Changeset 6497 for trunk/DOC/TexFiles
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trunk/DOC/TexFiles/Chapters/Chap_DIA.tex
r6289 r6497 1409 1409 1410 1410 % ------------------------------------------------------------------------------------------------------------- 1411 % 25 hour mean and hourly Surface, Mid and Bed1412 % -------------------------------------------------------------------------------------------------------------1413 \section{25 hour mean output for tidal models }1414 1415 A module is available to compute a crudely detided M2 signal by obtaining a 25 hour mean.1416 The 25 hour mean is available for daily runs by summing up the 25 hourly instantananeous hourly values from1417 midnight at the start of the day to midight at the day end.1418 This diagnostic is actived with the logical $ln\_dia25h$1419 1420 %------------------------------------------nam_dia25h------------------------------------------------------1421 \namdisplay{nam_dia25h}1422 %----------------------------------------------------------------------------------------------------------1423 1424 \section{Top Middle and Bed hourly output }1425 1426 A module is available to output the surface (top), mid water and bed diagnostics of a set of standard variables.1427 This can be a useful diagnostic when hourly or sub-hourly output is required in high resolution tidal outputs.1428 The tidal signal is retained but the overall data usage is cut to just three vertical levels. Also the bottom level1429 is calculated for each cell.1430 This diagnostic is actived with the logical $ln\_diatmb$1431 1432 %------------------------------------------nam_diatmb-----------------------------------------------------1433 \namdisplay{nam_diatmb}1434 %----------------------------------------------------------------------------------------------------------1435 1436 % -------------------------------------------------------------------------------------------------------------1437 1411 % Sections transports 1438 1412 % ------------------------------------------------------------------------------------------------------------- … … 1440 1414 \label{DIA_diag_dct} 1441 1415 1416 %------------------------------------------namdct---------------------------------------------------- 1417 \namdisplay{namdct} 1418 %------------------------------------------------------------------------------------------------------------- 1419 1442 1420 A module is available to compute the transport of volume, heat and salt through sections. 1443 1421 This diagnostic is actived with \key{diadct}. … … 1459 1437 and the time scales over which they are averaged, as well as the level of output for debugging: 1460 1438 1461 %------------------------------------------namdct----------------------------------------------------1462 \namdisplay{namdct}1463 %-------------------------------------------------------------------------------------------------------------1464 1465 1439 \np{nn\_dct}: frequency of instantaneous transports computing 1466 1440 … … 1469 1443 \np{nn\_debug}: debugging of the section 1470 1444 1471 \subsubsection{ To createa binary file containing the pathway of each section }1472 1473 In \texttt{NEMOGCM/TOOLS/SECTIONS\_DIADCT/run}, the file \text tt{ {list\_sections.ascii\_global}}1445 \subsubsection{ Creating a binary file containing the pathway of each section } 1446 1447 In \texttt{NEMOGCM/TOOLS/SECTIONS\_DIADCT/run}, the file \textit{ {list\_sections.ascii\_global}} 1474 1448 contains a list of all the sections that are to be computed (this list of sections is based on MERSEA project metrics). 1475 1449 … … 1583 1557 \texttt{=/0, =/ 1000.} & diagonal & eastward & westward & postive: eastward \\ \hline 1584 1558 \end{tabular} 1585 1586 1587 1588 % -------------------------------------------------------------------------------------------------------------1589 % Other Diagnostics1590 % -------------------------------------------------------------------------------------------------------------1591 \section{Other Diagnostics (\key{diahth}, \key{diaar5})}1592 \label{DIA_diag_others}1593 1594 1595 Aside from the standard model variables, other diagnostics can be computed1596 on-line. The available ready-to-add diagnostics routines can be found in directory DIA.1597 Among the available diagnostics the following ones are obtained when defining1598 the \key{diahth} CPP key:1599 1600 - the mixed layer depth (based on a density criterion \citep{de_Boyer_Montegut_al_JGR04}) (\mdl{diahth})1601 1602 - the turbocline depth (based on a turbulent mixing coefficient criterion) (\mdl{diahth})1603 1604 - the depth of the 20\deg C isotherm (\mdl{diahth})1605 1606 - the depth of the thermocline (maximum of the vertical temperature gradient) (\mdl{diahth})1607 1608 The poleward heat and salt transports, their advective and diffusive component, and1609 the meriodional stream function can be computed on-line in \mdl{diaptr}1610 \np{ln\_diaptr} to true (see the \textit{\ngn{namptr} } namelist below).1611 When \np{ln\_subbas}~=~true, transports and stream function are computed1612 for the Atlantic, Indian, Pacific and Indo-Pacific Oceans (defined north of 30\deg S)1613 as well as for the World Ocean. The sub-basin decomposition requires an input file1614 (\ifile{subbasins}) which contains three 2D mask arrays, the Indo-Pacific mask1615 been deduced from the sum of the Indian and Pacific mask (Fig~\ref{Fig_mask_subasins}).1616 1617 %------------------------------------------namptr----------------------------------------------------1618 \namdisplay{namptr}1619 %-------------------------------------------------------------------------------------------------------------1620 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>1621 \begin{figure}[!t] \begin{center}1622 \includegraphics[width=1.0\textwidth]{./TexFiles/Figures/Fig_mask_subasins.pdf}1623 \caption{ \label{Fig_mask_subasins}1624 Decomposition of the World Ocean (here ORCA2) into sub-basin used in to compute1625 the heat and salt transports as well as the meridional stream-function: Atlantic basin (red),1626 Pacific basin (green), Indian basin (bleue), Indo-Pacific basin (bleue+green).1627 Note that semi-enclosed seas (Red, Med and Baltic seas) as well as Hudson Bay1628 are removed from the sub-basins. Note also that the Arctic Ocean has been split1629 into Atlantic and Pacific basins along the North fold line. }1630 \end{center} \end{figure}1631 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>1632 1633 In addition, a series of diagnostics has been added in the \mdl{diaar5}.1634 They corresponds to outputs that are required for AR5 simulations1635 (see Section \ref{DIA_steric} below for one of them).1636 Activating those outputs requires to define the \key{diaar5} CPP key.1637 \\1638 \\1639 1640 \section{Courant numbers}1641 Courant numbers provide a theoretical indication of the model's numerical stability. The advective Courant numbers can be calculated according to1642 \begin{equation}1643 \label{eq:CFL}1644 C_u = |u|\frac{\rdt}{e_{1u}}, \quad C_v = |v|\frac{\rdt}{e_{2v}}, \quad C_w = |w|\frac{\rdt}{e_{3w}}1645 \end{equation}1646 in the zonal, meridional and vertical directions respectively. The vertical component is included although it is not strictly valid as the vertical velocity is calculated from the continuity equation rather than as a prognostic variable. Physically this represents the rate at which information is propogated across a grid cell. Values greater than 1 indicate that information is propagated across more than one grid cell in a single time step.1647 1648 The variables can be activated by setting the \np{nn\_diacfl} namelist parameter to 1 in the \ngn{namctl} namelist. The diagnostics will be written out to an ascii file named cfl\_diagnostics.ascii. In this file the maximum value of $C_u$, $C_v$, and $C_w$ are printed at each timestep along with the coordinates of where the maximum value occurs. At the end of the model run the maximum value of $C_u$, $C_v$, and $C_w$ for the whole model run is printed along with the coordinates of each. The maximum values from the run are also copied to the ocean.output file.1649 1559 1650 1560 … … 1802 1712 the \key{diaar5} defined to be called. 1803 1713 1714 1715 1716 % ------------------------------------------------------------------------------------------------------------- 1717 % Other Diagnostics 1718 % ------------------------------------------------------------------------------------------------------------- 1719 \section{Other Diagnostics (\key{diahth}, \key{diaar5})} 1720 \label{DIA_diag_others} 1721 1722 1723 Aside from the standard model variables, other diagnostics can be computed on-line. 1724 The available ready-to-add diagnostics modules can be found in directory DIA. 1725 1726 \subsection{Depth of various quantities (\mdl{diahth})} 1727 1728 Among the available diagnostics the following ones are obtained when defining 1729 the \key{diahth} CPP key: 1730 1731 - the mixed layer depth (based on a density criterion \citep{de_Boyer_Montegut_al_JGR04}) (\mdl{diahth}) 1732 1733 - the turbocline depth (based on a turbulent mixing coefficient criterion) (\mdl{diahth}) 1734 1735 - the depth of the 20\deg C isotherm (\mdl{diahth}) 1736 1737 - the depth of the thermocline (maximum of the vertical temperature gradient) (\mdl{diahth}) 1738 1739 % ----------------------------------------------------------- 1740 % Poleward heat and salt transports 1741 % ----------------------------------------------------------- 1742 1743 \subsection{Poleward heat and salt transports (\mdl{diaptr})} 1744 1745 %------------------------------------------namptr----------------------------------------- 1746 \namdisplay{namptr} 1747 %----------------------------------------------------------------------------------------- 1748 1749 The poleward heat and salt transports, their advective and diffusive component, and 1750 the meriodional stream function can be computed on-line in \mdl{diaptr} 1751 \np{ln\_diaptr} to true (see the \textit{\ngn{namptr} } namelist below). 1752 When \np{ln\_subbas}~=~true, transports and stream function are computed 1753 for the Atlantic, Indian, Pacific and Indo-Pacific Oceans (defined north of 30\deg S) 1754 as well as for the World Ocean. The sub-basin decomposition requires an input file 1755 (\ifile{subbasins}) which contains three 2D mask arrays, the Indo-Pacific mask 1756 been deduced from the sum of the Indian and Pacific mask (Fig~\ref{Fig_mask_subasins}). 1757 1758 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 1759 \begin{figure}[!t] \begin{center} 1760 \includegraphics[width=1.0\textwidth]{./TexFiles/Figures/Fig_mask_subasins.pdf} 1761 \caption{ \label{Fig_mask_subasins} 1762 Decomposition of the World Ocean (here ORCA2) into sub-basin used in to compute 1763 the heat and salt transports as well as the meridional stream-function: Atlantic basin (red), 1764 Pacific basin (green), Indian basin (bleue), Indo-Pacific basin (bleue+green). 1765 Note that semi-enclosed seas (Red, Med and Baltic seas) as well as Hudson Bay 1766 are removed from the sub-basins. Note also that the Arctic Ocean has been split 1767 into Atlantic and Pacific basins along the North fold line. } 1768 \end{center} \end{figure} 1769 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 1770 1771 1772 % ----------------------------------------------------------- 1773 % CMIP specific diagnostics 1774 % ----------------------------------------------------------- 1775 \subsection{CMIP specific diagnostics (\mdl{diaar5})} 1776 1777 A series of diagnostics has been added in the \mdl{diaar5}. 1778 They corresponds to outputs that are required for AR5 simulations (CMIP5) 1779 (see also Section \ref{DIA_steric} for one of them). 1780 Activating those outputs requires to define the \key{diaar5} CPP key. 1781 1782 1783 % ----------------------------------------------------------- 1784 % 25 hour mean and hourly Surface, Mid and Bed 1785 % ----------------------------------------------------------- 1786 \subsection{25 hour mean output for tidal models } 1787 1788 %------------------------------------------nam_dia25h------------------------------------- 1789 \namdisplay{nam_dia25h} 1790 %----------------------------------------------------------------------------------------- 1791 1792 A module is available to compute a crudely detided M2 signal by obtaining a 25 hour mean. 1793 The 25 hour mean is available for daily runs by summing up the 25 hourly instantananeous hourly values from 1794 midnight at the start of the day to midight at the day end. 1795 This diagnostic is actived with the logical $ln\_dia25h$ 1796 1797 1798 % ----------------------------------------------------------- 1799 % Top Middle and Bed hourly output 1800 % ----------------------------------------------------------- 1801 \subsection{Top Middle and Bed hourly output } 1802 1803 %------------------------------------------nam_diatmb----------------------------------------------------- 1804 \namdisplay{nam_diatmb} 1805 %---------------------------------------------------------------------------------------------------------- 1806 1807 A module is available to output the surface (top), mid water and bed diagnostics of a set of standard variables. 1808 This can be a useful diagnostic when hourly or sub-hourly output is required in high resolution tidal outputs. 1809 The tidal signal is retained but the overall data usage is cut to just three vertical levels. Also the bottom level 1810 is calculated for each cell. 1811 This diagnostic is actived with the logical $ln\_diatmb$ 1812 1813 1814 1815 % ----------------------------------------------------------- 1816 % Courant numbers 1817 % ----------------------------------------------------------- 1818 \subsection{Courant numbers} 1819 Courant numbers provide a theoretical indication of the model's numerical stability. The advective Courant numbers can be calculated according to 1820 \begin{equation} 1821 \label{eq:CFL} 1822 C_u = |u|\frac{\rdt}{e_{1u}}, \quad C_v = |v|\frac{\rdt}{e_{2v}}, \quad C_w = |w|\frac{\rdt}{e_{3w}} 1823 \end{equation} 1824 in the zonal, meridional and vertical directions respectively. The vertical component is included although it is not strictly valid as the vertical velocity is calculated from the continuity equation rather than as a prognostic variable. Physically this represents the rate at which information is propogated across a grid cell. Values greater than 1 indicate that information is propagated across more than one grid cell in a single time step. 1825 1826 The variables can be activated by setting the \np{nn\_diacfl} namelist parameter to 1 in the \ngn{namctl} namelist. The diagnostics will be written out to an ascii file named cfl\_diagnostics.ascii. In this file the maximum value of $C_u$, $C_v$, and $C_w$ are printed at each timestep along with the coordinates of where the maximum value occurs. At the end of the model run the maximum value of $C_u$, $C_v$, and $C_w$ for the whole model run is printed along with the coordinates of each. The maximum values from the run are also copied to the ocean.output file. 1827 1828 1804 1829 % ================================================================ 1805 1830 -
trunk/DOC/TexFiles/Chapters/Chap_DOM.tex
r6320 r6497 486 486 The last choice in terms of vertical coordinate concerns the presence (or not) in the model domain 487 487 of ocean cavities beneath ice shelves. Setting \np{ln\_isfcav} to true allows to manage ocean cavities, 488 otherwise they are filled in. 488 otherwise they are filled in. This option is currently only available in $z$- or $zps$-coordinate, 489 and partial step are also applied at the ocean/ice shelf interface. 489 490 490 491 Contrary to the horizontal grid, the vertical grid is computed in the code and no … … 772 773 \end{equation} 773 774 774 where $s_{min}$ is the depth at which the s-coordinate stretching starts and775 allows a z-coordinate to placed on top of the stretched coordinate,776 and zis the depth (negative down from the asea surface).775 where $s_{min}$ is the depth at which the $s$-coordinate stretching starts and 776 allows a $z$-coordinate to placed on top of the stretched coordinate, 777 and $z$ is the depth (negative down from the asea surface). 777 778 778 779 \begin{equation} … … 886 887 that do not communicate with another ocean point at the same level are eliminated. 887 888 888 In case of ice shelf cavities, as for the representation of bathymetry, a 2D integer array, misfdep, is created. 889 misfdep defines the level of the first wet $t$-point (ie below the ice-shelf/ocean interface). All the cells between $k=1$ and $misfdep(i,j)-1$ are masked. 890 By default, $misfdep(:,:)=1$ and no cells are masked. 891 Modifications of the model bathymetry and ice shelf draft into 889 As for the representation of bathymetry, a 2D integer array, misfdep, is created. 890 misfdep defines the level of the first wet $t$-point. All the cells between $k=1$ and $misfdep(i,j)-1$ are masked. 891 By default, misfdep(:,:)=1 and no cells are masked. 892 893 In case of ice shelf cavities, modifications of the model bathymetry and ice shelf draft into 892 894 the cavities are performed in the \textit{zgr\_isf} routine. The compatibility between ice shelf draft and bathymetry is checked. 893 895 All the locations where the isf cavity is thinnest than \np{rn\_isfhmin} meters are grounded ($i.e.$ masked). … … 903 905 vmask(i,j,k) &= \; tmask(i,j,k) \ * \ tmask(i,j+1,k) \\ 904 906 fmask(i,j,k) &= \; tmask(i,j,k) \ * \ tmask(i+1,j,k) \\ 905 &\ \ \, * tmask(i,j,k) \ * \ tmask(i+1,j,k) \\907 & \ \ \, * tmask(i,j,k) \ * \ tmask(i+1,j,k) \\ 906 908 wmask(i,j,k) &= \; tmask(i,j,k) \ * \ tmask(i,j,k-1) \text{ with } wmask(i,j,1) = tmask(i,j,1) 907 909 \end{align*} 908 910 909 Note, wmask is now defined. It allows, in case of ice shelves, 910 to deal with the top boundary (ice shelf/ocean interface) exactly in the same way as for the bottom boundary. 911 Note that, without ice shelves cavities, masks at $t-$ and $w-$points are identical with 912 the numerical indexing used (\S~\ref{DOM_Num_Index}). Nevertheless, $wmask$ are required 913 with oceean cavities to deal with the top boundary (ice shelf/ocean interface) 914 exactly in the same way as for the bottom boundary. 911 915 912 916 The specification of closed lateral boundaries requires that at least the first and last … … 916 920 (and so too the mask arrays) (see \S~\ref{LBC_jperio}). 917 921 918 %%%919 \gmcomment{ \colorbox{yellow}{Add one word on tricky trick !} mbathy in further modified in zdfbfr{\ldots}. }920 %%%921 922 922 923 % ================================================================ -
trunk/DOC/TexFiles/Chapters/Chap_SBC.tex
r6320 r6497 128 128 The ocean model provides, at each time step, to the surface module (\mdl{sbcmod}) 129 129 the surface currents, temperature and salinity. 130 These variables are averaged over \np{n f\_sbc} time-step (\ref{Tab_ssm}),130 These variables are averaged over \np{nn\_fsbc} time-step (\ref{Tab_ssm}), 131 131 and it is these averaged fields which are used to computes the surface fluxes 132 at a frequency of \np{n f\_sbc} time-step.132 at a frequency of \np{nn\_fsbc} time-step. 133 133 134 134 … … 144 144 \caption{ \label{Tab_ssm} 145 145 Ocean variables provided by the ocean to the surface module (SBC). 146 The variable are averaged over n f{\_}sbc time step, $i.e.$ the frequency of147 computation of surface fluxes.}146 The variable are averaged over nn{\_}fsbc time step, 147 $i.e.$ the frequency of computation of surface fluxes.} 148 148 \end{center} \end{table} 149 149 %-------------------------------------------------------------------------------------------------------------- … … 592 592 or larger than the one of the input atmospheric fields. 593 593 594 The \np{sn\_wndi}, \np{sn\_wndj}, \np{sn\_qsr}, \np{sn\_qlw}, \np{sn\_tair}, \np{sn\_humi}, 595 \np{sn\_prec}, \np{sn\_snow}, \np{sn\_tdif} parameters describe the fields 596 and the way they have to be used (spatial and temporal interpolations). 597 598 \np{cn\_dir} is the directory of location of bulk files 599 \np{ln\_taudif} is the flag to specify if we use Hight Frequency (HF) tau information (.true.) or not (.false.) 600 \np{rn\_zqt}: is the height of humidity and temperature measurements (m) 601 \np{rn\_zu}: is the height of wind measurements (m) 602 603 Three multiplicative factors are availables : 604 \np{rn\_pfac} and \np{rn\_efac} allows to adjust (if necessary) the global freshwater budget 605 by increasing/reducing the precipitations (total and snow) and or evaporation, respectively. 606 The third one,\np{rn\_vfac}, control to which extend the ice/ocean velocities are taken into account 607 in the calculation of surface wind stress. Its range should be between zero and one, 608 and it is recommended to set it to 0. 609 594 610 % ------------------------------------------------------------------------------------------------------------- 595 611 % CLIO Bulk formulea … … 926 942 \begin{description} 927 943 \item[\np{nn\_isf}~=~1] 928 The ice shelf cavity is represented (\np{ln\_isfcav}~=~true needed). The fwf and heat flux are computed. Two different bulk formula are available: 944 The ice shelf cavity is represented (\np{ln\_isfcav}~=~true needed). The fwf and heat flux are computed. 945 Two different bulk formula are available: 929 946 \begin{description} 930 947 \item[\np{nn\_isfblk}~=~1] … … 988 1005 This parameter is only used if \np{nn\_isf}~=~1 or \np{nn\_isf}~=~4 989 1006 990 If \np{rn\_hisf\_tbl} = 0. 0, the fluxes are put in the top level whatever is its tickness.991 992 If \np{rn\_hisf\_tbl} $>$ 0. 0, the fluxes are spread over the first \np{rn\_hisf\_tbl} m (ie over one or several cells).\\1007 If \np{rn\_hisf\_tbl} = 0., the fluxes are put in the top level whatever is its tickness. 1008 1009 If \np{rn\_hisf\_tbl} $>$ 0., the fluxes are spread over the first \np{rn\_hisf\_tbl} m (ie over one or several cells).\\ 993 1010 994 1011 The ice shelf melt is implemented as a volume flux with in the same way as for the runoff. -
trunk/DOC/TexFiles/Chapters/Chap_STO.tex
r6289 r6497 5 5 \label{STO} 6 6 7 Authors: P.-A. Bouttier 8 7 9 \minitoc 8 10 11 \newpage 9 12 10 \newpage 11 $\ $\newline % force a new line 13 14 The stochastic parametrization module aims to explicitly simulate uncertainties in the model. 15 More particularly, \cite{Brankart_OM2013} has shown that, 16 because of the nonlinearity of the seawater equation of state, unresolved scales represent 17 a major source of uncertainties in the computation of the large scale horizontal density gradient 18 (from T/S large scale fields), and that the impact of these uncertainties can be simulated 19 by random processes representing unresolved T/S fluctuations. 20 21 The stochastic formulation of the equation of state can be written as: 22 \begin{equation} 23 \label{eq:eos_sto} 24 \rho = \frac{1}{2} \sum_{i=1}^m\{ \rho[T+\Delta T_i,S+\Delta S_i,p_o(z)] + \rho[T-\Delta T_i,S-\Delta S_i,p_o(z)] \} 25 \end{equation} 26 where $p_o(z)$ is the reference pressure depending on the depth and, 27 $\Delta T_i$ and $\Delta S_i$ are a set of T/S perturbations defined as the scalar product 28 of the respective local T/S gradients with random walks $\mathbf{\xi}$: 29 \begin{equation} 30 \label{eq:sto_pert} 31 \Delta T_i = \mathbf{\xi}_i \cdot \nabla T \qquad \hbox{and} \qquad \Delta S_i = \mathbf{\xi}_i \cdot \nabla S 32 \end{equation} 33 $\mathbf{\xi}_i$ are produced by a first-order autoregressive processes (AR-1) with 34 a parametrized decorrelation time scale, and horizontal and vertical standard deviations $\sigma_s$. 35 $\mathbf{\xi}$ are uncorrelated over the horizontal and fully correlated along the vertical. 36 37 38 \section{Stochastic processes} 39 \label{STO_the_details} 40 41 The starting point of our implementation of stochastic parameterizations 42 in NEMO is to observe that many existing parameterizations are based 43 on autoregressive processes, which are used as a basic source of randomness 44 to transform a deterministic model into a probabilistic model. 45 A generic approach is thus to add one single new module in NEMO, 46 generating processes with appropriate statistics 47 to simulate each kind of uncertainty in the model 48 (see \cite{Brankart_al_GMD2015} for more details). 49 50 In practice, at every model grid point, independent Gaussian autoregressive 51 processes~$\xi^{(i)},\,i=1,\ldots,m$ are first generated 52 using the same basic equation: 53 54 \begin{equation} 55 \label{eq:autoreg} 56 \xi^{(i)}_{k+1} = a^{(i)} \xi^{(i)}_k + b^{(i)} w^{(i)} + c^{(i)} 57 \end{equation} 58 59 \noindent 60 where $k$ is the index of the model timestep; and 61 $a^{(i)}$, $b^{(i)}$, $c^{(i)}$ are parameters defining 62 the mean ($\mu^{(i)}$) standard deviation ($\sigma^{(i)}$) 63 and correlation timescale ($\tau^{(i)}$) of each process: 64 65 \begin{itemize} 66 \item for order~1 processes, $w^{(i)}$ is a Gaussian white noise, 67 with zero mean and standard deviation equal to~1, and the parameters 68 $a^{(i)}$, $b^{(i)}$, $c^{(i)}$ are given by: 69 70 \begin{equation} 71 \label{eq:ord1} 72 \left\{ 73 \begin{array}{l} 74 a^{(i)} = \varphi \\ 75 b^{(i)} = \sigma^{(i)} \sqrt{ 1 - \varphi^2 } 76 \qquad\qquad\mbox{with}\qquad\qquad 77 \varphi = \exp \left( - 1 / \tau^{(i)} \right) \\ 78 c^{(i)} = \mu^{(i)} \left( 1 - \varphi \right) \\ 79 \end{array} 80 \right. 81 \end{equation} 82 83 \item for order~$n>1$ processes, $w^{(i)}$ is an order~$n-1$ autoregressive process, 84 with zero mean, standard deviation equal to~$\sigma^{(i)}$; correlation timescale 85 equal to~$\tau^{(i)}$; and the parameters $a^{(i)}$, $b^{(i)}$, $c^{(i)}$ are given by: 86 87 \begin{equation} 88 \label{eq:ord2} 89 \left\{ 90 \begin{array}{l} 91 a^{(i)} = \varphi \\ 92 b^{(i)} = \frac{n-1}{2(4n-3)} \sqrt{ 1 - \varphi^2 } 93 \qquad\qquad\mbox{with}\qquad\qquad 94 \varphi = \exp \left( - 1 / \tau^{(i)} \right) \\ 95 c^{(i)} = \mu^{(i)} \left( 1 - \varphi \right) \\ 96 \end{array} 97 \right. 98 \end{equation} 99 100 \end{itemize} 101 102 \noindent 103 In this way, higher order processes can be easily generated recursively using 104 the same piece of code implementing Eq.~(\ref{eq:autoreg}), 105 and using succesively processes from order $0$ to~$n-1$ as~$w^{(i)}$. 106 The parameters in Eq.~(\ref{eq:ord2}) are computed so that this recursive application 107 of Eq.~(\ref{eq:autoreg}) leads to processes with the required standard deviation 108 and correlation timescale, with the additional condition that 109 the $n-1$ first derivatives of the autocorrelation function 110 are equal to zero at~$t=0$, so that the resulting processes 111 become smoother and smoother as $n$ is increased. 112 113 Overall, this method provides quite a simple and generic way of generating 114 a wide class of stochastic processes. 115 However, this also means that new model parameters are needed to specify each of 116 these stochastic processes. As in any parameterization of lacking physics, 117 a very important issues then to tune these new parameters using either first principles, 118 model simulations, or real-world observations. 119 120 \section{Implementation details} 121 \label{STO_thech_details} 122 12 123 %---------------------------------------namsbc-------------------------------------------------- 13 124 \namdisplay{namsto} 14 125 %-------------------------------------------------------------------------------------------------------------- 15 $\ $\newline % force a new ligne16 126 127 The computer code implementing stochastic parametrisations can be found in the STO directory. 128 It involves three modules : 129 \begin{description} 130 \item[\mdl{stopar}] : define the Stochastic parameters and their time evolution. 131 \item[\mdl{storng}] : a random number generator based on (and includes) the 64-bit KISS 132 (Keep It Simple Stupid) random number generator distributed by George Marsaglia 133 (see \href{https://groups.google.com/forum/#!searchin/comp.lang.fortran/64-bit$20KISS$20RNGs}{here}) 134 \item[\mdl{stopts}] : stochastic parametrisation associated with the non-linearity of the equation of seawater, 135 implementing Eq~\ref{eq:sto_pert} and specific piece of code in the equation of state implementing Eq~\ref{eq:eos_sto}. 136 \end{description} 17 137 18 See \cite{Brankart_OM2013} and \cite{Brankart_al_GMD2015} papers for a description of the parameterization. 138 The \mdl{stopar} module has 3 public routines to be called by the model (in our case, NEMO): 139 140 The first routine (\rou{sto\_par}) is a direct implementation of Eq.~(\ref{eq:autoreg}), 141 applied at each model grid point (in 2D or 3D), 142 and called at each model time step ($k$) to update 143 every autoregressive process ($i=1,\ldots,m$). 144 This routine also includes a filtering operator, applied to $w^{(i)}$, 145 to introduce a spatial correlation between the stochastic processes. 146 147 The second routine (\rou{sto\_par\_init}) is an initialization routine mainly dedicated 148 to the computation of parameters $a^{(i)}, b^{(i)}, c^{(i)}$ 149 for each autoregressive process, as a function of the statistical properties 150 required by the model user (mean, standard deviation, time correlation, 151 order of the process,\ldots). 152 153 Parameters for the processes can be specified through the following \ngn{namsto} namelist parameters: 154 \begin{description} 155 \item[\np{nn\_sto\_eos}] : number of independent random walks 156 \item[\np{rn\_eos\_stdxy}] : random walk horz. standard deviation (in grid points) 157 \item[\np{rn\_eos\_stdz}] : random walk vert. standard deviation (in grid points) 158 \item[\np{rn\_eos\_tcor}] : random walk time correlation (in timesteps) 159 \item[\np{nn\_eos\_ord}] : order of autoregressive processes 160 \item[\np{nn\_eos\_flt}] : passes of Laplacian filter 161 \item[\np{rn\_eos\_lim}] : limitation factor (default = 3.0) 162 \end{description} 163 This routine also includes the initialization (seeding) of the random number generator. 164 165 The third routine (\rou{sto\_rst\_write}) writes a restart file (which suffix name is 166 given by \np{cn\_storst\_out} namelist parameter) containing the current value of 167 all autoregressive processes to allow restarting a simulation from where it has been interrupted. 168 This file also contains the current state of the random number generator. 169 When \np{ln\_rststo} is set to \textit{true}), the restart file (which suffix name is 170 given by \np{cn\_storst\_in} namelist parameter) is read by the initialization routine 171 (\rou{sto\_par\_init}). The simulation will continue exactly as if it was not interrupted 172 only when \np{ln\_rstseed} is set to \textit{true}, $i.e.$ when the state of 173 the random number generator is read in the restart file. -
trunk/DOC/TexFiles/Chapters/Chap_TRA.tex
r6320 r6497 734 734 (see \S\ref{SBC_rnf} for further detail of how it acts on temperature and salinity tendencies) 735 735 736 $\bullet$ \textit{fwfisf}, the mass flux associated with ice shelf melt, (see \S\ref{SBC_isf} for further details737 on how the ice shelf melt is computed and applied).736 $\bullet$ \textit{fwfisf}, the mass flux associated with ice shelf melt, 737 (see \S\ref{SBC_isf} for further details on how the ice shelf melt is computed and applied). 738 738 739 739 The surface boundary condition on temperature and salinity is applied as follows: … … 840 840 ($i.e.$ the inverses of the extinction length scales) are tabulated over 61 nonuniform 841 841 chlorophyll classes ranging from 0.01 to 10 g.Chl/L (see the routine \rou{trc\_oce\_rgb} 842 in \mdl{trc\_oce} module). Three types of chlorophyll can be chosen in the RGB formulation: 843 (1) a constant 0.05 g.Chl/L value everywhere (\np{nn\_chdta}=0) ; (2) an observed 844 time varying chlorophyll (\np{nn\_chdta}=1) ; (3) simulated time varying chlorophyll 845 by TOP biogeochemical model (\np{ln\_qsr\_bio}=true). In the latter case, the RGB 846 formulation is used to calculate both the phytoplankton light limitation in PISCES 847 or LOBSTER and the oceanic heating rate. 848 842 in \mdl{trc\_oce} module). Four types of chlorophyll can be chosen in the RGB formulation: 843 \begin{description} 844 \item[\np{nn\_chdta}=0] 845 a constant 0.05 g.Chl/L value everywhere ; 846 \item[\np{nn\_chdta}=1] 847 an observed time varying chlorophyll deduced from satellite surface ocean color measurement 848 spread uniformly in the vertical direction ; 849 \item[\np{nn\_chdta}=2] 850 same as previous case except that a vertical profile of chlorophyl is used. 851 Following \cite{Morel_Berthon_LO89}, the profile is computed from the local surface chlorophyll value ; 852 \item[\np{ln\_qsr\_bio}=true] 853 simulated time varying chlorophyll by TOP biogeochemical model. 854 In this case, the RGB formulation is used to calculate both the phytoplankton 855 light limitation in PISCES or LOBSTER and the oceanic heating rate. 856 \end{description} 849 857 The trend in \eqref{Eq_tra_qsr} associated with the penetration of the solar radiation 850 858 is added to the temperature trend, and the surface heat flux is modified in routine \mdl{traqsr}. … … 1385 1393 I've changed "derivative" to "difference" and "mean" to "average"} 1386 1394 1387 With partial cells (\np{ln\_zps}=true) at bottom and top (\np{ln\_isfcav}=true), in general, tracers in horizontally1388 adjacent cells live at different depths. Horizontal gradients of tracers are needed1389 for horizontal diffusion (\mdl{traldf} module) and for the hydrostatic pressure1390 gradient (\mdl{dynhpg} module) to be active. The partial cell properties1391 at the top (\np{ln\_isfcav}=true) are computed in the same way as for the bottom. So, only the bottom interpolation is shown. 1392 \gmcomment{STEVEN from gm : question: not sure of what -to be active- means} 1395 With partial cells (\np{ln\_zps}=true) at bottom and top (\np{ln\_isfcav}=true), in general, 1396 tracers in horizontally adjacent cells live at different depths. 1397 Horizontal gradients of tracers are needed for horizontal diffusion (\mdl{traldf} module) 1398 and the hydrostatic pressure gradient calculations (\mdl{dynhpg} module). 1399 The partial cell properties at the top (\np{ln\_isfcav}=true) are computed in the same way as for the bottom. 1400 So, only the bottom interpolation is explained below. 1393 1401 1394 1402 Before taking horizontal gradients between the tracers next to the bottom, a linear -
trunk/DOC/TexFiles/Chapters/Chap_ZDF.tex
r6320 r6497 262 262 \end{equation} 263 263 264 At the ocean surface, a non zero length scale is set through the \np{rn\_ lmin0} namelist264 At the ocean surface, a non zero length scale is set through the \np{rn\_mxl0} namelist 265 265 parameter. Usually the surface scale is given by $l_o = \kappa \,z_o$ 266 266 where $\kappa = 0.4$ is von Karman's constant and $z_o$ the roughness 267 267 parameter of the surface. Assuming $z_o=0.1$~m \citep{Craig_Banner_JPO94} 268 leads to a 0.04~m, the default value of \np{rn\_ lsurf}. In the ocean interior268 leads to a 0.04~m, the default value of \np{rn\_mxl0}. In the ocean interior 269 269 a minimum length scale is set to recover the molecular viscosity when $\bar{e}$ 270 270 reach its minimum value ($1.10^{-6}= C_k\, l_{min} \,\sqrt{\bar{e}_{min}}$ ). … … 295 295 As the surface boundary condition on TKE is prescribed through $\bar{e}_o = e_{bb} |\tau| / \rho_o$, 296 296 with $e_{bb}$ the \np{rn\_ebb} namelist parameter, setting \np{rn\_ebb}~=~67.83 corresponds 297 to $\alpha_{CB} = 100$. further setting \np{ln\_lsurf} to true applies \eqref{ZDF_Lsbc}298 as surface boundary condition on length scale, with $\beta$ hard coded to the Stace t's value.297 to $\alpha_{CB} = 100$. Further setting \np{ln\_mxl0} to true applies \eqref{ZDF_Lsbc} 298 as surface boundary condition on length scale, with $\beta$ hard coded to the Stacey's value. 299 299 Note that a minimal threshold of \np{rn\_emin0}$=10^{-4}~m^2.s^{-2}$ (namelist parameters) 300 300 is applied on surface $\bar{e}$ value. … … 852 852 The bottom friction represents the friction generated by the bathymetry. 853 853 The top friction represents the friction generated by the ice shelf/ocean interface. 854 As the friction processes at the top and bottom are represented similarly, only the bottom friction is described in detail below.\\ 854 As the friction processes at the top and bottom are treated in similar way, 855 only the bottom friction is described in detail below. 855 856 856 857 … … 926 927 $H = 4000$~m, the resulting friction coefficient is $r = 4\;10^{-4}$~m\;s$^{-1}$. 927 928 This is the default value used in \NEMO. It corresponds to a decay time scale 928 of 115~days. It can be changed by specifying \np{rn\_bfri c1} (namelist parameter).929 of 115~days. It can be changed by specifying \np{rn\_bfri1} (namelist parameter). 929 930 930 931 For the linear friction case the coefficients defined in the general … … 936 937 \end{split} 937 938 \end{equation} 938 When \np{nn\_botfr}=1, the value of $r$ used is \np{rn\_bfri c1}.939 When \np{nn\_botfr}=1, the value of $r$ used is \np{rn\_bfri1}. 939 940 Setting \np{nn\_botfr}=0 is equivalent to setting $r=0$ and leads to a free-slip 940 941 bottom boundary condition. These values are assigned in \mdl{zdfbfr}. … … 943 944 in the \ifile{bfr\_coef} input NetCDF file. The mask values should vary from 0 to 1. 944 945 Locations with a non-zero mask value will have the friction coefficient increased 945 by $mask\_value$*\np{rn\_bfrien}*\np{rn\_bfri c1}.946 by $mask\_value$*\np{rn\_bfrien}*\np{rn\_bfri1}. 946 947 947 948 % ------------------------------------------------------------------------------------------------------------- … … 963 964 $e_b = 2.5\;10^{-3}$m$^2$\;s$^{-2}$, while the FRAM experiment \citep{Killworth1992} 964 965 uses $C_D = 1.4\;10^{-3}$ and $e_b =2.5\;\;10^{-3}$m$^2$\;s$^{-2}$. 965 The CME choices have been set as default values (\np{rn\_bfri c2} and \np{rn\_bfeb2}966 The CME choices have been set as default values (\np{rn\_bfri2} and \np{rn\_bfeb2} 966 967 namelist parameters). 967 968 … … 978 979 \end{equation} 979 980 980 The coefficients that control the strength of the non-linear bottom friction are 981 initialised as namelist parameters: $C_D$= \np{rn\_bfri2}, and $e_b$ =\np{rn\_bfeb2}. 982 Note for applications which treat tides explicitly a low or even zero value of 983 \np{rn\_bfeb2} is recommended. From v3.2 onwards a local enhancement of $C_D$ 984 is possible via an externally defined 2D mask array (\np{ln\_bfr2d}=true). 985 See previous section for details. 981 The coefficients that control the strength of the non-linear bottom friction are 982 initialised as namelist parameters: $C_D$= \np{rn\_bfri2}, and $e_b$ =\np{rn\_bfeb2}. 983 Note for applications which treat tides explicitly a low or even zero value of 984 \np{rn\_bfeb2} is recommended. From v3.2 onwards a local enhancement of $C_D$ is possible 985 via an externally defined 2D mask array (\np{ln\_bfr2d}=true). This works in the same way 986 as for the linear bottom friction case with non-zero masked locations increased by 987 $mask\_value$*\np{rn\_bfrien}*\np{rn\_bfri2}. 988 989 % ------------------------------------------------------------------------------------------------------------- 990 % Bottom Friction Log-layer 991 % ------------------------------------------------------------------------------------------------------------- 992 \subsection{Log-layer Bottom Friction enhancement (\np{nn\_botfr} = 2, \np{ln\_loglayer} = .true.)} 993 \label{ZDF_bfr_loglayer} 994 995 In the non-linear bottom friction case, the drag coefficient, $C_D$, can be optionally 996 enhanced using a "law of the wall" scaling. If \np{ln\_loglayer} = .true., $C_D$ is no 997 longer constant but is related to the thickness of the last wet layer in each column by: 998 999 \begin{equation} 1000 C_D = \left ( {\kappa \over {\rm log}\left ( 0.5e_{3t}/rn\_bfrz0 \right ) } \right )^2 1001 \end{equation} 1002 1003 \noindent where $\kappa$ is the von-Karman constant and \np{rn\_bfrz0} is a roughness 1004 length provided via the namelist. 1005 1006 For stability, the drag coefficient is bounded such that it is kept greater or equal to 1007 the base \np{rn\_bfri2} value and it is not allowed to exceed the value of an additional 1008 namelist parameter: \np{rn\_bfri2\_max}, i.e.: 1009 1010 \begin{equation} 1011 rn\_bfri2 \leq C_D \leq rn\_bfri2\_max 1012 \end{equation} 1013 1014 \noindent Note also that a log-layer enhancement can also be applied to the top boundary 1015 friction if under ice-shelf cavities are in use (\np{ln\_isfcav}=.true.). In this case, the 1016 relevant namelist parameters are \np{rn\_tfrz0}, \np{rn\_tfri2} 1017 and \np{rn\_tfri2\_max}. 986 1018 987 1019 % ------------------------------------------------------------------------------------------------------------- … … 1267 1299 1268 1300 % ================================================================ 1301 % Internal wave-driven mixing 1302 % ================================================================ 1303 \section{Internal wave-driven mixing (\key{zdftmx\_new})} 1304 \label{ZDF_tmx_new} 1305 1306 %--------------------------------------------namzdf_tmx_new------------------------------------------ 1307 \namdisplay{namzdf_tmx_new} 1308 %-------------------------------------------------------------------------------------------------------------- 1309 1310 The parameterization of mixing induced by breaking internal waves is a generalization 1311 of the approach originally proposed by \citet{St_Laurent_al_GRL02}. 1312 A three-dimensional field of internal wave energy dissipation $\epsilon(x,y,z)$ is first constructed, 1313 and the resulting diffusivity is obtained as 1314 \begin{equation} \label{Eq_Kwave} 1315 A^{vT}_{wave} = R_f \,\frac{ \epsilon }{ \rho \, N^2 } 1316 \end{equation} 1317 where $R_f$ is the mixing efficiency and $\epsilon$ is a specified three dimensional distribution 1318 of the energy available for mixing. If the \np{ln\_mevar} namelist parameter is set to false, 1319 the mixing efficiency is taken as constant and equal to 1/6 \citep{Osborn_JPO80}. 1320 In the opposite (recommended) case, $R_f$ is instead a function of the turbulence intensity parameter 1321 $Re_b = \frac{ \epsilon}{\nu \, N^2}$, with $\nu$ the molecular viscosity of seawater, 1322 following the model of \cite{Bouffard_Boegman_DAO2013} 1323 and the implementation of \cite{de_lavergne_JPO2016_efficiency}. 1324 Note that $A^{vT}_{wave}$ is bounded by $10^{-2}\,m^2/s$, a limit that is often reached when the mixing efficiency is constant. 1325 1326 In addition to the mixing efficiency, the ratio of salt to heat diffusivities can chosen to vary 1327 as a function of $Re_b$ by setting the \np{ln\_tsdiff} parameter to true, a recommended choice). 1328 This parameterization of differential mixing, due to \cite{Jackson_Rehmann_JPO2014}, 1329 is implemented as in \cite{de_lavergne_JPO2016_efficiency}. 1330 1331 The three-dimensional distribution of the energy available for mixing, $\epsilon(i,j,k)$, is constructed 1332 from three static maps of column-integrated internal wave energy dissipation, $E_{cri}(i,j)$, 1333 $E_{pyc}(i,j)$, and $E_{bot}(i,j)$, combined to three corresponding vertical structures 1334 (de Lavergne et al., in prep): 1335 \begin{align*} 1336 F_{cri}(i,j,k) &\propto e^{-h_{ab} / h_{cri} }\\ 1337 F_{pyc}(i,j,k) &\propto N^{n\_p}\\ 1338 F_{bot}(i,j,k) &\propto N^2 \, e^{- h_{wkb} / h_{bot} } 1339 \end{align*} 1340 In the above formula, $h_{ab}$ denotes the height above bottom, 1341 $h_{wkb}$ denotes the WKB-stretched height above bottom, defined by 1342 \begin{equation*} 1343 h_{wkb} = H \, \frac{ \int_{-H}^{z} N \, dz' } { \int_{-H}^{\eta} N \, dz' } \; , 1344 \end{equation*} 1345 The $n_p$ parameter (given by \np{nn\_zpyc} in \ngn{namzdf\_tmx\_new} namelist) controls the stratification-dependence of the pycnocline-intensified dissipation. 1346 It can take values of 1 (recommended) or 2. 1347 Finally, the vertical structures $F_{cri}$ and $F_{bot}$ require the specification of 1348 the decay scales $h_{cri}(i,j)$ and $h_{bot}(i,j)$, which are defined by two additional input maps. 1349 $h_{cri}$ is related to the large-scale topography of the ocean (etopo2) 1350 and $h_{bot}$ is a function of the energy flux $E_{bot}$, the characteristic horizontal scale of 1351 the abyssal hill topography \citep{Goff_JGR2010} and the latitude. 1352 1353 % ================================================================ 1354 1355 1356
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