Changeset 10092

Timestamp:

2018-09-05T18:53:05+02:00 (5 years ago)

Author:

jchanut

Message:

Update Tidal forcing documentation

Location:

NEMO/trunk/doc

Files:

• tex_main/NEMO_manual.bib (modified) (1 diff)
• tex_sub/chap_SBC.tex (modified) (2 diffs)

NEMO/trunk/doc/tex_main/NEMO_manual.bib

@@ -142 +142 @@
   volume = {109},  number = {1},
   pages = {18--36}
+}
+
+@ARTICLE{Arbic2004,
+  author = {B. Arbic and S. Garner and R. Hallberg and H. Simmons},
+  title = {The accuracy of surface elevations in forward global barotropic and baroclinic tide models},
+  journal = DSR,
+  year = {2004},
+  volume = {51},
+  pages = {3069-3101}
 }
 

NEMO/trunk/doc/tex_sub/chap_SBC.tex

@@ -756 +756 @@
 
 % ================================================================
-%        Tidal Potential
-% ================================================================
-\section{Tidal potential (\protect\mdl{sbctide})}
+%        Surface Tides Forcing
+% ================================================================
+\section{Surface tides (\protect\mdl{sbctide})}
 \label{sec:SBC_tide}
 
@@ -765 +765 @@
 %-----------------------------------------------------------------------------------------
 
-A module is available to compute the tidal potential and use it in the momentum equation.
-This option is activated when \np{ln\_tide} is set to true in \ngn{nam\_tide}.
-
-Some parameters are available in namelist \ngn{nam\_tide}:
-
-- \np{ln\_tide\_load} activate the load potential forcing and \np{filetide\_load} is  the associated file 
-
-- \np{ln\_tide\_pot} activate the tidal potential forcing
-
-- \np{nb\_harmo} is the number of constituent used
-
-- \np{clname} is the name of constituent
-
-The tide is generated by the forces of gravity ot the Earth-Moon and Earth-Sun sytem;
-they are expressed as the gradient of the astronomical potential ($\vec{\nabla}\Pi_{a}$). \\
-
-The potential astronomical expressed, for the three types of tidal frequencies
-following, by : \\
-Tide long period :
+The tidal forcing, generated by the gravity forces of the Earth-Moon and Earth-Sun sytems, is activated if \np{ln\_tide} and \np{ln\_tide\_pot} are both set to \np{.true.} in \ngn{nam\_tide}. This translates as an additional barotropic force in the momentum equations \ref{eq:PE_dyn} such that:
+\begin{equation}     \label{eq:PE_dyn_tides}
+\frac{\partial {\rm {\bf U}}_h }{\partial t}= ...
++g\nabla (\Pi_{eq} + \Pi_{sal}) 
+\end{equation} 
+where $\Pi_{eq}$ stands for the equilibrium tidal forcing and $\Pi_{sal}$ a self-attraction and loading term (SAL). 
+ 
+The equilibrium tidal forcing is expressed as a sum over the chosen constituents $l$ in \ngn{nam\_tide}. The constituents are defined such that \np{clname(1) = 'M2', clname(2)='S2', etc...}. For the three types of tidal frequencies it reads : \\
+Long period tides :
 \begin{equation}
-\Pi_{a}=gA_{k}(\frac{1}{2}-\frac{3}{2}sin^{2}\phi)cos(\omega_{k}t+V_{0k})
+\Pi_{eq}(l)=A_{l}(1+k-h)(\frac{1}{2}-\frac{3}{2}sin^{2}\phi)cos(\omega_{l}t+V_{l})
 \end{equation}
-diurnal Tide :
+diurnal tides :
 \begin{equation}
-\Pi_{a}=gA_{k}(sin 2\phi)cos(\omega_{k}t+\lambda+V_{0k})
+\Pi_{eq}(l)=A_{l}(1+k-h)(sin 2\phi)cos(\omega_{l}t+\lambda+V_{l})
 \end{equation}
-Semi-diurnal tide:
+Semi-diurnal tides:
 \begin{equation}
-\Pi_{a}=gA_{k}(cos^{2}\phi)cos(\omega_{k}t+2\lambda+V_{0k})
+\Pi_{eq}(l)=A_{l}(1+k-h)(cos^{2}\phi)cos(\omega_{l}t+2\lambda+V_{l})
 \end{equation}
-
-
-$A_{k}$ is the amplitude of the wave k, $\omega_{k}$ the pulsation of the wave k, $V_{0k}$ the astronomical phase of the wave
-$k$ to Greenwich.
-
-We make corrections to the astronomical potential.
-We obtain : 
+Here $A_{l}$ is the amplitude, $\omega_{l}$ is the frequency, $\phi$ the latitude, $\lambda$ the longitude, $V_{0l}$ a phase shift with respect to Greenwich meridian and $t$ the time. The Love number factor $(1+k-h)$ is here taken as a constant (0.7).
+
+The SAL term should in principle be computed online as it depends on the model tidal prediction itself (see \citet{Arbic2004} for a discussion about the practical implementation of this term). Nevertheless, the complex calculations involved would make this computationally too expensive. Here, practical solutions are whether to read complex estimates $\Pi_{sal}(l)$ from an external model (\np{ln\_read\_load=.true.}) or use a ``scalar approximation'' (\np{ln\_scal\_load=.true.}). In the latter case, it reads:\\
 \begin{equation}
-\Pi-g\delta = (1+k-h) \Pi_{A}(\lambda,\phi)
+\Pi_{sal} = \beta \eta
 \end{equation}
-with $k$ a number of Love estimated to 0.6 which parameterised the astronomical tidal land,
-and $h$ a number of Love to 0.3 which parameterised the parameterisation due to the astronomical tidal land.
-
-A description of load potential can be found in  \citet{Arbic2010}
+where $\beta$ (\np{rn\_scal\_load}, $\approx0.09$) is a spatially constant scalar, often chosen to minimize tidal prediction errors. Setting both \np{ln\_read\_load} and \np{ln\_scal\_load} to false removes the SAL contribution.
 
 % ================================================================