1 |
% $Header: /u/gcmpack/manual/part3/case_studies/advection_in_gyre_circulation/adv_gyre.tex,v 1.12 2008/01/16 19:08:41 jahn Exp $ |
2 |
% $Name: $ |
3 |
|
4 |
\bodytext{bgcolor="#FFFFFFFF"} |
5 |
|
6 |
|
7 |
\section[Gyre Advection Example]{Ocean Gyre Advection Schemes} |
8 |
\label{www:tutorials} |
9 |
\label{sect:eg-adv-gyre} |
10 |
\begin{rawhtml} |
11 |
<!-- CMIREDIR:eg-adv-gyre: --> |
12 |
\end{rawhtml} |
13 |
|
14 |
Author: Oliver Jahn and Chris Hill |
15 |
|
16 |
|
17 |
|
18 |
This set of examples is based on the barotropic and baroclinic gyre MITgcm configurations, |
19 |
that are described in the tutorial sections \ref{sect:eg-baro} and \ref{sect:eg-fourlayer}. |
20 |
The examples in this section explain how to introduce a passive tracer into the flow |
21 |
field of the barotropic and baroclinic gyre setups and looks at how the time evolution |
22 |
of the passive tracer depends on the advection or transport scheme that is selected |
23 |
for the tracer. |
24 |
|
25 |
Passive tracers are useful in many numerical experiments. In some cases tracers are |
26 |
used to track flow pathways, for example in \cite{Dutay02} a passive tracer is used |
27 |
to track pathways of CFC-11 in 13 global ocean models, using a numerical |
28 |
configuration similar to the example described in section \ref{sect:eg-offline-cfc}). |
29 |
In other cases tracers are used as a way |
30 |
to infer bulk mixing coefficients for a turbulent flow field, for example in |
31 |
\cite{marsh06} a tracer is used to infer eddy mixing coefficients in the |
32 |
Antarctic Circumpolar Current region. In biogeochemical and ecological simulations large numbers |
33 |
of tracers are used that carry the concentrations of biological nutrients and concentrations of |
34 |
biological species, for example in .... |
35 |
When using tracers for these and other purposes it is useful to have a feel for the role |
36 |
that the advection scheme employed plays in determining properties of the tracer distribution. |
37 |
In particular, in a discrete numerical model tracer advection only approximates the |
38 |
continuum behavior in space and time and different advection schemes introduce diferent |
39 |
approximations so that the resulting tracer distributions vary. In the following |
40 |
text we illustrate how |
41 |
to use the different advection schemes available in MITgcm here, and discuss which properties |
42 |
are well represented by each one. The advection schemes selections also apply to active |
43 |
tracers (e.g. $T$ and $S$) and the character of the schemes also affect their distributions |
44 |
and behavior. |
45 |
|
46 |
\subsection{Advection and tracer transport} |
47 |
|
48 |
In general, the tracer problem we want to solve can be written |
49 |
|
50 |
\begin{equation} |
51 |
\label{EQ:eg-adv-gyre-generic-tracer} |
52 |
\frac{\partial C}{partial t} = -U \cdot \nabla C + S |
53 |
\end{equation} |
54 |
|
55 |
where $C$ is the tracer concentration in a model cell, $U$ is the model three-dimensional |
56 |
flow field ( $U=(u,v,w)$ ). In (\ref{EQ:eg-adv-gyre-generic-tracer}) $S$ represents source, sink |
57 |
and tendency terms not associated with advective transport. Example of terms in $S$ include |
58 |
(i) air-sea fluxes for a dissolved gas, (ii) biological grazing and growth terms (for a |
59 |
biogeochemical problem) or (iii) convective mixing and other sub-grid parameterizations of |
60 |
mixing. In this section we are primarily concerned with |
61 |
\begin{enumerate} |
62 |
\item how to introduce the tracer term, $C$, into an integration |
63 |
\item the different discretized forms of |
64 |
the $-U \cdot \nabla C$ term that are available |
65 |
\end{enumerate} |
66 |
|
67 |
|
68 |
\subsection{Introducing a tracer into the flow} |
69 |
|
70 |
The MITgcm ptracers package (see section \ref{sec:pkg:ptracers} for a more complete discussion |
71 |
of the ptracers package and section \ref{sec:pkg:using} for a general introduction to MITgcm |
72 |
packages) provides pre-coded support for a simple passive tracer with an initial |
73 |
distribution at simulation time $t=0$ of $C_0(x,y,z)$. The steps required to use this capability |
74 |
are |
75 |
\begin{enumerate} |
76 |
\item{\bf Activating the ptracers package.} This simply requires adding the line {\tt ptracers} to |
77 |
the {\tt packages.conf} file in the {\it code/} directory for the experiment. |
78 |
\item{\bf Setting an initial tracer distribution.} |
79 |
\end{enumerate} |
80 |
|
81 |
Once the two steps above are complete we can proceed to examine how the tracer we have created is |
82 |
carried by the flow field and what properties of the tracer distribution are preserved under |
83 |
different advection schemes. |
84 |
|
85 |
\subsection{Selecting an advection scheme} |
86 |
|
87 |
- flags in data and data.ptracers |
88 |
|
89 |
- overlap width |
90 |
|
91 |
- CPP GAD\_ALLOW\_SOM\_ADVECT required for SOM case |
92 |
|
93 |
\subsection{Comparison of different advection schemes} |
94 |
|
95 |
\begin{enumerate} |
96 |
\item{Conservation} |
97 |
\item{Dispersion} |
98 |
\item{Diffusion} |
99 |
\item{Positive definite} |
100 |
\end{enumerate} |
101 |
|
102 |
\input part3/case_studies/advection_in_gyre_circulation/adv_gyre_figure.tex |
103 |
|
104 |
\begin{figure} |
105 |
\begin{center} |
106 |
\includegraphics*[width=\textwidth]{part3/case_studies/advection_in_gyre_circulation/stats.eps} |
107 |
\end{center} |
108 |
\caption{Maxima, minima and standard deviation (from left) as a function of time (in months) |
109 |
for the gyre circulation experiment from figure~\ref{fig:adv-gyre-all}.} |
110 |
\label{fig:adv-gyre-stats} |
111 |
\end{figure} |
112 |
|
113 |
\subsection{Code and Parameters files for this tutorial} |
114 |
|
115 |
The code and parameters for the experiments can be found in the MITgcm example experiments |
116 |
directory {\it verification/tutorial\_advection\_in\_gyre/}. |
117 |
|
118 |
|
119 |
|
120 |
|
121 |
|
122 |
|
123 |
|