Changeset 10614 for NEMO/trunk/doc/latex/NEMO/subfiles/chap_SBC.tex
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 20190131T18:10:55+01:00 (3 years ago)
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NEMO/trunk/doc/latex/NEMO/subfiles/chap_SBC.tex
r10468 r10614 815 815 816 816 The tidal forcing, generated by the gravity forces of the EarthMoon and EarthSun sytems, 817 is activated if \np{ln\_tide} and \np{ln\_tide\_pot} are both set to \ np{.true.} in \ngn{nam\_tide}.817 is activated if \np{ln\_tide} and \np{ln\_tide\_pot} are both set to \forcode{.true.} in \ngn{nam\_tide}. 818 818 This translates as an additional barotropic force in the momentum equations \ref{eq:PE_dyn} such that: 819 819 \[ … … 822 822 +g\nabla (\Pi_{eq} + \Pi_{sal}) 823 823 \] 824 where $\Pi_{eq}$ stands for the equilibrium tidal forcing and $\Pi_{sal}$ a selfattraction and loading term (SAL). 824 where $\Pi_{eq}$ stands for the equilibrium tidal forcing and 825 $\Pi_{sal}$ is a selfattraction and loading term (SAL). 825 826 826 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 \[ 831 \Pi_{eq}(l)=A_{l}(1+kh)(\frac{1}{2}\frac{3}{2}sin^{2}\phi)cos(\omega_{l}t+V_{l}) 832 \] 833 diurnal tides : 834 \[ 835 \Pi_{eq}(l)=A_{l}(1+kh)(sin 2\phi)cos(\omega_{l}t+\lambda+V_{l}) 836 \] 837 Semidiurnal tides: 838 \[ 839 \Pi_{eq}(l)=A_{l}(1+kh)(cos^{2}\phi)cos(\omega_{l}t+2\lambda+V_{l}) 840 \] 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 $(1+kh)$ 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. 827 The equilibrium tidal forcing is expressed as a sum over a subset of 828 constituents chosen from the set of available tidal constituents 829 defined in file \rou{SBC/tide.h90} (this comprises the tidal 830 constituents \textit{M2, N2, 2N2, S2, K2, K1, O1, Q1, P1, M4, Mf, Mm, 831 Msqm, Mtm, S1, MU2, NU2, L2}, and \textit{T2}). Individual 832 constituents 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} 835 and \textit{S2}). Optionally, when \np{ln\_tide\_ramp} is set to 836 \forcode{.true.}, the equilibrium tidal forcing can be ramped up 837 linearly from zero during the initial \np{rdttideramp} days of the 838 model run. 839 840 The SAL term should in principle be computed online as it depends on 841 the model tidal prediction itself (see \citet{Arbic2004} for a 842 discussion about the practical implementation of this term). 843 Nevertheless, the complex calculations involved would make this 844 computationally 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 847 used (\np{ln\_scal\_load=.true.}). In the latter case 848 \[ 849 \Pi_{sal} = \beta \eta, 850 \] 851 where $\beta$ (\np{rn\_scal\_load} with a default value of 0.094) is a 852 spatially constant scalar, often chosen to minimize tidal prediction 853 errors. Setting both \np{ln\_read\_load} and \np{ln\_scal\_load} to 854 \forcode{.false.} removes the SAL contribution. 857 855 858 856 % ================================================================
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