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\section[Gyre Advection Example]{Ocean Gyre Advection Schemes} |
\section[Gyre Advection Example]{Ocean Gyre Advection Schemes} |
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\label{sect:eg-adv-gyre} |
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\label{www:tutorials} |
\label{www:tutorials} |
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\label{sect:eg-adv-gyre} |
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\begin{rawhtml} |
\begin{rawhtml} |
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<!-- CMIREDIR:eg-adv-gyre: --> |
<!-- CMIREDIR:eg-adv-gyre: --> |
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\end{rawhtml} |
\end{rawhtml} |
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\begin{center} |
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(in directory: {\it verification/tutorial\_advection\_in\_gyre/}) |
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\end{center} |
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Author: Oliver Jahn and Chris Hill |
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This set of examples is based on the barotropic and baroclinic gyre MITgcm configurations, |
This set of examples is based on the barotropic and baroclinic gyre MITgcm configurations, |
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that are described in the tutorial sections \label{sect:eg-baro} and \label{sect:eg-fourlayer}. |
that are described in the tutorial sections \ref{sect:eg-baro} and \ref{sect:eg-fourlayer}. |
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The example in this section explains how to introduce a passive tracer into the flow |
The examples in this section explain how to introduce a passive tracer into the flow |
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field of the barotropic and baroclinic gyre setups and looks at how the time evolution |
field of the barotropic and baroclinic gyre setups and looks at how the time evolution |
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of the passive tracer depends on the advection or transport scheme that is selected |
of the passive tracer depends on the advection or transport scheme that is selected |
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for the tracer. |
for the tracer. |
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Passive tracers are useful in many numerical experiments. In some cases tracers are |
Passive tracers are useful in many numerical experiments. In some cases tracers are |
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used to track flow pathways, for example in \cite{Dutay02} a passive tracer is used |
used to track flow pathways, for example in \cite{Dutay02} a passive tracer is used |
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to track pathways of CFC-11 in 13 global ocean models (similar to the example |
to track pathways of CFC-11 in 13 global ocean models, using a numerical |
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described in section \ref{sect:eg-offline-cfc}). |
configuration similar to the example described in section \ref{sect:eg-offline-cfc}). |
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In other cases tracers are used as a way |
In other cases tracers are used as a way |
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to infer bulk mixing coefficients for a turbulent flow field, for example in ...... In |
to infer bulk mixing coefficients for a turbulent flow field, for example in |
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biogeochemical and ecological simulations large numbers of tracers are used that carry the |
\cite{marsh06} a tracer is used to infer eddy mixing coefficients in the |
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concentrations of biological nutrients and concentrations of biological species. |
Antarctic Circumpolar Current region. In biogeochemical and ecological simulations large numbers |
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of tracers are used that carry the concentrations of biological nutrients and concentrations of |
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biological species, for example in .... |
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When using tracers for these and other purposes it is useful to have a feel for the role |
When using tracers for these and other purposes it is useful to have a feel for the role |
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that the advection scheme employed plays in determining properties of the tracer distribution. |
that the advection scheme employed plays in determining properties of the tracer distribution. |
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In particular, in a discrete numerical model tracer advection only approximates the |
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continuum behavior in space and time and different advection schemes introduce diferent |
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approximations so that the resulting tracer distributions vary. In the following |
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text we illustrate how |
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to use the different advection schemes available in MITgcm here, and discuss which properties |
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are well represented by each one. The advection schemes selections also apply to active |
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tracers (e.g. $T$ and $S$) and the character of the schemes also affect their distributions |
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and behavior. |
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\subsection{Advection and tracer transport} |
\subsection{Advection and tracer transport} |
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In general, the tracer problem we want to solve can be written |
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\begin{equation} |
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\label{EQ:eg-adv-gyre-generic-tracer} |
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\frac{\partial C}{partial t} = -U \cdot \nabla C + S |
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\end{equation} |
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where $C$ is the tracer concentration in a model cell, $U$ is the model three-dimensional |
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flow field ( $U=(u,v,w)$ ). In (\ref{EQ:eg-adv-gyre-generic-tracer}) $S$ represents source, sink |
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and tendency terms not associated with advective transport. Example of terms in $S$ include |
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(i) air-sea fluxes for a dissolved gas, (ii) biological grazing and growth terms (for a |
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biogeochemical problem) or (iii) convective mixing and other sub-grid parameterizations of |
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mixing. In this section we are primarily concerned with |
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\begin{enumerate} |
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\item how to introduce the tracer term, $C$, into an integration |
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\item the different discretized forms of |
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the $-U \cdot \nabla C$ term that are available |
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\end{enumerate} |
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\subsection{Introducing a tracer into the flow} |
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The MITgcm ptracers package (see section \ref{sec:pkg:ptracers} for a more complete discussion |
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of the ptracers package and section \ref{sec:pkg:using} for a general introduction to MITgcm |
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packages) provides pre-coded support for a simple passive tracer with an initial |
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distribution at simulation time $t=0$ of $C_0(x,y,z)$. The steps required to use this capability |
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are |
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\begin{enumerate} |
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\item{\bf Activating the ptracers package.} This simply requires adding the line {\tt ptracers} to |
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the {\tt packages.conf} file in the {\it code/} directory for the experiment. |
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\item{\bf Setting an initial tracer distribution.} |
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\end{enumerate} |
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Once the two steps above are complete we can proceed to examine how the tracer we have created is |
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carried by the flow field and what properties of the tracer distribution are preserved under |
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different advection schemes. |
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\subsection{Selecting an advection scheme} |
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- flags in data and data.ptracers |
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- overlap width |
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- CPP GAD\_ALLOW\_SOM\_ADVECT required for SOM case |
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\subsection{Comparison of different advection schemes} |
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\begin{enumerate} |
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\item{Conservation} |
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\item{Dispersion} |
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\item{Diffusion} |
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\item{Positive definite} |
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\end{enumerate} |
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\input{s_examples/advection_in_gyre/adv_gyre_figure.tex} |
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\begin{figure} |
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\begin{center} |
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\includegraphics*[width=\textwidth]{s_examples/advection_in_gyre/stats.eps} |
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\end{center} |
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\caption{Maxima, minima and standard deviation (from left) as a function of time (in months) |
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for the gyre circulation experiment from figure~\ref{fig:adv-gyre-all}.} |
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\label{fig:adv-gyre-stats} |
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\end{figure} |
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\subsection{Code and Parameters files for this tutorial} |
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The code and parameters for the experiments can be found in the MITgcm example experiments |
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directory {\it verification/tutorial\_advection\_in\_gyre/}. |
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