--- manual/s_overview/text/manual.tex 2001/11/21 14:13:17 1.14 +++ manual/s_overview/text/manual.tex 2006/04/05 02:27:32 1.24 @@ -1,4 +1,4 @@ -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.14 2001/11/21 14:13:17 cnh Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.24 2006/04/05 02:27:32 edhill Exp $ % $Name: $ %tci%\documentclass[12pt]{book} @@ -34,12 +34,10 @@ % Section: Overview -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.14 2001/11/21 14:13:17 cnh Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.24 2006/04/05 02:27:32 edhill Exp $ % $Name: $ -\section{Introduction} - -This documentation provides the reader with the information necessary to +This document provides the reader with the information necessary to carry out numerical experiments using MITgcm. It gives a comprehensive description of the continuous equations on which the model is based, the numerical algorithms the model employs and a description of the associated @@ -49,6 +47,12 @@ both process and general circulation studies of the atmosphere and ocean are also presented. +\section{Introduction} +\begin{rawhtml} + +\end{rawhtml} + + MITgcm has a number of novel aspects: \begin{itemize} @@ -83,10 +87,10 @@ computational platforms. \end{itemize} -Key publications reporting on and charting the development of the model are: +Key publications reporting on and charting the development of the model are +\cite{hill:95,marshall:97a,marshall:97b,adcroft:97,marshall:98,adcroft:99,hill:99,maro-eta:99,adcroft:04a,adcroft:04b,marshall:04}: \begin{verbatim} - Hill, C. and J. Marshall, (1995) Application of a Parallel Navier-Stokes Model to Ocean Circulation in Parallel Computational Fluid Dynamics @@ -95,7 +99,7 @@ Elsevier Science B.V.: New York Marshall, J., C. Hill, L. Perelman, and A. Adcroft, (1997) -Hydrostatic, quasi-hydrostatic, and nonhydrostatic ocean modeling, +Hydrostatic, quasi-hydrostatic, and nonhydrostatic ocean modeling J. Geophysical Res., 102(C3), 5733-5752. Marshall, J., A. Adcroft, C. Hill, L. Perelman, and C. Heisey, (1997) @@ -128,18 +132,17 @@ application to Atlantic heat transport variability J. Geophysical Res., 104(C12), 29,529-29,547. - \end{verbatim} We begin by briefly showing some of the results of the model in action to give a feel for the wide range of problems that can be addressed using it. -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.14 2001/11/21 14:13:17 cnh Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.24 2006/04/05 02:27:32 edhill Exp $ % $Name: $ \section{Illustrations of the model in action} -The MITgcm has been designed and used to model a wide range of phenomena, +MITgcm has been designed and used to model a wide range of phenomena, from convection on the scale of meters in the ocean to the global pattern of atmospheric winds - see figure \ref{fig:all-scales}. To give a flavor of the kinds of problems the model has been used to study, we briefly describe some @@ -151,6 +154,11 @@ described in detail in the documentation. \subsection{Global atmosphere: `Held-Suarez' benchmark} +\begin{rawhtml} + +\end{rawhtml} + + A novel feature of MITgcm is its ability to simulate, using one basic algorithm, both atmospheric and oceanographic flows at both small and large scales. @@ -187,6 +195,12 @@ %% CNHend \subsection{Ocean gyres} +\begin{rawhtml} + +\end{rawhtml} +\begin{rawhtml} + +\end{rawhtml} Baroclinic instability is a ubiquitous process in the ocean, as well as the atmosphere. Ocean eddies play an important role in modifying the @@ -213,6 +227,9 @@ \subsection{Global ocean circulation} +\begin{rawhtml} + +\end{rawhtml} Figure \ref{fig:large-scale-circ} (top) shows the pattern of ocean currents at the surface of a 4$^{\circ }$ @@ -231,6 +248,10 @@ %%CNHend \subsection{Convection and mixing over topography} +\begin{rawhtml} + +\end{rawhtml} + Dense plumes generated by localized cooling on the continental shelf of the ocean may be influenced by rotation when the deformation radius is smaller @@ -250,6 +271,9 @@ %%CNHend \subsection{Boundary forced internal waves} +\begin{rawhtml} + +\end{rawhtml} The unique ability of MITgcm to treat non-hydrostatic dynamics in the presence of complex geometry makes it an ideal tool to study internal wave @@ -269,6 +293,9 @@ %%CNHend \subsection{Parameter sensitivity using the adjoint of MITgcm} +\begin{rawhtml} + +\end{rawhtml} Forward and tangent linear counterparts of MITgcm are supported using an `automatic adjoint compiler'. These can be used in parameter sensitivity and @@ -289,22 +316,30 @@ %%CNHend \subsection{Global state estimation of the ocean} +\begin{rawhtml} + +\end{rawhtml} + An important application of MITgcm is in state estimation of the global ocean circulation. An appropriately defined `cost function', which measures the departure of the model from observations (both remotely sensed and in-situ) over an interval of time, is minimized by adjusting `control parameters' such as air-sea fluxes, the wind field, the initial conditions -etc. Figure \ref{fig:assimilated-globes} shows an estimate of the time-mean -surface elevation of the ocean obtained by bringing the model in to +etc. Figure \ref{fig:assimilated-globes} shows the large scale planetary +circulation and a Hopf-Muller plot of Equatorial sea-surface height. +Both are obtained from assimilation bringing the model in to consistency with altimetric and in-situ observations over the period -1992-1997. {\bf CHANGE THIS TEXT - FIG FROM PATRICK/CARL/DETLEF} +1992-1997. %% CNHbegin \input{part1/assim_figure} %% CNHend \subsection{Ocean biogeochemical cycles} +\begin{rawhtml} + +\end{rawhtml} MITgcm is being used to study global biogeochemical cycles in the ocean. For example one can study the effects of interannual changes in meteorological @@ -320,9 +355,12 @@ %%CNHend \subsection{Simulations of laboratory experiments} +\begin{rawhtml} + +\end{rawhtml} Figure \ref{fig:lab-simulation} shows MITgcm being used to simulate a -laboratory experiment inquiring in to the dynamics of the Antarctic Circumpolar Current (ACC). An +laboratory experiment inquiring into the dynamics of the Antarctic Circumpolar Current (ACC). An initially homogeneous tank of water ($1m$ in diameter) is driven from its free surface by a rotating heated disk. The combined action of mechanical and thermal forcing creates a lens of fluid which becomes baroclinically @@ -334,10 +372,13 @@ \input{part1/lab_figure} %%CNHend -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.14 2001/11/21 14:13:17 cnh Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.24 2006/04/05 02:27:32 edhill Exp $ % $Name: $ \section{Continuous equations in `r' coordinates} +\begin{rawhtml} + +\end{rawhtml} To render atmosphere and ocean models from one dynamical core we exploit `isomorphisms' between equation sets that govern the evolution of the @@ -346,8 +387,8 @@ and encoded. The model variables have different interpretations depending on whether the atmosphere or ocean is being studied. Thus, for example, the vertical coordinate `$r$' is interpreted as pressure, $p$, if we are -modeling the atmosphere (left hand side of figure \ref{fig:isomorphic-equations}) -and height, $z$, if we are modeling the ocean (right hand side of figure +modeling the atmosphere (right hand side of figure \ref{fig:isomorphic-equations}) +and height, $z$, if we are modeling the ocean (left hand side of figure \ref{fig:isomorphic-equations}). %%CNHbegin @@ -368,11 +409,11 @@ \input{part1/vertcoord_figure.tex} %%CNHend -\begin{equation*} +\begin{equation} \frac{D\vec{\mathbf{v}_{h}}}{Dt}+\left( 2\vec{\Omega}\times \vec{\mathbf{v}} \right) _{h}+\mathbf{\nabla }_{h}\phi =\mathcal{F}_{\vec{\mathbf{v}_{h}}} \text{ horizontal mtm} \label{eq:horizontal_mtm} -\end{equation*} +\end{equation} \begin{equation} \frac{D\dot{r}}{Dt}+\widehat{k}\cdot \left( 2\vec{\Omega}\times \vec{\mathbf{ @@ -471,12 +512,12 @@ at fixed and moving $r$ surfaces we set (see figure \ref{fig:zandp-vert-coord}): \begin{equation} -\dot{r}=0atr=R_{fixed}(x,y)\text{ (ocean bottom, top of the atmosphere)} +\dot{r}=0 \text{\ at\ } r=R_{fixed}(x,y)\text{ (ocean bottom, top of the atmosphere)} \label{eq:fixedbc} \end{equation} \begin{equation} -\dot{r}=\frac{Dr}{Dt}atr=R_{moving}\text{ \ +\dot{r}=\frac{Dr}{Dt} \text{\ at\ } r=R_{moving}\text{ \ (ocean surface,bottom of the atmosphere)} \label{eq:movingbc} \end{equation} @@ -570,9 +611,11 @@ atmosphere)} \label{eq:moving-bc-atmos} \end{eqnarray} -Then the (hydrostatic form of) equations (\ref{eq:horizontal_mtm}-\ref{eq:humidity_salt}) -yields a consistent set of atmospheric equations which, for convenience, are written out in $p$ -coordinates in Appendix Atmosphere - see eqs(\ref{eq:atmos-prime}). +Then the (hydrostatic form of) equations +(\ref{eq:horizontal_mtm}-\ref{eq:humidity_salt}) yields a consistent +set of atmospheric equations which, for convenience, are written out +in $p$ coordinates in Appendix Atmosphere - see +eqs(\ref{eq:atmos-prime}). \subsection{Ocean} @@ -614,6 +657,10 @@ \subsection{Hydrostatic, Quasi-hydrostatic, Quasi-nonhydrostatic and Non-hydrostatic forms} +\begin{rawhtml} + +\end{rawhtml} + Let us separate $\phi $ in to surface, hydrostatic and non-hydrostatic terms: @@ -621,7 +668,9 @@ \phi (x,y,r)=\phi _{s}(x,y)+\phi _{hyd}(x,y,r)+\phi _{nh}(x,y,r) \label{eq:phi-split} \end{equation} -and write eq(\ref{eq:incompressible}) in the form: +%and write eq(\ref{eq:incompressible}) in the form: +% ^- this eq is missing (jmc) ; replaced with: +and write eq( \ref{eq:horizontal_mtm}) in the form: \begin{equation} \frac{\partial \vec{\mathbf{v}_{h}}}{\partial t}+\mathbf{\nabla }_{h}\phi @@ -721,15 +770,16 @@ \subsubsection{Shallow atmosphere approximation} -Most models are based on the `hydrostatic primitive equations' (HPE's) in -which the vertical momentum equation is reduced to a statement of -hydrostatic balance and the `traditional approximation' is made in which the -Coriolis force is treated approximately and the shallow atmosphere -approximation is made.\ The MITgcm need not make the `traditional -approximation'. To be able to support consistent non-hydrostatic forms the -shallow atmosphere approximation can be relaxed - when dividing through by $ -r $ in, for example, (\ref{eq:gu-speherical}), we do not replace $r$ by $a$, -the radius of the earth. +Most models are based on the `hydrostatic primitive equations' (HPE's) +in which the vertical momentum equation is reduced to a statement of +hydrostatic balance and the `traditional approximation' is made in +which the Coriolis force is treated approximately and the shallow +atmosphere approximation is made. MITgcm need not make the +`traditional approximation'. To be able to support consistent +non-hydrostatic forms the shallow atmosphere approximation can be +relaxed - when dividing through by $ r $ in, for example, +(\ref{eq:gu-speherical}), we do not replace $r$ by $a$, the radius of +the earth. \subsubsection{Hydrostatic and quasi-hydrostatic forms} \label{sec:hydrostatic_and_quasi-hydrostatic_forms} @@ -766,7 +816,7 @@ \subsubsection{Non-hydrostatic and quasi-nonhydrostatic forms} -The MIT model presently supports a full non-hydrostatic ocean isomorph, but +MITgcm presently supports a full non-hydrostatic ocean isomorph, but only a quasi-non-hydrostatic atmospheric isomorph. \paragraph{Non-hydrostatic Ocean} @@ -1051,8 +1101,9 @@ \subsection{Vector invariant form} -For some purposes it is advantageous to write momentum advection in eq(\ref -{eq:horizontal_mtm}) and (\ref{eq:vertical_mtm}) in the (so-called) `vector invariant' form: +For some purposes it is advantageous to write momentum advection in +eq(\ref {eq:horizontal_mtm}) and (\ref{eq:vertical_mtm}) in the +(so-called) `vector invariant' form: \begin{equation} \frac{D\vec{\mathbf{v}}}{Dt}=\frac{\partial \vec{\mathbf{v}}}{\partial t} @@ -1073,7 +1124,7 @@ Tangent linear and adjoint counterparts of the forward model are described in Chapter 5. -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.14 2001/11/21 14:13:17 cnh Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.24 2006/04/05 02:27:32 edhill Exp $ % $Name: $ \section{Appendix ATMOSPHERE} @@ -1163,6 +1214,7 @@ surface ($\phi $ is imposed and $\omega \neq 0$). \subsubsection{Splitting the geo-potential} +\label{sec:hpe-p-geo-potential-split} For the purposes of initialization and reducing round-off errors, the model deals with perturbations from reference (or ``standard'') profiles. For @@ -1192,7 +1244,8 @@ The final form of the HPE's in p coordinates is then: \begin{eqnarray} \frac{D\vec{\mathbf{v}}_{h}}{Dt}+f\hat{\mathbf{k}}\times \vec{\mathbf{v}} -_{h}+\mathbf{\nabla }_{p}\phi ^{\prime } &=&\vec{\mathbf{\mathcal{F}}} \label{eq:atmos-prime} \\ +_{h}+\mathbf{\nabla }_{p}\phi ^{\prime } &=&\vec{\mathbf{\mathcal{F}}} +\label{eq:atmos-prime} \\ \frac{\partial \phi ^{\prime }}{\partial p}+\alpha ^{\prime } &=&0 \\ \mathbf{\nabla }_{p}\cdot \vec{\mathbf{v}}_{h}+\frac{\partial \omega }{ \partial p} &=&0 \\ @@ -1200,7 +1253,7 @@ \frac{D\theta }{Dt} &=&\frac{\mathcal{Q}}{\Pi } \end{eqnarray} -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.14 2001/11/21 14:13:17 cnh Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.24 2006/04/05 02:27:32 edhill Exp $ % $Name: $ \section{Appendix OCEAN} @@ -1238,8 +1291,9 @@ _{\theta ,S}\frac{Dp}{Dt} \label{EOSexpansion} \end{equation} -Note that $\frac{\partial \rho }{\partial p}=\frac{1}{c_{s}^{2}}$ is the -reciprocal of the sound speed ($c_{s}$) squared. Substituting into \ref{eq-zns-cont} gives: +Note that $\frac{\partial \rho }{\partial p}=\frac{1}{c_{s}^{2}}$ is +the reciprocal of the sound speed ($c_{s}$) squared. Substituting into +\ref{eq-zns-cont} gives: \begin{equation} \frac{1}{\rho c_{s}^{2}}\frac{Dp}{Dt}+\mathbf{\nabla }_{z}\cdot \vec{\mathbf{ v}}+\partial _{z}w\approx 0 \label{eq-zns-pressure} @@ -1416,7 +1470,7 @@ _{nh}=0$ form of these equations that are used throughout the ocean modeling community and referred to as the primitive equations (HPE). -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.14 2001/11/21 14:13:17 cnh Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.24 2006/04/05 02:27:32 edhill Exp $ % $Name: $ \section{Appendix:OPERATORS}