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Timestamp:
2019-01-31T18:10:55+01:00 (3 years ago)
Author:
smueller
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Merge of changeset [10613] into the trunk

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  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_SBC.tex

    r10468 r10614  
    815815 
    816816The tidal forcing, generated by the gravity forces of the Earth-Moon and Earth-Sun sytems, 
    817 is activated if \np{ln\_tide} and \np{ln\_tide\_pot} are both set to \np{.true.} in \ngn{nam\_tide}. 
     817is activated if \np{ln\_tide} and \np{ln\_tide\_pot} are both set to \forcode{.true.} in \ngn{nam\_tide}. 
    818818This translates as an additional barotropic force in the momentum equations \ref{eq:PE_dyn} such that: 
    819819\[ 
     
    822822  +g\nabla (\Pi_{eq} + \Pi_{sal}) 
    823823\] 
    824 where $\Pi_{eq}$ stands for the equilibrium tidal forcing and $\Pi_{sal}$ a self-attraction and loading term (SAL).  
     824where $\Pi_{eq}$ stands for the equilibrium tidal forcing and 
     825$\Pi_{sal}$ is a self-attraction and loading term (SAL). 
    825826  
    826 The equilibrium tidal forcing is expressed as a sum over the chosen constituents $l$ in \ngn{nam\_tide}. 
    827 The constituents are defined such that \np{clname(1) = 'M2', clname(2)='S2', etc...}. 
    828 For the three types of tidal frequencies it reads: \\ 
    829 Long period tides : 
    830 \[ 
    831   \Pi_{eq}(l)=A_{l}(1+k-h)(\frac{1}{2}-\frac{3}{2}sin^{2}\phi)cos(\omega_{l}t+V_{l}) 
    832 \] 
    833 diurnal tides : 
    834 \[ 
    835   \Pi_{eq}(l)=A_{l}(1+k-h)(sin 2\phi)cos(\omega_{l}t+\lambda+V_{l}) 
    836 \] 
    837 Semi-diurnal tides: 
    838 \[ 
    839   \Pi_{eq}(l)=A_{l}(1+k-h)(cos^{2}\phi)cos(\omega_{l}t+2\lambda+V_{l}) 
    840 \] 
    841 Here $A_{l}$ is the amplitude, $\omega_{l}$ is the frequency, $\phi$ the latitude, $\lambda$ the longitude, 
    842 $V_{0l}$ a phase shift with respect to Greenwich meridian and $t$ the time. 
    843 The Love number factor $(1+k-h)$ is here taken as a constant (0.7). 
    844  
    845 The SAL term should in principle be computed online as it depends on the model tidal prediction itself 
    846 (see \citet{Arbic2004} for a discussion about the practical implementation of this term). 
    847 Nevertheless, the complex calculations involved would make this computationally too expensive. 
    848 Here, practical solutions are whether to read complex estimates $\Pi_{sal}(l)$ from an external model 
    849 (\np{ln\_read\_load=.true.}) or use a ``scalar approximation'' (\np{ln\_scal\_load=.true.}). 
    850 In the latter case, it reads:\\ 
    851 \[ 
    852   \Pi_{sal} = \beta \eta 
    853 \] 
    854 where $\beta$ (\np{rn\_scal\_load}, $\approx0.09$) is a spatially constant scalar, 
    855 often chosen to minimize tidal prediction errors. 
    856 Setting both \np{ln\_read\_load} and \np{ln\_scal\_load} to false removes the SAL contribution. 
     827The equilibrium tidal forcing is expressed as a sum over a subset of 
     828constituents chosen from the set of available tidal constituents 
     829defined in file \rou{SBC/tide.h90} (this comprises the tidal 
     830constituents \textit{M2, N2, 2N2, S2, K2, K1, O1, Q1, P1, M4, Mf, Mm, 
     831  Msqm, Mtm, S1, MU2, NU2, L2}, and \textit{T2}). Individual 
     832constituents are selected by including their names in the array 
     833\np{clname} in \ngn{nam\_tide} (e.g., \np{clname(1) = 'M2', 
     834  clname(2)='S2'} to select solely the tidal consituents \textit{M2} 
     835and \textit{S2}). Optionally, when \np{ln\_tide\_ramp} is set to 
     836\forcode{.true.}, the equilibrium tidal forcing can be ramped up 
     837linearly from zero during the initial \np{rdttideramp} days of the 
     838model run. 
     839 
     840The SAL term should in principle be computed online as it depends on 
     841the model tidal prediction itself (see \citet{Arbic2004} for a 
     842discussion about the practical implementation of this term). 
     843Nevertheless, the complex calculations involved would make this 
     844computationally too expensive.  Here, two options are available: 
     845$\Pi_{sal}$ generated by an external model can be read in 
     846(\np{ln\_read\_load=.true.}), or a ``scalar approximation'' can be 
     847used (\np{ln\_scal\_load=.true.}). In the latter case 
     848\[ 
     849  \Pi_{sal} = \beta \eta, 
     850\] 
     851where $\beta$ (\np{rn\_scal\_load} with a default value of 0.094) is a 
     852spatially constant scalar, often chosen to minimize tidal prediction 
     853errors. Setting both \np{ln\_read\_load} and \np{ln\_scal\_load} to 
     854\forcode{.false.} removes the SAL contribution. 
    857855 
    858856% ================================================================ 
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