Discretized numerical models of the atmosphere are usually intended to faithfully represent an underlying set of continuous equations, but this necessary condition is violated sometimes by subtle pathologies that have crept into the discretized equations. Such pathologies can introduce undesirable artifacts, such as sawtooth noise, into the model solutions. The presence of these pathologies can be detected by numerical convergence testing. This study employs convergence testing to verify the discretization of the Cloud Layers Unified By Binormals (CLUBB) model of clouds and turbulence. That convergence testing identifies two aspects of CLUBB’s equation set that contribute to undesirable noise in the solutions. First, numerical limiters (i.e. clipping) used by CLUBB introduce discontinuities or slope discontinuities in model fields. Second, nonlinear numerical diffusion employed for improving numerical stability can introduce unintended small-scale features into the solution of the model equations. Smoothing the limiters and using linear diffusion (low-order hyperdiffusion) reduces the noise and restores the expected first-order convergence in CLUBB’s solutions. These model reformulations enhance our confidence in the trustworthiness of solutions from CLUBB by eliminating the unphysical oscillations in high-resolution simulations. The improvements in the results at coarser, near-operational grid spacing and timestep are also seen in cumulus cloud and dry turbulence tests. In addition, convergence testing is proven to be a valuable tool for detecting pathologies, including unintended discontinuities and grid dependence, in the model equation set.

The higher-order turbulence scheme, Cloud Layers Unified by Binormals (CLUBB), is known for effectively simulating the transition from cumulus to stratocumulus clouds within leading atmospheric climate models. This study investigates an underexplored aspect of CLUBB: its capacity to simulate near-surface winds and the Planetary Boundary Layer (PBL), with a particular focus on its coupling with surface momentum flux. Using the GFDL atmospheric climate model (AM4), we examine two distinct coupling strategies, distinguished by their handling of surface momentum flux during the CLUBB’s stability-driven substepping performed at each atmospheric time step. The static coupling maintains a constant surface momentum flux, while the dynamic coupling adjusts the surface momentum flux at each CLUBB substep based on the CLUBB-computed zonal and meridional wind speed tendencies. Our 30-year present-day climate simulations (1980-2010) show that static coupling overestimates 10-m wind speeds compared to both control AM4 simulations and reanalysis, particularly over the Southern Ocean (SO) and other midlatitude ocean regions. Conversely, dynamic coupling corrects the static coupling 10-m winds biases in the midlatitude regions, resulting in CLUBB simulations achieving there an excellent agreement with AM4 simulations. Furthermore, analysis of PBL vertical profiles over the SO reveals that dynamic coupling reduces downward momentum transport, consistent with the found wind-speed reductions. Instead, near the tropics, dynamic coupling results in minimal changes in near-surface wind speeds and associated turbulent momentum transport structure. Notably, the wind turning angle serves as a valuable qualitative metric for assessing the impact of changes in surface momentum flux representation on global circulation patterns.

This work documents version two of the Department of Energy’s Energy Exascale Earth System Model (E3SM). E3SM version 2 (E3SMv2) is a significant evolution from its predecessor E3SMv1, resulting in a model that is nearly twice as fast and with a simulated climate that is improved in many metrics. We describe the physical climate model in its lower horizontal resolution configuration consisting of 110 km atmosphere, 165 km land, 0.5° river routing model, and an ocean and sea ice with mesh spacing varying between 60 km in the mid-latitudes and 30 km at the equator and poles. The model performance is evaluated by means of a standard set of Coupled Model Intercomparison Project Phase 6 (CMIP6) Diagnosis, Evaluation, and Characterization of Klima (DECK) simulations augmented with historical simulations as well as simulations to evaluate impacts of different forcing agents. The simulated climate is generally realistic, with notable improvements in clouds and precipitation compared to E3SMv1. E3SMv1 suffered from an excessively high equilibrium climate sensitivity (ECS) of 5.3 K. In E3SMv2, ECS is reduced to 4.0 K which is now within the plausible range based on a recent World Climate Research Programme (WCRP) assessment. However, E3SMv2 significantly underestimates the global mean surface temperature in the second half of the historical record. An analysis of single-forcing simulations indicates that correcting the historical temperature bias would require a substantial reduction in the magnitude of the aerosol-related forcing.

Discretized numerical models of the atmosphere are usually intended to faithfully represent an underlying set of continuous equations, but this necessary condition is violated sometimes by subtle pathologies that have crept into the discretized equations. Such pathologies can introduce undesirable artifacts, such as sawtooth noise, into the model solutions. The presence of these pathologies can be detected by numerical convergence testing. This study employs convergence testing to verify the discretization of the Cloud Layers Unified By Binormals (CLUBB) model of clouds and turbulence. That convergence testing identifies two aspects of CLUBB’s equation set that contribute to undesirable noise in the solutions. First, numerical limiters (i.e. clipping) used by CLUBB introduce discontinuities or slope discontinuities in model fields. Second, this noise can be amplified by an advective term in CLUBB’s background diffusion. Smoothing the limiters and removing the advective component of the background diffusion reduces the noise and restores the expected first-order convergence in CLUBB’s solutions. These model reformulations improve the results at coarser, near-operational grid spacing and time step in cumulus cloud and dry turbulence tests. In addition, convergence testing is proved to be a valuable tool for detecting pathologies, including unintended discontinuities and grid dependence, in the model equation set.

Nudging is a ubiquitous capability of numerical weather and climate models that is widely used in a variety of applications (e.g. crude data assimilation, “intelligent’ interpolation between analysis times, constraining flow in tracer advection/diffusion simulations). Here, the focus is on the momentum nudging tendencies themselves, rather than the atmospheric state that results from application of the method. The initial intent was to interpret these tendencies as a quantitative estimation of model error (net parameterization error in particular). However, it was found that nudging tendencies depend strongly on the nudging time scale chosen, which is the primary result presented here. Reducing the nudging time scale reduces the difference between the model state and the target state, but much less so than the reduction in the nudging time scale, resulting in increased nudging tendencies. The dynamical core, in particular, appears to increasingly oppose nudging tendencies as the nudging time scale is reduced. These results suggest nudging tendencies cannot be quantitatively interpreted as model error. Still, nudging tendencies do contain some information on model errors and/or missing physical processes and still might be useful in model development and tuning, even if only qualitatively.