surface components), and these fluxes are then treated as constant boundary conditions by the atmosphere component until they are updated on the next coupling time step. One risk of this approach is that different components may have an inconsistent view of the current model state or its physical interpretation, leading to unphysical model behavior.

A clear example of this can be seen in time series of surface stress and near-surface wind speed over land in E3SM. The surface stress over land is calculated using Monin-Obukhov similarity theory (MOST), which diagnoses surface fluxes under the assumption that the atmosphere’s surface layer is in a roughly steady state. However, the atmosphere model treats near-surface wind as a prognostic variable that can change significantly within a single coupling time step. We find that this discrepancy can lead to numerical instability, and as a consequence wind speeds tend to oscillate between high and low values with a period of twice the model’s coupling time step. We explore this phenomenon using a simplified model of turbulent diffusion of momentum in an atmospheric column, which predicts that for some regimes, explicit flux coupling is only stable for sufficiently small time step sizes, where communication between components is frequent enough that the near-surface atmospheric layers can relax toward a near-steady-state compatible with MOST. This helps us identify potential solutions to evaluate in E3SM.

We also mention three issues present in the gustiness parameterization used in E3SMv2, which we have addressed in E3SMv3. The first issue involves a somewhat subtle conceptual distinction between the speed of the mean wind, and the mean of wind speed (“vector” vs. “scalar” averages). The atmosphere and surface components did not agree on which of these quantities was being communicated between components, requiring cross-component modifications to correct. The second issue was due to a mistake in transcribing formulas from the literature that produced an incorrect scaling of mean wind with gustiness (a linear sum of quantities rather than the desired root-sum-square). The third issue involved both the atmosphere and land models adding gustiness due to boundary-layer turbulence, effectively double-counting this form of sub-grid-scale variability. Fixing these issues has a moderate effect on boundary layer physics that predominantly affects the tropics, and decreases the sensitivity of E3SMv3 to the time step of its boundary layer parameterization