Changeset 12377 for NEMO/trunk/doc/latex/NEMO/subfiles/chap_SBC.tex
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NEMO/trunk/doc/latex/NEMO/subfiles/chap_SBC.tex
r11693 r12377 1 1 \documentclass[../main/NEMO_manual]{subfiles} 2 \usepackage{fontspec} 3 \usepackage{fontawesome} 2 4 3 5 \begin{document} … … 45 47 46 48 \begin{itemize} 47 \item a bulk formulation (\np[=.true.]{ln_blk}{ln\_blk} with four possible bulk algorithms),49 \item a bulk formulation (\np[=.true.]{ln_blk}{ln\_blk}), featuring a selection of four bulk parameterization algorithms, 48 50 \item a flux formulation (\np[=.true.]{ln_flx}{ln\_flx}), 49 51 \item a coupled or mixed forced/coupled formulation (exchanges with a atmospheric model via the OASIS coupler), … … 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} 538 539 % L. Brodeau, December 2019... % 525 540 526 541 \begin{listing} … … 530 545 \end{listing} 531 546 532 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 547 If the bulk formulation is selected (\np[=.true.]{ln_blk}{ln\_blk}), the air-sea 548 fluxes associated with surface boundary conditions are estimated by means of the 549 traditional \emph{bulk formulae}. As input, bulk formulae rely on a prescribed 550 near-surface atmosphere state (typically extracted from a weather reanalysis) 551 and the prognostic sea (-ice) surface state averaged over \np{nn_fsbc}{nn\_fsbc} 552 time-step(s). 553 554 % Turbulent air-sea fluxes are computed using the sea surface properties and 555 % atmospheric SSVs at height $z$ above the sea surface, with the traditional 556 % aerodynamic bulk formulae: 557 558 Note: all the NEMO Fortran routines involved in the present section have been 559 initially developed (and are still developed in parallel) in 560 the \href{https://brodeau.github.io/aerobulk/}{\texttt{AeroBulk}} open-source project 561 \citep{brodeau.barnier.ea_JPO17}. 562 563 %%% Bulk formulae are this: 564 \subsection{Bulk formulae}\label{subsec:SBC_blkform} 565 % 566 In NEMO, the set of equations that relate each component of the surface fluxes 567 to the near-surface atmosphere and sea surface states writes 568 % 569 \begin{subequations}\label{eq_bulk} 570 \label{eq:SBC_bulk_form} 571 \begin{eqnarray} 572 \mathbf{\tau} &=& \rho~ C_D ~ \mathbf{U}_z ~ U_B \\ 573 Q_H &=& \rho~C_H~C_P~\big[ \theta_z - T_s \big] ~ U_B \\ 574 E &=& \rho~C_E ~\big[ q_s - q_z \big] ~ U_B \\ 575 Q_L &=& -L_v \, E \\ 576 % 577 Q_{sr} &=& (1 - a) Q_{sw\downarrow} \\ 578 Q_{ir} &=& \delta (Q_{lw\downarrow} -\sigma T_s^4) 579 \end{eqnarray} 580 \end{subequations} 581 % 582 with 583 \[ \theta_z \simeq T_z+\gamma z \] 584 \[ q_s \simeq 0.98\,q_{sat}(T_s,p_a ) \] 585 % 586 from which, the the non-solar heat flux is \[ Q_{ns} = Q_L + Q_H + Q_{ir} \] 587 % 588 where $\mathbf{\tau}$ is the wind stress vector, $Q_H$ the sensible heat flux, 589 $E$ the evaporation, $Q_L$ the latent heat flux, and $Q_{ir}$ the net longwave 590 flux. 591 % 592 $Q_{sw\downarrow}$ and $Q_{lw\downarrow}$ are the surface downwelling shortwave 593 and longwave radiative fluxes, respectively. 594 % 595 Note: a positive sign for $\mathbf{\tau}$, $Q_H$, $Q_L$, $Q_{sr}$ or $Q_{ir}$ 596 implies a gain of the relevant quantity for the ocean, while a positive $E$ 597 implies a freshwater loss for the ocean. 598 % 599 $\rho$ is the density of air. $C_D$, $C_H$ and $C_E$ are the bulk transfer 600 coefficients for momentum, sensible heat, and moisture, respectively. 601 % 602 $C_P$ is the heat capacity of moist air, and $L_v$ is the latent heat of 603 vaporization of water. 604 % 605 $\theta_z$, $T_z$ and $q_z$ are the potential temperature, absolute temperature, 606 and specific humidity of air at height $z$ above the sea surface, 607 respectively. $\gamma z$ is a temperature correction term which accounts for the 608 adiabatic lapse rate and approximates the potential temperature at height 609 $z$ \citep{josey.gulev.ea_2013}. 610 % 611 $\mathbf{U}_z$ is the wind speed vector at height $z$ above the sea surface 612 (possibly referenced to the surface current $\mathbf{u_0}$, 613 section \ref{s_res1}.\ref{ss_current}). 614 % 615 The bulk scalar wind speed, namely $U_B$, is the scalar wind speed, 616 $|\mathbf{U}_z|$, with the potential inclusion of a gustiness contribution. 617 % 618 $a$ and $\delta$ are the albedo and emissivity of the sea surface, respectively.\\ 619 % 620 %$p_a$ is the mean sea-level pressure (SLP). 621 % 622 $T_s$ is the sea surface temperature. $q_s$ is the saturation specific humidity 623 of air at temperature $T_s$; it includes a 2\% reduction to account for the 624 presence of salt in seawater \citep{sverdrup.johnson.ea_1942,kraus.businger_QJRMS96}. 625 Depending on the bulk parametrization used, $T_s$ can either be the temperature 626 at the air-sea interface (skin temperature, hereafter SSST) or at typically a 627 few tens of centimeters below the surface (bulk sea surface temperature, 628 hereafter SST). 629 % 630 The SSST differs from the SST due to the contributions of two effects of 631 opposite sign, the \emph{cool skin} and \emph{warm layer} (hereafter CS and WL, 632 respectively, see section\,\ref{subsec:SBC_skin}). 633 % 634 Technically, when the ECMWF or COARE* bulk parametrizations are selected 635 (\np[=.true.]{ln_ECMWF}{ln\_ECMWF} or \np[=.true.]{ln_COARE*}{ln\_COARE\*}), 636 $T_s$ is the SSST, as opposed to the NCAR bulk parametrization 637 (\np[=.true.]{ln_NCAR}{ln\_NCAR}) for which $T_s$ is the bulk SST (\ie~temperature 638 at first T-point level). 639 640 For more details on all these aspects the reader is invited to refer 641 to \citet{brodeau.barnier.ea_JPO17}. 642 643 644 645 \subsection{Bulk parametrizations}\label{subsec:SBC_blk_ocean} 646 %%%\label{subsec:SBC_param} 647 648 Accuracy of the estimate of surface turbulent fluxes by means of bulk formulae 649 strongly relies on that of the bulk transfer coefficients: $C_D$, $C_H$ and 650 $C_E$. They are estimated with what we refer to as a \emph{bulk 651 parametrization} algorithm. When relevant, these algorithms also perform the 652 height adjustment of humidity and temperature to the wind reference measurement 653 height (from \np{rn_zqt}{rn\_zqt} to \np{rn_zu}{rn\_zu}). 654 655 656 657 For the open ocean, four bulk parametrization algorithms are available in NEMO: 658 \begin{itemize} 659 \item NCAR, formerly known as CORE, \citep{large.yeager_rpt04,large.yeager_CD09} 660 \item COARE 3.0 \citep{fairall.bradley.ea_JC03} 661 \item COARE 3.6 \citep{edson.jampana.ea_JPO13} 662 \item ECMWF (IFS documentation, cy45) 663 \end{itemize} 664 665 666 With respect to version 3, the principal advances in version 3.6 of the COARE 667 bulk parametrization are built around improvements in the representation of the 668 effects of waves on 669 fluxes \citep{edson.jampana.ea_JPO13,brodeau.barnier.ea_JPO17}. This includes 670 improved relationships of surface roughness, and whitecap fraction on wave 671 parameters. It is therefore recommended to chose version 3.6 over 3. 672 673 674 675 676 \subsection{Cool-skin and warm-layer parametrizations}\label{subsec:SBC_skin} 677 %\subsection[Cool-skin and warm-layer parameterizations 678 %(\forcode{ln_skin_cs} \& \forcode{ln_skin_wl})]{Cool-skin and warm-layer parameterizations (\protect\np{ln_skin_cs}{ln\_skin\_cs} \& \np{ln_skin_wl}{ln\_skin\_wl})} 679 %\label{subsec:SBC_skin} 680 % 681 As opposed to the NCAR bulk parametrization, more advanced bulk 682 parametrizations such as COARE3.x and ECMWF are meant to be used with the skin 683 temperature $T_s$ rather than the bulk SST (which, in NEMO is the temperature at 684 the first T-point level, see section\,\ref{subsec:SBC_blkform}). 685 % 686 As such, the relevant cool-skin and warm-layer parametrization must be 687 activated through \np[=T]{ln_skin_cs}{ln\_skin\_cs} 688 and \np[=T]{ln_skin_wl}{ln\_skin\_wl} to use COARE3.x or ECMWF in a consistent 689 way. 690 691 \texttt{\#LB: ADD BLBLA ABOUT THE TWO CS/WL PARAMETRIZATIONS (ECMWF and COARE) !!!} 692 693 For the cool-skin scheme parametrization COARE and ECMWF algorithms share the same 694 basis: \citet{fairall.bradley.ea_JGR96}. With some minor updates based 695 on \citet{zeng.beljaars_GRL05} for ECMWF, and \citet{fairall.ea_19} for COARE 696 3.6. 697 698 For the warm-layer scheme, ECMWF is based on \citet{zeng.beljaars_GRL05} with a 699 recent update from \citet{takaya.bidlot.ea_JGR10} (consideration of the 700 turbulence input from Langmuir circulation). 701 702 Importantly, COARE warm-layer scheme \citep{fairall.ea_19} includes a prognostic 703 equation for the thickness of the warm-layer, while it is considered as constant 704 in the ECWMF algorithm. 705 706 707 \subsection{Appropriate use of each bulk parametrization} 708 709 \subsubsection{NCAR} 710 711 NCAR bulk parametrizations (formerly known as CORE) is meant to be used with the 712 CORE II atmospheric forcing \citep{large.yeager_CD09}. The expected sea surface 713 temperature is the bulk SST. Hence the following namelist parameters must be 714 set: 715 % 716 \begin{verbatim} 717 ... 718 ln_NCAR = .true. 719 ... 720 rn_zqt = 10. ! Air temperature & humidity reference height (m) 721 rn_zu = 10. ! Wind vector reference height (m) 722 ... 723 ln_skin_cs = .false. ! use the cool-skin parameterization 724 ln_skin_wl = .false. ! use the warm-layer parameterization 725 ... 726 ln_humi_sph = .true. ! humidity "sn_humi" is specific humidity [kg/kg] 727 \end{verbatim} 728 729 730 \subsubsection{ECMWF} 731 % 732 With an atmospheric forcing based on a reanalysis of the ECMWF, such as the 733 Drakkar Forcing Set \citep{brodeau.barnier.ea_OM10}, we strongly recommend to 734 use the ECMWF bulk parametrizations with the cool-skin and warm-layer 735 parametrizations activated. In ECMWF reanalyzes, since air temperature and 736 humidity are provided at the 2\,m height, and given that the humidity is 737 distributed as the dew-point temperature, the namelist must be tuned as follows: 738 % 739 \begin{verbatim} 740 ... 741 ln_ECMWF = .true. 742 ... 743 rn_zqt = 2. ! Air temperature & humidity reference height (m) 744 rn_zu = 10. ! Wind vector reference height (m) 745 ... 746 ln_skin_cs = .true. ! use the cool-skin parameterization 747 ln_skin_wl = .true. ! use the warm-layer parameterization 748 ... 749 ln_humi_dpt = .true. ! humidity "sn_humi" is dew-point temperature [K] 750 ... 751 \end{verbatim} 752 % 753 Note: when \np{ln_ECMWF}{ln\_ECMWF} is selected, the selection 754 of \np{ln_skin_cs}{ln\_skin\_cs} and \np{ln_skin_wl}{ln\_skin\_wl} implicitly 755 triggers the use of the ECMWF cool-skin and warm-layer parametrizations, 756 respectively (found in \textit{sbcblk\_skin\_ecmwf.F90}). 757 758 759 \subsubsection{COARE 3.x} 760 % 761 Since the ECMWF parametrization is largely based on the COARE* parametrization, 762 the two algorithms are very similar in terms of structure and closure 763 approach. As such, the namelist tuning for COARE 3.x is identical to that of 764 ECMWF: 765 % 766 \begin{verbatim} 767 ... 768 ln_COARE3p6 = .true. 769 ... 770 ln_skin_cs = .true. ! use the cool-skin parameterization 771 ln_skin_wl = .true. ! use the warm-layer parameterization 772 ... 773 \end{verbatim} 774 775 Note: when \np[=T]{ln_COARE3p0}{ln\_COARE3p0} is selected, the selection 776 of \np{ln_skin_cs}{ln\_skin\_cs} and \np{ln_skin_wl}{ln\_skin\_wl} implicitly 777 triggers the use of the COARE cool-skin and warm-layer parametrizations, 778 respectively (found in \textit{sbcblk\_skin\_coare.F90}). 779 780 781 %lulu 782 783 784 785 % In a typical bulk algorithm, the BTCs under neutral stability conditions are 786 % defined using \emph{in-situ} flux measurements while their dependence on the 787 % stability is accounted through the \emph{Monin-Obukhov Similarity Theory} and 788 % the \emph{flux-profile} relationships \citep[\eg{}][]{Paulson_1970}. BTCs are 789 % functions of the wind speed and the near-surface stability of the atmospheric 790 % surface layer (hereafter ASL), and hence, depend on $U_B$, $T_s$, $T_z$, $q_s$ 791 % and $q_z$. 792 793 794 795 \subsection{Prescribed near-surface atmospheric state} 796 797 The atmospheric fields used depend on the bulk formulae used. In forced mode, 798 when a sea-ice model is used, a specific bulk formulation is used. Therefore, 799 different bulk formulae are used for the turbulent fluxes computation over the 800 ocean and over sea-ice surface. 801 % 802 803 %The choice is made by setting to true one of the following namelist 804 %variable: \np{ln_NCAR}{ln\_NCAR}, \np{ln_COARE_3p0}{ln\_COARE\_3p0}, \np{ln_COARE_3p6}{ln\_COARE\_3p6} 805 %and \np{ln_ECMWF}{ln\_ECMWF}. 545 806 546 807 Common options are defined through the \nam{sbc_blk}{sbc\_blk} namelist variables. … … 553 814 Variable description & Model variable & Units & point \\ 554 815 \hline 555 i-component of the 10m air velocity & utau& $m.s^{-1}$ & T \\816 i-component of the 10m air velocity & wndi & $m.s^{-1}$ & T \\ 556 817 \hline 557 j-component of the 10m air velocity & vtau& $m.s^{-1}$ & T \\818 j-component of the 10m air velocity & wndj & $m.s^{-1}$ & T \\ 558 819 \hline 559 10m air temperature & tair & \r{}$K$& T \\820 10m air temperature & tair & $K$ & T \\ 560 821 \hline 561 Specific humidity & humi & \% & T \\ 822 Specific humidity & humi & $-$ & T \\ 823 Relative humidity & ~ & $\%$ & T \\ 824 Dew-point temperature & ~ & $K$ & T \\ 562 825 \hline 563 Incoming long wave radiation& qlw & $W.m^{-2}$ & T \\826 Downwelling longwave radiation & qlw & $W.m^{-2}$ & T \\ 564 827 \hline 565 Incoming short wave radiation& qsr & $W.m^{-2}$ & T \\828 Downwelling shortwave radiation & qsr & $W.m^{-2}$ & T \\ 566 829 \hline 567 830 Total precipitation (liquid + solid) & precip & $Kg.m^{-2}.s^{-1}$ & T \\ … … 584 847 585 848 \np{cn_dir}{cn\_dir} is the directory of location of bulk files 586 \np{ln_taudif}{ln\_taudif} is the flag to specify if we use HightFrequency (HF) tau information (.true.) or not (.false.)849 %\np{ln_taudif}{ln\_taudif} is the flag to specify if we use High Frequency (HF) tau information (.true.) or not (.false.) 587 850 \np{rn_zqt}{rn\_zqt}: is the height of humidity and temperature measurements (m) 588 851 \np{rn_zu}{rn\_zu}: is the height of wind measurements (m) … … 595 858 Its range must be between zero and one, and it is recommended to set it to 0 at low-resolution (ORCA2 configuration). 596 859 597 As for the flux formulation, information about the input data required by the model is provided in860 As for the flux parametrization, information about the input data required by the model is provided in 598 861 the namsbc\_blk namelist (see \autoref{subsec:SBC_fldread}). 599 862 600 %% ================================================================================================= 601 \subsection[Ocean-Atmosphere Bulk formulae (\textit{sbcblk\_algo\_coare.F90, sbcblk\_algo\_coare3p5.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})} 602 \label{subsec:SBC_blk_ocean} 603 604 Four different bulk algorithms are available to compute surface turbulent momentum and heat fluxes over the ocean. 605 COARE 3.0, COARE 3.5 and ECMWF schemes mainly differ by their roughness lenghts computation and consequently 606 their neutral transfer coefficients relationships with neutral wind. 607 \begin{itemize} 608 \item NCAR (\np[=.true.]{ln_NCAR}{ln\_NCAR}): The NCAR bulk formulae have been developed by \citet{large.yeager_rpt04}. 609 They have been designed to handle the NCAR forcing, a mixture of NCEP reanalysis and satellite data. 610 They use an inertial dissipative method to compute the turbulent transfer coefficients 611 (momentum, sensible heat and evaporation) from the 10m wind speed, air temperature and specific humidity. 612 This \citet{large.yeager_rpt04} dataset is available through 613 the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/NCAR.html}{GFDL web site}. 614 Note that substituting ERA40 to NCEP reanalysis fields does not require changes in the bulk formulea themself. 615 This is the so-called DRAKKAR Forcing Set (DFS) \citep{brodeau.barnier.ea_OM10}. 616 \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 details 618 \item ECMWF (\np[=.true.]{ln_ECMWF}{ln\_ECMWF}): Based on \href{https://www.ecmwf.int/node/9221}{IFS (Cy31)} implementation and documentation. 619 Surface roughness lengths needed for the Obukhov length are computed following \citet{beljaars_QJRMS95}. 620 \end{itemize} 863 864 \subsubsection{Air humidity} 865 866 Air humidity can be provided as three different parameters: specific humidity 867 [kg/kg], relative humidity [\%], or dew-point temperature [K] (LINK to namelist 868 parameters)... 869 870 871 ~\\ 872 873 874 875 876 877 878 879 880 881 882 %% ================================================================================================= 883 %\subsection[Ocean-Atmosphere Bulk formulae (\textit{sbcblk\_algo\_coare3p0.F90, sbcblk\_algo\_coare3p6.F90, %sbcblk\_algo\_ecmwf.F90, sbcblk\_algo\_ncar.F90})]{Ocean-Atmosphere Bulk formulae (\mdl{sbcblk\_algo\_coare3p0}, %\mdl{sbcblk\_algo\_coare3p6}, \mdl{sbcblk\_algo\_ecmwf}, \mdl{sbcblk\_algo\_ncar})} 884 %\label{subsec:SBC_blk_ocean} 885 886 %Four different bulk algorithms are available to compute surface turbulent momentum and heat fluxes over the ocean. 887 %COARE 3.0, COARE 3.6 and ECMWF schemes mainly differ by their roughness lenghts computation and consequently 888 %their neutral transfer coefficients relationships with neutral wind. 889 %\begin{itemize} 890 %\item NCAR (\np[=.true.]{ln_NCAR}{ln\_NCAR}): The NCAR bulk formulae have been developed by \citet{large.yeager_rpt04}. 891 % They have been designed to handle the NCAR forcing, a mixture of NCEP reanalysis and satellite data. 892 % They use an inertial dissipative method to compute the turbulent transfer coefficients 893 % (momentum, sensible heat and evaporation) from the 10m wind speed, air temperature and specific humidity. 894 % This \citet{large.yeager_rpt04} dataset is available through 895 % the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/NCAR.html}{GFDL web site}. 896 % Note that substituting ERA40 to NCEP reanalysis fields does not require changes in the bulk formulea themself. 897 % This is the so-called DRAKKAR Forcing Set (DFS) \citep{brodeau.barnier.ea_OM10}. 898 %\item COARE 3.0 (\np[=.true.]{ln_COARE_3p0}{ln\_COARE\_3p0}): See \citet{fairall.bradley.ea_JC03} for more details 899 %\item COARE 3.6 (\np[=.true.]{ln_COARE_3p6}{ln\_COARE\_3p6}): See \citet{edson.jampana.ea_JPO13} for more details 900 %\item ECMWF (\np[=.true.]{ln_ECMWF}{ln\_ECMWF}): Based on \href{https://www.ecmwf.int/node/9204}{IFS (Cy40r1)} %implementation and documentation. 901 % Surface roughness lengths needed for the Obukhov length are computed 902 % following \citet{beljaars_QJRMS95}. 903 %\end{itemize} 621 904 622 905 %% ================================================================================================= 623 906 \subsection{Ice-Atmosphere Bulk formulae} 624 907 \label{subsec:SBC_blk_ice} 908 909 910 \texttt{\#out\_of\_place:} 911 For sea-ice, three possibilities can be selected: 912 a constant transfer coefficient (1.4e-3; default 913 value), \citet{lupkes.gryanik.ea_JGR12} (\np{ln_Cd_L12}{ln\_Cd\_L12}), 914 and \citet{lupkes.gryanik_JGR15} (\np{ln_Cd_L15}{ln\_Cd\_L15}) parameterizations 915 \texttt{\#out\_of\_place.} 916 917 918 625 919 626 920 Surface turbulent fluxes between sea-ice and the atmosphere can be computed in three different ways:
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