Baylor Fox-Kemper

Parameterization of Mixed Layer Eddies. Part I: Theory and Diagnosis

Ageostrophic baroclinic instabilities develop within the surface mixed layer of the ocean at horizontal fronts and efficiently restratify the upper ocean. In this paper a parameterization for the restratification driven by finite-amplitude baroclinic instabilities of the mixed layer is proposed in terms of an overturning streamfunction that tilts isopycnals from the vertical to the horizontal. The streamfunction is proportional to the product of the horizontal density gradient, the mixed layer depth squared, and the inertial period. Hence restratification proceeds faster at strong fronts in deep mixed layers with a weak latitude dependence. In this paper the parameterization is theoretically motivated, confirmed to perform well for a wide range of mixed layer depths, rotation rates, and vertical and horizontal stratifications. It is shown to be superior to alternative extant parameterizations of baroclinic instability for the problem of mixed layer restratification. Two companion papers discuss the numerical implementation and the climate impacts of this parameterization.

Mixed Layer Instabilities and Restratification

Abstract The restratification of the oceanic surface mixed layer that results from lateral gradients in the surface density field is studied. The lateral gradients are shown to be unstable to ageostrophic baroclinic instabilities and slump from the horizontal to the vertical. These instabilities, which are referred to as mixed layer instabilities (MLIs), differ from instabilities in the ocean interior because of the weak surface stratification. Spatial scales are O(1–10) km, and growth time scales are on the order of a day. Linear stability analysis and fully nonlinear simulations are used to study MLIs and their impact on mixed layer restratification. The main result is that MLIs are a leading-order process in the ML heat budget acting to constantly restratify the surface ocean. Climate and regional ocean models do not resolve the scales associated with MLIs and are likely to underestimate the rate of ML restratification and consequently suffer from a bias in sea surface temperatures and ML depths. In a ...

A global perspective on Langmuir turbulence in the ocean surface boundary layer

The turbulent mixing in thin ocean surface boundary layers (OSBL), which occupy the upper 100 m or so of the ocean, control the exchange of heat and trace gases between the atmosphere and ocean. Here we show that current parameterizations of this turbulent mixing lead to systematic and substantial errors in the depth of the OSBL in global climate models, which then leads to biases in sea surface temperature. One reason, we argue, is that current parameterizations are missing key surface-wave processes that force Langmuir turbulence that deepens the OSBL more rapidly than steady wind forcing. Scaling arguments are presented to identify two dimensionless parameters that measure the importance of wave forcing against wind forcing, and against buoyancy forcing. A global perspective on the occurrence of wave-forced turbulence is developed using re-analysis data to compute these parameters globally. The diagnostic study developed here suggests that turbulent energy available for mixing the OSBL is under-estimated without forcing by surface waves. Wave-forcing and hence Langmuir turbulence could be important over wide areas of the ocean and in all seasons in the Southern Ocean. We conclude that surface-wave-forced Langmuir turbulence is an important process in the OSBL that requires parameterization. Citation: Belcher, S. E., et al. (2012), A global perspective on Langmuir turbulence in the ocean surface boundary layer, Geophys. Res. Lett., 39, L18605, doi: 10.1029/2012GL052932.

Will There Be a Significant Change to El Niño in the Twenty-First Century?

AbstractThe El Nino–Southern Oscillation (ENSO) response to anthropogenic climate change is assessed in the following 1° nominal resolution Community Climate System Model, version 4 (CCSM4) Coupled Model Intercomparison Project phase 5 (CMIP5) simulations: twentieth-century ensemble, preindustrial control, twenty-first-century projections, and stabilized 2100–2300 “extension runs.” ENSO variability weakens slightly with CO2; however, various significance tests reveal that changes are insignificant at all but the highest CO2 levels. Comparison with the 1850 control simulation suggests that ENSO changes may become significant on centennial time scales; the lack of signal in the twentieth- versus twenty-first-century ensembles is due to their limited duration. Changes to the mean state are consistent with previous studies: a weakening of the subtropical wind stress curl, an eastward shift of the tropical convective cells, a reduction in the zonal SST gradient, and an increase in vertical thermal stratificati...

Parameterization of Mixed Layer Eddies. Part II: Prognosis and Impact

Abstract The authors propose a parameterization for restratification by mixed layer eddies that develop from baroclinic instabilities of ocean fronts. The parameterization is cast as an overturning streamfunction that is proportional to the product of horizontal buoyancy gradient, mixed layer depth, and inertial period. The parameterization has remarkable skill for an extremely wide range of mixed layer depths, rotation rates, and vertical and horizontal stratifications. In this paper a coarse resolution prognostic model of the parameterization is compared with submesoscale mixed layer eddy resolving simulations. The parameterization proves accurate in predicting changes to the buoyancy. The climate implications of the proposed parameterization are estimated by applying the restratification scaling to observations: the mixed layer depth is estimated from climatology, and the buoyancy gradients are from satellite altimetry. The vertical fluxes are comparable to monthly mean air–sea fluxes in large areas of...

Wind Waves in the Coupled Climate System

The role waves play in modulating interactions between oceans and atmosphere is emphasized. All exchanges (e.g., momentum, energy, heat, mass, radiation fluxes) are influenced by the geometrical and physical characteristics of the ocean surface, which separates the atmospheric and oceanic boundary layers. A qualitative overview of the main relevant surface gravity wave–driven processes at the air–sea interface that may have an important role in the coupled climate system in general and the atmospheric and oceanic boundary layers in particular is provided.

Can Large Eddy Simulation Techniques Improve Mesoscale Rich Ocean Models

Large-eddy simulations (LES) differ from other fluid flow computations in that the largest eddies are explicitly resolved and the smaller eddies are modeled (as engineers call it) or parameterized (as oceanographers call it). Modeling the ocean and atmosphere inspired the first large-eddy simulations, but true large-eddy simulations of the ocean and atmosphere are surprisingly rare. Ocean models almost always have eddy parameterizations, be they just larger than natural values of constant diffusivities and viscosities, perhaps oriented along isopycnal surfaces [Redi, 1982], or more sophisticated models such as the eddy extraction of potential energy by along-isopycnal bolus flux model of Gent and McWilliams [1990], perhaps with nonlinear transfer coefficient scaling [Visbeck et al., 1997; Held and Larichev, 1996], the “Neptune” effect parameterizing eddy-topography interaction [Holloway, 1993], or parameterizations based on linear instability analysis [Stone, 1972; Branscome, 1983; Killworth, 2005]. All of these parameterizations are designed for situations where eddies are not present or weak, and, as a result, the model resolution does not appear explicitly. The Herculean—perhaps Sisyphean—task of parameterizing the important effects of eddies in ocean models is done by offline theoretical analysis in lieu of resolved eddies. It is no wonder that there is enormous model sensitivity to the parameterization choices made [e.g., Steiner et al., 2004]. Leaving all to theory seems very unlikely to succeed, as eddies are sensitive to difficult to quantify parameters, such as interaction with unresolved topography [Holloway, 1993], regional variations of hydrodynamic instability [Killworth, 2005], bottom drag [Arbic and Flierl, 2004a; Thompson and Young, 2006], and subtle sensitivity to the Coriolis parameter variation [Arbic and Flierl, 2004b; Thompson and Young, 2007]. Subgrid-scale parameterizations for LES are quite different in character because they attempt only to represent the effects Can Large Eddy Simulation Techniques Improve Mesoscale Rich Ocean Models?

Langmuir–Submesoscale Interactions: Descriptive Analysis of Multiscale Frontal Spindown Simulations

AbstractThe interactions between boundary layer turbulence, including Langmuir turbulence, and submesoscale processes in the oceanic mixed layer are described using large-eddy simulations of the spindown of a temperature front in the presence of submesoscale eddies, winds, and waves. The simulations solve the surface-wave-averaged Boussinesq equations with Stokes drift wave forcing at a resolution that is sufficiently fine to capture small-scale Langmuir turbulence. A simulation without Stokes drift forcing is also performed for comparison. Spatial and spectral properties of temperature, velocity, and vorticity fields are described, and these fields are scale decomposed in order to examine multiscale fluxes of momentum and buoyancy. Buoyancy flux results indicate that Langmuir turbulence counters the restratifying effects of submesoscale eddies, leading to small-scale vertical transport and mixing that is 4 times greater than in the simulations without Stokes drift forcing. The observed fluxes are also sh...

On the Indeterminacy of Rotational and Divergent Eddy Fluxes

Abstract The decomposition of an eddy flux into a divergent flux component and a rotational flux component is not unique in a bounded or singly periodic domain. Therefore, assertions made under the assumption of uniqueness, implicit or explicit, may be meaningless. Nondivergent, irrotational perturbations are allowed to any decomposition that may affect naive interpretation of the flux field. These perturbations are restricted, however, so that unique diagnostics can be formed from the flux field.

ENSO Model Validation Using Wavelet Probability Analysis

A new method to quantify changes in El Nino-Southern Oscillation (ENSO) variability is presented, using the overlap between probability distributions of the wavelet spectrum as measured by the wavelet probability index (WPI). Examples are provided using long integrations of three coupled climate models. When subsets of Nino-3.4 time series are compared, the width of the confidence interval on WPI has an exponential de- pendence on the length of the subset used, with a statistically identical slope for all three models. This ex- ponential relationship describes the rate at which the system converges toward equilibrium and may be used to determine the necessary simulation length for robust statistics. For the three models tested, a minimum of 250 model years is required to obtain 90% convergence for Nino-3.4, longer than typical Intergovernmental Panel on Climate Change (IPCC) simulations. Applying the same decay relationship to observational data indicates that measuring ENSO variability with 90% confidence requires approximately 240 years of ob- servations, which is substantially longer than the modern SST record. Applying hypothesis testing techniques to the WPI distributions from model subsetsand from comparisons of model subsetsto the historicalNino-3.4 index then allows statistically robust comparisons of relative model agreement with appropriate confidence levels given the length of the data record and model simulation.