Changeset 12178 for NEMO/branches/2019/dev_r11078_OSMOSIS_IMMERSE_Nurser/doc/latex/NEMO/subfiles/chap_DIU.tex
- Timestamp:
- 2019-12-11T12:02:38+01:00 (4 years ago)
- Location:
- NEMO/branches/2019/dev_r11078_OSMOSIS_IMMERSE_Nurser/doc
- Files:
-
- 5 edited
Legend:
- Unmodified
- Added
- Removed
-
NEMO/branches/2019/dev_r11078_OSMOSIS_IMMERSE_Nurser/doc
- Property svn:ignore deleted
-
Property
svn:externals
set to
^/utils/badges badges
^/utils/logos logos
-
NEMO/branches/2019/dev_r11078_OSMOSIS_IMMERSE_Nurser/doc/latex
- Property svn:ignore deleted
-
NEMO/branches/2019/dev_r11078_OSMOSIS_IMMERSE_Nurser/doc/latex/NEMO
-
Property
svn:externals
set to
^/utils/figures/NEMO figures
-
Property
svn:externals
set to
-
NEMO/branches/2019/dev_r11078_OSMOSIS_IMMERSE_Nurser/doc/latex/NEMO/subfiles
-
Property
svn:ignore
set to
*.ind
*.ilg
-
Property
svn:ignore
set to
-
NEMO/branches/2019/dev_r11078_OSMOSIS_IMMERSE_Nurser/doc/latex/NEMO/subfiles/chap_DIU.tex
r11123 r12178 2 2 3 3 \begin{document} 4 % ================================================================ 5 % Diurnal SST models (DIU) 6 % Edited by James While 7 % ================================================================ 4 8 5 \chapter{Diurnal SST Models (DIU)} 9 6 \label{chap:DIU} 10 7 11 \ minitoc8 \thispagestyle{plain} 12 9 10 \chaptertoc 13 11 14 \newpage 15 $\ $\newline % force a new line 12 \paragraph{Changes record} ~\\ 13 14 {\footnotesize 15 \begin{tabularx}{\textwidth}{l||X|X} 16 Release & Author(s) & Modifications \\ 17 \hline 18 {\em 4.0} & {\em ...} & {\em ...} \\ 19 {\em 3.6} & {\em ...} & {\em ...} \\ 20 {\em 3.4} & {\em ...} & {\em ...} \\ 21 {\em <=3.4} & {\em ...} & {\em ...} 22 \end{tabularx} 23 } 24 25 \clearpage 16 26 17 27 Code to produce an estimate of the diurnal warming and cooling of the sea surface skin 18 temperature (skin SST) is found in the DIU directory. 28 temperature (skin SST) is found in the DIU directory. 19 29 The skin temperature can be split into three parts: 20 30 \begin{itemize} 21 \item 22 A foundation SST which is free from diurnal warming. 23 \item 24 A warm layer, typically ~3\,m thick, 31 \item A foundation SST which is free from diurnal warming. 32 \item A warm layer, typically ~3\,m thick, 25 33 where heating from solar radiation can cause a warm stably stratified layer during the daytime 26 \item 27 A cool skin, a thin layer, approximately ~1\, mm thick, 34 \item A cool skin, a thin layer, approximately ~1\, mm thick, 28 35 where long wave cooling is dominant and cools the immediate ocean surface. 29 36 \end{itemize} 30 37 31 38 Models are provided for both the warm layer, \mdl{diurnal\_bulk}, and the cool skin, \mdl{cool\_skin}. 32 Foundation SST is not considered as it can be obtained either from the main NEMOmodel33 (\ie from the temperature of the top few model levels) or from some other source.39 Foundation SST is not considered as it can be obtained either from the main \NEMO\ model 40 (\ie\ from the temperature of the top few model levels) or from some other source. 34 41 It must be noted that both the cool skin and warm layer models produce estimates of the change in temperature 35 ($\Delta T_{\ rm{cs}}$ and $\Delta T_{\rm{wl}}$) and42 ($\Delta T_{\mathrm{cs}}$ and $\Delta T_{\mathrm{wl}}$) and 36 43 both must be added to a foundation SST to obtain the true skin temperature. 37 44 38 Both the cool skin and warm layer models are controlled through the namelist \n gn{namdiu}:45 Both the cool skin and warm layer models are controlled through the namelist \nam{diu}{diu}: 39 46 40 \nlst{namdiu} 47 \begin{listing} 48 \nlst{namdiu} 49 \caption{\forcode{&namdiu}} 50 \label{lst:namdiu} 51 \end{listing} 52 41 53 This namelist contains only two variables: 42 54 \begin{description} 43 \item[\np{ln\_diurnal}] 44 A logical switch for turning on/off both the cool skin and warm layer. 45 \item[\np{ln\_diurnal\_only}] 46 A logical switch which if \forcode{.true.} will run the diurnal model without the other dynamical parts of NEMO. 47 \np{ln\_diurnal\_only} must be \forcode{.false.} if \np{ln\_diurnal} is \forcode{.false.}. 55 \item [{\np{ln_diurnal}{ln\_diurnal}}] A logical switch for turning on/off both the cool skin and warm layer. 56 \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. 57 \np{ln_diurnal_only}{ln\_diurnal\_only} must be \forcode{.false.} if \np{ln_diurnal}{ln\_diurnal} is \forcode{.false.}. 48 58 \end{description} 49 59 … … 53 63 Initialisation is through the restart file. 54 64 Specifically the code will expect the presence of the 2-D variable ``Dsst'' to initialise the warm layer. 55 The cool skin model, which is determined purely by the instantaneous fluxes, has no initialisation variable. 65 The cool skin model, which is determined purely by the instantaneous fluxes, has no initialisation variable. 56 66 57 % ===============================================================67 %% ================================================================================================= 58 68 \section{Warm layer model} 59 \label{sec:warm_layer_sec} 60 %=============================================================== 69 \label{sec:DIU_warm_layer_sec} 61 70 62 71 The warm layer is calculated using the model of \citet{takaya.bidlot.ea_JGR10} (TAKAYA10 model hereafter). 63 72 This is a simple flux based model that is defined by the equations 64 73 \begin{align} 65 \frac{\partial{\Delta T_{\ rm{wl}}}}{\partial{t}}&=&\frac{Q(\nu+1)}{D_T\rho_w c_p74 \frac{\partial{\Delta T_{\mathrm{wl}}}}{\partial{t}}&=&\frac{Q(\nu+1)}{D_T\rho_w c_p 66 75 \nu}-\frac{(\nu+1)ku^*_{w}f(L_a)\Delta T}{D_T\Phi\!\left(\frac{D_T}{L}\right)} \mbox{,} 67 \label{eq: ecmwf1} \\68 L&=&\frac{\rho_w c_p u^{*^3}_{w}}{\kappa g \alpha_w Q }\mbox{,}\label{eq: ecmwf2}76 \label{eq:DIU_ecmwf1} \\ 77 L&=&\frac{\rho_w c_p u^{*^3}_{w}}{\kappa g \alpha_w Q }\mbox{,}\label{eq:DIU_ecmwf2} 69 78 \end{align} 70 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.71 In equation (\autoref{eq: ecmwf1}) $\alpha_w=2\times10^{-4}$ is the thermal expansion coefficient of water,79 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. 80 In equation (\autoref{eq:DIU_ecmwf1}) $\alpha_w=2\times10^{-4}$ is the thermal expansion coefficient of water, 72 81 $\kappa=0.4$ is von K\'{a}rm\'{a}n's constant, $c_p$ is the heat capacity at constant pressure of sea water, 73 82 $\rho_w$ is the water density, and $L$ is the Monin-Obukhov length. 74 83 The tunable variable $\nu$ is a shape parameter that defines the expected subskin temperature profile via 75 $T(z) = T(0) - \left( \frac{z}{D_T} \right)^\nu \Delta T_{\ rm{wl}}$,84 $T(z) = T(0) - \left( \frac{z}{D_T} \right)^\nu \Delta T_{\mathrm{wl}}$, 76 85 where $T$ is the absolute temperature and $z\le D_T$ is the depth below the top of the warm layer. 77 86 The influence of wind on TAKAYA10 comes through the magnitude of the friction velocity of the water $u^*_{w}$, … … 79 88 the relationship $u^*_{w} = u_{10}\sqrt{\frac{C_d\rho_a}{\rho_w}}$, where $C_d$ is the drag coefficient, 80 89 and $\rho_a$ is the density of air. 81 The symbol $Q$ in equation (\autoref{eq: ecmwf1}) is the instantaneous total thermal energy flux into90 The symbol $Q$ in equation (\autoref{eq:DIU_ecmwf1}) is the instantaneous total thermal energy flux into 82 91 the diurnal layer, \ie 83 92 \[ 84 Q = Q_{\ rm{sol}} + Q_{\rm{lw}} + Q_{\rm{h}}\mbox{,}85 % \label{eq: e_flux_eqn}93 Q = Q_{\mathrm{sol}} + Q_{\mathrm{lw}} + Q_{\mathrm{h}}\mbox{,} 94 % \label{eq:DIU_e_flux_eqn} 86 95 \] 87 where $Q_{\ rm{h}}$ is the sensible and latent heat flux, $Q_{\rm{lw}}$ is the long wave flux,88 and $Q_{\ rm{sol}}$ is the solar flux absorbed within the diurnal warm layer.89 For $Q_{\ rm{sol}}$ the 9 term representation of \citet{gentemann.minnett.ea_JGR09} is used.90 In equation \autoref{eq: ecmwf1} the function $f(L_a)=\max(1,L_a^{\frac{2}{3}})$,96 where $Q_{\mathrm{h}}$ is the sensible and latent heat flux, $Q_{\mathrm{lw}}$ is the long wave flux, 97 and $Q_{\mathrm{sol}}$ is the solar flux absorbed within the diurnal warm layer. 98 For $Q_{\mathrm{sol}}$ the 9 term representation of \citet{gentemann.minnett.ea_JGR09} is used. 99 In equation \autoref{eq:DIU_ecmwf1} the function $f(L_a)=\max(1,L_a^{\frac{2}{3}})$, 91 100 where $L_a=0.3$\footnote{ 92 101 This is a global average value, more accurately $L_a$ could be computed as $L_a=(u^*_{w}/u_s)^{\frac{1}{2}}$, … … 99 108 4\zeta^2}{1+3\zeta+0.25\zeta^2} &(\zeta \ge 0) \\ 100 109 (1 - 16\zeta)^{-\frac{1}{2}} & (\zeta < 0) \mbox{,} 101 \end{array} \right. \label{eq: stab_func_eqn}110 \end{array} \right. \label{eq:DIU_stab_func_eqn} 102 111 \end{equation} 103 where $\zeta=\frac{D_T}{L}$. It is clear that the first derivative of (\autoref{eq: stab_func_eqn}),104 and thus of (\autoref{eq: ecmwf1}), is discontinuous at $\zeta=0$ (\ie$Q\rightarrow0$ in105 equation (\autoref{eq: ecmwf2})).112 where $\zeta=\frac{D_T}{L}$. It is clear that the first derivative of (\autoref{eq:DIU_stab_func_eqn}), 113 and thus of (\autoref{eq:DIU_ecmwf1}), is discontinuous at $\zeta=0$ (\ie\ $Q\rightarrow0$ in 114 equation (\autoref{eq:DIU_ecmwf2})). 106 115 107 The two terms on the right hand side of (\autoref{eq: ecmwf1}) represent different processes.116 The two terms on the right hand side of (\autoref{eq:DIU_ecmwf1}) represent different processes. 108 117 The first term is simply the diabatic heating or cooling of the diurnal warm layer due to 109 118 thermal energy fluxes into and out of the layer. … … 111 120 In practice the second term acts as a relaxation on the temperature. 112 121 113 %=============================================================== 114 122 %% ================================================================================================= 115 123 \section{Cool skin model} 116 \label{sec:cool_skin_sec} 117 118 %=============================================================== 124 \label{sec:DIU_cool_skin_sec} 119 125 120 126 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 $u^*_{w}$. 121 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 $\Delta T_{\ rm{cs}}$ becomes127 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 122 128 \[ 123 % \label{eq: sunders_eqn}124 \Delta T_{\ rm{cs}}=\frac{Q_{\rm{ns}}\delta}{k_t} \mbox{,}129 % \label{eq:DIU_sunders_eqn} 130 \Delta T_{\mathrm{cs}}=\frac{Q_{\mathrm{ns}}\delta}{k_t} \mbox{,} 125 131 \] 126 where $Q_{\ rm{ns}}$ is the, usually negative, non-solar heat flux into the ocean and132 where $Q_{\mathrm{ns}}$ is the, usually negative, non-solar heat flux into the ocean and 127 133 $k_t$ is the thermal conductivity of sea water. 128 134 $\delta$ is the thickness of the skin layer and is given by 129 135 \begin{equation} 130 \label{eq: sunders_thick_eqn}136 \label{eq:DIU_sunders_thick_eqn} 131 137 \delta=\frac{\lambda \mu}{u^*_{w}} \mbox{,} 132 138 \end{equation} … … 134 140 \citet{saunders_JAS67} suggested varied between 5 and 10. 135 141 136 The value of $\lambda$ used in equation (\autoref{eq: sunders_thick_eqn}) is that of \citet{artale.iudicone.ea_JGR02},142 The value of $\lambda$ used in equation (\autoref{eq:DIU_sunders_thick_eqn}) is that of \citet{artale.iudicone.ea_JGR02}, 137 143 which is shown in \citet{tu.tsuang_GRL05} to outperform a number of other parametrisations at 138 144 both low and high wind speeds. 139 145 Specifically, 140 146 \[ 141 % \label{eq: artale_lambda_eqn}147 % \label{eq:DIU_artale_lambda_eqn} 142 148 \lambda = \frac{ 8.64\times10^4 u^*_{w} k_t }{ \rho c_p h \mu \gamma }\mbox{,} 143 149 \] … … 145 151 $\gamma$ is a dimensionless function of wind speed $u$: 146 152 \[ 147 % \label{eq: artale_gamma_eqn}153 % \label{eq:DIU_artale_gamma_eqn} 148 154 \gamma = 149 155 \begin{cases} … … 154 160 \] 155 161 156 \biblio 157 158 \pindex 162 \onlyinsubfile{\input{../../global/epilogue}} 159 163 160 164 \end{document}
Note: See TracChangeset
for help on using the changeset viewer.