Index: NEMO/branches/2019/dev_r11078_OSMOSIS_IMMERSE_Nurser/doc/latex/NEMO/subfiles/chap_DIU.tex
===================================================================
--- NEMO/branches/2019/dev_r11078_OSMOSIS_IMMERSE_Nurser/doc/latex/NEMO/subfiles/chap_DIU.tex	(revision 11139)
+++ NEMO/branches/2019/dev_r11078_OSMOSIS_IMMERSE_Nurser/doc/latex/NEMO/subfiles/chap_DIU.tex	(revision 12178)
@@ -2,48 +2,58 @@
 
 \begin{document}
-% ================================================================
-% Diurnal SST models (DIU)
-% Edited by James While
-% ================================================================
+
 \chapter{Diurnal SST Models (DIU)}
 \label{chap:DIU}
 
-\minitoc
+\thispagestyle{plain}
 
+\chaptertoc
 
-\newpage
-$\ $\newline % force a new line
+\paragraph{Changes record} ~\\
+
+{\footnotesize
+  \begin{tabularx}{\textwidth}{l||X|X}
+    Release & Author(s) & Modifications \\
+    \hline
+    {\em   4.0} & {\em ...} & {\em ...} \\
+    {\em   3.6} & {\em ...} & {\em ...} \\
+    {\em   3.4} & {\em ...} & {\em ...} \\
+    {\em <=3.4} & {\em ...} & {\em ...}
+  \end{tabularx}
+}
+
+\clearpage
 
 Code to produce an estimate of the diurnal warming and cooling of the sea surface skin
-temperature (skin SST) is found in the DIU directory.  
+temperature (skin SST) is found in the DIU directory.
 The skin temperature can be split into three parts:
 \begin{itemize}
-\item
-  A foundation SST which is free from diurnal warming.
-\item
-  A warm layer, typically ~3\,m thick,
+\item A foundation SST which is free from diurnal warming.
+\item A warm layer, typically ~3\,m thick,
   where heating from solar radiation can cause a warm stably stratified layer during the daytime
-\item
-  A cool skin, a thin layer, approximately ~1\, mm thick,
+\item A cool skin, a thin layer, approximately ~1\, mm thick,
   where long wave cooling is dominant and cools the immediate ocean surface.
 \end{itemize}
 
 Models are provided for both the warm layer, \mdl{diurnal\_bulk}, and the cool skin, \mdl{cool\_skin}.
-Foundation SST is not considered as it can be obtained either from the main NEMO model
-(\ie from the temperature of the top few model levels) or from some other source.  
+Foundation SST is not considered as it can be obtained either from the main \NEMO\ model
+(\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.
 
-Both the cool skin and warm layer models are controlled through the namelist \ngn{namdiu}:
+Both the cool skin and warm layer models are controlled through the namelist \nam{diu}{diu}:
 
-\nlst{namdiu}
+\begin{listing}
+  \nlst{namdiu}
+  \caption{\forcode{&namdiu}}
+  \label{lst:namdiu}
+\end{listing}
+
 This namelist contains only two variables:
 \begin{description}
-\item[\np{ln\_diurnal}]
-  A logical switch for turning on/off both the cool skin and warm layer.
-\item[\np{ln\_diurnal\_only}]
-  A logical switch which if \forcode{.true.} will run the diurnal model without the other dynamical parts of NEMO.
-  \np{ln\_diurnal\_only} must be \forcode{.false.} if \np{ln\_diurnal} is \forcode{.false.}.
+\item [{\np{ln_diurnal}{ln\_diurnal}}] A logical switch for turning on/off both the cool skin and warm layer.
+\item [{\np{ln_diurnal_only}{ln\_diurnal\_only}}] A logical switch which if \forcode{.true.} will run the diurnal model without the other dynamical parts of \NEMO.
+  \np{ln_diurnal_only}{ln\_diurnal\_only} must be \forcode{.false.} if \np{ln_diurnal}{ln\_diurnal} is \forcode{.false.}.
 \end{description}
 
@@ -53,25 +63,24 @@
 Initialisation is through the restart file.
 Specifically the code will expect the presence of the 2-D variable ``Dsst'' to initialise the warm layer.
-The cool skin model, which is determined purely by the instantaneous fluxes, has no initialisation variable.  
+The cool skin model, which is determined purely by the instantaneous fluxes, has no initialisation variable.
 
-%===============================================================
+%% =================================================================================================
 \section{Warm layer model}
-\label{sec:warm_layer_sec}
-%===============================================================
+\label{sec:DIU_warm_layer_sec}
 
 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}
+\label{eq:DIU_ecmwf1} \\
+L&=&\frac{\rho_w c_p u^{*^3}_{w}}{\kappa g \alpha_w Q }\mbox{,}\label{eq:DIU_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.
-In equation (\autoref{eq:ecmwf1}) $\alpha_w=2\times10^{-4}$ is the thermal expansion coefficient of water,
+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:DIU_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 $u^*_{w}$,
@@ -79,14 +88,14 @@
 the relationship $u^*_{w} = u_{10}\sqrt{\frac{C_d\rho_a}{\rho_w}}$, where $C_d$ is the drag coefficient,
 and $\rho_a$ is the density of air.
-The symbol $Q$ in equation (\autoref{eq:ecmwf1}) is the instantaneous total thermal energy flux into
+The symbol $Q$ in equation (\autoref{eq:DIU_ecmwf1}) is the instantaneous total thermal energy flux into
 the diurnal layer, \ie
 \[
-  Q = Q_{\rm{sol}} + Q_{\rm{lw}} + Q_{\rm{h}}\mbox{,}
-  % \label{eq:e_flux_eqn}
+  Q = Q_{\mathrm{sol}} + Q_{\mathrm{lw}} + Q_{\mathrm{h}}\mbox{,}
+  % \label{eq:DIU_e_flux_eqn}
 \]
-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.minnett.ea_JGR09} is used.
-In equation \autoref{eq:ecmwf1} the function $f(L_a)=\max(1,L_a^{\frac{2}{3}})$,
+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:DIU_ecmwf1} the function $f(L_a)=\max(1,L_a^{\frac{2}{3}})$,
 where $L_a=0.3$\footnote{
   This is a global average value, more accurately $L_a$ could be computed as $L_a=(u^*_{w}/u_s)^{\frac{1}{2}}$,
@@ -99,11 +108,11 @@
 4\zeta^2}{1+3\zeta+0.25\zeta^2} &(\zeta \ge 0) \\
                                     (1 - 16\zeta)^{-\frac{1}{2}} & (\zeta < 0) \mbox{,}
-                                    \end{array} \right. \label{eq:stab_func_eqn}
+                                    \end{array} \right. \label{eq:DIU_stab_func_eqn}
 \end{equation}
-where $\zeta=\frac{D_T}{L}$.  It is clear that the first derivative of (\autoref{eq:stab_func_eqn}),
-and thus of (\autoref{eq:ecmwf1}), is discontinuous at $\zeta=0$ (\ie $Q\rightarrow0$ in
-equation (\autoref{eq:ecmwf2})).
+where $\zeta=\frac{D_T}{L}$.  It is clear that the first derivative of (\autoref{eq:DIU_stab_func_eqn}),
+and thus of (\autoref{eq:DIU_ecmwf1}), is discontinuous at $\zeta=0$ (\ie\ $Q\rightarrow0$ in
+equation (\autoref{eq:DIU_ecmwf2})).
 
-The two terms on the right hand side of (\autoref{eq:ecmwf1}) represent different processes.
+The two terms on the right hand side of (\autoref{eq:DIU_ecmwf1}) represent different processes.
 The first term is simply the diabatic heating or cooling of the diurnal warm layer due to
 thermal energy fluxes into and out of the layer.
@@ -111,22 +120,19 @@
 In practice the second term acts as a relaxation on the temperature.
 
-%===============================================================
-
+%% =================================================================================================
 \section{Cool skin model}
-\label{sec:cool_skin_sec}
-
-%===============================================================
+\label{sec:DIU_cool_skin_sec}
 
 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 $\Delta T_{\rm{cs}}$ becomes
+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
 \[
-  % \label{eq:sunders_eqn}
-  \Delta T_{\rm{cs}}=\frac{Q_{\rm{ns}}\delta}{k_t} \mbox{,}
+  % \label{eq:DIU_sunders_eqn}
+  \Delta T_{\mathrm{cs}}=\frac{Q_{\mathrm{ns}}\delta}{k_t} \mbox{,}
 \]
-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
 \begin{equation}
-\label{eq:sunders_thick_eqn}
+\label{eq:DIU_sunders_thick_eqn}
 \delta=\frac{\lambda \mu}{u^*_{w}} \mbox{,}
 \end{equation}
@@ -134,10 +140,10 @@
 \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.iudicone.ea_JGR02},
+The value of $\lambda$ used in equation (\autoref{eq:DIU_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,
 \[
-  % \label{eq:artale_lambda_eqn}
+  % \label{eq:DIU_artale_lambda_eqn}
   \lambda = \frac{ 8.64\times10^4 u^*_{w} k_t }{ \rho c_p h \mu \gamma }\mbox{,}
 \]
@@ -145,5 +151,5 @@
 $\gamma$ is a dimensionless function of wind speed $u$:
 \[
-  % \label{eq:artale_gamma_eqn}
+  % \label{eq:DIU_artale_gamma_eqn}
   \gamma =
   \begin{cases}
@@ -154,7 +160,5 @@
 \]
 
-\biblio
-
-\pindex
+\onlyinsubfile{\input{../../global/epilogue}}
 
 \end{document}
