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A Neutral Density Variable for the World's Oceans

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A Neutral Density Variable for the World's Oceans FEBRUARY 1997 JACKETT AND MCDOUGALL 237 A Neutral Density Variable for the World's Oceans DAVID R. JACKETT AND TREVOR J. MCDOUGALL Antarctic CRC, University of Tasmania and Division of Oceanography, CSIRO, Hobart, Tasmania, Australia (Manuscript received 20 June 1995, in ®nal form 13 March 1996) 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 ®tting 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 gn, which is a continuous analog of these discretely referenced potential density surfaces. The level surfaces of gn 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 eval- uating gn 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: salinity, temperature, and pressure, but also of longitude and latitude. The spatial dependence of gn is achieved by accurately labeling a global hydrographic dataset with neutral density. Arbitrary hydrographic data can then be labeled with reference to this global gn ®eld. The global dataset is derived from the Levitus climatology of the world's oceans, with minor modi®cations made to ensure static stability and an adequate representation of the densest seawater. An initial ®eld of gn is obtained by solving, using a combination of numerical techniques, a system of differential equations that describe the fundamental neutral surface property. This global ®eld of gn values is further iterated in the characteristic coordinate system of the neutral surfaces to reduce any errors incurred during this solution procedure and to distribute the inherent path-dependent error associated with the de®nition of neutral surfaces over the entire globe. Comparisons are made between neutral surfaces calculated from gn and the present best isopycnal surfaces along independent sections of hydrographic data. The development of this neutral density variable increases the accuracy of the best-practice isopycnal surfaces currently in use but, more importantly, provides oceanographers with a much easier method of ®tting such surfaces to hydrographic data. 1. Introduction inverse models are faced with the problem of ®nding the actual positions of the surfaces in the model domain. The role of ``density'' surfaces in models of the ocean Even in the case of the prognostic level models, vali- is fundamental. These models range from the analysis dation of these models can only be made by comparison of hydrographic data on the most appropriate mixing surfaces (Reid 1986, 1989, 1994; McCartney 1982) to with data from the real ocean. It must be borne in mind the inversion of hydrographic data to obtain ocean cir- that the strong lateral mixing of these prognostic models culation and mixing (Schott and Stommel 1978; Wunsch occurs along neutral surfaces. As such, maps of prop- 1978; Killworth 1986; Zhang and Hogg 1992) to prog- erties along neutral surfaces and the heights of neutral nostic ``level'' or ``layer'' models (Bleck et al. 1992; surfaces are the most relevant variables from the real Hirst and Wenju 1994), which integrate forward in time ocean to be compared with the model output. the basic momentum and tracer conservation equations. Historically, the ®rst surfaces used for oceanic models All of these models have as their goal a description of were in situ density surfaces. Wust (1933) and Mont- the oceanic circulation and all use the concept of mixing gomery (1938) ®rst realized the inadequacy of these surfaces, between or along which the underlying physics surfaces for describing the circulation even at shallow governing oceanic ¯ow is analyzed. While prognostic depth, and they proposed a new variable, potential den- level models can adequately cope with these mixing sity, for quantitatively describing the isopycnal spread- surfaces (they only require the direction of the gradient ing of water masses in the ocean. Despite the widespread of the surfaces in order to align the mixing tensor), acceptance of this isopycnal mixing, de®ciencies in po- tential density surfaces for accurately describing precise isopycnal ¯ow have been known for some time. For example, McDougall (1987a) shows a surface across the Corresponding author address: Dr. David R. Jackett, Division of Oceanography, CSIRO, GPO Box 1538, Hobart, Tasmania 7001, Aus- North Atlantic Ocean where potential density and neu- tralia. tral surfaces diverge by 1500 m. Lynn and Reid (1968), q1997 American Meteorological Society Unauthenticated | Downloaded 09/28/21 11:32 AM UTC 238 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 27 Reid and Lynn (1971), and Ivers (1975) have all used while McDougall (1987a) made a detailed analysis of a series of potential density surfaces, referred to three the properties of these surfaces. These surfaces were different reference pressures, namely, 0, 2000, and 4000 de®ned by McDougall in terms of gradients of salinity db. In more recent work, Reid (1994) has found it nec- S and potential temperature u in the neutral surface, essary when describing the geostrophic circulation of while in McDougall and Jackett (1988) it was shown the Atlantic Ocean to further re®ne the de®nition of that the normal to these surfaces is in the direction of isopycnal surfaces by using potential density surfaces b=S 2 a=u, where a and b are the thermal expansion referred to a range of reference pressures, with incre- and saline contraction coef®cients, respectively. It is this ments in some regions of as little as 500 db. latter property that motivates the de®nition of neutral The reduction of the errors associated with a single surfaces that is most useful for our purposes, namely, reference pressure by the introduction of a range of that they are the surfaces everywhere perpendicular to reference pressures makes the actual computation of the the vector r(b=S 2 a=u). It is important to note that isopycnal surfaces dif®cult. Reid (1989, 1994), for ex- the z component of r(b=S 2 a=u) is simply 2g21rN2, ample, has de®ned 10 isopycnal surfaces in the North where g is the acceleration due to gravity and N is the and South Atlantic Oceans with 88 different sn values, buoyancy or Brunt±VaÈisaÈllaÈ frequency. where n 5 0, 0.5, 1, 1.5, 2, 3, 4, and 5 (corresponding Since r(b=S 2 a=u) in the real ocean is a well- to reference pressures up to 5000 db), depending on the de®ned function of three-dimensional space, the exis- spatial location of the water involved (there being 11 tence of neutral tangent planes as the planes perpen- different spatial regions). The choice of the number of dicular to r(b=S 2 a=u) is guaranteed. Unfortunately, these sn values and the de®nitions of the corresponding the envelope of all such tangent planes is not a math- regions is subjective. The assignment of sn values is ematically well-de®ned surface. For such a surface to based on a match between differing sn values as one exist, A 5 r(b=S 2 a=u) must satisfy the condition progresses from one spatial region to the next. When of integrability (Phillips 1956), that is, its helicity (Lilly following such an ``isopycnal'' surface from one ref- 1986) H must be zero; erence pressure to another (say from a given s value 1 H 5 A´= 3 A 5 0. (1) to a desired s2 value), data at the mid pressure (1500 db in this case) from all the casts in the region is plotted This condition is satis®ed exactly when there is an in- on a s1 versus s2 diagram and a straight line is ®tted tegrating factor b 5 b(x, y, z) with the property that by least squares. The desired s2 value is then found as br(b=S 2 a=u) is irrotational [see also Eqs. (10) and the value on the straight line at the speci®ed s1 value. (11) of McDougall and Jackett 1988]. Under these con- The addition of further isopycnal surfaces requires the ditions, a scalar potential gn exists that satis®es choice of additional s values and regions based on this n =gn 5 br(b=S 2 a=u). (2) matching procedure. The computation of these isopyc- nal surfaces for a range of reference pressures is both Formally, it can be shown that (i) the existence of neutral time consuming and far from straightforward. Also, surfaces orthogonal to r(b=S 2 a=u), (ii) zero helicity there are nearly always discontinuities in the slopes of [as de®ned in (1)], and (iii) the existence of the scalar these isopycnal surfaces across the de®ning regions. potential gn and integrating factor b satisfying (2) are In this paper we de®ne a new density variable, neutral all equivalent. density, denoted by gn, which is a function of salinity Another way of looking at the above de®nition of S (psu), in situ temperature T (8C), pressure p (db), neutral density is to apply the classical result from vector longitude, and latitude. Surfaces of constant gn de®ne analysis known as Helmholtz's theorem (see Phillips the neutral surfaces, which provide the proper frame- 1956). This states that an arbitrary vector, V, can be work for an ocean model's calculations and analysis.
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