Changeset 12019 for NEMO/branches/2019/dev_r11085_ASINTER-05_Brodeau_Advanced_Bulk/doc/latex/NEMO/subfiles/chap_SBC.tex
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NEMO/branches/2019/dev_r11085_ASINTER-05_Brodeau_Advanced_Bulk/doc/latex/NEMO/subfiles/chap_SBC.tex
r11831 r12019 1 1 \documentclass[../main/NEMO_manual]{subfiles} 2 \usepackage{fontspec} 3 \usepackage{fontawesome} 2 4 3 5 \begin{document} … … 504 506 \label{sec:SBC_flx} 505 507 508 % Laurent: DO NOT mix up ``bulk formulae'' (the classic equation) and the ``bulk 509 % parameterization'' (i.e NCAR, COARE, ECMWF...) 510 506 511 \begin{listing} 507 512 \nlst{namsbc_flx} … … 520 525 See \autoref{subsec:SBC_ssr} for its specification. 521 526 522 %% ================================================================================================= 527 528 529 530 531 532 533 %% ================================================================================================= 534 \pagebreak 535 \newpage 523 536 \section[Bulk formulation (\textit{sbcblk.F90})]{Bulk formulation (\protect\mdl{sbcblk})} 524 537 \label{sec:SBC_blk} … … 530 543 \end{listing} 531 544 532 In the bulk formulation, the surface boundary condition fields are computed with bulk formulae using atmospheric fields 533 and ocean (and sea-ice) variables averaged over \np{nn_fsbc}{nn\_fsbc} time-step. 534 535 The atmospheric fields used depend on the bulk formulae used. 536 In forced mode, when a sea-ice model is used, a specific bulk formulation is used. 537 Therefore, different bulk formulae are used for the turbulent fluxes computation 538 over the ocean and over sea-ice surface. 539 For the ocean, four bulk formulations are available thanks to the \href{https://brodeau.github.io/aerobulk/}{Aerobulk} package (\citet{brodeau.barnier.ea_JPO16}): 540 the NCAR (formerly named CORE), COARE 3.0, COARE 3.5 and ECMWF bulk formulae. 541 The choice is made by setting to true one of the following namelist variable: 542 \np{ln_NCAR}{ln\_NCAR}, \np{ln_COARE_3p0}{ln\_COARE\_3p0}, \np{ln_COARE_3p5}{ln\_COARE\_3p5} and \np{ln_ECMWF}{ln\_ECMWF}. 543 For sea-ice, three possibilities can be selected: 544 a constant transfer coefficient (1.4e-3; default value), \citet{lupkes.gryanik.ea_JGR12} (\np{ln_Cd_L12}{ln\_Cd\_L12}), and \citet{lupkes.gryanik_JGR15} (\np{ln_Cd_L15}{ln\_Cd\_L15}) parameterizations 545 In the bulk formulation, the surface boundary condition fields are computed with 546 bulk formulae using prescribed atmospheric fields and prognostic ocean (and 547 sea-ice) surface variables averaged over \np{nn_fsbc}{nn\_fsbc} time-step. 548 549 % Turbulent air-sea fluxes are computed using the sea surface properties and 550 % atmospheric SSVs at height $z$ above the sea surface, with the traditional 551 % aerodynamic bulk formulae: 552 553 554 %%% Bulk formulae are this: 555 \subsection{Bulk formulae} 556 % 557 In NEMO, when the bulk formulation is selected, surface fluxes are computed by means of the traditional bulk formulae: 558 % 559 \begin{subequations}\label{eq_bulk} 560 \begin{eqnarray} 561 \mathbf{\tau} &=& \rho~ C_D ~ \mathbf{U}_z ~ U_B \label{eq_b_t} \\ 562 Q_H &=& \rho~C_H~C_P~\big[ \theta_z - T_s \big] ~ U_B \label{eq_b_qh} \\ 563 E &=& \rho~C_E ~\big[ q_s - q_z \big] ~ U_B \label{eq_b_e} \\ 564 Q_L &=& -L_v \, E \label{eq_b_qe} \\ 565 % 566 Q_{sr} &=& (1 - a) Q_{sw\downarrow} \\ 567 Q_{ir} &=& \delta (Q_{lw\downarrow} -\sigma T_s^4) 568 \end{eqnarray} 569 \end{subequations} 570 %lulu 571 % 572 From which, the the non-solar heat flux is \[ Q_{ns} = Q_L + Q_H + Q_{ir} \] 573 % 574 \[ \theta_z \simeq T_z+\gamma z \] 575 \[ q_s \simeq 0.98\,q_{sat}(T_s,p_a ) \] 576 577 578 579 where $\mathbf{\tau}$ is the wind stress vector, $Q_H$ the sensible heat flux, 580 $E$ the evaporation, $Q_L$ the latent heat flux, and $Q_{ir}$ the net longwave 581 flux. 582 % 583 $Q_{sw\downarrow}$ and $Q_{lw\downarrow}$ are the surface downwelling shortwave 584 and longwave radiative fluxes, respectively. 585 % 586 Note: a positive sign of $\mathbf{\tau}$, $Q_H$, and $Q_L$ means a gain of the 587 relevant quantity for the ocean, while a positive $E$ implies a freshwater loss 588 for the ocean. 589 % 590 $\rho$ is the density of air. $C_D$, $C_H$ and $C_E$ are the BTCs for momentum, 591 sensible heat, and moisture, respectively. $C_P$ is the heat capacity of moist 592 air, and $L_v$ is the latent heat of vaporization of water. $\theta_z$, $T_z$ 593 and $q_z$ are the potential temperature, temperature, and specific humidity of 594 air at height $z$, respectively. $\gamma z$ is a temperature correction term 595 which accounts for the adiabatic lapse rate and approximates the potential 596 temperature at height $z$ \citep{Josey_al_2013}. $\mathbf{U}_z$ is the wind 597 speed vector at height $z$ (possibly referenced to the surface current 598 $\mathbf{u_0}$, section \ref{s_res1}.\ref{ss_current}). The bulk scalar wind 599 speed, $U_B$, is the scalar wind speed, $|\mathbf{U}_z|$, with the potential 600 inclusion of a gustiness contribution (section 601 \ref{s_res2}.\ref{ss_calm}). 602 $P_0$ is the mean sea-level pressure (SLP). 603 $T_s$ is the sea surface temperature. $q_s$ is the saturation specific humidity 604 of air at temperature $T_s$ and includes a 2\% reduction to account for the 605 presence of salt in seawater \citep{Sverdrup_al_1942,Kraus_Businger_1996}. 606 Depending on the bulk parameterization used, $T_s$ can be the temperature at the 607 air-sea interface (skin temperature, hereafter SSST) or at a few tens of 608 centimeters below the surface (bulk sea surface temperature, hereafter SST). 609 The SSST differs from the SST due to the contributions of two effects of 610 opposite sign, the \emph{cool skin} and \emph{warm layer} (hereafter CSWL). The 611 \emph{cool skin} refers to the cooling of the millimeter-scale uppermost layer 612 of the ocean, in which the net upward flux of heat to the atmosphere is 613 ineffectively sustained by molecular diffusion. As such, a steep vertical 614 gradient of temperature must exist to ensure the heat flux continuity with 615 underlying layers in which the same flux is sustained by turbulence. 616 The \emph{warm layer} refers to the warming of the upper few meters of the ocean 617 under sunny conditions. 618 The CSWL effects are most significant under weak wind conditions due to the 619 absence of substancial surface vertical mixing (caused by \eg breaking waves). 620 The impact of the CSWL on the computed TASFs is discussed in section 621 \ref{s_res1}.\ref{ss_skin}. 622 623 624 %%%% Second set of equations (rad): 625 where $a$ and $\delta$ are the albedo and emissivity of the sea surface, 626 respectively. 627 Thus, we use the computed $Q_L$ and $Q_H$ and the 3-hourly surface downwelling 628 shortwave and longwave radiative fluxes ($Q_{sw\downarrow}$ and 629 $Q_{lw\downarrow}$, respectively) from ERA-Interim to correct the daily SST 630 every 3 hours. Due to the implicitness of the problem implied by the dependence 631 of $Q_{nsol}$ on $T_s$, this correction is done iteratively during the 632 computation of the TASFs. 633 634 635 \subsection{Bulk parameterizations} 636 637 Accuracy of the estimate of surface turbulent fluxes by means of bulk formulae 638 strongly relies on that of the bulk transfer coefficients: $C_D$, $C_H$ and 639 $C_E$. They are estimated with what we refer to as a \emph{bulk 640 parameterization} algorithm. 641 642 ... also to adjust humidity and temperature of air to the wind reference measurement 643 height (generally 10\,m). 644 645 Over the open ocean, four bulk parameterization algorithms are available: 646 \begin{itemize} 647 \item NCAR, formerly known as CORE, \citep{large.yeager_rpt04} 648 \item COARE 3.0 \citep{fairall.bradley.ea_JC03} 649 \item COARE 3.6 \citep{edson.jampana.ea_JPO13} 650 \item ECMWF (IFS documentation, cy41) 651 \end{itemize} 652 653 ~ 654 655 % In a typical bulk algorithm, the BTCs under neutral stability conditions are 656 % defined using \emph{in-situ} flux measurements while their dependence on the 657 % stability is accounted through the \emph{Monin-Obukhov Similarity Theory} and 658 % the \emph{flux-profile} relationships \citep[\eg{}][]{Paulson_1970}. BTCs are 659 % functions of the wind speed and the near-surface stability of the atmospheric 660 % surface layer (hereafter ASL), and hence, depend on $U_B$, $T_s$, $T_z$, $q_s$ 661 % and $q_z$. 662 663 664 665 666 \subsection{Cool-skin and warm-layer parameterizations} 667 668 As oposed to the NCAR bulk parameterization, more advanced bulk 669 parameterizations such as COARE3.x and ECMWF are meant to be used with the skin 670 temperature $T_s$ rather than the bulk SST (which, in NEMO is the temperature at 671 the first T-point level). 672 % 673 So that, technically, the cool-skin and warm-layer parameterization must be 674 activated (XXX) to use COARE3.x and ECMWF in a consistant way. 675 676 677 \subsection{Air humidity} 678 679 Air humidity can be provided as three different parameters: specific humidity 680 [kg/kg], relative humidity [\%], or dew-point temperature [K] (LINK to namelist 681 parameters)... 682 683 684 ~\\ 685 686 687 688 689 The atmospheric fields used depend on the bulk formulae used. In forced mode, 690 when a sea-ice model is used, a specific bulk formulation is used. Therefore, 691 different bulk formulae are used for the turbulent fluxes computation over the 692 ocean and over sea-ice surface. 693 % 694 695 696 thanks to the \href{https://brodeau.github.io/aerobulk/}{Aerobulk} package 697 (\citet{brodeau.barnier.ea_JPO16}): 698 699 The choice is made by setting to true one of the following namelist 700 variable: \np{ln_NCAR}{ln\_NCAR}, \np{ln_COARE_3p0}{ln\_COARE\_3p0}, \np{ln_COARE_3p6}{ln\_COARE\_3p6} 701 and \np{ln_ECMWF}{ln\_ECMWF}. For sea-ice, three possibilities can be selected: 702 a constant transfer coefficient (1.4e-3; default 703 value), \citet{lupkes.gryanik.ea_JGR12} (\np{ln_Cd_L12}{ln\_Cd\_L12}), 704 and \citet{lupkes.gryanik_JGR15} (\np{ln_Cd_L15}{ln\_Cd\_L15}) parameterizations 545 705 546 706 Common options are defined through the \nam{sbc_blk}{sbc\_blk} namelist variables. … … 557 717 j-component of the 10m air velocity & vtau & $m.s^{-1}$ & T \\ 558 718 \hline 559 10m air temperature & tair & \r{}$K$& T \\719 10m air temperature & tair & $K$ & T \\ 560 720 \hline 561 Specific humidity & humi & \% & T \\ 721 Specific humidity & humi & $-$ & T \\ 722 Relative humidity & ~ & $\%$ & T \\ 723 Dew-point temperature & ~ & $K$ & T \\ 562 724 \hline 563 Incoming long wave radiation& qlw & $W.m^{-2}$ & T \\725 Downwelling longwave radiation & qlw & $W.m^{-2}$ & T \\ 564 726 \hline 565 Incoming short wave radiation& qsr & $W.m^{-2}$ & T \\727 Downwelling shortwave radiation & qsr & $W.m^{-2}$ & T \\ 566 728 \hline 567 729 Total precipitation (liquid + solid) & precip & $Kg.m^{-2}.s^{-1}$ & T \\ … … 595 757 Its range must be between zero and one, and it is recommended to set it to 0 at low-resolution (ORCA2 configuration). 596 758 597 As for the flux formulation, information about the input data required by the model is provided in759 As for the flux parameterization, information about the input data required by the model is provided in 598 760 the namsbc\_blk namelist (see \autoref{subsec:SBC_fldread}). 599 761 600 762 %% ================================================================================================= 601 \subsection[Ocean-Atmosphere Bulk formulae (\textit{sbcblk\_algo\_coare.F90, sbcblk\_algo\_coare3p 5.F90, sbcblk\_algo\_ecmwf.F90, sbcblk\_algo\_ncar.F90})]{Ocean-Atmosphere Bulk formulae (\mdl{sbcblk\_algo\_coare}, \mdl{sbcblk\_algo\_coare3p5}, \mdl{sbcblk\_algo\_ecmwf}, \mdl{sbcblk\_algo\_ncar})}763 \subsection[Ocean-Atmosphere Bulk formulae (\textit{sbcblk\_algo\_coare.F90, sbcblk\_algo\_coare3p6.F90, sbcblk\_algo\_ecmwf.F90, sbcblk\_algo\_ncar.F90})]{Ocean-Atmosphere Bulk formulae (\mdl{sbcblk\_algo\_coare}, \mdl{sbcblk\_algo\_coare3p6}, \mdl{sbcblk\_algo\_ecmwf}, \mdl{sbcblk\_algo\_ncar})} 602 764 \label{subsec:SBC_blk_ocean} 603 765 604 766 Four different bulk algorithms are available to compute surface turbulent momentum and heat fluxes over the ocean. 605 COARE 3.0, COARE 3. 5and ECMWF schemes mainly differ by their roughness lenghts computation and consequently767 COARE 3.0, COARE 3.6 and ECMWF schemes mainly differ by their roughness lenghts computation and consequently 606 768 their neutral transfer coefficients relationships with neutral wind. 607 769 \begin{itemize} … … 615 777 This is the so-called DRAKKAR Forcing Set (DFS) \citep{brodeau.barnier.ea_OM10}. 616 778 \item COARE 3.0 (\np[=.true.]{ln_COARE_3p0}{ln\_COARE\_3p0}): See \citet{fairall.bradley.ea_JC03} for more details 617 \item COARE 3. 5 (\np[=.true.]{ln_COARE_3p5}{ln\_COARE\_3p5}): See \citet{edson.jampana.ea_JPO13} for more details779 \item COARE 3.6 (\np[=.true.]{ln_COARE_3p6}{ln\_COARE\_3p6}): See \citet{edson.jampana.ea_JPO13} for more details 618 780 \item ECMWF (\np[=.true.]{ln_ECMWF}{ln\_ECMWF}): Based on \href{https://www.ecmwf.int/node/9221}{IFS (Cy31)} implementation and documentation. 619 781 Surface roughness lengths needed for the Obukhov length are computed following \citet{beljaars_QJRMS95}.
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