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branches/DEV_r1826_DOC/DOC/TexFiles/Chapters/Chap_SBC.tex
r1320 r1831 17 17 \item the two components of the surface ocean stress $\left( {\tau _u \;,\;\tau _v} \right)$ 18 18 \item the incoming solar and non solar heat fluxes $\left( {Q_{ns} \;,\;Q_{sr} } \right)$ 19 \item the surface freshwater budget $\left( {\text {EMP},\;\text{EMP}_S } \right)$19 \item the surface freshwater budget $\left( {\textit{emp},\;\textit{emp}_S } \right)$ 20 20 \end{itemize} 21 21 … … 28 28 the \np{nf\_sbc} namelist parameter. 29 29 When the fields are supplied from data files (flux and bulk formulations), the input fields 30 need not be supplied on the model grid. Instead a file of coordinates and weights can be supplied which31 maps the data from the supplied grid to the model points (so called "Interpolation on the Fly"). 32 In addition, the resulting fields can be further modified using 33 several namelist options. These options control the rotation of vector components 34 supplied relative to an east-north coordinate system onto the local grid directions in the model; 35 the addition of a surface restoring36 term to observed SST and/or SSS (\np{ln\_ssr}=true); the modification of fluxes30 need not be supplied on the model grid. Instead a file of coordinates and weights can 31 be supplied which maps the data from the supplied grid to the model points 32 (so called "Interpolation on the Fly"). 33 In addition, the resulting fields can be further modified using several namelist options. 34 These options control the rotation of vector components supplied relative to an east-north 35 coordinate system onto the local grid directions in the model; the addition of a surface 36 restoring term to observed SST and/or SSS (\np{ln\_ssr}=true); the modification of fluxes 37 37 below ice-covered areas (using observed ice-cover or a sea-ice model) 38 38 (\np{nn\_ice}=0,1, 2 or 3); the addition of river runoffs as surface freshwater … … 42 42 cycle (\np{ln\_dm2dc}=true). 43 43 44 In this chapter, we first discuss where the surface boundary condition 45 appears in the model equations. Then we present the four ways of providing 46 the surface boundary condition. Next the scheme for interpolation on the fly is described. 47 Finally, the different options that further modify 48 the fluxes applied to the ocean are discussed. 44 In this chapter, we first discuss where the surface boundary condition appears in the 45 model equations. Then we present the four ways of providing the surface boundary condition. 46 Next the scheme for interpolation on the fly is described. 47 Finally, the different options that further modify the fluxes applied to the ocean are discussed. 49 48 50 49 … … 75 74 \begin{equation} \label{Eq_sbc_trasbc_q} 76 75 \frac{\partial T}{\partial t}\equiv \cdots \;+\;\left. {\frac{Q_{ns} }{\rho 77 _o \;C_p \;e_{3 T} }} \right|_{k=1} \quad76 _o \;C_p \;e_{3t} }} \right|_{k=1} \quad 78 77 \end{equation} 79 78 $Q_{sr}$ is the penetrative part of the heat flux. It is applied as a 3D … … 81 80 82 81 \begin{equation} \label{Eq_sbc_traqsr} 83 \frac{\partial T}{\partial t}\equiv \cdots \;+\frac{Q_{sr} }{\rho _o C_p 84 \,e_{3T} }\delta _k \left[ {I_w } \right] 82 \frac{\partial T}{\partial t}\equiv \cdots \;+\frac{Q_{sr} }{\rho_o C_p \,e_{3t} }\delta _k \left[ {I_w } \right] 85 83 \end{equation} 86 84 where $I_w$ is a non-dimensional function that describes the way the light … … 88 86 exponentials (see \S\ref{TRA_qsr}). 89 87 90 The surface freshwater budget is provided by fields: EMP and EMP$_S$ which88 The surface freshwater budget is provided by fields: \textit{emp} and $\textit{emp}_S$ which 91 89 may or may not be identical. Indeed, a surface freshwater flux has two effects: 92 90 it changes the volume of the ocean and it changes the surface concentration of 93 91 salt (and other tracers). Therefore it appears in the sea surface height as a volume 94 flux, EMP(\textit{dynspg\_xxx} modules), and in the salinity time evolution equations92 flux, \textit{emp} (\textit{dynspg\_xxx} modules), and in the salinity time evolution equations 95 93 as a concentration/dilution effect, 96 EMP$_{S}$ (\mdl{trasbc} module).94 $\textit{emp}_{S}$ (\mdl{trasbc} module). 97 95 \begin{equation} \label{Eq_trasbc_emp} 98 96 \begin{aligned} 99 &\frac{\partial \eta }{\partial t}\equiv \cdots \;+\;\text {EMP}\quad \\97 &\frac{\partial \eta }{\partial t}\equiv \cdots \;+\;\textit{emp}\quad \\ 100 98 \\ 101 &\frac{\partial S}{\partial t}\equiv \cdots \;+\left. {\frac{\text {EMP}_S \;S}{e_{3T} }} \right|_{k=1} \\99 &\frac{\partial S}{\partial t}\equiv \cdots \;+\left. {\frac{\textit{emp}_S \;S}{e_{3t} }} \right|_{k=1} \\ 102 100 \end{aligned} 103 101 \end{equation} 104 102 105 In the real ocean, EMP$=$EMP$_S$ and the ocean salt content is conserved,103 In the real ocean, $\textit{emp}=\textit{emp}_S$ and the ocean salt content is conserved, 106 104 but it exist several numerical reasons why this equality should be broken. 107 105 For example: 108 106 109 107 When the rigid-lid assumption is made, the ocean volume becomes constant and 110 thus, EMP$=$0, not EMP$_{S }$.108 thus, $\textit{emp}=0$, not $\textit{emp}_S$. 111 109 112 110 When the ocean is coupled to a sea-ice model, the water exchanged between ice and 113 111 ocean is slightly salty (mean sea-ice salinity is $\sim $\textit{4 psu}). In this case, 114 EMP$_{S}$ take into account both concentration/dilution effect associated with115 freezing/melting and the salt flux between ice and ocean, while EMPis116 only the volume flux. In addition, in the current version of \NEMO, the 117 sea-ice is assumed to be above the ocean. Freezing/melting does not change118 the ocean volume (no impact on EMP) but it modifies the SSS.112 $\textit{emp}_{S}$ take into account both concentration/dilution effect associated with 113 freezing/melting and the salt flux between ice and ocean, while \textit{emp} is 114 only the volume flux. In addition, in the current version of \NEMO, the sea-ice is 115 assumed to be above the ocean (the so-called levitating sea-ice). Freezing/melting does 116 not change the ocean volume (no impact on \textit{emp}) but it modifies the SSS. 119 117 %gm \colorbox{yellow}{(see {\S} on LIM sea-ice model)}. 120 118 … … 127 125 associated with precipitation! Precipitation can change the ocean volume and thus the 128 126 ocean heat content. It is therefore associated with a heat flux (not yet 129 diagnosed in the model) \citep{Roullet 2000}).127 diagnosed in the model) \citep{Roullet_Madec_JGR00}). 130 128 131 129 %\colorbox{yellow}{Miss: } … … 193 191 be uniform in space. They take constant values given in the namelist 194 192 namsbc{\_}ana by the variables \np{rn\_utau0}, \np{rn\_vtau0}, \np{rn\_qns0}, 195 \np{rn\_qsr0}, and \np{rn\_emp0} ( EMP$=$EMP$_S$). The runoff is set to zero.193 \np{rn\_qsr0}, and \np{rn\_emp0} ($\textit{emp}=\textit{emp}_S$). The runoff is set to zero. 196 194 In addition, the wind is allowed to reach its nominal value within a given number 197 195 of time steps (\np{nn\_tau000}). … … 267 265 %------------------------------------------------------------------------------------------------------------- 268 266 269 The CORE bulk formulae have been developed by \citet{Large Yeager2004}.267 The CORE bulk formulae have been developed by \citet{Large_Yeager_Rep04}. 270 268 They have been designed to handle the CORE forcing, a mixture of NCEP 271 269 reanalysis and satellite data. They use an inertial dissipative method to compute … … 408 406 The symbolic algorithm used to calculate values on the model grid is now: 409 407 410 \begin{multline*} 411 f_{m}(i,j) = f_{m}(i,j) + \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))} 412 \\ 413 + \sum_{k=5}^{8} {wgt(k)\left.\frac{\partial f}{\partial i}\right| _{idx(src(k))} } 414 \\ 415 + \sum_{k=9}^{12} {wgt(k)\left.\frac{\partial f}{\partial j}\right| _{idx(src(k))} } 416 \\ 417 + \sum_{k=13}^{16} {wgt(k)\left.\frac{\partial ^2 f}{\partial i \partial j}\right| _{idx(src(k))} } 418 \end{multline*} 408 \begin{equation*} \begin{split} 409 f_{m}(i,j) = f_{m}(i,j) +& \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))} 410 + \sum_{k=5}^{8} {wgt(k)\left.\frac{\partial f}{\partial i}\right| _{idx(src(k))} } \\ 411 +& \sum_{k=9}^{12} {wgt(k)\left.\frac{\partial f}{\partial j}\right| _{idx(src(k))} } 412 + \sum_{k=13}^{16} {wgt(k)\left.\frac{\partial ^2 f}{\partial i \partial j}\right| _{idx(src(k))} } 413 \end{split} 414 \end{equation*} 419 415 The gradients here are taken with respect to the horizontal indices and not distances since the spatial dependency has been absorbed into the weights. 420 416 … … 515 511 516 512 \begin{equation} \label{Eq_sbc_dmp_emp} 517 EMP = EMP_o + \gamma_s^{-1} e_{3t} \frac{ \left(\left.S\right|_{k=1}-SSS_{Obs}\right)}513 \textit{emp} = \textit{emp}_o + \gamma_s^{-1} e_{3t} \frac{ \left(\left.S\right|_{k=1}-SSS_{Obs}\right)} 518 514 {\left.S\right|_{k=1}} 519 515 \end{equation} 520 516 521 where EMP$_{o }$ is a net surface fresh water flux (observed, climatological or an517 where $\textit{emp}_{o }$ is a net surface fresh water flux (observed, climatological or an 522 518 atmospheric model product), \textit{SSS}$_{Obs}$ is a sea surface salinity (usually a time 523 519 interpolation of the monthly mean Polar Hydrographic Climatology \citep{Steele2001}), … … 602 598 \item[\np{nn\_fwb}=0] no control at all. The mean sea level is free to drift, and will 603 599 certainly do so. 604 \item[\np{nn\_fwb}=1] global mean EMPset to zero at each model time step.600 \item[\np{nn\_fwb}=1] global mean \textit{emp} set to zero at each model time step. 605 601 %Note that with a sea-ice model, this technique only control the mean sea level with linear free surface (\key{vvl} not defined) and no mass flux between ocean and ice (as it is implemented in the current ice-ocean coupling). 606 602 \item[\np{nn\_fwb}=2] freshwater budget is adjusted from the previous year annual
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