Changeset 10092


Ignore:
Timestamp:
2018-09-05T18:53:05+02:00 (22 months ago)
Author:
jchanut
Message:

Update Tidal forcing documentation

Location:
NEMO/trunk/doc
Files:
2 edited

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  • NEMO/trunk/doc/tex_main/NEMO_manual.bib

    r9394 r10092  
    142142  volume = {109},  number = {1}, 
    143143  pages = {18--36} 
     144} 
     145 
     146@ARTICLE{Arbic2004, 
     147  author = {B. Arbic and S. Garner and R. Hallberg and H. Simmons}, 
     148  title = {The accuracy of surface elevations in forward global barotropic and baroclinic tide models}, 
     149  journal = DSR, 
     150  year = {2004}, 
     151  volume = {51}, 
     152  pages = {3069-3101} 
    144153} 
    145154 
  • NEMO/trunk/doc/tex_sub/chap_SBC.tex

    r9407 r10092  
    756756 
    757757% ================================================================ 
    758 %        Tidal Potential 
    759 % ================================================================ 
    760 \section{Tidal potential (\protect\mdl{sbctide})} 
     758%        Surface Tides Forcing 
     759% ================================================================ 
     760\section{Surface tides (\protect\mdl{sbctide})} 
    761761\label{sec:SBC_tide} 
    762762 
     
    765765%----------------------------------------------------------------------------------------- 
    766766 
    767 A module is available to compute the tidal potential and use it in the momentum equation. 
    768 This option is activated when \np{ln\_tide} is set to true in \ngn{nam\_tide}. 
    769  
    770 Some parameters are available in namelist \ngn{nam\_tide}: 
    771  
    772 - \np{ln\_tide\_load} activate the load potential forcing and \np{filetide\_load} is  the associated file  
    773  
    774 - \np{ln\_tide\_pot} activate the tidal potential forcing 
    775  
    776 - \np{nb\_harmo} is the number of constituent used 
    777  
    778 - \np{clname} is the name of constituent 
    779  
    780 The tide is generated by the forces of gravity ot the Earth-Moon and Earth-Sun sytem; 
    781 they are expressed as the gradient of the astronomical potential ($\vec{\nabla}\Pi_{a}$). \\ 
    782  
    783 The potential astronomical expressed, for the three types of tidal frequencies 
    784 following, by : \\ 
    785 Tide long period : 
     767The 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: 
     768\begin{equation}     \label{eq:PE_dyn_tides} 
     769\frac{\partial {\rm {\bf U}}_h }{\partial t}= ... 
     770+g\nabla (\Pi_{eq} + \Pi_{sal})  
     771\end{equation}  
     772where $\Pi_{eq}$ stands for the equilibrium tidal forcing and $\Pi_{sal}$ a self-attraction and loading term (SAL).  
     773  
     774The 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 : \\ 
     775Long period tides : 
    786776\begin{equation} 
    787 \Pi_{a}=gA_{k}(\frac{1}{2}-\frac{3}{2}sin^{2}\phi)cos(\omega_{k}t+V_{0k}) 
     777\Pi_{eq}(l)=A_{l}(1+k-h)(\frac{1}{2}-\frac{3}{2}sin^{2}\phi)cos(\omega_{l}t+V_{l}) 
    788778\end{equation} 
    789 diurnal Tide : 
     779diurnal tides : 
    790780\begin{equation} 
    791 \Pi_{a}=gA_{k}(sin 2\phi)cos(\omega_{k}t+\lambda+V_{0k}) 
     781\Pi_{eq}(l)=A_{l}(1+k-h)(sin 2\phi)cos(\omega_{l}t+\lambda+V_{l}) 
    792782\end{equation} 
    793 Semi-diurnal tide: 
     783Semi-diurnal tides: 
    794784\begin{equation} 
    795 \Pi_{a}=gA_{k}(cos^{2}\phi)cos(\omega_{k}t+2\lambda+V_{0k}) 
     785\Pi_{eq}(l)=A_{l}(1+k-h)(cos^{2}\phi)cos(\omega_{l}t+2\lambda+V_{l}) 
    796786\end{equation} 
    797  
    798  
    799 $A_{k}$ is the amplitude of the wave k, $\omega_{k}$ the pulsation of the wave k, $V_{0k}$ the astronomical phase of the wave 
    800 $k$ to Greenwich. 
    801  
    802 We make corrections to the astronomical potential. 
    803 We obtain :  
     787Here $A_{l}$ 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). 
     788 
     789The 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:\\ 
    804790\begin{equation} 
    805 \Pi-g\delta = (1+k-h) \Pi_{A}(\lambda,\phi) 
     791\Pi_{sal} = \beta \eta 
    806792\end{equation} 
    807 with $k$ a number of Love estimated to 0.6 which parameterised the astronomical tidal land, 
    808 and $h$ a number of Love to 0.3 which parameterised the parameterisation due to the astronomical tidal land. 
    809  
    810 A description of load potential can be found in  \citet{Arbic2010} 
     793where $\beta$ (\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. 
    811794 
    812795% ================================================================ 
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