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We present the formulation and optimization of a Runge–Kutta-type time-stepping scheme for solving the shallow-water equations, aimed at substantially increasing the effective allowable time step over that of comparable methods. This scheme, called FB-RK(3,2), uses weighted forward–backward averaging of thickness data to advance the momentum equation. The weights for this averaging are chosen with an optimization process that employs a von Neumann–type analysis, ensuring that the weights maximize the admittable Courant number. Through a simplified local truncation error analysis and numerical experiments, we show that the method is at least second-order in time for any choice of weights and exhibits low dispersion and dissipation errors for well-resolved waves. Further, we show that an optimized FB-RK(3,2) can take time steps up to 2.8 times as large as a popular three-stage, third-order strong stability-preserving Runge–Kutta method in a quasi-linear test case. In fully nonlinear shallow-water test cases relevant to oceanic and atmospheric flows, FB-RK(3,2) outperforms SSPRK3 in admittable time step by factors roughly between 1.6 and 2.2, making the scheme approximately twice as computationally efficient with little to no effect on solution quality.

The purpose of this work is to develop and optimize time-stepping schemes for models relevant to oceanic and atmospheric flows. Specifically, for the shallow-water equations we optimize for schemes that can take time steps as large as possible while retaining solution quality. We find that our optimized schemes can take time steps between 1.6 and 2.2 times larger than schemes that cost the same number of floating point operations, translating directly to a corresponding speedup. Our ultimate goal is to use these schemes in climate-scale simulations.

 

The Southern Ocean overturning circulation is driven by winds, heat fluxes, and freshwater sources. Among these sources of freshwater, Antarctic sea-ice formation and melting play the dominant role. Even though ice-shelf melt is relatively small in magnitude, it is located close to regions of convection, where it may influence dense water formation. Here, we explore the impacts of ice-shelf melting on Southern Ocean water mass transformation (WMT) using simulations from the Energy Exascale Earth System Model (E3SM) both with and without the explicit representation of melt fluxes from beneath Antarctic ice shelves. We find that ice-shelf melting enhances transformation of Upper Circumpolar Deep Water (UCDW), converting it to lower density values. While the overall differences in Southern Ocean WMT between the two simulations are moderate, freshwater fluxes produced by ice-shelf melting have a further, indirect impact on the Southern Ocean overturning circulation through their interaction with sea-ice formation and melting, which also cause considerable upwelling. We further find that surface freshening and cooling by ice-shelf melting causes increased Antarctic sea-ice production and stronger density stratification near the Antarctic coast. In addition, ice-shelf melting causes decreasing air temperature, which may be directly related to sea-ice expansion. The increased stratification reduces vertical heat transport from the deeper ocean. Although the addition of ice-shelf melting processes leads to no significant changes in Southern Ocean WMT, the simulations and analysis conducted here point to a relationship between increased Antarctic ice-shelf melting and the increased role of sea ice in Southern Ocean overturning. 

This work documents version two of the Department of Energy's Energy Exascale Earth System Model (E3SM). 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 with Coupled Model Intercomparison Project Phase 6 Diagnosis, Evaluation, and Characterization of Klima simulations augmented with historical simulations as well as simulations to evaluate impacts of different forcing agents. The simulated climate has many realistic features of the climate system, 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 Program assessment. However, a number of important biases remain including a weak Atlantic Meridional Overturning Circulation, deficiencies in the characteristics and spectral distribution of tropical atmospheric variability, and a significant underestimation of the observed warming in the second half of the historical period. 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.