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1\include{Preamble}
2
3\begin{document}
4
5\title{Draft description of NEMO wetting and drying scheme:     29 November 2017 }
6
7\author{ Enda O'Dea, Hedong Liu, Jason Holt, Andrew Coward  and Michael J. Bell  }
8
9%------------------------------------------------------------------------
10% End of temporary latex header (to be removed)
11%------------------------------------------------------------------------
12
13% ================================================================
14% Chapter Ocean Dynamics (DYN)
15% ================================================================
16\chapter{Ocean Dynamics (DYN)}
17\label{DYN}
18\minitoc
19
20% add a figure for  dynvor ens, ene latices
21
22$\ $\newline    % force a new ligne
23
24% ================================================================
25% Wetting and drying
26% ================================================================
27 
28%----------------------------------------------------------------------------------------
29%      The WAD test cases
30%----------------------------------------------------------------------------------------
31\section   [The WAD test cases (\textit{usrdef\_zgr})]
32         {The WAD test cases (\mdl{usrdef\_zgr})}
33\label{WAD_test_cases}
34
35This section contains details of the seven test cases that can be run as part of the
36WAD\_TEST\_CASES configuration. All the test cases are shallow (less than 10m deep),
37basins or channels with 4m high walls and some of topography that can wet and dry up to
382.5m above sea-level. The horizontal grid is uniform with a 1km resolution and measures
3952km by 34km. These dimensions are determined by a combination of code in the
40\mdl{usrdef\_nam} module located in the WAD\_TEST\_CASES/MY\_SRC directory and setting
41read in from the namusr\_def namelist. The first six test cases are closed systems with no
42rotation or external forcing and motion is simply initiated by an initial ssh slope. The
43seventh test case introduces and open boundary at the right-hand end of the channel which
44is forced with sinousoidally varying ssh and barotropic velocities.
45
46\namdisplay{nam_wad_usr}
47
48The $\mathrm{nn\_wad\_test}$ parameter can takes values 1 to 7 and it is this parameter
49that determines which of the test cases will be run. Most cases can be run with the
50default settings but the simple linear slope cases (tests 1 and 5) can be run with lower
51values of $\mathrm{rn\_wdmin1}$. Any recommended changes to the default namelist settings
52will be stated in the individual subsections.
53
54Test case 7 requires additional {\tt namelist\_cfg} changes to activate the open boundary
55and lengthen the duration of the run (in order to demonstrate the full forcing cycle).
56There is also a simple python script which needs to be run in order to generate the
57boundary forcing files.  Full details are given in subsection (\ref{WAD_test_case7}).
58
59\clearpage
60\subsection [WAD test case 1 : A simple linear slope]
61                    {WAD test case 1 : A simple linear slope}
62\label{WAD_test_case1}
63
64The first test case is a simple linear slope (in the x-direction, uniform in y) with an
65adverse SSH gradient that, when released, creates a surge up the slope. The parameters are
66chosen such that the surge rises above sea-level before falling back and oscillating
67towards an equilibrium position. This case can be run with $\mathrm{rn\_wdmin1}$ values as
68low as 0.075m. I.e. the following change may be made to the default values in {\tt
69namelist\_cfg} (for this test only):
70
71\namdisplay{nam_wad_tc1}
72
73%>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
74\begin{figure}[htb] \begin{center}
75\includegraphics[width=0.8\textwidth]{Fig_WAD_TC1}
76\caption{ \label{Fig_WAD_TC1}
77The evolution of the sea surface height in WAD\_TEST\_CASE 1 from the initial state (t=0)
78over the first three hours of simulation. Note that in this time-frame the resultant surge
79reaches to nearly 2m above sea-level before retreating.}
80\end{center}\end{figure}
81%>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
82
83\clearpage
84\subsection [WAD test case 2 : A parabolic channel ]
85                    {WAD test case 2 : A parabolic channel}
86\label{WAD_test_case2}
87
88The second and third test cases use a closed channel which is parabolic in x and uniform
89in y.  Test case 2 uses a gentler initial SSH slope which nevertheless demonstrates the
90ability to wet and dry on both sides of the channel. This solution requires values of
91$\mathrm{rn\_wdmin1}$ at least 0.3m ({\it Q.: A function of the maximum topographic
92slope?})
93
94\namdisplay{nam_wad_tc2}
95
96%>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
97\begin{figure}[htb] \begin{center}
98\includegraphics[width=0.8\textwidth]{Fig_WAD_TC2}
99\caption{ \label{Fig_WAD_TC2}
100The evolution of the sea surface height in WAD\_TEST\_CASE 2 from the initial state (t=0)
101over the first three hours of simulation. Note that in this time-frame the resultant sloshing
102causes wetting and drying on both sides of the parabolic channel.}
103\end{center}\end{figure}
104%>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
105
106\clearpage
107\subsection [WAD test case 3 : A parabolic channel (extreme slope) ]
108                    {WAD test case 3 : A parabolic channel (extreme slope)}
109\label{WAD_test_case3}
110
111Similar to test case 2 but with a steeper initial SSH slope. The solution is similar but more vigorous.
112
113\namdisplay{nam_wad_tc3}
114
115%>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
116\begin{figure}[htb] \begin{center}
117\includegraphics[width=0.8\textwidth]{Fig_WAD_TC3}
118\caption{ \label{Fig_WAD_TC3}
119The evolution of the sea surface height in WAD\_TEST\_CASE 3 from the initial state (t=0)
120over the first three hours of simulation. Note that in this time-frame the resultant sloshing
121causes wetting and drying on both sides of the parabolic channel.}
122\end{center}\end{figure}
123%>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
124
125\clearpage
126\subsection [WAD test case 4 : A parabolic bowl ]
127                    {WAD test case 4 : A parabolic bowl}
128\label{WAD_test_case4}
129
130Test case 4 includes variation in the y-direction in the form of a parabolic bowl. The
131initial condition is now a raised bulge centred over the bowl. Figure \ref{Fig_WAD_TC4}
132shows a cross-section of the SSH in the X-direction but features can be seen to propagate
133in all directions and interfere when return paths cross.
134
135\namdisplay{nam_wad_tc4}
136
137%>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
138\begin{figure}[htb] \begin{center}
139\includegraphics[width=0.8\textwidth]{Fig_WAD_TC4}
140\caption{ \label{Fig_WAD_TC4}
141The evolution of the sea surface height in WAD\_TEST\_CASE 4 from the initial state (t=0)
142over the first three hours of simulation. Note that this test case is a parabolic bowl with
143variations occurring in the y-direction too (not shown here).}
144\end{center}\end{figure}
145%>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
146
147\clearpage
148\subsection [WAD test case 5 : A double slope with shelf channel ]
149                    {WAD test case 5 : A double slope with shelf channel}
150\label{WAD_test_case5}
151
152Similar in nature to test case 1 but with a change in slope and a mid-depth shelf.
153
154\namdisplay{nam_wad_tc5}
155
156%>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
157\begin{figure}[htb] \begin{center}
158\includegraphics[width=0.8\textwidth]{Fig_WAD_TC5}
159\caption{ \label{Fig_WAD_TC5}
160The evolution of the sea surface height in WAD\_TEST\_CASE 5 from the initial state (t=0)
161over the first three hours of simulation. The surge resulting in this case wets to the full
162depth permitted (2.5m above sea-level) and is only halted by the 4m high side walls.}
163\end{center}\end{figure}
164%>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
165
166\clearpage
167\subsection [WAD test case 6 : A parabolic channel with central bar ]
168                    {WAD test case 6 : A parabolic channel with central bar}
169\label{WAD_test_case6}
170
171Test cases 1 to 5 have all used uniform T and S conditions. The dashed line in each plot
172shows the surface salinity along the y=17 line which remains satisfactorily constant. Test
173case 6 introduces variation in salinity by taking a parabolic channel divided by a central
174bar (gaussian) and using two different salinity values in each half of the channel. This
175step change in salinity is initially enforced by the central bar but the bar is
176subsequently over-topped after the initial SSH gradient is released. The time series in
177this case shows the SSH evolution with the water coloured according to local salinity
178values. Encroachment of the high salinity (red) waters into the low salinity (blue) basin
179can clearly be seen.
180
181\namdisplay{nam_wad_tc6}
182
183%>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
184\begin{figure}[htb] \begin{center}
185\includegraphics[width=0.8\textwidth]{Fig_WAD_TC6}
186\caption{ \label{Fig_WAD_TC6}
187The evolution of the sea surface height in WAD\_TEST\_CASE 6 from the initial state (t=0)
188over the first three hours of simulation. Water is coloured according to local salinity
189values. Encroachment of the high salinity (red) waters into the low salinity (blue) basin
190can clearly be seen although the largest influx occurs early in the sequence between the
191frames shown.}
192\end{center}\end{figure}
193%>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
194
195\clearpage
196\subsection [WAD test case 7 : A double slope with shelf, open-ended channel ]
197                    {WAD test case 7 : A double slope with shelf, open-ended channel}
198\label{WAD_test_case7}
199
200Similar in nature to test case 5 but with an open boundary forced with a sinusoidally
201varying ssh. This test case has been introduced to emulate a typical coastal application
202with a tidally forced open boundary. The bathymetry and setup is identical to test case 5
203except the right hand end of the channel is now open and has simple ssh and barotropic
204velocity boundary conditions applied at the open boundary. Several additional steps and
205namelist changes are required to run this test.
206
207\namdisplay{nam_wad_tc7}
208
209In addition, the boundary condition files must be generated using the python script
210provided.
211
212\begin{verbatim}
213python ./makebdy_tc7.py
214\end{verbatim}
215
216will create the following boundary files for this test (assuming a suitably configured
217python environment: python2.7 with netCDF4 and numpy):
218
219\begin{verbatim}
220  bdyssh_tc7_m12d30.nc   bdyuv_tc7_m12d30.nc
221  bdyssh_tc7_m01d01.nc   bdyuv_tc7_m01d01.nc
222  bdyssh_tc7_m01d02.nc   bdyuv_tc7_m01d02.nc
223  bdyssh_tc7_m01d03.nc   bdyuv_tc7_m01d03.nc
224\end{verbatim}
225
226These are sufficient for up to a three day simulation; the script is easily adapted if
227longer periods are required.
228
229%>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
230\begin{sidewaysfigure}[htb] \begin{center}
231\includegraphics[width=0.8\textwidth]{Fig_WAD_TC7}
232\caption{ \label{Fig_WAD_TC7}
233The evolution of the sea surface height in WAD\_TEST\_CASE 7 from the initial state (t=0)
234over the first 24 hours of simulation. After the initial surge the solution settles into a
235simulated tidal cycle with an amplitude of 5m. This is enough to repeatedly wet and dry
236both shelves.}
237
238\end{center}\end{sidewaysfigure}
239%>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
240
241
242% ================================================================
243
244%\bibliographystyle{wileyqj}
245%\bibliographystyle{../../../doc/latex/NEMO/main/ametsoc.bst}
246%\bibliography{references}
247
248\end{document}
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