The use of coarse resolution and strong grid-scale dissipation has prevented global ocean models from simulating the correct kinetic energy level. Recently parameterizing energy backscatter has been proposed to energize the model simulations. Parameterizing backscatter reduces long-standing North Atlantic sea surface temperature (SST) and associated surface current biases, but the underlying mechanism remains unclear. Here, we apply backscatter in different geographic regions to distinguish the different physical processes at play. We show that an improved Gulf Stream path is due to backscatter acting north of the Grand Banks to maintain a strong deep western boundary current. An improved North Atlantic Current path is due to backscatter acting around the Flemish Cap, with likely an improved nearby topography-flow interactions. These results suggest that the SST improvement with backscatter is partly due to the resulted strengthening of resolved currents, whereas the role of improved eddy physics requires further research.

Atmospheric macroturbulence transports energy down the equator-to-pole gradient. This is represented by diffusion in energy balance models (EBMs), and EBMs have proven valuable for understanding and quantifying the pattern of surface temperature change. They typically assume climate-state-independent diffusivity, chosen to well represent the current climate, and find that this is sufficient to emulate warming response in general circulation models (GCMs). Meanwhile, model diagnoses of GCM simulations have shown that the diffusivity changes with climate. There is also ongoing development for diffusivity theories based on atmospheric dynamics. Here, we examine the role that changes in diffusivity play in the large-scale equator-to-pole contrast in surface warming in EBMs, building on previous analytic EBM theories for polar-amplified warming. New analytic theories for two formulations of climate-state-dependent diffusivity capture the results of numerical EBM solutions. For reasonable choices of parameter values, the success of the new analytic theories reveals why the change of diffusivity is limited in response to radiative forcing and does not eliminate polar-amplified warming.

An idealized aquaplanet moist global atmospheric model with realistic radiative transfer but no clouds and no convective parameterization is found to possess multiple climate equilibria. When forced symmetrically about the equator, in some cases the Inter Tropical Convergence Zone (ITCZ) migrates to an off-equatorial equilibrium position. Mechanism denial experiments prescribing relative humidity imply that radiation-circulation coupling is essential to this instability. The cross-equatorial asymmetry occurs only when the underlying slab ocean is sufficiently deep and the atmosphere's spectral dynamical core is sufficiently coarse (∼T170 or less with our control parameters). At higher resolutions, initializing with an asymmetric state indicates metastability with very slow (thousands of days) return to hemispheric symmetry. There is some sensitivity to the model timestep, which affects the time required to transition to the asymmetric state, with little effect on the equilibrium climate. The instability is enhanced when the planetary boundary layer scheme favors deeper layers or by a prescribed meridional heat transport away from the equator within the slab. The instability is not present when the model is run with a convective parameterization scheme commonly utilized in idealized moist models. We argue that the instability occurs when the asymmetric heating associated with a spontaneous ITCZ shift drives a circulation that rises poleward of the perturbed ITCZ. These results serve as a warning of the potential for instability and non-uniqueness of climate that may complicate studies with idealized models of the tropical response to perturbations in forcing.

Chang, Chiung-Yin, and Isaac M Held, June 2022: A scaling theory for the diffusivity of poleward eddy heat transport based on Rhines scaling and the global entropy budget. Journal of the Atmospheric Sciences, 79(6), DOI:10.1175/JAS-D-21-0242.11743-1758. Abstract

Diffusive theories for the meridional atmospheric energy transport can summarize our understanding of this central aspect of the general circulation. They can also be utilized in simple models of Earth’s energy balance to help interpret the response of the system to perturbations. A theory for this diffusivity of eddy heat transport is described based on Rhines scaling and the global entropy budget, each of which provides a constraint between the kinetic energy dissipation and the diffusivity. An expression for the diffusivity is then obtained by eliminating the dissipation from this set of two constraints. The theory can be thought of as a generalization of the theories of Held–Larichev and Barry–Craig–Thuburn. The theory is compared to simulations of the Held–Suarez idealized dry atmospheric model. Limitations of the theory are emphasized. The form of the theory allows it to be readily generalized to a moist atmosphere.

We describe an idealized primitive-equation model for studying mesoscale turbulence and leverage a hierarchy of grid resolutions to make eddy-resolving calculations on the finest grids more affordable. The model has intermediate complexity, incorporating basin-scale geometry with idealized Atlantic and Southern oceans and with non-uniform ocean depth to allow for mesoscale eddy interactions with topography. The model is perfectly adiabatic and spans the Equator and thus fills a gap between quasi-geostrophic models, which cannot span two hemispheres, and idealized general circulation models, which generally include diabatic processes and buoyancy forcing. We show that the model solution is approaching convergence in mean kinetic energy for the ocean mesoscale processes of interest and has a rich range of dynamics with circulation features that emerge only due to resolving mesoscale turbulence.

Although classical theories of midlatitude momentum fluxes focus on the wave–mean flow interaction, wave–wave interactions may be important for generating long waves. It is shown in this study that this nonlinear generation has implications for eddy momentum fluxes in some regimes. Using a two-layer quasigeostrophic model of a baroclinic jet on a β plane, statistically steady states are explored in which the vertically integrated eddy momentum flux is divergent at the center of the jet, rather than convergent as in Earthlike climates. One moves toward this less familiar climate from more Earthlike settings by reducing either β, frictional drag, or the width of the baroclinic zone, or by increasing the upper bound of resolvable wavelengths by lengthening the zonal channel. Even in Earthlike settings, long waves diverge momentum from the jet, but they are too weak to compete with short unstable waves that converge momentum. We argue that long waves are generated by breaking of short unstable waves near their critical latitudes, where long waves converge momentum while diverging momentum at the center of the jet. Quasi-linear models with no wave–wave interaction can qualitatively capture the Earthlike regime but not the regime with momentum flux divergence at the center of the jet, because the nonlinear wave breaking and long-wave generation processes are missing. Therefore, a more comprehensive theory of atmospheric eddy momentum fluxes should take into account the nonlinear dynamics of long waves.

Chang, Chiung-Yin, and Isaac M Held, June 2019: The control of surface friction on the scales of baroclinic eddies in a homogeneous quasigeostrophic two-layer model. Journal of the Atmospheric Sciences, 76(6), DOI:10.1175/JAS-D-18-0333.1. Abstract

In idealized models of the extratropical troposphere, both β and surface friction can control the equilibrated scales of baroclinic eddies by stopping the inverse cascade. A scaling theory on how surface friction alone sets these scales is proposed by Held (1999) in the case of a quadratic drag law. However, the theory breaks down when friction is modeled by linear damping, and there are other reasons to suspect that it is oversimplified. An ideal system to test the theory is the homogeneous two-layer quasigeostrophic model in the β = 0 limit with quadratic damping. This study investigates some numerical simulations of the model to analyze two causes of the theory’s breakdown. They are 1) the asymmetry between two layers due to confinement of friction to the lower layer, and 2) deviation from a spectrally local inverse energy cascade due to the spread of wavenumbers over which energy is input into the barotropic mode. The former is studied by comparing the simulations with drag appearing asymmetrically or symmetrically between the two layers. The latter is addressed with a heuristic modification of the theory. A regime where eddies equilibrate without an inverse cascade is also examined. A comparison is then made between quadratic and linear drag simulations. The connection to a competing theory based on the dynamics of equivalent barotropic vortices with thermal signatures is further discussed. Finally, we present an example of an inhomogeneous statistically steady state to argue that the diffusivity obtained from the homogeneous model has relevance to more realistic configurations.