[707] | 1 | % ================================================================ |
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| 2 | % Chapter Ñ Surface Boundary Condition (SBC) |
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| 3 | % ================================================================ |
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| 4 | \chapter{Surface Boundary Condition (SBC) } |
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| 5 | \label{SBC} |
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| 6 | \minitoc |
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| 7 | |
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| 8 | \begin{verbatim} |
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| 9 | At the time of this writing, the new surface module |
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| 10 | that is described in this chapter (SBC) is not yet part |
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| 11 | of the current distribution. The current way to specify |
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| 12 | the surface boundary condition is such a mess that we |
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| 13 | did not attempt to describe it. Nevertheless, apart from |
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| 14 | the way the surface forcing is implemented, the infor- |
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| 15 | mation given here are relevant for a NEMO v2.3 user. |
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| 16 | \end{verbatim} |
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| 17 | |
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| 18 | The ocean needs 7 fields as surface boundary condition: |
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| 19 | |
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| 20 | The two components of the surface ocean stress $\left( {\tau _u \;,\;\tau _v} \right)$ |
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| 21 | |
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| 22 | The incoming solar and non solar heat fluxes $\left( {Q_{ns} \;,\;Q_{sr} } \right)$ |
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| 23 | |
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| 24 | The surface freshwater budget $\left( {\text{EMP}\;,\;\text{EMP}_S } \right)$ |
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| 25 | |
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| 26 | \colorbox {yellow}{ The river runoffs (RUNOFF)} |
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| 27 | |
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| 28 | Four different ways are offered to provide those 7 fields to the ocean: an |
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| 29 | analytical formulation, a flux formulation, a bulk formulae formulation |
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| 30 | (CORE or CLIO bulk formulae) and a coupled formulation (exchanges with a |
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| 31 | atmospheric model via OASIS coupler). In addition, the resulting fields can |
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| 32 | be further modified on used demand via several namelist option. These option |
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| 33 | control the addition of a surface restoring term to observed SST and/or SSS, |
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| 34 | the modification of fluxes below ice-covered area (using observed ice-cover |
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| 35 | or a sea-ice model), the addition of river runoffs as surface freshwater |
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| 36 | fluxes, and the addition of a freshwater flux adjustment on order to avoid a |
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| 37 | mean sea-level drift. |
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| 38 | |
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| 39 | In this chapter we first discuss where the surface boundary condition |
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| 40 | appears in the model equations. Then we present the four ways of providing |
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| 41 | the surface boundary condition. Finally, the different options that modify |
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| 42 | the fluxes inside the ocean are discussed. |
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| 43 | |
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| 44 | |
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| 45 | |
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| 46 | |
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| 47 | |
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| 48 | |
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| 49 | |
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| 50 | |
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| 51 | |
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| 52 | |
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| 53 | |
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| 54 | % ================================================================ |
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| 55 | % Surface boundary condition for the ocean |
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| 56 | % ================================================================ |
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| 57 | \section{Surface boundary condition for the ocean} |
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| 58 | \label{SBC_general} |
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| 59 | |
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| 60 | |
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| 61 | The surface ocean stress is the stress exerted by the wind and the sea-ice |
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| 62 | on the ocean. Their two components are assumed to be interpolated on the |
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| 63 | ocean mesh, i.e. provided at U- and V-points and projected onto the |
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| 64 | (\textbf{i},\textbf{j}) referential. They are applied as a surface boundary |
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| 65 | condition of the computation of the momentum vertical mixing trend |
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| 66 | (\textbf{dynzdf} module) : |
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| 67 | \begin{equation} \label{Eq_sbc_dynzdf} |
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| 68 | \left.{\left( {\frac{A^{vm} }{e_3 }\ \frac{\partial \textbf{U}_h}{\partial k}} \right)} \right|_{z=1} |
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| 69 | = \frac{1}{\rho _o} \binom{\tau _u}{\tau _v } |
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| 70 | \end{equation} |
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| 71 | where $(\tau _u ,\;\tau _v )=(utau,vtau)$ are the two components of the wind |
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| 72 | stress vector in the $(\textbf{i},\textbf{j})$ coordinate system. |
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| 73 | |
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| 74 | The surface heat flux is decomposed in two parts, a non solar and solar heat |
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| 75 | fluxes. The former is the non penetrative part of the heat flux (i.e. |
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| 76 | sensible plus latent plus long wave heat fluxes). It is applied as a surface |
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| 77 | boundary condition trend of the first level temperature time evolution |
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| 78 | equation (\mdl{trasbc} module). |
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| 79 | \begin{equation} \label{Eq_sbc_trasbc_q} |
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| 80 | \frac{\partial T}{\partial t}\equiv \cdots \;+\;\left. {\frac{Q_{ns} }{\rho |
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| 81 | _o \;C_p \;e_{3T} }} \right|_{k=1} \quad |
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| 82 | \end{equation} |
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| 83 | |
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| 84 | The latter is the penetrative part of the heat flux. It is applied as a 3D |
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| 85 | trends of the temperature equation (\mdl{traqsr} module) when \np{ln\_traqsr}=T. |
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| 86 | |
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| 87 | \begin{equation} \label{Eq_sbc_traqsr} |
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| 88 | \frac{\partial T}{\partial t}\equiv \cdots \;+\frac{Q_{sr} }{\rho _o C_p |
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| 89 | \,e_{3T} }\delta _k \left[ {I_w } \right] |
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| 90 | \end{equation} |
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| 91 | |
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| 92 | where $I_w$ is an adimensional function that describes the way the light |
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| 93 | penetrates inside the water column. It is generally a sum of decreasing |
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| 94 | exponential (see \S\ref{TRA_qsr}). |
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| 95 | |
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| 96 | The surface freshwater budget is provided through two non-necessary |
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| 97 | identical fields EMP and EMP$_S $. Indeed, a surface freshwater |
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| 98 | flux has two effects: it changes the volume of the ocean and it changes the |
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| 99 | surface concentration of salt (an others tracers). Therefore it appears in |
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| 100 | the sea surface height and salinity time evolution equations as a volume |
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| 101 | flux, EMP (\textit{dynspg\_xxx} modules), and concentration/dilution effect, |
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| 102 | EMP$_{S}$ (\mdl{trasbc} module), respectively. |
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| 103 | \begin{equation} \label{Eq_trasbc_emp} |
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| 104 | \begin{aligned} |
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| 105 | &\frac{\partial \eta }{\partial t}\equiv \cdots \;+\;\text{EMP}\quad \\ |
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| 106 | \\ |
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| 107 | &\frac{\partial S}{\partial t}\equiv \cdots \;+\left. {\frac{\text{EMP}_S \;S}{e_{3T} }} \right|_{k=1} \\ |
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| 108 | \end{aligned} |
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| 109 | \end{equation} |
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| 110 | |
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| 111 | In the real ocean, EMP=EMP$_S$ and the ocean salt content is conserved, |
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| 112 | but it exist several numerical reason why this equality should be broken. |
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| 113 | For example: |
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| 114 | |
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| 115 | When rigid-lid assumption is made, the ocean volume becomes constant and |
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| 116 | thus, EMP=0, not EMP$_{S }$. |
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| 117 | |
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| 118 | When a sea-ice model is considered, the water exchanged between ice and |
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| 119 | ocean is not fresh as mean ice salinity is $\sim $\textit{4 psu}. In this case, |
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| 120 | EMP$_{S}$ take into account both concentration/dilution effect associated with |
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| 121 | freezing/melting together with salt flux between ice and ocean, while EMP is |
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| 122 | only the volume flux. In addition, in the current version of \NEMO, the |
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| 123 | sea-ice is assumed to be above the ocean. Freezing/melting does not change |
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| 124 | the ocean volume (not impact on EMP) while it modifies the SSS |
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| 125 | \colorbox{yellow}{(see {\S} on LIM sea-ice model)}. |
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| 126 | |
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| 127 | Note that SST can also be modified by a freshwater flux. Precipitations (in |
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| 128 | particular solid one) may have a temperature significantly different from |
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| 129 | the SST. Due to the lack of information about the temperature of |
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| 130 | precipitations, we assume it is equal to the SST. Therefore, no |
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| 131 | concentration/dilution term appears in the temperature equation. It has to |
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| 132 | be emphasised that this absence does not mean that there is not heat flux |
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| 133 | associated with precipitation! An excess of precipitation will change the |
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| 134 | ocean heat content and is therefore associated with a heat flux (not |
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| 135 | diagnosed in the model) \citep{Roullet2000}). |
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| 136 | |
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| 137 | \colorbox{yellow}{Miss: } |
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| 138 | |
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| 139 | A extensive description of all namsbc namelist (parameter that have to be |
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| 140 | created!) |
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| 141 | |
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| 142 | Especially the \np{nf\_sbc}, the \mdl{sbc\_oce} module (fluxes + mean sst sss ssu |
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| 143 | ssv) i.e. information required by flux computation or sea-ice |
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| 144 | |
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| 145 | \colorbox{red}{Add nqsr = 0 / 1 replace key{\_}traqsr} |
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| 146 | |
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| 147 | \mdl{sbc\_oce} containt the definition in memory of the 7 fields (6+runoff), add |
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| 148 | a word on runoff: included in surface bc or add as lateral obc{\ldots}. |
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| 149 | |
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| 150 | Sbcmod manage the ``providing'' (fourniture) to the ocean the 7 fields |
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| 151 | |
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| 152 | Fluxes update only each nf{\_}sbc time step (namsbc) explain relation |
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| 153 | between nf{\_}sbc and nf{\_}ice, do we define nf{\_}blk??? ? only one |
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| 154 | nf{\_}sbc |
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| 155 | |
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| 156 | Explain here all the namlist namsbc variable{\ldots}. |
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| 157 | |
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| 158 | \colorbox{yellow}{End Miss } |
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| 159 | |
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| 160 | The ocean model provides the following variables averaged over nf{\_}sbc |
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| 161 | time-step: |
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| 162 | |
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| 163 | %-------------------------------------------------TABLE--------------------------------------------------- |
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| 164 | \begin{table}[htbp] \label{Tab_ssm} |
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| 165 | \begin{center} |
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| 166 | \begin{tabular}{|l|l|l|l|} |
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| 167 | \hline |
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| 168 | Variable desciption & Computer name & Units & point \\ \hline |
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| 169 | i-component of the surface current & ssu\_u & $m.s^{-1}$ & U \\ \hline |
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| 170 | j-component of the surface current & ssv\_m & $m.s^{-1}$ & V \\ \hline |
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| 171 | Sea surface temperature & sst\_m & \r{}$K$ & T \\ \hline |
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| 172 | Sea surface salinty & sss\_m & $psu$ & T \\ \hline |
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| 173 | \end{tabular} |
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| 174 | \end{center} |
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| 175 | \end{table} |
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| 176 | %-------------------------------------------------------------------------------------------------------------- |
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| 177 | |
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| 178 | The mean computation is done in sbcmod ( |
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| 179 | |
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| 180 | \colorbox{yellow}{Penser a} mettre dans le restant l'info nf{\_}sbc ET nf{\_}sbc*rdt de sorte de |
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| 181 | reinitialiser la moyenne si on change la frequence ou le pdt |
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| 182 | |
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| 183 | NB: creer cn{\_}sbc{\_}ice (cn{\_} = character in the namelist) with 3 |
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| 184 | cases: |
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| 185 | |
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| 186 | = `noice' no specific call |
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| 187 | |
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| 188 | = `iceif ` ``ice-if'' sea ice, i.e. read observed ice-cover and modified sbc |
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| 189 | bellow those area. |
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| 190 | |
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| 191 | = `lim' LIM sea-ice model is called which update the sbc fields in ice |
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| 192 | covered area |
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| 193 | |
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| 194 | ? modify the nsbc{\_}ice variable depending of this parameter (from --1, 0 |
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| 195 | to 1) |
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| 196 | \colorbox{yellow}{End Penser a} |
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| 197 | |
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| 198 | % ================================================================ |
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| 199 | % Analytical formulation (sbcana module) |
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| 200 | % ================================================================ |
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| 201 | \section{Analytical formulation (\textit{sbcana} module) } |
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| 202 | \label{SBC_ana} |
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| 203 | |
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| 204 | %---------------------------------------namtau - namflx-------------------------------------------------- |
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| 205 | \namdisplay{namtau} |
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| 206 | \namdisplay{namflx} |
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| 207 | %-------------------------------------------------------------------------------------------------------------- |
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| 208 | |
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| 209 | |
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| 210 | The analytical formulation of the surface boundary condition is set by |
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| 211 | default. In this case, all the 6 fluxes needed by the ocean are assumed to |
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| 212 | be uniform in space. They take constant values given in the namlist |
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| 213 | namsbc{\_}ana : \textit{utau0}, \textit{vtau0}, \textit{qns0}, \textit{qsr0}, \textit{emp0} and \textit{emps0}. while the runoff is set to zero. In addition, |
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| 214 | the wind is allowed to reach its nominal value within a given number of time |
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| 215 | step (\textit{ntau000}). |
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| 216 | |
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| 217 | If a user wants to applied a different analytical forcing, \mdl{sbcana} |
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| 218 | module is the very place to do that. As an example, one can have a look to |
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| 219 | the \mdl{sbc\_ana\_gyre} routine which provides the analytical forcing of the |
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| 220 | GYRE configuration (see GYRE configuration manual, in preparation). |
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| 221 | |
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| 222 | |
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| 223 | % ================================================================ |
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| 224 | % Flux formulation |
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| 225 | % ================================================================ |
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| 226 | \section{Flux formulation (\mdl{sbcflx} module, \key{sbcflx}) } |
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| 227 | \label{SBC_flx} |
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| 228 | |
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| 229 | In the flux formulation (\key{sbcflx} defined), the surface boundary |
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| 230 | condition fields are directly read from input files. The user has to define |
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| 231 | in the namelist namsbc{\_}flx the name of the file, the name of the variable |
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| 232 | read in the file, the time frequency at which it is given, and a logical |
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| 233 | setting whether a time interpolation to the model time step is asked are not |
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| 234 | for this field). (fld\_i namelist structure). |
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| 235 | |
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| 236 | \colorbox{yellow}{ Describe the information given? } |
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| 237 | |
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| 238 | \colorbox{yellow}{ Add an info about on-line interpolation or not ? at with which scale{\ldots} } |
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| 239 | |
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| 240 | |
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| 241 | \textbf{Caution}: when the frequency is set to --12, the data are monthly |
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| 242 | values. There are assumed to be climatological values, so time interpolation |
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| 243 | between December the 15$^{th}$ and January the 15$^{th}$ is done using |
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| 244 | record 12 and 1 |
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| 245 | |
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| 246 | When higher frequency is set and time interpolation is demanded, the model |
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| 247 | will try to read the last (first) record of previous (next) year in a file |
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| 248 | having the same name but a suffix {\_}prev{\_}year (next{\_}year) being |
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| 249 | added. These file must only content a single record. If they don't exist, |
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| 250 | the will assume that the previous year last record is equal to the first |
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| 251 | record of the previous year, and similarly, that the first record of the |
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| 252 | next year is equal to the last record of the current year. This will cause |
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| 253 | the forcing to remain constant over the first and last half fld\_frequ |
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| 254 | hours. |
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| 255 | |
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| 256 | Note that in general, a flux formulation is used in associated with a |
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| 257 | damping term to observed SST and/or SSS. See \S\ref{SBC_ssr} for its |
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| 258 | specification. |
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| 259 | |
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| 260 | |
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| 261 | % ================================================================ |
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| 262 | % Bulk formulation |
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| 263 | % ================================================================ |
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| 264 | \section{Bulk formulation (\mdl{sbcblk\_core} or\mdl{sbcblk\_clio} module) } |
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| 265 | \label{SBC_blk} |
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| 266 | |
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| 267 | In the bulk formulation, the surface boundary condition fields are computed |
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| 268 | using bulk formulae and atmospheric fields and ocean (and ice) variables. |
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| 269 | |
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| 270 | The atmospheric fields used depends on the bulk formulae used. Two of them |
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| 271 | are available : the CORE and CLIO bulk formulea. The choice is made by |
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| 272 | activating the CPP key \key{sbcblk\_core} or |
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| 273 | \key{sbcblk\_clio}, respectively. |
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| 274 | |
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| 275 | \colorbox{yellow}{Note : if a sea-ice model is used then blah blah blah{\ldots}} |
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| 276 | |
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| 277 | CORE bulk formulea |
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| 278 | |
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| 279 | The CORE bulk formulae have been developed by \citet{LargeYeager2004}. They |
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| 280 | have been design to handle the CORE forcing, a mixture of NCEP reanalysis |
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| 281 | and satellite data. They use an inertial dissipative method to compute the |
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| 282 | turbulent transfer coefficients (momentum, sensible heat and evaporation) |
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| 283 | from the 10 meter wind speed, air temperature and specific humidity). |
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| 284 | |
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| 285 | The required 8 input fields are: |
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| 286 | |
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| 287 | %--------------------------------------------------TABLE-------------------------------------------------- |
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| 288 | \begin{table}[htbp] \label{Tab_CORE} |
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| 289 | \begin{center} |
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| 290 | \begin{tabular}{|l|l|l|l|} |
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| 291 | \hline |
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| 292 | Variable desciption & Computer name & Units & point \\ \hline |
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| 293 | i-component of the 10m air velocity & utau & $m.s^{-1}$ & T or U \\ \hline |
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| 294 | j-component of the 10m air velocity & vtau & $m.s^{-1}$ & T or V \\ \hline |
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| 295 | 10m air temperature & tair & \r{}$K$ & T \\ \hline |
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| 296 | Specific humidity & humi & \% & T \\ \hline |
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| 297 | Incoming long wave radiation & qlw & $W.m^{-2}$ & T \\ \hline |
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| 298 | Incoming short wave radiation & qsr & $W.m^{-2}$ & T \\ \hline |
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| 299 | Total precipitation (liquid + solid) & precip & $Kg.m^{-2}.s^{-1}$ & T \\ \hline |
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| 300 | Solid precipitation & snow & $Kg.m^{-2}.s^{-1}$ & T \\ \hline |
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| 301 | \end{tabular} |
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| 302 | \end{center} |
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| 303 | \end{table} |
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| 304 | %-------------------------------------------------------------------------------------------------------------- |
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| 305 | |
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| 306 | Note that the air velocity can be provided at either tracer ocean point or |
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| 307 | velocity ocean point. |
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| 308 | |
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| 309 | \colorbox{yellow}{Explain low resolution, better to provide it at U-V, high resolution better} |
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| 310 | |
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| 311 | \colorbox{yellow}{at T-point{\ldots} Explain why, scheme?} |
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| 312 | |
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| 313 | \colorbox{yellow}{Add a namelist parameter to provide a switch from U/V or T (or I??) point} |
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| 314 | |
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| 315 | \colorbox{yellow}{ for utau/vtau} |
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| 316 | |
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| 317 | CLIO bulk formulea |
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| 318 | |
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| 319 | The CLIO bulk formulae have been developed several years ago for the |
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| 320 | Louvain-la-neuve coupled ice-ocean model (CLIO, Goosse et al. 1997). It is a |
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| 321 | simpler bulk formulae that assumed the stress to be known and computes the |
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| 322 | radiative fluxes from a climatological cloud cover. |
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| 323 | |
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| 324 | The required 7 input fields are: |
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| 325 | |
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| 326 | %--------------------------------------------------TABLE-------------------------------------------------- |
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| 327 | \begin{table}[htbp] \label{Tab_CLIO} |
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| 328 | \begin{center} |
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| 329 | \begin{tabular}{|l|l|l|l|} |
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| 330 | \hline |
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| 331 | Variable desciption & Computer name & Units & point \\ \hline |
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| 332 | i-component of the ocean stress & utau & $N.m^{-2}$ & U \\ \hline |
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| 333 | j-component of the ocean stress & vtau & $N.m^{-2}$ & V \\ \hline |
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| 334 | Wind speed module & vatm & $m.s^{-1}$ & T \\ \hline |
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| 335 | 10m air temperature & tair & \r{}$K$ & T \\ \hline |
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| 336 | Secific humidity & humi & \% & T \\ \hline |
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| 337 | Cloud cover & & \% & T \\ \hline |
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| 338 | Total precipitation (liquid + solid) & precip & $Kg.m^{-2}.s^{-1}$ & T \\ \hline |
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| 339 | Solid precipitation & snow & $Kg.m^{-2}.s^{-1}$ & T \\ \hline |
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| 340 | \end{tabular} |
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| 341 | \end{center} |
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| 342 | \end{table} |
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| 343 | %-------------------------------------------------------------------------------------------------------------- |
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| 344 | |
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| 345 | As for the flux formulation, the input data information required by the |
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| 346 | model is provided in the namsbc\_blk\_core or namsbc\_blk\_clio |
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| 347 | namelist (via the structure fld\_i). The same assumption is made about the |
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| 348 | value of the first and last record in each file. |
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| 349 | |
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| 350 | |
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| 351 | % ================================================================ |
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| 352 | % Coupled formulation |
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| 353 | % ================================================================ |
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| 354 | \section{Coupled formulation (\mdl{sbccpl} module)} |
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| 355 | \label{SBC_cpl} |
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| 356 | |
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| 357 | In the coupled formulation of the surface boundary condition, the fluxes are |
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| 358 | provided by the OASIS coupler at each \np{nf\_cpl} time-step, while sea and ice |
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| 359 | surface temperature, ocean and ice albedo, and ocean currents are sent to |
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| 360 | the atmospheric component. |
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| 361 | |
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| 362 | |
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| 363 | % ================================================================ |
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| 364 | % Miscellanea options |
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| 365 | % ================================================================ |
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| 366 | \section{Miscellanea options} |
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| 367 | \label{SBC_misc} |
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| 368 | |
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| 369 | % ------------------------------------------------------------------------------------------------------------- |
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| 370 | % Surface restoring to observed SST and/or SSS |
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| 371 | % ------------------------------------------------------------------------------------------------------------- |
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| 372 | \subsection{Surface restoring to observed SST and/or SSS (\mdl{sbcssr})} |
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| 373 | \label{SBC_ssr} |
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| 374 | |
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| 375 | In forced mode using flux formulation (default option or \key{flx} defined), a |
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| 376 | feedback term \emph{must} be added to the specified surface heat flux $Q_{ns}^o$: |
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| 377 | \begin{equation} \label{Eq_sbc_dmp_q} |
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| 378 | Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right|_{k=1} - SST_{Obs} \right) |
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| 379 | \end{equation} |
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| 380 | where SST is a sea surface temperature field (observed or climatological), $T$ is |
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| 381 | the model surface layer temperature and $\frac{dQ}{dT}$ is a negative feedback |
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| 382 | coefficient usually taken equal to $-40~W.m^{-2}.$\r{}K$^{-1}$. For a $50~m$ mixed-layer depth, |
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| 383 | this value corresponds to a relaxation time scale of two months. This term |
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| 384 | ensures that if $T$ perfectly fits SST then $Q$ is equal to $Q_o$. |
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| 385 | |
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| 386 | In the fresh water budget, a feedback term can also be added: |
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| 387 | |
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| 388 | \begin{equation} \label{Eq_sbc_dmp_emp} |
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| 389 | EMP = EMP_o +\gamma_s^{-1} \left(S-SSS_{Obs}\right)\left|S\right. |
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| 390 | \end{equation} |
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| 391 | |
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| 392 | where EMP$_{o }$ is a net surface fresh water flux (observed, climatological or |
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| 393 | atmospheric model product), \textit{SSS}$_{Obs}$is a sea surface salinity (usually a time |
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| 394 | interpolation of the monthly mean PHC climatology \citep{Steele2001}, $S$ is the model |
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| 395 | surface layer salinity and $\gamma_s$ is a negative feedback coefficient |
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| 396 | which is provided as a namelist parameter. Unlike heat flux, there is no |
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| 397 | physical justification for the feedback term in (III.4.4) as the atmosphere |
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| 398 | does not care about ocean surface salinity \citep{Madec1997}. The |
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| 399 | SSS restoring term can only be view as a flux correction on freshwater |
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| 400 | fluxes to reduce the uncertainties we have on the observed freshwater |
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| 401 | budget. |
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| 402 | |
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| 403 | % ------------------------------------------------------------------------------------------------------------- |
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| 404 | % Handling of ice-covered area |
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| 405 | % ------------------------------------------------------------------------------------------------------------- |
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| 406 | \subsection{Handling of ice-covered area} |
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| 407 | \label{SBC_ice-cover} |
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| 408 | The presence of sea-ice at the top of the ocean |
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| 409 | strongly modify the surface fluxes |
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| 410 | |
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| 411 | The presence at the sea surface of an ice cover area modified all the fluxes |
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| 412 | transmitted to the ocean. There is two cases whereas a sea-ice model is used |
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| 413 | or not. |
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| 414 | |
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| 415 | Without sea ice model, the information of ice-cover / open ocean is read in |
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| 416 | a file (either the directly the ice-cover or the observed SST from which |
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| 417 | ice-cover is deduced using a criteria on freezing point temperature). |
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| 418 | |
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| 419 | % ------------------------------------------------------------------------------------------------------------- |
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| 420 | % Addition of river runoffs |
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| 421 | % ------------------------------------------------------------------------------------------------------------- |
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| 422 | \subsection{Addition of river runoffs (\mdl{sbcrnf})} |
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| 423 | \label{SBC_rnf} |
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| 424 | |
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| 425 | It is convenient to introduce the river runoff in the model as a surface |
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| 426 | fresh water fluxes. \colorbox{yellow}{{\ldots} blah blah{\ldots}.} |
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| 427 | |
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| 428 | \colorbox{yellow}{Nevertheless, Pb of vertical resolution and increase of Kz in vicinity of } |
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| 429 | |
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| 430 | \colorbox{yellow}{river mouths{\ldots}} |
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| 431 | |
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| 432 | Control of the mean sea level |
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| 433 | |
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| 434 | % ------------------------------------------------------------------------------------------------------------- |
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| 435 | % Addition of river runoffs |
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| 436 | % ------------------------------------------------------------------------------------------------------------- |
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| 437 | \subsection{Freshwater budget control (\mdl{sbcfwb})} |
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| 438 | \label{SBC_fwb} |
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| 439 | %--------------------------------------------namfwb-------------------------------------------------------- |
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| 440 | \namdisplay{namfwb} |
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| 441 | %-------------------------------------------------------------------------------------------------------------- |
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| 442 | |
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| 443 | \colorbox{yellow}{freshwater budget correction{\ldots}} |
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| 444 | |
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| 445 | |
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| 446 | |
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| 447 | |
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