Trevor J. McDougall

Parameterizing Eddy-Induced Tracer Transports in Ocean Circulation Models

Abstract It is shown that the effects of mesoscale eddies on tracer transports can be parameterized in a large-scale model by additional advection and diffusion of tracers. Thus, tracers are advected by the effective transport velocity, which is the sum of the large-scale velocity and the eddy-induced transport velocity. The density and continuity equations are the familiar equations for adiabatic, Boussinesq, and incompressible flow with the effective transport velocity replacing the large-scale velocity. One of the main points of this paper is to show how simple the parameterization of Gent and McWilliams appears when interpreted in terms of the effective transport velocity. This was not done in their original 1990 paper. It is also shown that, with the Gent and McWilliams parameterization, potential vorticity in the planetary geostrophic model satisfies an equation close to that for tracers. The analogy of this parameterization with vertical mixing of momentum is then described. The effect of the Gent ...

A Neutral Density Variable for the World’s Oceans

Abstract The use of density surfaces in the analysis of oceanographic data and in models of the ocean circulation is widespread. The present best method of fitting these isopycnal surfaces to hydrographic data is based on a linked sequence of potential density surfaces referred to a discrete set of reference pressures. This method is both time consuming and cumbersome in its implementation. In this paper the authors introduce a new density variable, neutral density γn, which is a continuous analog of these discretely referenced potential density surfaces. The level surfaces of γn form neutral surfaces, which are the most appropriate surfaces within which an ocean model’s calculations should be performed or analyzed. The authors have developed a computational algorithm for evaluating γn from a given hydrographic observation so that the formation of neutral density surfaces requires a simple call to a computational function. Neutral density is of necessity not only a function of the three state variables: s...

Minimal Adjustment of Hydrographic Profiles to Achieve Static Stability

Abstract Hydrographic data, be it raw or highly averaged observational data, contain substantial regions having vertical density inversions. An algorithm is described that minimally modifies such data so that the resulting hydrographic casts have vertical buoyancy frequency profiles larger than a specified lower bound. The method underlying the algorithm is based on the solution of a constrained weighted least-squares problem and maximizes the smoothness of the resulting salinity-potential temperature diagram. Examples are provided that demonstrate the effectiveness of the technique in minimally altering hydrographic data only in the immediate vicinity of the data that do not already satisfy the buoyancy frequency constraint. A modified equation of state, identical in form to the international equation of state of seawater but written in terms of potential rather than in situ temperature, is also provided, enabling rapid computation of the thermal expansion and saline contraction coefficients.

Diagnosing Climate Change and Ocean Ventilation Using Hydrographic Data

Abstract Changes in atmospheric forcing can affect the subsurface water column of the ocean by three different mechanisms. First, warmed mixed-layer water that is subducted into the ocean interior will cause subsurface warming; second, the subducted surface water can be freshened through changes in evaporation and precipitation; and third, the properties at a given depth may be changed by the vertical displacement of isotherms and isohalines without changes of water masses. These vertical displacements of the water column can be caused either by changes in the rates of renewal of water masses or by dynamical changes (such as changes in wind stress). A method for analysing the subsurface temporal changes in hydrographic data is described in terms of these three processes: “pure warming,” “pure freshening,” and “pure heave.” Linear relations are derived for the relative strength of each process in terms of the observed changes of potential temperature and salinity in two different coordinate frames: (i) con...

Decadal changes along an Indian Ocean section at 32°S and their interpretation

In the Indian Ocean subtropical gyre, historical temperature, salinity, and oxygen data with a median date of 1962 are compared with a hydrographic section taken at a mean latitude of 32°S in October-November 1987. Significant basinwide changes in all three hydrographic fields are observed below the mixed layer. On isobaric surfaces the main changes are (i) a warming of the upper 900 dbar of the water column with a maximum change in the sectional mean of 0.5°C, (ii) a freshening between 500 and 1500 dbar with a maximum freshening of 0.05 psu, and (iii) a pronounced decrease in oxygen concentration between 300 and 1000 dbar. Examination of water mass properties shows that very significant water mass changes have occurred. On isopycnals subantarctic mode water (SAMW) and Antarctic Intermediate Water (AAIW) have freshened and cooled. Both of these water masses are on average deeper in 1987. Using the analysis of Bindoff and McDougall (1994), the changes of temperature at constant depth and at constant density are used to show that the water mass changes can most simply be explained by a surface warming in the source region of SAMW and by increased precipitation in the source region of AAIW. The decrease in oxygen concentration can be explained simply by a slight slowing of the subtropical gyre allowing more time for biological consumption to decrease the oxygen concentration by water parcel translation from the formation area to the observation point. Estimates show that over the last 25 years there is an apparent decrease of the gyre spin rate of about 20% at the depth levels of SAMW; the estimated spin rate change decreases almost linearly with greater depth to zero at the oxygen minimum in Indian Deep Water (IDW). Below IDW the observed changes in oxygen concentration (and also the changes of temperature and salinity) are associated with the upward movement of isopycnals with no significant water mass change. The differences in temperature and salinity in the SAMW and AAIW are consistent with the relatively young age of these water masses inferred from CFC data.

The Temporal-Residual-Mean Velocity. Part II: Isopycnal Interpretation and the Tracer and Momentum Equations

Abstract Mesoscale eddies mix fluid parcels in a way that is highly constrained by the stratified nature of the fluid. The temporal-residual-mean (TRM) theory provides the link between the different views that are apparent from temporally averaging these turbulent flow fields in height coordinates and in density coordinates. Here the original TRM theory is modified so that it applies to unsteady flows. This requires a modification not only to the streamfunction (and hence the velocity vector) but also a specific interpretation of the density field; it is not the Eulerian-mean density. The TRM theory reduces the problem of parameterizing the eddy flux from three dimensions to two dimensions. The three-dimensional TRM velocity is shown to be the same as is obtained by averaging with respect to instantaneous density surfaces and the averaged conservation equations in height coordinates and in density coordinates are the same except for a nondivergent flux that is identified and explained. The TRM theory demo...

Potential Enthalpy: A Conservative Oceanic Variable for Evaluating Heat Content and Heat Fluxes

Abstract Potential temperature is used in oceanography as though it is a conservative variable like salinity; however, turbulent mixing processes conserve enthalpy and usually destroy potential temperature. This negative production of potential temperature is similar in magnitude to the well-known production of entropy that always occurs during mixing processes. Here it is shown that potential enthalpy—the enthalpy that a water parcel would have if raised adiabatically and without exchange of salt to the sea surface—is more conservative than potential temperature by two orders of magnitude. Furthermore, it is shown that a flux of potential enthalpy can be called “the heat flux” even though potential enthalpy is undefined up to a linear function of salinity. The exchange of heat across the sea surface is identically the flux of potential enthalpy. This same flux is not proportional to the flux of potential temperature because of variations in heat capacity of up to 5%. The geothermal heat flux across the o...

Accurate and Computationally Efficient Algorithms for Potential Temperature and Density of Seawater

Abstract An equation of state for seawater is presented that contains 25 terms and is an excellent fit to the Feistel and Hagen equation of state. It is written in terms of potential temperature (rather than in situ temperature), as required for efficient ocean model integrations. The maximum density error of the fit is 3 × 10–3 kg m–3 in the oceanographic ranges of temperature, salinity, and pressure. The corresponding maximum error in the thermal expansion coefficient is 4 × 10–7 °C–1, which is a factor of 12 less than the corresponding maximum difference between the Feistel and Hagen equation of state and the widely used but less accurate international equation of state. A method is presented to convert between potential temperature and in situ temperature using specific entropy based on the Gibbs function of Feistel and Hagen. The resulting values of potential temperature are substantially more accurate than those based on the lapse rate derived from the international equation of state.

The Relative Roles of Diapycnal and Isopycnal Mixing on Subsurface Water Mass Conversion

Abstract Fluid motion in the sea is known to occur predominantly along quasi-horizontal neutral surfaces but the very small diapycnal (i.e., across isopycnal) velocities often make a significant contribution to the conversation equations of heat, salt and tracer. By eliminating the diapycnal advection term between the conservation equations for (i) heat and (ii) salt, an equation is derived for the rate of change (Lagrangian derivative) of potential temperature θ on a neutral surface which has terms caused by (a) turbulent mixing along isopycnal surfaces (i.e., isopycnal mixing), (b) diapycnal turbulent mixing and (c) double-diffusive convection. Bemuse of the nature of the isopycnal reference frame, the diapycnal mixing terms do not take their expected forms. For example, the diapycnal turbulent mixing term is proportional to the diapycnal eddy diffusivity D multiplied by the curvature of the θ-S curve, d2S/dθ2, rather than the usual form (Dθx)x. If the θ−S curve is locally straight, small-scale turbulen...

Measurements of turbulence in a zero-mean-shear mixed layer

This paper is concerned with laboratory measurements of turbulence in a mixed layer and through a density interface, in the absence of a mean flow. The present results confirm the conclusion of Hopfinger & Toly (1976) that the turbulence in a mixed layer is not significantly affected by the slow entrainment of fluid across the bounding density interface. In a homogeneous fluid the turbulence intensity is found to be surprisingly non-uniform, even two grid mesh distances away from the grid. Velocity measurements have also been taken through a density interface (at the entraining boundary of a mixed layer) and the turbulence here varies in a manner that bears some resemblance to the theory of Hunt & Graham (1978). These velocity measurements were taken with a laser-Doppler anemometer and they were made possible by a novel experimental technique which eliminates the refractive index variations which normally occur in a turbulent, density-stratified liquid flow.