--- manual/s_overview/text/manual.tex 2001/10/25 15:24:01 1.8 +++ manual/s_overview/text/manual.tex 2004/03/23 15:29:39 1.18 @@ -1,4 +1,4 @@ -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.8 2001/10/25 15:24:01 cnh Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.18 2004/03/23 15:29:39 afe 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 1.8 2001/10/25 15:24:01 cnh Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.18 2004/03/23 15:29:39 afe 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} @@ -84,12 +88,56 @@ \end{itemize} Key publications reporting on and charting the development of the model are -listed in an Appendix. +\cite{hill:95,marshall:97a,marshall:97b,adcroft:97,marshall:98,adcroft:99,hill:99,maro-eta:99}: + +\begin{verbatim} +Hill, C. and J. Marshall, (1995) +Application of a Parallel Navier-Stokes Model to Ocean Circulation in +Parallel Computational Fluid Dynamics +In Proceedings of Parallel Computational Fluid Dynamics: Implementations +and Results Using Parallel Computers, 545-552. +Elsevier Science B.V.: New York + +Marshall, J., C. Hill, L. Perelman, and A. Adcroft, (1997) +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) +A finite-volume, incompressible Navier Stokes model for studies of the ocean +on parallel computers, +J. Geophysical Res., 102(C3), 5753-5766. + +Adcroft, A.J., Hill, C.N. and J. Marshall, (1997) +Representation of topography by shaved cells in a height coordinate ocean +model +Mon Wea Rev, vol 125, 2293-2315 + +Marshall, J., Jones, H. and C. Hill, (1998) +Efficient ocean modeling using non-hydrostatic algorithms +Journal of Marine Systems, 18, 115-134 + +Adcroft, A., Hill C. and J. Marshall: (1999) +A new treatment of the Coriolis terms in C-grid models at both high and low +resolutions, +Mon. Wea. Rev. Vol 127, pages 1928-1936 + +Hill, C, Adcroft,A., Jamous,D., and J. Marshall, (1999) +A Strategy for Terascale Climate Modeling. +In Proceedings of the Eighth ECMWF Workshop on the Use of Parallel Processors +in Meteorology, pages 406-425 +World Scientific Publishing Co: UK + +Marotzke, J, Giering,R., Zhang, K.Q., Stammer,D., Hill,C., and T.Lee, (1999) +Construction of the adjoint MIT ocean general circulation model and +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 1.8 2001/10/25 15:24:01 cnh Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.18 2004/03/23 15:29:39 afe Exp $ % $Name: $ \section{Illustrations of the model in action} @@ -102,10 +150,15 @@ numerical algorithm and implementation that lie behind these calculations is given later. Indeed many of the illustrative examples shown below can be easily reproduced: simply download the model (the minimum you need is a PC -running linux, together with a FORTRAN\ 77 compiler) and follow the examples +running Linux, together with a FORTRAN\ 77 compiler) and follow the examples 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. @@ -126,7 +179,7 @@ %% CNHend As described in Adcroft (2001), a `cubed sphere' is used to discretize the -globe permitting a uniform gridding and obviated the need to Fourier filter. +globe permitting a uniform griding and obviated the need to Fourier filter. The `vector-invariant' form of MITgcm supports any orthogonal curvilinear grid, of which the cubed sphere is just one of many choices. @@ -142,6 +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 @@ -163,11 +222,14 @@ visible. %% CNHbegin -\input{part1/ocean_gyres_figure} +\input{part1/atl6_figure} %% CNHend \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$^{\circ }$ @@ -186,12 +248,16 @@ %%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 than the width of the cooling region. Rather than gravity plumes, the mechanism for moving dense fluid down the shelf is then through geostrophic -eddies. The simulation shown in the figure \ref{fig::convect-and-topo} +eddies. The simulation shown in the figure \ref{fig:convect-and-topo} (blue is cold dense fluid, red is warmer, lighter fluid) employs the non-hydrostatic capability of MITgcm to trigger convection by surface cooling. The cold, dense water falls down the @@ -205,6 +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 @@ -224,6 +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 @@ -231,7 +303,7 @@ As one example of application of the MITgcm adjoint, Figure \ref{fig:hf-sensitivity} maps the gradient $\frac{\partial J}{\partial \mathcal{H}}$where $J$ is the magnitude -of the overturning streamfunction shown in figure \ref{fig:large-scale-circ} +of the overturning stream-function shown in figure \ref{fig:large-scale-circ} at 60$^{\circ }$N and $ \mathcal{H}(\lambda,\varphi)$ is the mean, local air-sea heat flux over a 100 year period. We see that $J$ is @@ -244,22 +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 -insitu) over an interval of time, is minimized by adjusting `control +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/globes_figure} +\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 @@ -275,9 +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 enquiring 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 @@ -289,10 +372,13 @@ \input{part1/lab_figure} %%CNHend -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.8 2001/10/25 15:24:01 cnh Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.18 2004/03/23 15:29:39 afe 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 @@ -301,8 +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 @@ -351,7 +437,7 @@ \begin{equation} \frac{DS}{Dt}=\mathcal{Q}_{S}\text{ humidity/salinity} -\label{eq:humidtity_salt} +\label{eq:humidity_salt} \end{equation} Here: @@ -426,13 +512,13 @@ 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{ \ -(oceansurface,bottomoftheatmosphere)} \label{eq:movingbc} +\dot{r}=\frac{Dr}{Dt} \text{\ at\ } r=R_{moving}\text{ \ +(ocean surface,bottom of the atmosphere)} \label{eq:movingbc} \end{equation} Here @@ -525,7 +611,7 @@ atmosphere)} \label{eq:moving-bc-atmos} \end{eqnarray} -Then the (hydrostatic form of) equations (\ref{eq:horizontal_mtm}-\ref{eq:humidity_slainty}) +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}). @@ -562,13 +648,17 @@ \end{eqnarray} where $\eta $ is the elevation of the free surface. -Then equations (\ref{eq:horizontal_mtm}-\ref{eq:humidity_slainty}) yield a consistent set +Then equations (\ref{eq:horizontal_mtm}-\ref{eq:humidity_salt}) yield a consistent set of oceanic equations which, for convenience, are written out in $z$ coordinates in Appendix Ocean - see eqs(\ref{eq:ocean-mom}) to (\ref{eq:ocean-salt}). \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: @@ -1028,7 +1118,7 @@ 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 1.8 2001/10/25 15:24:01 cnh Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.18 2004/03/23 15:29:39 afe Exp $ % $Name: $ \section{Appendix ATMOSPHERE} @@ -1155,7 +1245,7 @@ \frac{D\theta }{Dt} &=&\frac{\mathcal{Q}}{\Pi } \end{eqnarray} -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.8 2001/10/25 15:24:01 cnh Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.18 2004/03/23 15:29:39 afe Exp $ % $Name: $ \section{Appendix OCEAN} @@ -1178,7 +1268,7 @@ \label{eq:non-boussinesq} \end{eqnarray} These equations permit acoustics modes, inertia-gravity waves, -non-hydrostatic motions, a geostrophic (Rossby) mode and a thermo-haline +non-hydrostatic motions, a geostrophic (Rossby) mode and a thermohaline mode. As written, they cannot be integrated forward consistently - if we step $\rho $ forward in (\ref{eq-zns-cont}), the answer will not be consistent with that obtained by stepping (\ref{eq-zns-heat}) and (\ref @@ -1371,7 +1461,7 @@ _{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 1.8 2001/10/25 15:24:01 cnh Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.18 2004/03/23 15:29:39 afe Exp $ % $Name: $ \section{Appendix:OPERATORS}