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\@writefile{toc}{\contentsline {chapter}{\chapnumberline {1}{On the Use of Hybrid Vertical Coordinates in Ocean Circulation Modeling}}{1}}
\@writefile{toc}{{\noindent\tocauthorfont \relax Rainer Bleck}}
\@writefile{toc}{\contentsline {section}{\numberline {1.}Introduction }{1}}
\@writefile{toc}{\contentsline {section}{\numberline {2.}The Grid Generator }{5}}
\newlabel{eqn:cnuity}{{1.1\relax }{6}}
\@writefile{lof}{\contentsline {figure}{\numberline {1.1\relax }{\ignorespaces \relax \fontsize  {8}{9.5}\selectfont  \abovedisplayskip 6\p@ plus2\p@ minus4\p@ \abovedisplayshortskip \z@ plus\p@ \belowdisplayshortskip 3\p@ plus\p@ minus2\p@ \def \leftmargin \leftmargini \parsep 4\p@ plus2\p@ minus\p@ \topsep 8\p@ plus2\p@ minus4\p@ \itemsep 4\p@ plus2\p@ minus\p@ {\leftmargin \leftmargini \topsep 3\p@ plus\p@ minus\p@ \parsep 2\p@ plus\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip Schematic illustrating numerical dispersion in a water column subjected to gravity wave-induced oscillatory vertical motion. Shown is a stack of three grid cells. The initial state, T=0, is chosen to coincide with the wave trough, at which time the middle cell is assumed to be filled with a tracer of concentration 100. The approaching wave crest causes water to be advected upward by a distance chosen in this example to correspond to one-fifth of the vertical cell size (T=1). In level models (a), the clock is stopped momentarily to allow the tracer to be reapportioned (``rezoned") among the original grid cells. The next wave trough causes the water column to return to its original position (T=2). After renewed rezoning, tracer concentration in the middle cell has fallen to 68, the remainder having seeped into cells above and below. In layer models (b), the periodic rezoning steps are skipped, so tracer concentration remains unaffected by the wave motion.}}{7}}
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\@writefile{lof}{\contentsline {figure}{\numberline {1.2\relax }{\ignorespaces \relax \fontsize  {8}{9.5}\selectfont  \abovedisplayskip 6\p@ plus2\p@ minus4\p@ \abovedisplayshortskip \z@ plus\p@ \belowdisplayshortskip 3\p@ plus\p@ minus2\p@ \def \leftmargin \leftmargini \parsep 4\p@ plus2\p@ minus\p@ \topsep 8\p@ plus2\p@ minus4\p@ \itemsep 4\p@ plus2\p@ minus\p@ {\leftmargin \leftmargini \topsep 3\p@ plus\p@ minus\p@ \parsep 2\p@ plus\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip Sample vertical section through HYCOM solution extending south from Montevideo into the eddy-rich Brazil and Malvinas Current confluence region. Heavy lines: Layer interfaces. Shaded contours: potential density anomaly ($\sigma _2$, kg\,m$^{-3}$). Tick marks along top and bottom indicate horizontal grid resolution [$0.225^\circ \times \mathop {\mathgroup \symoperators cos}\nolimits (lat.)$, approx. 15\,km]. Vertical scale: 1000\,m. Crowded isopycnals on continental shelf (upper left corner) are due to Rio de la Plata inflow.}}{9}}
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\@writefile{toc}{\contentsline {section}{\numberline {3.}Mutually consistent T/S/$\rho $ advection }{9}}
\@writefile{lof}{\contentsline {figure}{\numberline {1.3\relax }{\ignorespaces \relax \fontsize  {8}{9.5}\selectfont  \abovedisplayskip 6\p@ plus2\p@ minus4\p@ \abovedisplayshortskip \z@ plus\p@ \belowdisplayshortskip 3\p@ plus\p@ minus2\p@ \def \leftmargin \leftmargini \parsep 4\p@ plus2\p@ minus\p@ \topsep 8\p@ plus2\p@ minus4\p@ \itemsep 4\p@ plus2\p@ minus\p@ {\leftmargin \leftmargini \topsep 3\p@ plus\p@ minus\p@ \parsep 2\p@ plus\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip $T,S$ diagrams showing ispopycnals referenced to 2000\,m (solid) and two renditions of linearized spiciness $\chi '$ (dashed). Left: $\lambda $=-0.13\,psu/$^\circ $C; right: $\lambda $=-0.26\,psu/$^\circ $C.}}{12}}
\newlabel{fig:chiprime}{{1.3\relax }{12}}
\newlabel{eqn:dchi}{{1.2\relax }{12}}
\newlabel{eqn:rho}{{1.3\relax }{12}}
\@writefile{lof}{\contentsline {figure}{\numberline {1.4\relax }{\ignorespaces \relax \fontsize  {8}{9.5}\selectfont  \abovedisplayskip 6\p@ plus2\p@ minus4\p@ \abovedisplayshortskip \z@ plus\p@ \belowdisplayshortskip 3\p@ plus\p@ minus2\p@ \def \leftmargin \leftmargini \parsep 4\p@ plus2\p@ minus\p@ \topsep 8\p@ plus2\p@ minus4\p@ \itemsep 4\p@ plus2\p@ minus\p@ {\leftmargin \leftmargini \topsep 3\p@ plus\p@ minus\p@ \parsep 2\p@ plus\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip Vertical section through the zonally averaged density field after a 100-year, global, coarse mesh integration of HYCOM forced by monthly climatology [mesh size $2^\circ \times \mathop {\mathgroup \symoperators cos}\nolimits (lat.)$]. Colors highlight differences in isopycnal layer depth resulting from using two different $\lambda $ values, -0.26 psu/$^\circ $C and 0. Blue/red: interfaces in $\lambda $=-0.26 psu/$^\circ $C run are at shallower/greater depth, respectively, than interfaces in $\lambda =0$ run.}}{13}}
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\newlabel{eqn:chi}{{1.4\relax }{13}}
\newlabel{eqn:chiprime}{{1.5\relax }{14}}
\@writefile{lof}{\contentsline {figure}{\numberline {1.5\relax }{\ignorespaces \relax \fontsize  {8}{9.5}\selectfont  \abovedisplayskip 6\p@ plus2\p@ minus4\p@ \abovedisplayshortskip \z@ plus\p@ \belowdisplayshortskip 3\p@ plus\p@ minus2\p@ \def \leftmargin \leftmargini \parsep 4\p@ plus2\p@ minus\p@ \topsep 8\p@ plus2\p@ minus4\p@ \itemsep 4\p@ plus2\p@ minus\p@ {\leftmargin \leftmargini \topsep 3\p@ plus\p@ minus\p@ \parsep 2\p@ plus\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip Time series of northern hemispheric ice mass in a coupled GISS-HYCOM simulation. Grey: results from $\rho ,S$-advecting model; black: results from $\rho ,\chi '$-advecting model using $\lambda $=-0.13\,psu/$^\circ $C. Courtesy: Dr. Shan Sun, Goddard Institute for Space Studies.}}{15}}
\newlabel{fig:icemass}{{1.5\relax }{15}}
\@writefile{toc}{\contentsline {section}{\numberline {4.}Closing Remarks }{15}}
\bibcite{bleck78}{bleck78}
\bibcite{bleck02}{bleck02}
\bibcite{bb81}{bb81}
\bibcite{brhs91}{brhs91}
\bibcite{brydon}{brydon}
\bibcite{cheng}{cheng}
\@writefile{toc}{\contentsline {spchapter}{\cnumberline {}Acknowledgments}{17}}
\@writefile{toc}{\contentsline {section}{References}{17}}
\bibcite{flament}{flament}
\bibcite{hirt}{hirt}
\bibcite{daveholland}{daveholland}
\bibcite{hollandlin1}{hollandlin1}
\bibcite{hollandlin2}{hollandlin2}
\bibcite{hu}{hu}
\bibcite{oberhuber}{oberhuber}
\bibcite{sun01}{sun01}
\bibcite{welander}{welander}