Changeset 14037 for NEMO/branches/2020/dev_r13333_KERNEL-08_techene_gm_HPG_SPG/doc/latex/NEMO/subfiles/chap_SBC.tex
- Timestamp:
- 2020-12-03T12:20:38+01:00 (3 years ago)
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- NEMO/branches/2020/dev_r13333_KERNEL-08_techene_gm_HPG_SPG
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NEMO/branches/2020/dev_r13333_KERNEL-08_techene_gm_HPG_SPG
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NEMO/branches/2020/dev_r13333_KERNEL-08_techene_gm_HPG_SPG/doc/latex/NEMO/subfiles/chap_SBC.tex
r13165 r14037 5 5 \begin{document} 6 6 7 \chapter{Surface Boundary Condition (SBC, SAS, ISF, ICB )}7 \chapter{Surface Boundary Condition (SBC, SAS, ISF, ICB, TDE)} 8 8 \label{chap:SBC} 9 9 … … 18 18 Release & Author(s) & Modifications \\ 19 19 \hline 20 {\em next} & {\em Simon M{\" u}ller} & {\em Update of \autoref{sec:SBC_TDE}}\\[2mm] 20 21 {\em 4.0} & {\em ...} & {\em ...} \\ 21 22 {\em 3.6} & {\em ...} & {\em ...} \\ … … 1013 1014 1014 1015 %% ================================================================================================= 1015 \section [Surface tides (\textit{sbctide.F90})]{Surface tides (\protect\mdl{sbctide})}1016 \label{sec:SBC_ tide}1016 \section{Surface tides (TDE)} 1017 \label{sec:SBC_TDE} 1017 1018 1018 1019 \begin{listing} … … 1022 1023 \end{listing} 1023 1024 1024 The tidal forcing, generated by the gravity forces of the Earth-Moon and Earth-Sun sytems, 1025 is activated if \np{ln_tide}{ln\_tide} and \np{ln_tide_pot}{ln\_tide\_pot} are both set to \forcode{.true.} in \nam{_tide}{\_tide}. 1026 This translates as an additional barotropic force in the momentum \autoref{eq:MB_PE_dyn} such that: 1025 \subsection{Tidal constituents} 1026 Ocean model component TDE provides the common functionality for tidal forcing 1027 and tidal analysis in the model framework. This includes the computation of the gravitational 1028 surface forcing, as well as support for lateral forcing at open boundaries (see 1029 \autoref{subsec:LBC_bdy_tides}) and tidal harmonic analysis (see 1030 \autoref{subsec:DIA_diamlr} and \autoref{subsec:DIA_diadetide}). The module is 1031 activated with \np[=.true.]{ln_tide}{ln\_tide} in namelist 1032 \nam{_tide}{\_tide}. It provides the same 34 tidal constituents that are 1033 included in the 1034 \href{https://www.aviso.altimetry.fr/en/data/products/auxiliary-products/global-tide-fes.html}{FES2014 1035 ocean tide model}: Mf, Mm, Ssa, Mtm, Msf, Msqm, Sa, K1, O1, P1, Q1, J1, S1, 1036 M2, S2, N2, K2, nu2, mu2, 2N2, L2, T2, eps2, lam2, R2, M3, MKS2, MN4, MS4, M4, 1037 N4, S4, M6, and M8; see file \hf{tide} and \mdl{tide\_mod} for further 1038 information and references\footnote{As a legacy option \np{ln_tide_var} can be 1039 set to \forcode{0}, in which case the 19 tidal constituents (M2, N2, 2N2, S2, 1040 K2, K1, O1, Q1, P1, M4, Mf, Mm, Msqm, Mtm, S1, MU2, NU2, L2, and T2; see file 1041 \hf{tide}) and associated parameters that have been available in NEMO version 1042 4.0 and earlier are available}. Constituents to be included in the tidal forcing 1043 (surface and lateral boundaries) are selected by enumerating their respective 1044 names in namelist array \np{sn_tide_cnames}{sn\_tide\_cnames}.\par 1045 1046 \subsection{Surface tidal forcing} 1047 Surface tidal forcing can be represented in the model through an additional 1048 barotropic force in the momentum equation (\autoref{eq:MB_PE_dyn}) such that: 1027 1049 \[ 1028 % \label{eq:SBC_PE_dyn_tides} 1029 \frac{\partial {\mathrm {\mathbf U}}_h }{\partial t}= ... 1030 +g\nabla (\Pi_{eq} + \Pi_{sal}) 1050 \frac{\partial {\mathrm {\mathbf U}}_h }{\partial t} = \ldots +g\nabla (\gamma 1051 \Pi_{eq} + \Pi_{sal}) 1031 1052 \] 1032 where $\Pi_{eq}$ stands for the equilibrium tidal forcing and 1033 $\Pi_{sal}$ is a self-attraction and loading term (SAL). 1034 1035 The equilibrium tidal forcing is expressed as a sum over a subset of 1036 constituents chosen from the set of available tidal constituents 1037 defined in file \hf{SBC/tide} (this comprises the tidal 1038 constituents \textit{M2, N2, 2N2, S2, K2, K1, O1, Q1, P1, M4, Mf, Mm, 1039 Msqm, Mtm, S1, MU2, NU2, L2}, and \textit{T2}). Individual 1040 constituents are selected by including their names in the array 1041 \np{clname}{clname} in \nam{_tide}{\_tide} (e.g., \np{clname}{clname}\forcode{(1)='M2', } 1042 \np{clname}{clname}\forcode{(2)='S2'} to select solely the tidal consituents \textit{M2} 1043 and \textit{S2}). Optionally, when \np{ln_tide_ramp}{ln\_tide\_ramp} is set to 1044 \forcode{.true.}, the equilibrium tidal forcing can be ramped up 1045 linearly from zero during the initial \np{rdttideramp}{rdttideramp} days of the 1046 model run. 1053 where $\gamma \Pi_{eq}$ stands for the equilibrium tidal forcing scaled by a spatially 1054 uniform tilt factor $\gamma$, and $\Pi_{sal}$ is an optional 1055 self-attraction and loading term (SAL). These additional terms are enabled when, 1056 in addition to \np[=.true.]{ln_tide}{ln\_tide}), 1057 \np[=.true.]{ln_tide_pot}{ln\_tide\_pot}.\par 1058 1059 The equilibrium tidal forcing is expressed as a sum over the subset of 1060 constituents listed in \np{sn_tide_cnames}{sn\_tide\_cnames} of 1061 \nam{_tide} (e.g., 1062 \begin{forlines} 1063 sn_tide_cnames(1) = 'M2' 1064 sn_tide_cnames(2) = 'K1' 1065 sn_tide_cnames(3) = 'S2' 1066 sn_tide_cnames(4) = 'O1' 1067 \end{forlines} 1068 to select the four tidal constituents of strongest equilibrium tidal 1069 potential). The tidal tilt factor $\gamma = 1 + k - h$ includes the 1070 Love numbers $k$ and $h$ \citep{love_prsla1909}; this factor is 1071 configurable using \np{rn_tide_gamma} (default value 0.7). Optionally, 1072 when \np[=.true.]{ln_tide_ramp}{ln\_tide\_ramp}, the equilibrium tidal 1073 forcing can be ramped up linearly from zero during the initial 1074 \np{rn_tide_ramp_dt}{rn\_tide\_ramp\_dt} days of the model run.\par 1047 1075 1048 1076 The SAL term should in principle be computed online as it depends on 1049 1077 the model tidal prediction itself (see \citet{arbic.garner.ea_DSR04} for a 1050 discussion about the practical implementation of this term). 1051 Nevertheless, the complex calculations involved would make this 1052 computationally too expensive. Here, two options are available: 1053 $\Pi_{sal}$ generated by an external model can be read in 1054 (\np[=.true.]{ln_read_load}{ln\_read\_load}), or a ``scalar approximation'' can be 1055 used (\np[=.true.]{ln_scal_load}{ln\_scal\_load}). In the latter case 1078 discussion about the practical implementation of this term). The complex 1079 calculations involved in such computations, however, are computationally very 1080 expensive. Here, two mutually exclusive simpler variants are available: 1081 amplitudes generated by an external model for oscillatory $\Pi_{sal}$ 1082 contributions from each of the selected tidal constituents can be read in 1083 (\np[=.true.]{ln_read_load}{ln\_read\_load}) from the file specified in 1084 \np{cn_tide_load}{cn\_tide\_load} (the variable names are comprised of the 1085 tidal-constituent name and suffixes \forcode{_z1} and \forcode{_z2} for the two 1086 orthogonal components, respectively); alternatively, a ``scalar approximation'' 1087 can be used (\np[=.true.]{ln_scal_load}{ln\_scal\_load}), where 1056 1088 \[ 1057 1089 \Pi_{sal} = \beta \eta, 1058 1090 \] 1059 where $\beta$ (\np{rn_scal_load}{rn\_scal\_load} with a default value of 0.094) is a 1060 spatially constant scalar, often chosen to minimize tidal prediction 1061 errors. Setting both \np{ln_read_load}{ln\_read\_load} and \np{ln_scal_load}{ln\_scal\_load} to 1062 \forcode{.false.} removes the SAL contribution. 1091 with a spatially uniform coefficient $\beta$, which can be configured 1092 via \np{rn_scal_load}{rn\_scal\_load} (default value 0.094) and is 1093 often tuned to minimize tidal prediction errors.\par 1094 1095 For diagnostic purposes, the forcing potential of the individual tidal 1096 constituents (incl. load ptential, if activated) and the total forcing 1097 potential (incl. load potential, if activated) can be made available 1098 as diagnostic output by setting 1099 \np[=.true.]{ln_tide_dia}{ln\_tide\_dia} (fields 1100 \forcode{tide_pot_<constituent>} and \forcode{tide_pot}).\par 1063 1101 1064 1102 %% =================================================================================================
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