Changeset 6347 for branches/2016/dev_r6325_SIMPLIF_1/DOC
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- 2016-02-24T08:56:48+01:00 (8 years ago)
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branches/2016/dev_r6325_SIMPLIF_1/DOC/TexFiles/Biblio/Biblio.bib
r6320 r6347 472 472 } 473 473 474 @article{bouffard_Boegman_DAO2013, 475 author = {D. Bouffard and L. Boegman}, 476 title = {A diapycnal diffusivity model for stratified environmental flows}, 477 volume = {61-62}, 478 issn = {03770265}, 479 url = {http://dx.doi.org/10.1016/j.dynatmoce.2013.02.002}, 480 doi = {10.1016/j.dynatmoce.2013.02.002}, 481 journal = DAO, 482 year = {2013}, 483 pages = {14--34}, 484 } 485 474 486 @ARTICLE{Bougeault1989, 475 487 author = {P. Bougeault and P. Lacarrere}, … … 787 799 volume = {34}, 788 800 pages = {8--13} 801 } 802 803 @article{de_lavergne_JPO2016_mixing, 804 author = {C. de Lavergne and G. Madec and J. Le Sommer and A. J. G. Nurser and A. C. Naveira Garabato }, 805 title = {On Antarctic Bottom Water consumption in the abyssal ocean}, 806 issn = {0022-3670}, 807 url = {http://dx.doi.org/10.1175/JPO-D-14-0201.1}, 808 doi = {10.1175/JPO-D-14-0201.1}, 809 abstract = {In studies of ocean mixing, it is generally assumed that small-scale turbulent overturns lose 15-20 \% of their energy in eroding the background stratification. Accumulating evidence that this energy fraction, or mixing efficiency Rf, significantly varies depending on flow properties challenges this assumption, however. Here, we examine the implications of a varying mixing efficiency for ocean energetics and deep water mass transformation. Combining current parameterizations of internal wave-driven mixing with a recent model expressing Rf as a function of a turbulence intensity parameter Reb = εν/νN2, we show that accounting for reduced mixing efficiencies in regions of weak stratification or energetic turbulence (high Reb) strongly limits the ability of breaking internal waves to supply oceanic potential energy and drive abyssal upwelling. Moving from a fixed Rf = 1/6 to a variable efficiency Rf(Reb) causes Antarctic Bottom Water upwelling induced by locally-dissipating internal tides and lee waves to fall from 9 to 4 Sv, and the corresponding potential energy source to plunge from 97 to 44 GW. When adding the contribution of remotely-dissipating internal tides under idealized distributions of energy dissipation, the total rate of Antarctic Bottom Water upwelling is reduced by about a factor of 2, reaching 5-15 Sv compared to 10-33 Sv for a fixed efficiency. Our results suggest that distributed mixing, overflow-related boundary processes and geothermal heating are more effective in consuming abyssal waters than topographically-enhanced mixing by breaking internal waves. Our calculations also point to the importance of accurately constraining Rf(Reb) and including the effect in ocean models.}, 810 journal = {Journal of Physical Oceanography}, 811 year = {2016}, 812 volume = {46}, pages = {635-–661} 813 } 814 815 @article{de_lavergne_JPO2016_efficiency, 816 author = {C. de Lavergne and G. Madec and J. Le Sommer and A. J. G. Nurser and A. C. Naveira Garabato }, 817 title = {The impact of a variable mixing efficiency on the abyssal overturning}, 818 issn = {0022-3670}, 819 url = {http://dx.doi.org//10.1175/JPO-D-14-0259.1}, 820 doi = {10.1175/JPO-D-14-0259.1}, 821 abstract = {In studies of ocean mixing, it is generally assumed that small-scale turbulent overturns lose 15-20 \% of their energy in eroding the background stratification. Accumulating evidence that this energy fraction, or mixing efficiency Rf, significantly varies depending on flow properties challenges this assumption, however. Here, we examine the implications of a varying mixing efficiency for ocean energetics and deep water mass transformation. Combining current parameterizations of internal wave-driven mixing with a recent model expressing Rf as a function of a turbulence intensity parameter Reb = εν/νN2, we show that accounting for reduced mixing efficiencies in regions of weak stratification or energetic turbulence (high Reb) strongly limits the ability of breaking internal waves to supply oceanic potential energy and drive abyssal upwelling. Moving from a fixed Rf = 1/6 to a variable efficiency Rf(Reb) causes Antarctic Bottom Water upwelling induced by locally-dissipating internal tides and lee waves to fall from 9 to 4 Sv, and the corresponding potential energy source to plunge from 97 to 44 GW. When adding the contribution of remotely-dissipating internal tides under idealized distributions of energy dissipation, the total rate of Antarctic Bottom Water upwelling is reduced by about a factor of 2, reaching 5-15 Sv compared to 10-33 Sv for a fixed efficiency. Our results suggest that distributed mixing, overflow-related boundary processes and geothermal heating are more effective in consuming abyssal waters than topographically-enhanced mixing by breaking internal waves. Our calculations also point to the importance of accurately constraining Rf(Reb) and including the effect in ocean models.}, 822 journal = {Journal of Physical Oceanography}, 823 year = {2016}, 824 volume = {46}, pages = {663-–681} 789 825 } 790 826 … … 1160 1196 } 1161 1197 1198 @article{goff_JGR2010, 1199 author = {J. A. Goff}, 1200 title = {Global prediction of abyssal hill root-mean-square heights from small-scale altimetric gravity variability}, 1201 issn = {2156-2202}, 1202 url = {http://dx.doi.org/10.1029/2010JB007867}, 1203 doi = {10.1029/2010JB007867}, 1204 abstract = {Abyssal hills, which are pervasive landforms on the seafloor of the Earth's oceans, represent a potential tectonic record of the history of mid-ocean ridge spreading. However, the most detailed global maps of the seafloor, derived from the satellite altimetry-based gravity field, cannot be used to deterministically characterize such small-scale ({\textless}10 km) morphology. Nevertheless, the small-scale variability of the gravity field can be related to the statistical properties of abyssal hill morphology using the upward continuation formulation. In this paper, I construct a global prediction of abyssal hill root-mean-square (rms) heights from the small-scale variability of the altimetric gravity field. The abyssal hill-related component of the gravity field is derived by first masking distinct features, such as seamounts, mid-ocean ridges, and continental margins, and then applying a newly designed adaptive directional filter algorithm to remove fracture zone/discontinuity fabric. A noise field is derived empirically by correlating the rms variability of the small-scale gravity field to the altimetric noise field in regions of very low relief, and the noise variance is subtracted from the small-scale gravity variance. Suites of synthetically derived, abyssal hill formed gravity fields are generated as a function of water depth, basement rms heights, and sediment thickness and used to predict abyssal hill seafloor rms heights from corrected small-scale gravity rms height. The resulting global prediction of abyssal hill rms heights is validated qualitatively by comparing against expected variations in abyssal hill morphology and quantitatively by comparing against actual measurements of rms heights. Although there is scatter, the prediction appears unbiased.}, 1205 volume = {115}, 1206 number = {B12}, 1207 journal = {Journal of Geophysical Research: Solid Earth}, 1208 year = {2010}, 1209 pages = {B12104}, 1210 } 1211 1162 1212 @ARTICLE{Goosse_al_JGR99, 1163 1213 author = {H. Goosse and E. Deleersnijder and T. Fichefet and M. England}, … … 1264 1314 1265 1315 @ARTICLE{Griffies_Hallberg_MWR00, 1266 author = {S.M. Griffies and R. H. Hallberg},1267 title = {Biharmonic friction with a smagorinsky-like viscosity for use in large-scale eddy-permitting ocean models},1316 author = {S.M. Griffies and R.W. Hallberg}, 1317 title = {Biharmonic friction with a Smagorinsky-like viscosity for use in large-scale eddy-permitting ocean models}, 1268 1318 journal = MWR, 1269 1319 year = {2000}, … … 1586 1636 volume = {12}, 1587 1637 pages = {381--389} 1638 } 1639 1640 @article{Jackson_Rehmann_JPO2014, 1641 author = {P. R. Jackson and C. R. Rehmann}, 1642 title = {Experiments on differential scalar mixing in turbulence in a sheared, stratified flow}, 1643 journal = JPO, 1644 volume = {44}, 1645 issn = {0022-3670}, 1646 url = {http://dx.doi.org/10.1175/JPO-D-14-0027.1}, 1647 doi = {10.1175/JPO-D-14-0027.1}, 1648 number = {10}, 1649 year = {2014}, 1650 pages = {2661--2680}, 1588 1651 } 1589 1652 … … 2430 2493 } 2431 2494 2495 @ARTICLE{Morel_Berthon_LO89, 2496 author = {A. Morel and J.-F. Berthon}, 2497 title = {Surface pigments, algal biomass profiles, and potential production of the euphotic layer: 2498 Relationships reinvestigated in view of remote-sensing applications}, 2499 journal = {Limnol. Oceanogr.}, 2500 year = {1989}, 2501 volume = {34(8)}, 2502 pages = {1545--1562} 2503 } 2504 2432 2505 @ARTICLE{Morel_Maritorena_JGR01, 2433 2506 author = {A. Morel and S. Maritorena}, … … 2478 2551 title = {Estimates of the local rate of vertical diffusion from dissipation measurements}, 2479 2552 journal = JPO, 2553 year = {1980}, 2480 2554 volume = {10}, 2481 2555 pages = {83--89} … … 2714 2788 } 2715 2789 2790 @ARTICLE{Rousset_GMD2015, 2791 author = {C. Rousset and M. Vancoppenolle and G. Madec and T. Fichefet and S. Flavoni 2792 and A. Barth\'{e}lemy and R. Benshila and J. Chanut and C. L\'{e}vy and S. Masson and F. Vivier }, 2793 title = {The Louvain-La-Neuve sea-ice model LIM3.6: Global and regional capabilities}, 2794 journal= {Geoscientific Model Development}, 2795 year = {2015}, 2796 volume = {8}, pages={2991--3005}, 2797 doi = {10.5194/gmd-8-2991-2015}, 2798 url = {http://dx.doi.org/10.5194/gmd-8-2991-2015} 2799 } 2800 2716 2801 @ARTICLE{Sadourny1975, 2717 2802 author = {R. Sadourny}, … … 2794 2879 year = {2004}, 2795 2880 pages = {245--263}, 2881 } 2882 2883 @INBOOK{Smagorinsky_93, 2884 author = {Smagorinsky, J.}, 2885 chapter = {Some historical remarks on the use of non-linear viscosities}, 2886 title = {Large Eddy Simulation of Complex Engineering and Geophysical Flows}, 2887 pages = {3--36}, 2888 year = {1993}, 2889 publisher = {Cambridge University Press, B. Galperin and S. A. Orszag (eds.)}, 2796 2890 } 2797 2891 -
branches/2016/dev_r6325_SIMPLIF_1/DOC/TexFiles/Chapters/Chap_DIA.tex
r6289 r6347 110 110 even without a parallel-enabled NetCDF4 library, simply by employing only one dedicated I/O server. 111 111 112 \subsection{XIOS: the I O\_SERVER}112 \subsection{XIOS: the I/O server} 113 113 114 114 \subsubsection{Attached or detached mode?} … … 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 -
branches/2016/dev_r6325_SIMPLIF_1/DOC/TexFiles/Chapters/Chap_DOM.tex
r6320 r6347 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 … … 494 495 \ifile{bathy\_meter} file, so that the computation of the number of wet ocean point 495 496 in each water column is by-passed}. 496 If \np{ln\_isfcav}~=~true, an extra file input file describing the ice shelf draft497 (in meters) (\ifile{isf\_draft\_meter}) is needed.498 499 497 After reading the bathymetry, the algorithm for vertical grid definition differs 500 498 between the different options: … … 760 758 as the minimum and maximum depths at which the terrain-following vertical coordinate is calculated. 761 759 762 Options for stretching the coordinate are provided as examples, but care must be taken to ensure763 t hat the vertical stretch used is appropriate for the application.760 Options for stretching the coordinate are provided as examples, but care must be taken 761 to ensure that the vertical stretch used is appropriate for the application. 764 762 765 763 The original default NEMO s-coordinate stretching is available if neither of the other options … … 772 770 \end{equation} 773 771 774 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).772 where $s_{min}$ is the depth at which the $s$-coordinate stretching starts and 773 allows a $z$-coordinate to placed on top of the stretched coordinate, 774 and $z$ is the depth (negative down from the asea surface). 777 775 778 776 \begin{equation} … … 886 884 that do not communicate with another ocean point at the same level are eliminated. 887 885 888 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 886 As for the representation of bathymetry, a 2D integer array, misfdep, is created. 887 misfdep defines the level of the first wet $t$-point. All the cells between $k=1$ and $misfdep(i,j)-1$ are masked. 888 By default, misfdep(:,:)=1 and no cells are masked. 889 890 In case of ice shelf cavities, modifications of the model bathymetry and ice shelf draft into 892 891 the cavities are performed in the \textit{zgr\_isf} routine. The compatibility between ice shelf draft and bathymetry is checked. 893 All the locations where the isf cavity is thinnest than \np{rn\_isfhmin} meters are grounded ($i.e.$ masked).894 892 If only one cell on the water column is opened at $t$-, $u$- or $v$-points, the bathymetry or the ice shelf draft is dug to fit this constrain. 895 893 If the incompatibility is too strong (need to dig more than 1 cell), the cell is masked.\\ 896 894 897 From the \textit{mbathy} a nd \textit{misfdep} array, the mask fields are defined as follows:895 From the \textit{mbathy} array, the mask fields are defined as follows: 898 896 \begin{align*} 899 897 tmask(i,j,k) &= \begin{cases} \; 0& \text{ if $k < misfdep(i,j) $ } \\ … … 903 901 vmask(i,j,k) &= \; tmask(i,j,k) \ * \ tmask(i,j+1,k) \\ 904 902 fmask(i,j,k) &= \; tmask(i,j,k) \ * \ tmask(i+1,j,k) \\ 905 &\ \ \, * tmask(i,j,k) \ * \ tmask(i+1,j,k) \\903 & \ \ \, * tmask(i,j,k) \ * \ tmask(i+1,j,k) \\ 906 904 wmask(i,j,k) &= \; tmask(i,j,k) \ * \ tmask(i,j,k-1) \text{ with } wmask(i,j,1) = tmask(i,j,1) 907 905 \end{align*} 908 906 909 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. 907 Note that, without ice shelves cavities, masks at $t-$ and $w-$points are identical with 908 the numerical indexing used (\S~\ref{DOM_Num_Index}). Nevertheless, $wmask$ are required 909 with oceean cavities to deal with the top boundary (ice shelf/ocean interface) 910 exactly in the same way as for the bottom boundary. 911 911 912 912 The specification of closed lateral boundaries requires that at least the first and last … … 916 916 (and so too the mask arrays) (see \S~\ref{LBC_jperio}). 917 917 918 %%%919 \gmcomment{ \colorbox{yellow}{Add one word on tricky trick !} mbathy in further modified in zdfbfr{\ldots}. }920 %%%921 918 922 919 % ================================================================ -
branches/2016/dev_r6325_SIMPLIF_1/DOC/TexFiles/Chapters/Chap_DYN.tex
r6320 r6347 637 637 ($e_{3w}$). 638 638 639 $\bullet$ Traditional coding with adaptation for ice shelf cavities (\np{ln\_dynhpg\_isf}=true).640 This scheme need the activation of ice shelf cavities (\np{ln\_isfcav}=true).641 642 639 $\bullet$ Pressure Jacobian scheme (prj) (a research paper in preparation) (\np{ln\_dynhpg\_prj}=true) 643 640 … … 667 664 668 665 $\bullet$ The ocean load is computed using the expression \eqref{Eq_dynhpg_sco} described in \ref{DYN_hpg_sco}. 666 A treatment of the partial cell for top and bottom similar to the one described in \ref{DYN_hpg_zps} is done 667 to reduce the residual circulation generated by the top partial cell. 669 668 670 669 %-------------------------------------------------------------------------------------------------------------- -
branches/2016/dev_r6325_SIMPLIF_1/DOC/TexFiles/Chapters/Chap_LDF.tex
r6289 r6347 397 397 \subsubsection{Space and Time Varying Mixing Coefficients} 398 398 399 There is no default specification of space and time varying mixing coefficient. 400 The only case available is specific to the ORCA2 and ORCA05 global ocean 401 configurations. It provides only a tracer 402 mixing coefficient for eddy induced velocity (ORCA2) or both iso-neutral and 403 eddy induced velocity (ORCA05) that depends on the local growth rate of 404 baroclinic instability. This specification is actually used when an ORCA key 399 There are no default specifications of space and time varying mixing coefficient. One 400 available case is specific to the ORCA2 and ORCA05 global ocean configurations. It 401 provides only a tracer mixing coefficient for eddy induced velocity (ORCA2) or both 402 iso-neutral and eddy induced velocity (ORCA05) that depends on the local growth rate of 403 baroclinic instability. This specification is actually used when an ORCA key 405 404 and both \key{traldf\_eiv} and \key{traldf\_c2d} are defined. 405 406 \subsubsection{Smagorinsky viscosity (\key{dynldf\_c3d} and \key{dynldf\_smag})} 407 408 The \key{dynldf\_smag} key activates a 3D, time-varying viscosity that depends on the 409 resolved motions. Following \citep{Smagorinsky_93} the viscosity coefficient is set 410 proportional to a local deformation rate based on the horizontal shear and tension, 411 namely: 412 413 \begin{equation} 414 A_{m_{Smag}} = \left(\frac{{\sf CM_{Smag}}}{\pi}\right)^2L^2\vert{D}\vert 415 \end{equation} 416 417 \noindent where the deformation rate $\vert{D}\vert$ is given by 418 419 \begin{equation} 420 \vert{D}\vert=\sqrt{\left({\frac{\partial{u}} {\partial{x}}} 421 -{\frac{\partial{v}} {\partial{y}}}\right)^2 422 + \left({\frac{\partial{u}} {\partial{y}}} 423 +{\frac{\partial{v}} {\partial{x}}}\right)^2} 424 \end{equation} 425 426 \noindent and $L$ is the local gridscale given by: 427 428 \begin{equation} 429 L^2 = \frac{2{e_1}^2 {e_2}^2}{\left ( {e_1}^2 + {e_2}^2 \right )} 430 \end{equation} 431 432 \citep{Griffies_Hallberg_MWR00} suggest values in the range 2.2 to 4.0 of the coefficient 433 $\sf CM_{Smag}$ for oceanic flows. This value is set via the \np{rn\_cmsmag\_1} namelist 434 parameter. An additional parameter: \np{rn\_cmsh} is included in NEMO for experimenting 435 with the contribution of the shear term. A value of 1.0 (the default) calculates the 436 deformation rate as above; a value of 0.0 will discard the shear term entirely. 437 438 For numerical stability, the calculated viscosity is bounded according to the following: 439 440 \begin{equation} 441 {\rm MIN}\left ({ L^2\over {8\Delta{t}}}, rn\_ahm\_m\_lap\right ) \geq A_{m_{Smag}} 442 \geq rn\_ahm\_0\_lap 443 \end{equation} 444 445 \noindent with both parameters for the upper and lower bounds being provided via the 446 indicated namelist parameters. 447 448 \bigskip When $ln\_dynldf\_bilap = .true.$, a biharmonic version of the Smagorinsky 449 viscosity is also available which sets a coefficient for the biharmonic viscosity as: 450 451 \begin{equation} 452 B_{m_{Smag}} = - \left(\frac{{\sf CM_{bSmag}}}{\pi}\right)^2 {L^4\over 8}\vert{D}\vert 453 \end{equation} 454 455 \noindent which is bounded according to: 456 457 \begin{equation} 458 {\rm MAX}\left (-{ L^4\over {64\Delta{t}}}, rn\_ahm\_m\_blp\right ) \leq B_{m_{Smag}} 459 \leq rn\_ahm\_0\_blp 460 \end{equation} 461 462 \noindent Note the reversal of the inequalities here because NEMO requires the biharmonic 463 coefficients as negative numbers. $\sf CM_{bSmag}$ is set via the \np{rn\_cmsmag\_2} 464 namelist parameter and the bounding values have corresponding entries in the namelist too. 465 466 \bigskip The current implementation in NEMO also allows for 3D, time-varying diffusivities 467 to be set using the Smagorinsky approach. Users should note that this option is not 468 recommended for many applications since diffusivities will tend to be largest near 469 boundaries (where shears are greatest) leading to spurious upwellings 470 (\citep{Griffies_Bk04}, chapter 18.3.4). Nevertheless the option is there for those 471 wishing to experiment. This choice requires both \key{traldf\_c3d} and \key{traldf\_smag} 472 and uses the \np{rn\_chsmag} (${\sf CH_{Smag}}$), \np{rn\_smsh} and \np{rn\_aht\_m} 473 namelist parameters in an analogous way to \np{rn\_cmsmag\_1}, \np{rn\_cmsh} and 474 \np{rn\_ahm\_m\_lap} (see above) to set the diffusion coefficient: 475 476 \begin{equation} 477 A_{h_{Smag}} = \left(\frac{{\sf CH_{Smag}}}{\pi}\right)^2L^2\vert{D}\vert 478 \end{equation} 479 480 481 For numerical stability, the calculated diffusivity is bounded according to the following: 482 483 \begin{equation} 484 {\rm MIN}\left ({ L^2\over {8\Delta{t}}}, rn\_aht\_m\right ) \geq A_{h_{Smag}} 485 \geq rn\_aht\_0 486 \end{equation} 487 406 488 407 489 $\ $\newline % force a new ligne -
branches/2016/dev_r6325_SIMPLIF_1/DOC/TexFiles/Chapters/Chap_SBC.tex
r6320 r6347 51 51 \item the modification of fluxes below ice-covered areas (using observed ice-cover or a sea-ice model) (\np{nn\_ice}~=~0,1, 2 or 3) ; 52 52 \item the addition of river runoffs as surface freshwater fluxes or lateral inflow (\np{ln\_rnf}~=~true) ; 53 \item the addition of isf melting as lateral inflow (parameterisation) or as fluxes applied at the land-ice ocean interface (\np{ln\_isf}) ; 53 \item the addition of isf melting as lateral inflow (parameterisation) (\np{nn\_isf}~=~2 or 3 and \np{ln\_isfcav}~=~false) 54 or as fluxes applied at the land-ice ocean interface (\np{nn\_isf}~=~1 or 4 and \np{ln\_isfcav}~=~true) ; 54 55 \item the addition of a freshwater flux adjustment in order to avoid a mean sea-level drift (\np{nn\_fwb}~=~0,~1~or~2) ; 55 56 \item the transformation of the solar radiation (if provided as daily mean) into a diurnal cycle (\np{ln\_dm2dc}~=~true) ; … … 128 129 The ocean model provides, at each time step, to the surface module (\mdl{sbcmod}) 129 130 the surface currents, temperature and salinity. 130 These variables are averaged over \np{n f\_sbc} time-step (\ref{Tab_ssm}),131 These variables are averaged over \np{nn\_fsbc} time-step (\ref{Tab_ssm}), 131 132 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.133 at a frequency of \np{nn\_fsbc} time-step. 133 134 134 135 … … 144 145 \caption{ \label{Tab_ssm} 145 146 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.}147 The variable are averaged over nn{\_}fsbc time step, 148 $i.e.$ the frequency of computation of surface fluxes.} 148 149 \end{center} \end{table} 149 150 %-------------------------------------------------------------------------------------------------------------- … … 557 558 reanalysis and satellite data. They use an inertial dissipative method to compute 558 559 the turbulent transfer coefficients (momentum, sensible heat and evaporation) 559 from the 10 met rewind speed, air temperature and specific humidity.560 from the 10 meters wind speed, air temperature and specific humidity. 560 561 This \citet{Large_Yeager_Rep04} dataset is available through the 561 562 \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/CORE.html}{GFDL web site}. … … 592 593 or larger than the one of the input atmospheric fields. 593 594 595 The \np{sn\_wndi}, \np{sn\_wndj}, \np{sn\_qsr}, \np{sn\_qlw}, \np{sn\_tair}, \np{sn\_humi}, 596 \np{sn\_prec}, \np{sn\_snow}, \np{sn\_tdif} parameters describe the fields 597 and the way they have to be used (spatial and temporal interpolations). 598 599 \np{cn\_dir} is the directory of location of bulk files 600 \np{ln\_taudif} is the flag to specify if we use Hight Frequency (HF) tau information (.true.) or not (.false.) 601 \np{rn\_zqt}: is the height of humidity and temperature measurements (m) 602 \np{rn\_zu}: is the height of wind measurements (m) 603 604 Three multiplicative factors are availables : 605 \np{rn\_pfac} and \np{rn\_efac} allows to adjust (if necessary) the global freshwater budget 606 by increasing/reducing the precipitations (total and snow) and or evaporation, respectively. 607 The third one,\np{rn\_vfac}, control to which extend the ice/ocean velocities are taken into account 608 in the calculation of surface wind stress. Its range should be between zero and one, 609 and it is recommended to set it to 0. 610 594 611 % ------------------------------------------------------------------------------------------------------------- 595 612 % CLIO Bulk formulea … … 926 943 \begin{description} 927 944 \item[\np{nn\_isf}~=~1] 928 The ice shelf cavit y is represented (\np{ln\_isfcav}~=~true needed). The fwf and heat flux are computed. Two different bulk formula are available:945 The ice shelf cavities are explicitly represented. The fwf and heat flux are computed. Two different bulk formula are available: 929 946 \begin{description} 930 947 \item[\np{nn\_isfblk}~=~1] … … 934 951 \item[\np{nn\_isfblk}~=~2] 935 952 The bulk formula used to compute the melt is based the one described in \citet{Jenkins1991}. 936 This formulation is based on a 3 equations formulation (a heat flux budget, a salt flux budget 937 and a linearised freezing point temperature equation). 953 This formulation is based on a 3 equations formulation (a heat flux budget, a salt flux budget and a linearised freezing point temperature equation). 938 954 \end{description} 939 955 … … 971 987 972 988 \item[\np{nn\_isf}~=~4] 973 The ice shelf cavity is opened (\np{ln\_isfcav}~=~true needed). However, the fwf is not computed but specified from file \np{sn\_fwfisf}).989 The ice shelf cavity is opened. However, the fwf is not computed but specified from file \np{sn\_fwfisf}). 974 990 The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.\\ 975 991 \end{description} … … 984 1000 coarse to have realistic melting or for studies where you need to control your heat and fw input.\\ 985 1001 986 A namelist parameters control over how many meters the heat and fw fluxes are spread. 987 \np{rn\_hisf\_tbl}] is the top boundary layer thickness as defined in \citet{Losch2008}. 1002 Two namelist parameters control how the heat and fw fluxes are passed to NEMO: \np{rn\_hisf\_tbl} and \np{ln\_divisf} 1003 \begin{description} 1004 \item[\np{rn\_hisf\_tbl}] is the top boundary layer thickness as defined in \citet{Losch2008}. 988 1005 This parameter is only used if \np{nn\_isf}~=~1 or \np{nn\_isf}~=~4 1006 It allows you to control over which depth you want to spread the heat and fw fluxes. 989 1007 990 1008 If \np{rn\_hisf\_tbl} = 0.0, the fluxes are put in the top level whatever is its tickness. 991 1009 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).\\ 993 994 The ice shelf melt is implemented as a volume flux with in the same way as for the runoff. 1010 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). 1011 1012 \item[\np{ln\_divisf}] is a flag to apply the fw flux as a volume flux or as a salt flux. 1013 1014 \np{ln\_divisf}~=~true applies the fwf as a volume flux. This volume flux is implemented with in the same way as for the runoff. 995 1015 The fw addition due to the ice shelf melting is, at each relevant depth level, added to the horizontal divergence 996 1016 (\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div}, called from \mdl{divcur}. 997 1017 See the runoff section \ref{SBC_rnf} for all the details about the divergence correction. 998 1018 999 1000 \section{ Ice sheet coupling} 1001 \label{SBC_iscpl} 1002 %------------------------------------------namsbc_iscpl---------------------------------------------------- 1003 \namdisplay{namsbc_iscpl} 1004 %-------------------------------------------------------------------------------------------------------- 1005 Ice sheet/ocean coupling is done through file exchange at the restart step. NEMO, at each restart step, 1006 read the bathymetry and ice shelf draft variable in a netcdf file. 1007 If \np{ln\_iscpl = ~true}, the isf draft is assume to be different at each restart step 1008 with potentially some new wet/dry cells due to the ice sheet dynamics/thermodynamics. 1009 The wetting and drying scheme applied on the restart is very simple and described below for the 6 different cases: 1010 \begin{description} 1011 \item[Thin a cell down:] 1012 T/S/ssh are unchanged and U/V in the top cell are corrected to keep the barotropic transport (bt) constant ($bt_b=bt_n$). 1013 \item[Enlarge a cell:] 1014 See case "Thin a cell down" 1015 \item[Dry a cell:] 1016 mask, T/S, U/V and ssh are set to 0. Furthermore, U/V into the water column are modified to satisfy ($bt_b=bt_n$). 1017 \item[Wet a cell:] 1018 mask is set to 1, T/S is extrapolated from neighbours, $ssh_n = ssh_b$ and U/V set to 0. If no neighbours along i,j and k, T/S/U/V and mask are set to 0. 1019 \item[Dry a column:] 1020 mask, T/S, U/V are set to 0 everywhere in the column and ssh set to 0. 1021 \item[Wet a column:] 1022 set mask to 1, T/S is extrapolated from neighbours, ssh is extrapolated from neighbours and U/V set to 0. If no neighbour, T/S/U/V and mask set to 0. 1019 \np{ln\_divisf}~=~false applies the fwf and heat flux directly on the salinity and temperature tendancy. 1020 1021 \item[\np{ln\_conserve}] is a flag for \np{nn\_isf}~=~1. A conservative boundary layer scheme as described in \citet{Jenkins2001} 1022 is used if \np{ln\_conserve}=true. It takes into account the fact that the melt water is at freezing T and needs to be warm up to ocean temperature. 1023 It is only relevant for \np{ln\_divisf}~=~false. 1024 If \np{ln\_divisf}~=~true, \np{ln\_conserve} has to be set to false to avoid a double counting of the contribution. 1025 1023 1026 \end{description} 1024 The extrapolation is call \np{nn\_drown} times. It means that if the grounding line retreat by more than \np{nn\_drown} cells between 2 coupling steps,1025 the code will be unable to fill all the new wet cells properly. The default number is set up for the MISOMIP idealised experiments.\\1026 This coupling procedure is able to take into account grounding line and calving front migration. However, it is a non-conservative processe.1027 This could lead to a trend in heat/salt content and volume. In order to remove the trend and keep the conservation level as close to 0 as possible,1028 a simple conservation scheme is available with \np{ln\_hsb = ~true}. The heat/salt/vol. gain/loss is diagnose, as well as the location.1029 Based on what is done on sbcrnf to prescribed a source of heat/salt/vol., the heat/salt/vol. gain/loss is removed/added,1030 over a period of \np{rn\_fiscpl} time step, into the system.1031 So after \np{rn\_fiscpl} time step, all the heat/salt/vol. gain/loss due to extrapolation process is canceled.\\1032 1033 As the before and now fields are not compatible (modification of the geometry), the restart time step is prescribed to be an euler time step instead of a leap frog and $fields_b = fields_n$.1034 1027 % 1035 1028 % ================================================================ -
branches/2016/dev_r6325_SIMPLIF_1/DOC/TexFiles/Chapters/Chap_STO.tex
r6289 r6347 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. -
branches/2016/dev_r6325_SIMPLIF_1/DOC/TexFiles/Chapters/Chap_TRA.tex
r6320 r6347 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 horizontally 1388 adjacent cells live at different depths. Horizontal gradients of tracers are needed 1389 for horizontal diffusion (\mdl{traldf} module) and for the hydrostatic pressure 1390 gradient (\mdl{dynhpg} module) to be active. The partial cell properties 1391 at the top (\np{ln\_isfcav}=true) are computed in the same way as for the bottom. So, only the bottom interpolation is shown. 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 for the hydrostatic pressure gradient (\mdl{dynhpg} module) to be active. 1392 1399 \gmcomment{STEVEN from gm : question: not sure of what -to be active- means} 1393 1394 1400 Before taking horizontal gradients between the tracers next to the bottom, a linear 1395 1401 interpolation in the vertical is used to approximate the deeper tracer as if it actually … … 1467 1473 \gmcomment{gm : this last remark has to be done} 1468 1474 %%% 1475 1476 If under ice shelf seas opened (\np{ln\_isfcav}=true), the partial cell properties 1477 at the top are computed in the same way as for the bottom. Some extra variables are, 1478 however, computed to reduce the flow generated at the top and bottom if $z*$ coordinates activated. 1479 The extra variables calculated and used by \S\ref{DYN_hpg_isf} are: 1480 1481 $\bullet$ $\overline{T}_k^{\,i+1/2}$ as described in \eqref{Eq_zps_hde} 1482 1483 $\bullet$ $\delta _{i+1/2} Z_{T_k} = \widetilde {Z}^{\,i}_{T_k}-Z^{\,i}_{T_k}$ to compute 1484 the pressure gradient correction term used by \eqref{Eq_dynhpg_sco} in \S\ref{DYN_hpg_isf}, 1485 with $\widetilde {Z}_{T_k}$ the depth of the point $\widetilde {T}_{k}$ in case of $z^*$ coordinates 1486 (this term = 0 in z-coordinates) -
branches/2016/dev_r6325_SIMPLIF_1/DOC/TexFiles/Chapters/Chap_ZDF.tex
r6320 r6347 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 represented similarly, 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 -
branches/2016/dev_r6325_SIMPLIF_1/DOC/TexFiles/clean.sh
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