Changeset 11263 for NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_DIU.tex

Timestamp:

2019-07-12T12:47:53+02:00 (5 years ago)

Author:

smasson

Message:

dev_r10984_HPC-13 : merge with trunk@11242, see #2285

Location:

NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc

Files:

• . (modified) (1 prop)
• latex (modified) (1 prop)
• latex/NEMO (modified) (1 prop)
• latex/NEMO/subfiles/chap_DIU.tex (modified) (5 diffs)

NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex

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-*.aux
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-*.out
-*.pdf
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+figures

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-*.aux
-*.bbl
-*.blg
-*.dvi
-*.fdb*
-*.fls
-*.idx
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-*.log
-*.maf
-*.mtc*
-*.out
-*.pdf
-*.toc
-_minted-*
+figures

NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_DIU.tex

@@ -33 +33 @@
 (\ie from the temperature of the top few model levels) or from some other source.  
 It must be noted that both the cool skin and warm layer models produce estimates of the change in temperature
-($\Delta T_{\rm{cs}}$ and $\Delta T_{\rm{wl}}$) and
+($\Delta T_{\mathrm{cs}}$ and $\Delta T_{\mathrm{wl}}$) and
 both must be added to a foundation SST to obtain the true skin temperature.
 
@@ -60 +60 @@
 %===============================================================
 
-The warm layer is calculated using the model of \citet{Takaya_al_JGR10} (TAKAYA10 model hereafter).
+The warm layer is calculated using the model of \citet{takaya.bidlot.ea_JGR10} (TAKAYA10 model hereafter).
 This is a simple flux based model that is defined by the equations
 \begin{align}
-\frac{\partial{\Delta T_{\rm{wl}}}}{\partial{t}}&=&\frac{Q(\nu+1)}{D_T\rho_w c_p
+\frac{\partial{\Delta T_{\mathrm{wl}}}}{\partial{t}}&=&\frac{Q(\nu+1)}{D_T\rho_w c_p
 \nu}-\frac{(\nu+1)ku^*_{w}f(L_a)\Delta T}{D_T\Phi\!\left(\frac{D_T}{L}\right)} \mbox{,}
 \label{eq:ecmwf1} \\
 L&=&\frac{\rho_w c_p u^{*^3}_{w}}{\kappa g \alpha_w Q }\mbox{,}\label{eq:ecmwf2}
 \end{align}
-where $\Delta T_{\rm{wl}}$ is the temperature difference between the top of the warm layer and the depth $D_T=3$\,m at which there is assumed to be no diurnal signal.
+where $\Delta T_{\mathrm{wl}}$ is the temperature difference between the top of the warm layer and the depth $D_T=3$\,m at which there is assumed to be no diurnal signal.
 In equation (\autoref{eq:ecmwf1}) $\alpha_w=2\times10^{-4}$ is the thermal expansion coefficient of water,
 $\kappa=0.4$ is von K\'{a}rm\'{a}n's constant, $c_p$ is the heat capacity at constant pressure of sea water,
 $\rho_w$ is the water density, and $L$ is the Monin-Obukhov length.
 The tunable variable $\nu$ is a shape parameter that defines the expected subskin temperature profile via
-$T(z) = T(0) - \left( \frac{z}{D_T} \right)^\nu \Delta T_{\rm{wl}}$,
+$T(z) = T(0) - \left( \frac{z}{D_T} \right)^\nu \Delta T_{\mathrm{wl}}$,
 where $T$ is the absolute temperature and $z\le D_T$ is the depth below the top of the warm layer.
 The influence of wind on TAKAYA10 comes through the magnitude of the friction velocity of the water $u^*_{w}$,
@@ -82 +82 @@
 the diurnal layer, \ie
 \[
-  Q = Q_{\rm{sol}} + Q_{\rm{lw}} + Q_{\rm{h}}\mbox{,}
+  Q = Q_{\mathrm{sol}} + Q_{\mathrm{lw}} + Q_{\mathrm{h}}\mbox{,}
   % \label{eq:e_flux_eqn}
 \]
-where $Q_{\rm{h}}$ is the sensible and latent heat flux, $Q_{\rm{lw}}$ is the long wave flux,
-and $Q_{\rm{sol}}$ is the solar flux absorbed within the diurnal warm layer.
-For $Q_{\rm{sol}}$ the 9 term representation of \citet{Gentemann_al_JGR09} is used.
+where $Q_{\mathrm{h}}$ is the sensible and latent heat flux, $Q_{\mathrm{lw}}$ is the long wave flux,
+and $Q_{\mathrm{sol}}$ is the solar flux absorbed within the diurnal warm layer.
+For $Q_{\mathrm{sol}}$ the 9 term representation of \citet{gentemann.minnett.ea_JGR09} is used.
 In equation \autoref{eq:ecmwf1} the function $f(L_a)=\max(1,L_a^{\frac{2}{3}})$,
 where $L_a=0.3$\footnote{
@@ -118 +118 @@
 %===============================================================
 
-The cool skin is modelled using the framework of \citet{Saunders_JAS82} who used a formulation of the near surface temperature difference based upon the heat flux and the friction velocity $u^*_{w}$.
-As the cool skin is so thin (~1\,mm) we ignore the solar flux component to the heat flux and the Saunders equation for the cool skin temperature difference $\Delta T_{\rm{cs}}$ becomes
+The cool skin is modelled using the framework of \citet{saunders_JAS67} who used a formulation of the near surface temperature difference based upon the heat flux and the friction velocity $u^*_{w}$.
+As the cool skin is so thin (~1\,mm) we ignore the solar flux component to the heat flux and the Saunders equation for the cool skin temperature difference $\Delta T_{\mathrm{cs}}$ becomes
 \[
   % \label{eq:sunders_eqn}
-  \Delta T_{\rm{cs}}=\frac{Q_{\rm{ns}}\delta}{k_t} \mbox{,}
+  \Delta T_{\mathrm{cs}}=\frac{Q_{\mathrm{ns}}\delta}{k_t} \mbox{,}
 \]
-where $Q_{\rm{ns}}$ is the, usually negative, non-solar heat flux into the ocean and
+where $Q_{\mathrm{ns}}$ is the, usually negative, non-solar heat flux into the ocean and
 $k_t$ is the thermal conductivity of sea water.
 $\delta$ is the thickness of the skin layer and is given by
@@ -132 +132 @@
 \end{equation}
 where $\mu$ is the kinematic viscosity of sea water and $\lambda$ is a constant of proportionality which
-\citet{Saunders_JAS82} suggested varied between 5 and 10.
+\citet{saunders_JAS67} suggested varied between 5 and 10.
 
-The value of $\lambda$ used in equation (\autoref{eq:sunders_thick_eqn}) is that of \citet{Artale_al_JGR02},
-which is shown in \citet{Tu_Tsuang_GRL05} to outperform a number of other parametrisations at
+The value of $\lambda$ used in equation (\autoref{eq:sunders_thick_eqn}) is that of \citet{artale.iudicone.ea_JGR02},
+which is shown in \citet{tu.tsuang_GRL05} to outperform a number of other parametrisations at
 both low and high wind speeds.
 Specifically,

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-*.aux
-*.bbl
-*.blg
-*.dvi
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-*.fls
-*.idx
-*.ilg
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-*.mtc*
-*.out
-*.pdf
-*.toc
-_minted-*
+figures