If model parameterizations of unresolved physics, such as the variety of upper ocean mixing processes, are to hold over the large range of time and space scales of importance to climate, they must be strongly physically based. Observations, theories, and models of oceanic vertical mixing are surveyed. Two distinct regimes are identified: ocean mixing in the boundary layer near the surface under a variety of surface forcing conditions (stabilizing, destabilizing, and wind driven), and mixing in the ocean interior due to internal waves, shear instability, and double diffusion (arising from the different molecular diffusion rates of heat and salt). Mixing schemes commonly applied to the upper ocean are shown not to contain some potentially important boundary layer physics. Therefore a new parameterization of oceanic boundary layer mixing is developed to accommodate some of this physics. It includes a scheme for determining the boundary layer depth h, where the turbulent contribution to the vertical shear of a bulk Richardson number is parameterized. Expressions for diffusivity and nonlocal transport throughout the boundary layer are given. The diffusivity is formulated to agree with similarity theory of turbulence in the surface layer and is subject to the conditions that both it and its vertical gradient match the interior values at h. This nonlocal “K profile parameterization” (KPP) is then verified and compared to alternatives, including its atmospheric counterparts. Its most important feature is shown to be the capability of the boundary layer to penetrate well into a stable thermocline in both convective and wind-driven situations. The diffusivities of the aforementioned three interior mixing processes are modeled as constants, functions of a gradient Richardson number (a measure of the relative importance of stratification to destabilizing shear), and functions of the double-diffusion density ratio, Rρ. Oceanic simulations of convective penetration, wind deepening, and diurnal cycling are used to determine appropriate values for various model parameters as weak functions of vertical resolution. Annual cycle simulations at ocean weather station Papa for 1961 and 1969–1974 are used to test the complete suite of parameterizations. Model and observed temperatures at all depths are shown to agree very well into September, after which systematic advective cooling in the ocean produces expected differences. It is argued that this cooling and a steady salt advection into the model are needed to balance the net annual surface heating and freshwater input. With these advections, good multiyear simulations of temperature and salinity can be achieved. These results and KPP simulations of the diurnal cycle at the Long-Term Upper Ocean Study (LOTUS) site are compared with the results of other models. It is demonstrated that the KPP model exchanges properties between the mixed layer and thermocline in a manner consistent with observations, and at least as well or better than alternatives.

Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization

A computationally efficient relocatable system for generalized inverse (GI) modeling of barotropic ocean tides is described. The GI penalty functional is minimized using a representer method, which requires repeated solution of the forward and adjoint linearized shallow water equations (SWEs). To make representer computations efficient, the SWEs are solved in the frequency domain by factoring the coefficient matrix for a finite-difference discretization of the second-order wave equation in elevation. Once this matrix is factored representers can be calculated rapidly. By retaining the first-order SWE system (defined in terms of both elevations and currents) in the definition of the discretized GI penalty functional, complete generality in the choice of dynamical error covariances is retained. This allows rational assumptions about errors in the SWE, with soft momentum balance constraints (e.g., to account for inaccurate parameterization of dissipation), but holds mass conservation constraints. Wh...

/pdf/efficient-inverse-modeling-of-barotropic-ocean-tides-2awn93pupi.pdf

Efficient Inverse Modeling of Barotropic Ocean Tides

Abyssal recipes II: energetics of tidal and wind mixing

It is now well understood that data on soil moisture and sea surface salinity (SSS) are required to improve meteorological and climate predictions. These two quantities are not yet available globally or with adequate temporal or spatial sampling. It is recognized that a spaceborne L-band radiometer with a suitable antenna is the most promising way of fulfilling this gap. With these scientific objectives and technical solution at the heart of a proposed mission concept the European Space Agency (ESA) selected the Soil Moisture and Ocean Salinity (SMOS) mission as its second Earth Explorer Opportunity Mission. The development of the SMOS mission was led by ESA in collaboration with the Centre National d'Etudes Spatiales (CNES) in France and the Centro para el Desarrollo Tecnologico Industrial (CDTI) in Spain. SMOS carries a single payload, an L-Band 2-D interferometric radiometer operating in the 1400-1427-MHz protected band . The instrument receives the radiation emitted from Earth's surface, which can then be related to the moisture content in the first few centimeters of soil over land, and to salinity in the surface waters of the oceans. SMOS will achieve an unprecedented maximum spatial resolution of 50 km at L-band over land (43 km on average over the field of view), providing multiangular dual polarized (or fully polarized) brightness temperatures over the globe. SMOS has a revisit time of less than 3 days so as to retrieve soil moisture and ocean salinity data, meeting the mission's science objectives. The caveat in relation to its sampling requirements is that SMOS will have a somewhat reduced sensitivity when compared to conventional radiometers. The SMOS satellite was launched successfully on November 2, 2009.

/pdf/the-smos-mission-new-tool-for-monitoring-key-elements-ofthe-1ekd44425c.pdf

The SMOS Mission: New Tool for Monitoring Key Elements ofthe Global Water Cycle

Atmospheric and Oceanic Fluid Dynamics

Ocean microstructure data show that turbulent mixing in the deep Brazil Basin of the South Atlantic Ocean is weak at all depths above smooth abyssal plains and the South American Continental Rise. The diapycnal diffusivity there was estimated to be less than or approximately equal to 0.1 x 10(-4) meters squared per second. In contrast, mixing rates are large throughout the water column above the rough Mid-Atlantic Ridge, and the diffusivity deduced for the bottom-most 150 meters exceeds 5 x 10(-4) meters squared per second. Such patterns in vertical mixing imply that abyssal circulations have complex spatial structures that are linked to the underlying bathymetry.

https://science.sciencemag.org/content/sci/276/5309/93.full.pdf

Spatial variability of turbulent mixing in the Abyssal Ocean

The overturning circulation of the ocean plays an important role in modulating the Earth's climate. But whereas the mechanisms for the vertical transport of water into the deep ocean--deep water formation at high latitudes--and horizontal transport in ocean currents have been largely identified, it is not clear how the compensating vertical transport of water from the depths to the surface is accomplished. Turbulent mixing across surfaces of constant density is the only viable mechanism for reducing the density of the water and enabling it to rise. However, measurements of the internal wave field, the main source of energy for mixing, and of turbulent dissipation rates, have typically implied diffusivities across surfaces of equal density of only approximately 0.1 cm2 s(-1), too small to account for the return flow. Here we report measurements of tracer dispersion and turbulent energy dissipation in the Brazil basin that reveal diffusivities of 2-4 cm2 s(-1) at a depth of 500 m above abyssal hills on the flank of the Mid-Atlantic Ridge, and approximately 10 cm2 s(-1) nearer the bottom. This amount of mixing, probably driven by breaking internal waves that are generated by tidal currents flowing over the rough bathymetry, may be large enough to close the buoyancy budget for the Brazil basin and suggests a mechanism for closing the global overturning circulation.

Evidence for enhanced mixing over rough topography in the abyssal ocean

The modern study of double-diffusive convection began with Melvin Stern's article on "The Salt Fountain and Thermohaline Convection" in 1960. In that paper, he showed how opposing stratifications of two component species could drive convection if their diffusivities differed. Stommel ct al (1956) had earlier noted that there was significant potential energy available in the decrease of salinity with depth found in much of the tropical and subtropical ocean. While they suggested that a flow (the salt fountain) would be driven in a thermally-conducting pipe, it was Stern who realized that the two orders of magnitude difference in heat and salt diffusivities allowed the ocean to form its own pipes. These later came to be known as "salt fingers." Stern also identified the potential for the oscillatory instability when cold, fresh water overlies warm, salty water in the 1960 paper, though only in a footnote. Turner & Stommel (1964) demonstrated the "diffusive-convection" process a few years later. From these beginnings in oceanography over three decades ago, double diffusion has come to be recognized as an important convection process in a wide variety of fluid media, including magmas, metals, and stellar interiors (Schmitt 1983, Turner 1985). However, it is interesting to note that about one hundred years before Stern's paper, W. S. Jevons (1857) reported on the observation of long, narrow convection cells formed when warm, salty water was introduced over cold, fresh water. He correctly attributed the phenomenon to a difference in the diffusivities for heat and

Double diffusion in oceanography

Fine- and microstructure data from a free fall profiler are analyzed to test models that relate the turbulent dissipation rate (e) to characteristics of the internal wave field. The data were obtained from several distinct been previously available. Observations from the ocean interior with negligible large-scale flow were examined to address the buoyancy scaling of e. These data exhibited a factor of 140 range in squared buoyancy frequency (N 2 ) with depth and uniform internal wave characteristics, consistent with the Garrett-Munk spectrum. The magnitude of e and its variation with N(∼N 2 ) was best described by the dynamical model of Henyey et al. A second dynamical model, by McComas and Muller, predicted an appropriate buoyancy scaling but overestimated the observed dissipation rates. Two kinematical dissipation parametrizations predicted buoyancy scalings of N 3/2 ; these are shown to be inconscient with the observations. Data from wave fields that depart from the canonical GM description are also examined an interpreted with reference to the dynamical models. The measurements came from a warm core ring dominated by strong near-inertial shears, a region of steep topography exhibiting high-frequency internal wave characteristics, and a midocean regime dominated at large wavelengths by an internal tide. Of the dissipation predictions examined, those of the Henyey et al. model in which eN − 2 scales as E 2 , where E is the nondimensional spectral shear level, were most consistent with observations. Nevertheless, the predictions for these cases exhibited departures from the observations by more than an order of magnitude. For the present data, these discrepancies appeared most sensitive to the distribution of internal wave frequency, inferred here from the ratio of shear spectral level to that for strain. Application of a frequency-based correction to the Henyey et al. model returned dissipation values consistent with observed estimates to within a factor of 2. These results indicate that the kinetic energy dissipation rate (and attendant turbulent mixing) is small for the background Garrett and Munk internal wave conditions (0.25eN −2 ∼ 0.7 × 10 − 5 m 2 s − 1). Dissipation and mixing become large when wave shear spectral levels are elevated, particularly by high-frequency waves. Thus, internal wave reflection/generation at steep topographic features appear promising candidates for achieving enhanced dissipation and strong diapycnal mixing in the deep ocean that appears required by box models and advection-diffusion balances

/pdf/finescale-parameterizations-of-turbulent-dissipation-2rptlqxmd9.pdf

Finescale parameterizations of turbulent dissipation

Profiles of diapycnal eddy diffusivity to a maximum depth of 4000 meters were derived from ocean velocity and temperature microstructure data obtained in conjunction with separate experiments in the Northeast Pacific and Northeast Atlantic oceans. These profiles indicate that in the ocean interior where the internal wave field is at background intensity, the diapycnal eddy diffusivity is small (on the order of 0.1 x 10(-4) meters squared per second) and independent of depth, in apparent contradiction with large-scale budget studies. Enhanced dissipation is observed in regions of elevated internal wave energy, particularly near steeply sloping boundaries (where the eddy diffusivity estimates exceed 1 x 10(-4) meters squared per second). These results suggest that basin-averaged mixing rates may be dominated by processes occurring near the ocean boundaries.

http://science.sciencemag.org/content/sci/264/5162/1120.full.pdf

Raymond W. Schmitt

Papers

Spatial variability of turbulent mixing in the Abyssal Ocean

Evidence for enhanced mixing over rough topography in the abyssal ocean

Double diffusion in oceanography

Finescale parameterizations of turbulent dissipation

Estimates of Diapycnal Mixing in the Abyssal Ocean