David R. Jackett

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.

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.

Algorithms for Density, Potential Temperature, Conservative Temperature, and the Freezing Temperature of Seawater

Algorithms are presented for density, potential temperature, conservative temperature, and the freezing temperature of seawater. The algorithms for potential temperature and density (in terms of potential temperature) are updates to routines recently published by McDougall et al., while the algorithms involving conservative temperature and the freezing temperatures of seawater are new. The McDougall et al. algorithms were based on the thermodynamic potential of Feistel and Hagen; the algorithms in this study are all based on the “new extended Gibbs thermodynamic potential of seawater” of Feistel. The algorithm for the computation of density in terms of salinity, pressure, and conservative temperature produces errors in density and in the corresponding thermal expansion coefficient of the same order as errors for the density equation using potential temperature, both being twice as accurate as the International Equation of State when compared with Feistel’s new equation of state. An inverse function relating potential temperature to conservative temperature is also provided. The difference between practical salinity and absolute salinity is discussed, and it is shown that the present practice of essentially ignoring the difference between these two different salinities is unlikely to cause significant errors in ocean models.

Using Sea Level Rise Projections for Urban Planning in Australia

Abstract This study deals with incorporating predictions of sea level rise into practical municipal planning. Predictions of global mean sea level rise can be made with more confidence than many other aspects of climate change science. The world has warmed in the past century, and as a result global mean sea level has risen and is expected to continue to rise. Even so, there are significant uncertainties regarding predictions of sea level. These arise from two main sources: the future amount of greenhouse gases in the atmosphere, and the ability of models to predict the impact of increasing concentrations of greenhouse gases. Current knowledge regarding the effect of global warming on sea level rise is reviewed. Global mean sea level is expected to rise by 3–30 cm by 2040, and 9–88 cm by 2100. An important remaining uncertainty is the future contribution of surface water storage (for example, lakes and reservoirs) to changes in sea level. In addition, there are also significant local sea level effects that need to be taken account in many regions of the globe, including isostatic and tectonic effects. The thermal expansion component of sea level rise is also likely to vary regionally, due to regional differences in the rate of downward mixing of heat and to changes in ocean currents. The current state of planning for sea level rise in Australia is reviewed. While not all coastal municipalities include sea level rise in their planning schemes, the recent adoption in a number of States of new planning schemes with statutory authority creates a changed planning environment for local government. Coastal urban planning needs to take sea level rise into account because its effects will be apparent during the typical replacement time of urban infrastructure such as buildings (before about 70 years). For local planning, ideally a risk assessment methodology may be employed to estimate the risk caused by sea level rise. In many locations, planning thresholds would also have to be considered in the light of possible changes in storm surge climatology due to changes in storm frequency and intensity, and (in some locations) changes to return periods of riverine flooding. In the medium term (decades), urban beaches will need beach re-nourishment and associated holding structures such as sea walls. Changes in storm and wave climatology are crucial factors for determining future coastal erosion.

A Model of Sea Level Rise Caused by Ocean Thermal Expansion

Abstract Warming of the atmosphere as a result of an increased concentration of greenhouse gases is expected to lead to a significant rise is global sea level. We present estimates of the component of this sea level rise caused by thermal expansion of the ocean. These estimates are based on the idea that the upper layers of the main gyres of the ocean are ventilated by the subduction of water at higher latitudes and its subsequent equatorward and downward flow into the main thermocline along surfaces of constant “density”. In this mechanism, heat enters the ocean by an advection process rather than by vertical diffusion, as in previous estimates of the component of sea level rise that is caused by thermal expansion. After the heat initially enters the subtropical gyres by subduction, it is then redistributed to preserve gradients of the depth-integrated pressure field, by an adjustment involving low vertical-mode baroclinic waves. Estimates of historical sea level rise based on this simple ventilation sch...

The Meridional Overturning Cells of a World Ocean Model in Neutral Density Coordinates

Abstract A comparison is made of the meridional overturning circulation in a coarse-resolution World Ocean model when the integration is performed along (i) level, (ii) potential density, and (iii) neutral density surfaces. In the level-surface calculation, all the usual cells are evident, including the Atlantic “conveyor,” the Deacon cell, and the direct Antarctic cell. In the potential or neutral density calculations, all cells remain present; however, the Deacon cell is greatly reduced in strength (to just a few Sverdrups). An analysis of the thermodynamics underlying the dianeutral motion is conducted. Most dianeutral motion results from fluxes associated with the vertical diffusivity and the (unphysical) horizontal diffusivity. Caballing is not important, despite the inclusion of isopycnal diffusivity. The mechanism of the residual Deacon cell involves densification near 40°5 resulting from fluxes associated with the horizontal diffusivity. Horizontal diffusivity results in substantial dianeutral mot...

An Assessment of Orthobaric Density in the Global Ocean

Abstract Orthobaric density has recently been advanced as a new density variable for displaying ocean data and as a coordinate for ocean modeling. Here the extent to which orthobaric density surfaces are neutral is quantified and it is found that orthobaric density surfaces are less neutral in the World Ocean than are potential density surfaces referenced to 2000 dbar. Another property that is important for a vertical coordinate of a layered model is the quasi-material nature of the coordinate and it is shown that orthobaric density surfaces are significantly non-quasi-material. These limitations of orthobaric density arise because of its inability to accurately accommodate differences between water masses at fixed values of pressure and in situ density such as occur between the Northern and Southern Hemisphere portions of the World Ocean. It is shown that special forms of orthobaric density can be quite accurate if they are formed for an individual ocean basin and used only in that basin. While orthobari...

Availability predictions by hepatic elimination models for Michaelis―Menten kinetics

Numerical methods have been used to compare the availability predictions of a number of hepatic elimination models when Michaelis-Menten kinetics is operative. Propranolol and galactose were used as model compounds. Lower availabilities were predicted by the dispersion model than by a segregated distribution model for both compounds. The differences in the predictions were most pronounced for models corresponding to a large variation in solute residence times in the liver. The predictions of the tank-in-series, dispersion model with mixed boundary conditions and dispersion model with Dankwerts boundary conditions were similar over all concentrations studied. Changes in blood flow and protein binding provided little discrimination between the model predictions. It is concluded that micromixing of blood between sinusoids and the anatomical sites of mixing are important determinants of availability when liver eliminating enzymes are partially saturated.

On the helical nature of neutral trajectories in the ocean

Abstract A neutral tangent plane is defined so that small isentropic and adiabatic displacements of a fluid parcel in this plane do not produce bouyant restoring forces on the parcel. This local stability argument can also be used to trace a neutral trajectory in space along some pre-determined path in latitude and longitude. If one integrates laterally around an entire ocean basin on a neutral trajectory, one can arrive at a different depth than that of the starting point on the original CTD cast. This means that the definition of a neutral surface is path-dependent. This is a real effect; it results from the complicated equation of state of seawater, and is not an artifact of errors in the lateral integration procedure. Dyed patches of fluid are mixed laterally by meso-scale eddies along these neutral helices, and at the same time they are smoothed and advected in the vertical direction by small-scale mixing processes. It is shown that, while a neutral surface is formally ill-defined mathematically (in the above path-dependent sense), this is of little importance for the purpose of constructing lateral maps of properties in the ocean, since the ambiguity in constructing a neutral surface is often less than the measurement accuracy of modern oceanographic instruments (≈0.003 kg m−3 in density). Path-dependence in the definition of a neutral surface occurs because α/β is a function of pressure (where α and β are the thermal expansion and haline contraction coefficients respectively). The local contribution to path-dependence is proportional to ▽ p · ▽ Sx ▽ Sx θ , representing the angle between an isobaric surface and the line of intersection of an isohaline surface and a surface of constant potential temperature. This, in turn, is proportional to ▽ n px ▽ n θ where ▽ n is the epineutral gradient operator for properties measured in a neutral tangent plane. That is, unless isobars and potential isotherms drawn in a neutral tangent plane are parallel, a neutral trajectory around this point will not lie in the plane, but will describe a helix in space. Although complete surfaces with the “neutral property” do not exist, the neutral tangent plane is everywhere well-defined. The lateral motion along helical neutral trajectories produces vertical advection in the ocean. A method is described in this paper of taking an approximately neutral surface and distributing the path-dependent effects over the surface in a least-squares sense. At each point in the ocean an error vector is found that represents the difference between the “best-fit” surface (which is a mathematically well-defined surface) and the local slope of the neutral tangent plane, providing a rational way of distributing the path-dependent vertical velocity on the surface. The vertical fluxes of heat, salt or tracer produced by the path-dependence of neutral surfaces do not have a signature in the dissipation rate of mechanical energy that can be measured with microstructure instrumentation.