Isopycnic Modeling of Ocean Circulation

Bleck, Rainer; Sun, Shan

doi:10.1590/2675-2824073.25024

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REVIEW • Ocean Coast. Res. 73 • 2025 • https://doi.org/10.1590/2675-2824073.25024 linkcopy

Isopycnic Modeling of Ocean Circulation

Authorship SCIMAGO INSTITUTIONS RANKINGS

The history of ocean circulation models utilizing sea water potential density as a vertical coordinate is described. After a brief review of several models belonging to this class, emphasis in this article shifts to the ocean models MICOM and HYCOM developed by the authors and others at the University of Miami during the period 1980 - 2010.

Keywords:
Ocean circulation modeling; isentropic coordinate; generalized vertical coordinates; global overturning circulation; MICOM; HYCOM

Authorship

person Rainer Bleck *

Conceptualization · Writing original draft

schoolCooperative Institute for Research in Environmental Sciences, University of Colorado Boulder, and NOAA/OAR/Global Systems Laboratory, Boulder, Colorado, USA,University of Colorado BoulderUSABoulder, Colorado, USACooperative Institute for Research in Environmental Sciences, University of Colorado Boulder, and NOAA/OAR/Global Systems Laboratory, Boulder, Colorado, USA,

0000-0001-7387-4620

person Shan Sun

Visualization · Writing Review and Editing

schoolNOAA/OAR/Global Systems Laboratory, Boulder, Colorado, USANOAAUSABoulder, Colorado, USANOAA/OAR/Global Systems Laboratory, Boulder, Colorado, USA

0000-0002-8595-7375

person*Corresponding author:
emailRainer.Bleck@noaa.gov

Editor:

Rubens Lopes

CONFLICTS OF INTEREST

The authors declare no conflict of interest.

SCIMAGO INSTITUTIONS RANKINGS

Cooperative Institute for Research in Environmental Sciences, University of Colorado Boulder, and NOAA/OAR/Global Systems Laboratory, Boulder, Colorado, USA,University of Colorado BoulderUSABoulder, Colorado, USACooperative Institute for Research in Environmental Sciences, University of Colorado Boulder, and NOAA/OAR/Global Systems Laboratory, Boulder, Colorado, USA,

NOAA/OAR/Global Systems Laboratory, Boulder, Colorado, USANOAAUSABoulder, Colorado, USANOAA/OAR/Global Systems Laboratory, Boulder, Colorado, USA

Figures | Formulas

Figures (4)
Formulas (9)

Thumbnail

Figure 1 Left: Layout of (x, y, s) coordinate surfaces, reproduced from Bleck (1978a). Right: Hybrid coordinate version D, reproduced from Bleck (1978b).

Thumbnail

Figure 2 Transport-induced vertical diffusion in (a) "level" models (models using a fixed-depth vertical coordinate) and (b) "layer" models (models using a material vertical coordinate).

Thumbnail

Figure 3 Illustration of vertical regridding, taken from a random grid location in an atmospheric model run. Black: original distribution of potential temperature (abscissa, K) as a function of pressure (ordinate, hPa). Red: piecewise linear curve fit based on Bleck (1984). Green: New stairsteps adhering to prescribed potential temperature target values 334K, 346K, 350K, etc.

Thumbnail

Figure 4 Simplified schematic of the “deep” global thermohaline circulation in the isopycnal ocean model of Sun & Bleck (2001), in a format inspired by Broecker (1991) and Schmitz (1995). Circled numbers represent transport in Sv (1 Sv = 10⁶ m ³ s ⁻¹ ). Reproduced from Sun & Bleck (2006a).

(1)

(2)

(3)

(4)

(5)

imageFigure 1 Left: Layout of (x, y, s) coordinate surfaces, reproduced from Bleck (1978a). Right: Hybrid coordinate version D, reproduced from Bleck (1978b). open_in_new

imageFigure 2 Transport-induced vertical diffusion in (a) "level" models (models using a fixed-depth vertical coordinate) and (b) "layer" models (models using a material vertical coordinate). open_in_new

imageFigure 3 Illustration of vertical regridding, taken from a random grid location in an atmospheric model run. Black: original distribution of potential temperature (abscissa, K) as a function of pressure (ordinate, hPa). Red: piecewise linear curve fit based on Bleck (1984). Green: New stairsteps adhering to prescribed potential temperature target values 334K, 346K, 350K, etc. open_in_new

imageFigure 4 Simplified schematic of the “deep” global thermohaline circulation in the isopycnal ocean model of Sun & Bleck (2001), in a format inspired by Broecker (1991) and Schmitz (1995). Circled numbers represent transport in Sv (1 Sv = 10⁶ m ³ s ⁻¹ ). Reproduced from Sun & Bleck (2006a). open_in_new

(1)

α {(\partial p / \partial x)}_{z} = {(\partial M / \partial x)}_{α}

(2)

d v = (\partial v / \partial x)_{y s t} d x + (\partial v / \partial y)_{x s t} d y + (\partial v / \partial s)_{x y t} d s + (\partial v / \partial t)_{x y s} d t

w \equiv d z / d t = (\partial z / \partial t)_{s} + v \cdot \nabla_{s} z + \dot{s} (\partial z / \partial s)

\partial w / \partial z = (\partial s / \partial z) (\partial w / \partial s) = (d / d t) \log (\partial z / \partial s) + (\partial v / \partial z) \cdot \nabla_{s} z + \partial \dot{s} / \partial s

(d / d t) \log ρ + \nabla_{z} \cdot v + \partial w / \partial z = (d / d t) \log (ρ \partial z / \partial s) + \nabla_{s} \cdot v + \partial \dot{s} / \partial s = 0

(3)

\frac{\partial}{\partial t} (\frac{\partial p}{\partial s}) + \nabla_{s} \cdot (v \frac{\partial p}{\partial s}) + \frac{\partial}{\partial s} (\dot{s} \frac{\partial p}{\partial s}) = 0

(4)

α' {(\frac{\partial p}{\partial x})}_{z} = {(\frac{\partial (g z + p α')}{\partial x})}_{α_{p o t}} - p {(\frac{\partial α'}{\partial x})}_{α_{p o t}}

(5)

(\begin{matrix} vertical \\ motion \\ OF \\ layer \\ interface \end{matrix}) + (\begin{matrix} vertical \\ motion \\ THROUGH \\ layer \\ interface \end{matrix}) = (\begin{matrix} vertically \\ integrated \\ horizontal \\ mass flux \\ divergence \end{matrix})

\frac{\partial v}{\partial p} [\dot{s} \frac{\partial p}{\partial s}] d t

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