# Bibliography - Malte Jansen

- Chai, Junyi, Malte Jansen, and Geoffrey K Vallis, August 2016:
**Equilibration of a baroclinic planetary atmosphere toward the limit of vanishing bottom friction**. *Journal of the Atmospheric Sciences*, **73(8)**, DOI:10.1175/JAS-D-15-0329.1 .

[ Abstract ]This paper discusses whether and how a baroclinic atmosphere can equilibrate with very small bottom friction in a dry, primitive equation, general circulation model. The model is forced by a Newtonian relaxation of temperature to a prescribed temperature profile, and it is damped by a linear friction near the lower boundary. When friction is decreased by four orders of magnitude, kinetic energy dissipation by friction gradually becomes negligible, while “energy recycling” becomes dominant. In this limit kinetic energy is converted back into potential energy at the largest scales, thus closing the energy cycle without significant frictional dissipation. The momentum fluxes are of opposite sign in the upper and lower atmosphere: in the upper atmosphere, eddies converge momentum into the westerly jets, however, in the lower atmosphere, the eddies diverge momentum out of the westerly jets. The secondary circulation driven by the meridional eddy momentum fluxes thus acts to increase the baroclinicity of the westerly jet. This regime may be relevant for the Jovian atmosphere, where the frictional time scale may be much larger than the radiative damping time scale.

- Jansen, Malte, and R Ferrari, January 2015:
**Diagnosing the Vertical Structure of the Eddy Diffusivity in Real and Idealized Atmospheres**. *Quarterly Journal of the Royal Meteorological Society*, **141(687)**, DOI:10.1002/qj.2387 .

[ Abstract ]Earth's extra-tropical troposphere is equilibrated by turbulent eddy fluxes of potential temperature and momentum. The equilibrated state has the remarkable characteristic that isentropic slopes leaving the surface in the sub-tropics reach the tropopause near the poles. It has been speculated that turbulent eddy fluxes maintain this state for a wide range of radiative forcing and planetary parameters. In a previous study the authors showed that this state needs to be associated with an eddy diffusivity of Ertel potential vorticity that is largest at the surface and decays through the troposphere to approximately zero at the tropopause. This result is confirmed in this study using atmospheric reanalysis and idealized numerical simulations. However, it is also shown that the vertical profile of the eddy diffusivity can change, resulting in different isentropic slopes and climates. This is illustrated with a series of idealized numerical simulations with varying planetary scales and rotation rates.

- Jansen, Malte, Alistair Adcroft, Robert Hallberg, and Isaac M Held, August 2015:
**Parameterization of eddy fluxes based on a mesoscale energy budget**. *Ocean Modelling*, **92**, DOI:10.1016/j.ocemod.2015.05.007 .

[ Abstract ]It has recently been proposed to formulate eddy diffusivities in ocean models based on a mesoscale eddy kinetic energy (EKE) budget. Given an appropriate length scale, the mesoscale EKE can be used to estimate an eddy diffusivity based on mixing length theory. This paper discusses some of the open questions associated with the formulation of an EKE budget and mixing length, and proposes an improved energy budget-based parameterization for the mesoscale eddy diffusivity. A series of numerical simulations is performed, using an idealized flat-bottomed β-plane channel configuration with quadratic bottom drag. The results stress the importance of the mixing length formulation, as well as the formulation for the bottom signature of the mesoscale EKE, which is important in determining the rate of EKE dissipation. In the limit of vanishing planetary vorticity gradient, the mixing length is ultimately controlled by bottom drag, though the frictional arrest scale predicted by barotropic turbulence theory needs to be modified to account for the effects of baroclinicity. Any significant planetary vorticity gradient, β, is shown to suppress mixing, and limit the effective mixing length to the Rhines scale. While the EKE remains moderated by bottom friction, the bottom signature of EKE is shown to decrease as the appropriately non-dimensionalized friction increases, which considerably weakens the impact of changes in the bottom friction compared to barotropic turbulence. For moderate changes in the bottom-friction, eddy fluxes are thus reasonably well approximated by the scaling relation proposed by Held, I.M., Larichev, V.D., 1996. A scaling theory for horizontally homogeneous baroclinically unstable ow on a beta plane. J. Atmos. Sci. 53, 946–952., which ignores the effect of bottom friction.

- Jansen, Malte, Alistair Adcroft, Robert Hallberg, and Isaac M Held, October 2015:
**Energy budget-based backscatter in an eddy permitting primitive equation model**. *Ocean Modelling*, **94**, DOI:10.1016/j.ocemod.2015.07.015 .

[ Abstract ]It has recently been proposed to formulate eddy diffusivities in ocean models based on a mesoscale eddy kinetic energy (EKE) budget. Given an appropriate length scale, the mesoscale EKE can be used to estimate an eddy diffusivity based on mixing length theory. This paper discusses some of the open questions associated with the formulation of an EKE budget and mixing length, and proposes an improved energy budget-based parameterization for the mesoscale eddy diffusivity. A series of numerical simulations is performed, using an idealized flat-bottomed β-plane channel configuration with quadratic bottom drag. The results stress the importance of the mixing length formulation, as well as the formulation for the bottom signature of the mesoscale EKE, which is important in determining the rate of EKE dissipation. In the limit of vanishing planetary vorticity gradient, the mixing length is ultimately controlled by bottom drag, though the frictional arrest scale predicted by barotropic turbulence theory needs to be modified to account for the effects of baroclinicity. Any significant planetary vorticity gradient, β, is shown to suppress mixing, and limit the effective mixing length to the Rhines scale. While the EKE remains moderated by bottom friction, the bottom signature of EKE is shown to decrease as the appropriately non-dimensionalized friction increases, which considerably weakens the impact of changes in the bottom friction compared to barotropic turbulence. For moderate changes in the bottom-friction, eddy fluxes are thus reasonably well approximated by the scaling relation proposed by Held and Larichev (1996), which ignores the effect of bottom friction.

- Zurita-Gotor, Pablo, Isaac M Held, and Malte Jansen, September 2015:
**Kinetic energy-conserving hyperdiffusion can improve low-resolution atmospheric models**. *Journal of Advances in Modeling Earth Systems*, **7(3)**, DOI:10.1002/2015MS000480 .

[ Abstract ]Motivated by findings that energetically-consistent subgrid dissipation schemes can improve eddy-permitting ocean simulations, this work investigates the impact of the subgrid dissipation scheme on low-resolution atmospheric dynamical cores. A kinetic energy-conserving dissipation scheme is implemented in the model adding a negative viscosity term that injects back into the eddy field the kinetic energy dissipated by horizontal hyperdiffusion. The kinetic energy-conserving scheme enhances numerical convergence when horizontal resolution is changed with fixed vertical resolution and gives superior low-resolution results. Improvements are most obvious for eddy kinetic energy but also found in other fields, particularly with strong or little scale-selective horizontal hyperdiffusion. One advantage of the kinetic energy-conserving scheme is that it reduces the sensitivity of the model to changes in the subgrid dissipation rate, providing more robust results.

- Ferrari, R, and Malte Jansen, et al., June 2014:
**Antarctic sea ice control on ocean circulation in present and glacial climates**. *Proceedings of the National Academy of Sciences*, **111(24)**, DOI:10.1073/pnas.1323922111 .

[ Abstract ]In the modern climate, the ocean below 2 km is mainly filled by waters sinking into the abyss around Antarctica and in the North Atlantic. Paleoproxies indicate that waters of North Atlantic origin were instead absent below 2 km at the Last Glacial Maximum, resulting in an expansion of the volume occupied by Antarctic origin waters. In this study we show that this rearrangement of deep water masses is dynamically linked to the expansion of summer sea ice around Antarctica. A simple theory further suggests that these deep waters only came to the surface under sea ice, which insulated them from atmospheric forcing, and were weakly mixed with overlying waters, thus being able to store carbon for long times. This unappreciated link between the expansion of sea ice and the appearance of a voluminous and insulated water mass may help quantify the ocean’s role in regulating atmospheric carbon dioxide on glacial–interglacial timescales. Previous studies pointed to many independent changes in ocean physics to account for the observed swings in atmospheric carbon dioxide. Here it is shown that many of these changes are dynamically linked and therefore must co-occur.

- Jansen, Malte, and Isaac M Held, August 2014:
**Parameterizing subgrid-scale eddy effects using energetically consistent backscatter**. *Ocean Modelling*, **80**, DOI:10.1016/j.ocemod.2014.06.002 .

[ Abstract ]In the near future we expect the resolution of many IPCC-class ocean models to enter the “eddy-permitting” regime. At this resolution models can produce reasonable eddy-like disturbances, but can still not properly resolve geostrophic eddies at all relevant scales. Adequate parameterizations representing sub-grid eddy effects are thus necessary. Most eddy-permitting models presently employ some kind of hyper-viscosity, which is shown to cause a significant amount of energy dissipation. However, comparison to higher resolution simulations shows that only enstrophy, but almost no energy, should be dissipated below the grid-scale. As a result of the artificial energy sink associated with viscous parameterizations, the eddy fields in eddy permitting models are generally not energetic enough.
To overcome this problem, we propose a class of sub-grid parameterizations which dissipate enstrophy but little or no energy. The idea is to combine a standard hyperviscous closure with some mechanism to return dissipated energy to the resolved flow. Enstrophy dissipation remains ensured because the energy is returned at larger scales. Two simple ways to return the energy are proposed: one using a stochastic excitation and one using a negative Laplacian viscosity. Both approaches are tested in an idealized two-layer quasi-geostrophic model. Either approach is shown to greatly improve the solutions in simulations with typical eddy-permitting resolutions. The adaptation of the proposed parameterization for use in realistic ocean models is discussed.

Direct link to page: http://www.gfdl.noaa.gov/bibliography/results.php?author=3988