Changeset 14113 for NEMO/trunk/doc/latex/NEMO/subfiles/chap_SBC.tex
 Timestamp:
 20201204T20:15:58+01:00 (2 years ago)
 File:

 1 edited
Legend:
 Unmodified
 Added
 Removed

NEMO/trunk/doc/latex/NEMO/subfiles/chap_SBC.tex
r13916 r14113 1 1 \documentclass[../main/NEMO_manual]{subfiles} 2 \usepackage{fontspec}3 \usepackage{fontawesome}4 2 5 3 \begin{document} … … 526 524 See \autoref{subsec:SBC_ssr} for its specification. 527 525 528 529 530 531 532 533 534 %% ================================================================================================= 535 \pagebreak 536 \newpage 526 %% ================================================================================================= 537 527 \section[Bulk formulation (\textit{sbcblk.F90})]{Bulk formulation (\protect\mdl{sbcblk})} 538 528 \label{sec:SBC_blk} … … 558 548 559 549 Note: all the NEMO Fortran routines involved in the present section have been 560 561 the \href{https://brodeau.github.io/aerobulk/}{\texttt{AeroBulk}} opensource project562 \citep{brodeau.barnier.ea_JPO1 7}.550 initially developed (and are still developed in parallel) in 551 the \href{https://brodeau.github.io/aerobulk}{\texttt{AeroBulk}} opensource project 552 \citep{brodeau.barnier.ea_JPO16}. 563 553 564 554 %%% Bulk formulae are this: 565 \subsection{Bulk formulae}\label{subsec:SBC_blkform} 566 % 555 \subsection{Bulk formulae} 556 \label{subsec:SBC_blkform} 557 567 558 In NEMO, the set of equations that relate each component of the surface fluxes 568 559 to the nearsurface atmosphere and sea surface states writes 569 % 570 \begin{subequations}\label{eq_bulk} 560 561 \begin{subequations} 562 \label{eq:SBC_bulk} 571 563 \label{eq:SBC_bulk_form} 572 \begin{eqnarray} 573 \mathbf{\tau} &=& \rho~ C_D ~ \mathbf{U}_z ~ U_B \\ 574 Q_H &=& \rho~C_H~C_P~\big[ \theta_z  T_s \big] ~ U_B \\ 575 E &=& \rho~C_E ~\big[ q_s  q_z \big] ~ U_B \\ 576 Q_L &=& L_v \, E \\ 577 % 578 Q_{sr} &=& (1  a) Q_{sw\downarrow} \\ 579 Q_{ir} &=& \delta (Q_{lw\downarrow} \sigma T_s^4) 580 \end{eqnarray} 564 \begin{align} 565 \mathbf{\tau} &= \rho~ C_D ~ \mathbf{U}_z ~ U_B \\ 566 Q_H &= \rho~C_H~C_P~\big[ \theta_z  T_s \big] ~ U_B \\ 567 E &= \rho~C_E ~\big[ q_s  q_z \big] ~ U_B \\ 568 Q_L &= L_v \, E \\ 569 Q_{sr} &= (1  a) Q_{sw\downarrow} \\ 570 Q_{ir} &= \delta (Q_{lw\downarrow} \sigma T_s^4) 571 \end{align} 581 572 \end{subequations} 582 % 573 583 574 with 584 575 \[ \theta_z \simeq T_z+\gamma z \] 585 576 \[ q_s \simeq 0.98\,q_{sat}(T_s,p_a ) \] 586 %587 577 from which, the the nonsolar heat flux is \[ Q_{ns} = Q_L + Q_H + Q_{ir} \] 588 %589 578 where $\mathbf{\tau}$ is the wind stress vector, $Q_H$ the sensible heat flux, 590 579 $E$ the evaporation, $Q_L$ the latent heat flux, and $Q_{ir}$ the net longwave 591 580 flux. 592 %593 581 $Q_{sw\downarrow}$ and $Q_{lw\downarrow}$ are the surface downwelling shortwave 594 582 and longwave radiative fluxes, respectively. 595 %596 583 Note: a positive sign for $\mathbf{\tau}$, $Q_H$, $Q_L$, $Q_{sr}$ or $Q_{ir}$ 597 584 implies a gain of the relevant quantity for the ocean, while a positive $E$ 598 585 implies a freshwater loss for the ocean. 599 %600 586 $\rho$ is the density of air. $C_D$, $C_H$ and $C_E$ are the bulk transfer 601 587 coefficients for momentum, sensible heat, and moisture, respectively. 602 %603 588 $C_P$ is the heat capacity of moist air, and $L_v$ is the latent heat of 604 589 vaporization of water. 605 %606 590 $\theta_z$, $T_z$ and $q_z$ are the potential temperature, absolute temperature, 607 591 and specific humidity of air at height $z$ above the sea surface, 608 592 respectively. $\gamma z$ is a temperature correction term which accounts for the 609 593 adiabatic lapse rate and approximates the potential temperature at height 610 $z$ \citep{josey.gulev.ea_2013}. 611 % 594 $z$ \citep{josey.gulev.ea_OCC13}. 612 595 $\mathbf{U}_z$ is the wind speed vector at height $z$ above the sea surface 613 (possibly referenced to the surface current $\mathbf{u_0}$, 614 section \ref{s_res1}.\ref{ss_current}). 615 % 596 (possibly referenced to the surface current $\mathbf{u_0}$).%, 597 %\autoref{s_res1}.\autoref{ss_current}). %% Undefined references 616 598 The bulk scalar wind speed, namely $U_B$, is the scalar wind speed, 617 599 $\mathbf{U}_z$, with the potential inclusion of a gustiness contribution. 618 %619 600 $a$ and $\delta$ are the albedo and emissivity of the sea surface, respectively.\\ 620 %621 601 %$p_a$ is the mean sealevel pressure (SLP). 622 %623 602 $T_s$ is the sea surface temperature. $q_s$ is the saturation specific humidity 624 603 of air at temperature $T_s$; it includes a 2\% reduction to account for the 625 presence of salt in seawater \citep{sverdrup.johnson.ea_ 1942,kraus.businger_QJRMS96}.604 presence of salt in seawater \citep{sverdrup.johnson.ea_bk42,kraus.businger_QJRMS96}. 626 605 Depending on the bulk parametrization used, $T_s$ can either be the temperature 627 606 at the airsea interface (skin temperature, hereafter SSST) or at typically a 628 607 few tens of centimeters below the surface (bulk sea surface temperature, 629 608 hereafter SST). 630 %631 609 The SSST differs from the SST due to the contributions of two effects of 632 610 opposite sign, the \emph{cool skin} and \emph{warm layer} (hereafter CS and WL, 633 respectively, see section\,\ref{subsec:SBC_skin}). 634 % 611 respectively, see \autoref{subsec:SBC_skin}). 635 612 Technically, when the ECMWF or COARE* bulk parametrizations are selected 636 613 (\np[=.true.]{ln_ECMWF}{ln\_ECMWF} or \np[=.true.]{ln_COARE*}{ln\_COARE\*}), … … 640 617 641 618 For more details on all these aspects the reader is invited to refer 642 to \citet{brodeau.barnier.ea_JPO17}. 643 644 645 646 \subsection{Bulk parametrizations}\label{subsec:SBC_blk_ocean} 619 to \citet{brodeau.barnier.ea_JPO16}. 620 621 \subsection{Bulk parametrizations} 622 \label{subsec:SBC_blk_ocean} 647 623 %%%\label{subsec:SBC_param} 648 624 … … 654 630 height (from \np{rn_zqt}{rn\_zqt} to \np{rn_zu}{rn\_zu}). 655 631 656 657 658 632 For the open ocean, four bulk parametrization algorithms are available in NEMO: 633 659 634 \begin{itemize} 660 \item NCAR, formerly known as CORE, \citep{large.yeager_ rpt04,large.yeager_CD09}635 \item NCAR, formerly known as CORE, \citep{large.yeager_trpt04,large.yeager_CD09} 661 636 \item COARE 3.0 \citep{fairall.bradley.ea_JC03} 662 637 \item COARE 3.6 \citep{edson.jampana.ea_JPO13} … … 664 639 \end{itemize} 665 640 666 667 641 With respect to version 3, the principal advances in version 3.6 of the COARE 668 642 bulk parametrization are built around improvements in the representation of the 669 643 effects of waves on 670 fluxes \citep{edson.jampana.ea_JPO13,brodeau.barnier.ea_JPO1 7}. This includes644 fluxes \citep{edson.jampana.ea_JPO13,brodeau.barnier.ea_JPO16}. This includes 671 645 improved relationships of surface roughness, and whitecap fraction on wave 672 646 parameters. It is therefore recommended to chose version 3.6 over 3. 673 647 674 675 676 677 \subsection{Coolskin and warmlayer parametrizations}\label{subsec:SBC_skin} 678 %\subsection[Coolskin and warmlayer parameterizations 679 %(\forcode{ln_skin_cs} \& \forcode{ln_skin_wl})]{Coolskin and warmlayer parameterizations (\protect\np{ln_skin_cs}{ln\_skin\_cs} \& \np{ln_skin_wl}{ln\_skin\_wl})} 680 %\label{subsec:SBC_skin} 681 % 648 \subsection{Coolskin and warmlayer parametrizations} 649 %\subsection[Coolskin and warmlayer parameterizations (\forcode{ln_skin_cs} \& \forcode{ln_skin_wl})]{Coolskin and warmlayer parameterizations (\protect\np{ln_skin_cs}{ln\_skin\_cs} \& \np{ln_skin_wl}{ln\_skin\_wl})} 650 \label{subsec:SBC_skin} 651 682 652 As opposed to the NCAR bulk parametrization, more advanced bulk 683 653 parametrizations such as COARE3.x and ECMWF are meant to be used with the skin 684 654 temperature $T_s$ rather than the bulk SST (which, in NEMO is the temperature at 685 the first Tpoint level, see section\,\ref{subsec:SBC_blkform}).686 % 655 the first Tpoint level, see \autoref{subsec:SBC_blkform}). 656 687 657 As such, the relevant coolskin and warmlayer parametrization must be 688 658 activated through \np[=T]{ln_skin_cs}{ln\_skin\_cs} … … 693 663 694 664 For the coolskin scheme parametrization COARE and ECMWF algorithms share the same 695 basis: \citet{fairall.bradley.ea_JGR 96}. With some minor updates based665 basis: \citet{fairall.bradley.ea_JGRO96}. With some minor updates based 696 666 on \citet{zeng.beljaars_GRL05} for ECMWF, and \citet{fairall.ea_19} for COARE 697 667 3.6. … … 704 674 equation for the thickness of the warmlayer, while it is considered as constant 705 675 in the ECWMF algorithm. 706 707 676 708 677 \subsection{Appropriate use of each bulk parametrization} … … 714 683 temperature is the bulk SST. Hence the following namelist parameters must be 715 684 set: 716 % 717 \begin{ verbatim}685 686 \begin{forlines} 718 687 ... 719 688 ln_NCAR = .true. … … 726 695 ... 727 696 ln_humi_sph = .true. ! humidity "sn_humi" is specific humidity [kg/kg] 728 \end{verbatim} 729 697 \end{forlines} 730 698 731 699 \subsubsection{ECMWF} 732 % 700 733 701 With an atmospheric forcing based on a reanalysis of the ECMWF, such as the 734 702 Drakkar Forcing Set \citep{brodeau.barnier.ea_OM10}, we strongly recommend to … … 737 705 humidity are provided at the 2\,m height, and given that the humidity is 738 706 distributed as the dewpoint temperature, the namelist must be tuned as follows: 739 % 740 \begin{ verbatim}707 708 \begin{forlines} 741 709 ... 742 710 ln_ECMWF = .true. … … 750 718 ln_humi_dpt = .true. ! humidity "sn_humi" is dewpoint temperature [K] 751 719 ... 752 \end{ verbatim}753 % 720 \end{forlines} 721 754 722 Note: when \np{ln_ECMWF}{ln\_ECMWF} is selected, the selection 755 723 of \np{ln_skin_cs}{ln\_skin\_cs} and \np{ln_skin_wl}{ln\_skin\_wl} implicitly … … 757 725 respectively (found in \textit{sbcblk\_skin\_ecmwf.F90}). 758 726 759 760 727 \subsubsection{COARE 3.x} 761 % 728 762 729 Since the ECMWF parametrization is largely based on the COARE* parametrization, 763 730 the two algorithms are very similar in terms of structure and closure 764 731 approach. As such, the namelist tuning for COARE 3.x is identical to that of 765 732 ECMWF: 766 % 767 \begin{ verbatim}733 734 \begin{forlines} 768 735 ... 769 736 ln_COARE3p6 = .true. … … 772 739 ln_skin_wl = .true. ! use the warmlayer parameterization 773 740 ... 774 \end{ verbatim}741 \end{forlines} 775 742 776 743 Note: when \np[=T]{ln_COARE3p0}{ln\_COARE3p0} is selected, the selection … … 779 746 respectively (found in \textit{sbcblk\_skin\_coare.F90}). 780 747 781 782 748 %lulu 783 784 785 749 786 750 % In a typical bulk algorithm, the BTCs under neutral stability conditions are … … 792 756 % and $q_z$. 793 757 794 795 796 758 \subsection{Prescribed nearsurface atmospheric state} 797 759 … … 800 762 different bulk formulae are used for the turbulent fluxes computation over the 801 763 ocean and over seaice surface. 802 %803 764 804 765 %The choice is made by setting to true one of the following namelist … … 862 823 the namsbc\_blk namelist (see \autoref{subsec:SBC_fldread}). 863 824 864 865 825 \subsubsection{Air humidity} 866 826 … … 868 828 [kg/kg], relative humidity [\%], or dewpoint temperature [K] (LINK to namelist 869 829 parameters)... 870 871 872 ~\\873 874 875 876 877 878 879 880 881 882 830 883 831 %% ================================================================================================= … … 889 837 %their neutral transfer coefficients relationships with neutral wind. 890 838 %\begin{itemize} 891 %\item NCAR (\np[=.true.]{ln_NCAR}{ln\_NCAR}): The NCAR bulk formulae have been developed by \citet{large.yeager_ rpt04}.839 %\item NCAR (\np[=.true.]{ln_NCAR}{ln\_NCAR}): The NCAR bulk formulae have been developed by \citet{large.yeager_trpt04}. 892 840 % They have been designed to handle the NCAR forcing, a mixture of NCEP reanalysis and satellite data. 893 841 % They use an inertial dissipative method to compute the turbulent transfer coefficients 894 842 % (momentum, sensible heat and evaporation) from the 10m wind speed, air temperature and specific humidity. 895 % This \citet{large.yeager_ rpt04} dataset is available through843 % This \citet{large.yeager_trpt04} dataset is available through 896 844 % the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/NCAR.html}{GFDL web site}. 897 845 % Note that substituting ERA40 to NCEP reanalysis fields does not require changes in the bulk formulea themself. … … 908 856 \label{subsec:SBC_blk_ice} 909 857 910 911 858 \texttt{\#out\_of\_place:} 912 859 For seaice, three possibilities can be selected: 913 860 a constant transfer coefficient (1.4e3; default 914 value), \citet{lupkes.gryanik.ea_JGR 12} (\np{ln_Cd_L12}{ln\_Cd\_L12}),861 value), \citet{lupkes.gryanik.ea_JGRA12} (\np{ln_Cd_L12}{ln\_Cd\_L12}), 915 862 and \citet{lupkes.gryanik_JGR15} (\np{ln_Cd_L15}{ln\_Cd\_L15}) parameterizations 916 863 \texttt{\#out\_of\_place.} 917 864 918 919 920 921 865 Surface turbulent fluxes between seaice and the atmosphere can be computed in three different ways: 922 866 923 867 \begin{itemize} 924 \item Constant value (\ np[ Cd_ice=1.4e3 ]{constant value}{constant\ value}):868 \item Constant value (\forcode{Cd_ice=1.4e3}): 925 869 default constant value used for momentum and heat neutral transfer coefficients 926 \item \citet{lupkes.gryanik.ea_JGR 12} (\np[=.true.]{ln_Cd_L12}{ln\_Cd\_L12}):870 \item \citet{lupkes.gryanik.ea_JGRA12} (\np[=.true.]{ln_Cd_L12}{ln\_Cd\_L12}): 927 871 This scheme adds a dependency on edges at leads, melt ponds and flows 928 872 of the constant neutral airice drag. After some approximations, … … 1260 1204 \begin{description} 1261 1205 \item [{\np[=1]{nn_isfblk}{nn\_isfblk}}]: The melt rate is based on a balance between the upward ocean heat flux and 1262 the latent heat flux at the ice shelf base. A complete description is available in \citet{hunter_ rpt06}.1206 the latent heat flux at the ice shelf base. A complete description is available in \citet{hunter_trpt06}. 1263 1207 \item [{\np[=2]{nn_isfblk}{nn\_isfblk}}]: The melt rate and the heat flux are based on a 3 equations formulation 1264 1208 (a heat flux budget at the ice base, a salt flux budget at the ice base and a linearised freezing point temperature equation). … … 1332 1276 The fw addition due to the ice shelf melting is, at each relevant depth level, added to 1333 1277 the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div}, called from \mdl{divhor}. 1334 See the runoff section \autoref{sec:SBC_rnf} for all the details about the divergence correction.\\1278 See \autoref{sec:SBC_rnf} for all the details about the divergence correction. 1335 1279 1336 1280 \begin{figure}[!t] … … 1503 1447 Then using the routine \rou{sbcblk\_algo\_ncar} and starting from the neutral drag coefficent provided, 1504 1448 the drag coefficient is computed according to the stable/unstable conditions of the 1505 airsea interface following \citet{large.yeager_ rpt04}.1449 airsea interface following \citet{large.yeager_trpt04}. 1506 1450 1507 1451 %% ================================================================================================= … … 1614 1558 1615 1559 The surface stress felt by the ocean is the atmospheric stress minus the net stress going 1616 into the waves \citep{janssen.breivik.ea_ rpt13}. Therefore, when waves are growing, momentum and energy is spent and is not1560 into the waves \citep{janssen.breivik.ea_trpt13}. Therefore, when waves are growing, momentum and energy is spent and is not 1617 1561 available for forcing the mean circulation, while in the opposite case of a decaying sea 1618 1562 state, more momentum is available for forcing the ocean.
Note: See TracChangeset
for help on using the changeset viewer.