- Timestamp:
- 2010-10-15T16:42:00+02:00 (14 years ago)
- File:
-
- 1 edited
Legend:
- Unmodified
- Added
- Removed
-
branches/nemo_v3_3_beta/DOC/TexFiles/Chapters/Chap_SBC.tex
r1320 r2282 1 %================================================================1 ================================================================ 2 2 % Chapter Ñ Surface Boundary Condition (SBC) 3 3 % ================================================================ … … 17 17 \item the two components of the surface ocean stress $\left( {\tau _u \;,\;\tau _v} \right)$ 18 18 \item the incoming solar and non solar heat fluxes $\left( {Q_{ns} \;,\;Q_{sr} } \right)$ 19 \item the surface freshwater budget $\left( {\text {EMP},\;\text{EMP}_S } \right)$19 \item the surface freshwater budget $\left( {\textit{emp},\;\textit{emp}_S } \right)$ 20 20 \end{itemize} 21 21 … … 28 28 the \np{nf\_sbc} namelist parameter. 29 29 When the fields are supplied from data files (flux and bulk formulations), the input fields 30 need not be supplied on the model grid. Instead a file of coordinates and weights can be supplied which31 maps the data from the supplied grid to the model points (so called "Interpolation on the Fly"). 32 In addition, the resulting fields can be further modified using 33 several namelist options. These options control the rotation of vector components 34 supplied relative to an east-north coordinate system onto the local grid directions in the model; 35 the addition of a surface restoring36 term to observed SST and/or SSS (\np{ln\_ssr}=true); the modification of fluxes30 need not be supplied on the model grid. Instead a file of coordinates and weights can 31 be supplied which maps the data from the supplied grid to the model points 32 (so called "Interpolation on the Fly"). 33 In addition, the resulting fields can be further modified using several namelist options. 34 These options control the rotation of vector components supplied relative to an east-north 35 coordinate system onto the local grid directions in the model; the addition of a surface 36 restoring term to observed SST and/or SSS (\np{ln\_ssr}=true); the modification of fluxes 37 37 below ice-covered areas (using observed ice-cover or a sea-ice model) 38 38 (\np{nn\_ice}=0,1, 2 or 3); the addition of river runoffs as surface freshwater … … 42 42 cycle (\np{ln\_dm2dc}=true). 43 43 44 In this chapter, we first discuss where the surface boundary condition 45 appears in the model equations. Then we present the four ways of providing 46 the surface boundary condition. Next the scheme for interpolation on the fly is described. 47 Finally, the different options that further modify 48 the fluxes applied to the ocean are discussed. 44 In this chapter, we first discuss where the surface boundary condition appears in the 45 model equations. Then we present the four ways of providing the surface boundary condition. 46 Next the scheme for interpolation on the fly is described. 47 Finally, the different options that further modify the fluxes applied to the ocean are discussed. 49 48 50 49 … … 75 74 \begin{equation} \label{Eq_sbc_trasbc_q} 76 75 \frac{\partial T}{\partial t}\equiv \cdots \;+\;\left. {\frac{Q_{ns} }{\rho 77 _o \;C_p \;e_{3 T} }} \right|_{k=1} \quad76 _o \;C_p \;e_{3t} }} \right|_{k=1} \quad 78 77 \end{equation} 79 78 $Q_{sr}$ is the penetrative part of the heat flux. It is applied as a 3D … … 81 80 82 81 \begin{equation} \label{Eq_sbc_traqsr} 83 \frac{\partial T}{\partial t}\equiv \cdots \;+\frac{Q_{sr} }{\rho _o C_p 84 \,e_{3T} }\delta _k \left[ {I_w } \right] 82 \frac{\partial T}{\partial t}\equiv \cdots \;+\frac{Q_{sr} }{\rho_o C_p \,e_{3t} }\delta _k \left[ {I_w } \right] 85 83 \end{equation} 86 84 where $I_w$ is a non-dimensional function that describes the way the light … … 88 86 exponentials (see \S\ref{TRA_qsr}). 89 87 90 The surface freshwater budget is provided by fields: EMP and EMP$_S$ which88 The surface freshwater budget is provided by fields: \textit{emp} and $\textit{emp}_S$ which 91 89 may or may not be identical. Indeed, a surface freshwater flux has two effects: 92 90 it changes the volume of the ocean and it changes the surface concentration of 93 91 salt (and other tracers). Therefore it appears in the sea surface height as a volume 94 flux, EMP(\textit{dynspg\_xxx} modules), and in the salinity time evolution equations92 flux, \textit{emp} (\textit{dynspg\_xxx} modules), and in the salinity time evolution equations 95 93 as a concentration/dilution effect, 96 EMP$_{S}$ (\mdl{trasbc} module).94 $\textit{emp}_{S}$ (\mdl{trasbc} module). 97 95 \begin{equation} \label{Eq_trasbc_emp} 98 96 \begin{aligned} 99 &\frac{\partial \eta }{\partial t}\equiv \cdots \;+\;\text {EMP}\quad \\97 &\frac{\partial \eta }{\partial t}\equiv \cdots \;+\;\textit{emp}\quad \\ 100 98 \\ 101 &\frac{\partial S}{\partial t}\equiv \cdots \;+\left. {\frac{\text {EMP}_S \;S}{e_{3T} }} \right|_{k=1} \\99 &\frac{\partial S}{\partial t}\equiv \cdots \;+\left. {\frac{\textit{emp}_S \;S}{e_{3t} }} \right|_{k=1} \\ 102 100 \end{aligned} 103 101 \end{equation} 104 102 105 In the real ocean, EMP$=$EMP$_S$ and the ocean salt content is conserved,103 In the real ocean, $\textit{emp}=\textit{emp}_S$ and the ocean salt content is conserved, 106 104 but it exist several numerical reasons why this equality should be broken. 107 For example: 108 109 When the rigid-lid assumption is made, the ocean volume becomes constant and 110 thus, EMP$=$0, not EMP$_{S }$. 111 112 When the ocean is coupled to a sea-ice model, the water exchanged between ice and 113 ocean is slightly salty (mean sea-ice salinity is $\sim $\textit{4 psu}). In this case, 114 EMP$_{S}$ take into account both concentration/dilution effect associated with 115 freezing/melting and the salt flux between ice and ocean, while EMP is 116 only the volume flux. In addition, in the current version of \NEMO, the 117 sea-ice is assumed to be above the ocean. Freezing/melting does not change 118 the ocean volume (no impact on EMP) but it modifies the SSS. 105 For example, when the ocean is coupled to a sea-ice model, the water exchanged between 106 ice and ocean is slightly salty (mean sea-ice salinity is $\sim $\textit{4 psu}). In this case, 107 $\textit{emp}_{S}$ take into account both concentration/dilution effect associated with 108 freezing/melting and the salt flux between ice and ocean, while \textit{emp} is 109 only the volume flux. In addition, in the current version of \NEMO, the sea-ice is 110 assumed to be above the ocean (the so-called levitating sea-ice). Freezing/melting does 111 not change the ocean volume (no impact on \textit{emp}) but it modifies the SSS. 119 112 %gm \colorbox{yellow}{(see {\S} on LIM sea-ice model)}. 120 113 … … 127 120 associated with precipitation! Precipitation can change the ocean volume and thus the 128 121 ocean heat content. It is therefore associated with a heat flux (not yet 129 diagnosed in the model) \citep{Roullet 2000}).122 diagnosed in the model) \citep{Roullet_Madec_JGR00}). 130 123 131 124 %\colorbox{yellow}{Miss: } … … 193 186 be uniform in space. They take constant values given in the namelist 194 187 namsbc{\_}ana by the variables \np{rn\_utau0}, \np{rn\_vtau0}, \np{rn\_qns0}, 195 \np{rn\_qsr0}, and \np{rn\_emp0} ( EMP$=$EMP$_S$). The runoff is set to zero.188 \np{rn\_qsr0}, and \np{rn\_emp0} ($\textit{emp}=\textit{emp}_S$). The runoff is set to zero. 196 189 In addition, the wind is allowed to reach its nominal value within a given number 197 190 of time steps (\np{nn\_tau000}). … … 267 260 %------------------------------------------------------------------------------------------------------------- 268 261 269 The CORE bulk formulae have been developed by \citet{Large Yeager2004}.262 The CORE bulk formulae have been developed by \citet{Large_Yeager_Rep04}. 270 263 They have been designed to handle the CORE forcing, a mixture of NCEP 271 264 reanalysis and satellite data. They use an inertial dissipative method to compute … … 361 354 362 355 % ================================================================ 356 % River runoffs 357 % ================================================================ 358 \section [river runoffs (\textit{sbcrnf})] 359 {river runoffs (\mdl{sbcrnf})} 360 \label{SBC_rnf} 361 %------------------------------------------namsbc_rnf---------------------------------------------------- 362 \namdisplay{namsbc_rnf} 363 %------------------------------------------------------------------------------------------------------------- 364 365 %River runoff generally enters the ocean at a nonzero depth rather than through the surface. 366 %Many models, however, have traditionally inserted river runoff to the top model cell. 367 %This was the case in \NEMO prior to the version 3.3. The switch toward a input of runoff 368 %throughout a nonzero depth has been motivated by the numerical and physical problems 369 %that arise when the top grid cells are of the order of one meter. This situation is common in 370 %coastal modelling and becomes more and more often open ocean and climate modelling 371 %\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are 372 %required to properly represent the diurnal cycle \citep{Bernie_al_JC05}. see also \S\ref{SBC_dcy}.}. 373 374 375 %To do this we need to treat evaporation/precipitation fluxes and river runoff differently in the 376 %\mdl{tra\_sbc} module. We decided to separate them throughout the code, so that the variable 377 %\textit{emp} represented solely evaporation minus precipitation fluxes, and a new 2d variable 378 %rnf was added which represents the volume flux of river runoff (in kg/m2s to remain consistent with 379 %emp). This meant many uses of emp and emps needed to be changed, a list of all modules which use 380 %emp or emps and the changes made are below: 381 382 383 %Rachel: 384 River runoff generally enters the ocean at a nonzero depth rather than through the surface. 385 Many models, however, have traditionally inserted river runoff to the top model cell. 386 This was the case in \NEMO prior to the version 3.3, and was combined with an option to increase vertical mixing near the river mouth. 387 388 However, with this method numerical and physical problems arise when the top grid cells are 389 of the order of one meter. This situation is common in coastal modelling and is becoming 390 more common in open ocean and climate modelling 391 \footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are 392 required to properly represent the diurnal cycle \citep{Bernie_al_JC05}. see also \S\ref{SBC_dcy}.}. 393 394 As such from VN3.3 onwards it is possible to add river runoff through a non-zero depth, and for the 395 temperature and salinity of the river to effect the surrounding ocean. 396 The user is able to specify, in a NetCDF input file, the temperature and salinity of the river, along with the 397 depth (in metres) which the river should be added to. 398 399 Namelist options, \np{ln\_rnf\_depth}, \np{ln\_rnf\_sal} and \np{ln\_rnf\_temp} control whether 400 the river attributes (depth, salinity and temperature) are read in and used. If these are set 401 as false the river is added to the surface box only, assumed to be fresh (0~psu), and/or 402 taken as surface temperature respectively. 403 404 The runoff value and attributes are read in in sbcrnf. 405 For temperature -999 is taken as missing data and the river temperature is taken to be the 406 surface temperatue at the river point. 407 For the depth parameter a value of -1 means the river is added to the surface box only, 408 and a value of -999 means the river is added through the entire water column. 409 After being read in the temperature and salinity variables are multiplied by the amount of runoff (converted into m/s) 410 to give the heat and salt content of the river runoff. 411 After the user specified depth is read ini, the number of grid boxes this corresponds to is 412 calculated and stored in the variable \np{nz\_rnf}. 413 The variable \np{h\_dep} is then calculated to be the depth (in metres) of the bottom of the 414 lowest box the river water is being added to (i.e. the total depth that river water is being added to in the model). 415 416 The mass/volume addition due to the river runoff is, at each relevant depth level, added to the horizontal divergence (\np{hdivn}) 417 in the subroutine \np{sbc\_rnf\_div} (called from \np{divcur}). 418 This increases the diffusion term in the vicinity of the river, thereby simulating a momentum flux. 419 The sea surface height is calculated using the sum of the horizontal divergence terms, and so the 420 river runoff indirectly forces an increase in sea surface height. 421 422 The \np{hdivn} terms are used in the tracer advection modules to force vertical velocities. 423 This causes a mass of water, equal to the amount of runoff, to be moved into the box above. 424 The heat and salt content of the river runoff is not included in this step, and so the tracer 425 concentrations are diluted as water of ocean temperature and salinity is moved upward out of the box 426 and replaced by the same volume of river water with no corresponding heat and salt addition. 427 428 For the linear free surface case, at the surface box the tracer advection causes a flux of water 429 (of equal volume to the runoff) through the sea surface out of the domain, which causes a salt and heat flux out of the model. 430 As such the volume of water does not change, but the water is diluted. 431 432 For the non-linear free surface case (vvl), no flux is allowed through the surface. 433 Instead in the surface box (as well as water moving up from the boxes below) a volume of runoff water 434 is added with no corresponding heat and salt addition and so as happens in the lower boxes there is a dilution effect. 435 (The runoff addition to the top box along with the water being moved up through boxes below means the surface box has a large 436 increase in volume, whilst all other boxes remain the same size) 437 438 In trasbc the addition of heat and salt due to the river runoff is added. 439 This is done in the same way for both vvl and non-vvl. 440 The temperature and salinity are increased through the specified depth according to the heat and salt content of the river. 441 442 In the non-linear free surface case (vvl), near the end of the time step the change in sea surface height is redistrubuted 443 through the grid boxes, so that the original ratios of grid box heights are restored. 444 In doing this water is moved into boxes below, throughout the water column, so the large volume addition to the surface box is spread between all the grid boxes. 445 446 It is also possible for runnoff to be specified as a negative value for modelling flow through straits, i.e. modelling the Baltic flow in and out of the North Sea. 447 When the flow is out of the domain there is no change in temperature and salinity, regardless of the namelist options used, as the ocean water leaving the domain removes heat and salt (at the same concentration) with it. 448 449 450 %\colorbox{yellow}{Nevertheless, Pb of vertical resolution and 3D input : increase vertical mixing near river mouths to mimic a 3D river 451 452 %All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and at the same temperature as the sea surface.} 453 454 %\colorbox{yellow}{river mouths{\ldots}} 455 456 %IF( ln_rnf ) THEN ! increase diffusivity at rivers mouths 457 % DO jk = 2, nkrnf ; avt(:,:,jk) = avt(:,:,jk) + rn_avt_rnf * rnfmsk(:,:) ; END DO 458 %ENDIF 459 460 %\gmcomment{ word doc of runoffs: 461 % 462 %In the current \NEMO setup river runoff is added to emp fluxes, these are then applied at just the sea surface as a volume change (in the variable volume case this is a literal volume change, and in the linear free surface case the free surface is moved) and a salt flux due to the concentration/dilution effect. There is also an option to increase vertical mixing near river mouths; this gives the effect of having a 3d river. All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and at the same temperature as the sea surface. 463 %Our aim was to code the option to specify the temperature and salinity of river runoff, (as well as the amount), along with the depth that the river water will affect. This would make it possible to model low salinity outflow, such as the Baltic, and would allow the ocean temperature to be affected by river runoff. 464 465 %The depth option makes it possible to have the river water affecting just the surface layer, throughout depth, or some specified point in between. 466 467 %To do this we need to treat evaporation/precipitation fluxes and river runoff differently in the tra_sbc module. We decided to separate them throughout the code, so that the variable emp represented solely evaporation minus precipitation fluxes, and a new 2d variable rnf was added which represents the volume flux of river runoff (in kg/m2s to remain consistent with emp). This meant many uses of emp and emps needed to be changed, a list of all modules which use emp or emps and the changes made are below: 468 469 } 470 471 472 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 473 \begin{figure}[!t] \label{Fig_SBC_diurnal} \begin{center} 474 \includegraphics[width=0.8\textwidth]{./TexFiles/Figures/Fig_SBC_diurnal.pdf} 475 \caption{Example of recontruction of the diurnal cycle variation of short wave flux 476 from daily mean values. The reconstructed diurnal cycle (black line) is chosen 477 as the mean value of the analytical cycle (blue line) over a time step, not 478 as the mid time step value of the analytically cycle (red square). From \citet{Bernie_al_CD07}.} 479 \end{center} \end{figure} 480 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 481 482 % ================================================================ 483 % Diurnal cycle 484 % ================================================================ 485 \section [Diurnal cycle (\textit{sbcdcy})] 486 {Diurnal cycle (\mdl{sbcdcy})} 487 \label{SBC_dcy} 488 %------------------------------------------namsbc_rnf---------------------------------------------------- 489 %\namdisplay{namsbc} 490 %------------------------------------------------------------------------------------------------------------- 491 492 \cite{Bernie_al_JC05} have shown that to capture 90$\%$ of the diurnal variability of 493 SST requires a vertical resolution in upper ocean of 1~m or better and a temporal resolution 494 of the surface fluxes of 3~h or less. Unfortunately high frequency forcing fields are rare, 495 not to say inexistent. Nevertheless, it is possible to obtain a reasonable diurnal cycle 496 of the SST knowning only short wave flux (SWF) at high frequency \citep{Bernie_al_CD07}. 497 Furthermore, only the knowledge of daily mean value of SWF is needed, 498 as higher frequency variations can be reconstructed from them, assuming that 499 the diurnal cycle of SWF is a scaling of the top of the atmosphere diurnal cycle 500 of incident SWF. The \cite{Bernie_al_CD07} reconstruction algorithm is available 501 in \NEMO by setting \np{ln\_dm2dc}=true (a \textit{namsbc} namelist parameter) when using 502 CORE bulk formulea (\np{ln\_blk\_core}=true) or the flux formulation (\np{ln\_flx}=true). 503 The reconstruction is performed in the \mdl{sbcdcy} module. The detail of the algoritm used 504 can be found in the appendix~A of \cite{Bernie_al_CD07}. The algorithm preserve the daily 505 mean incomming SWF as the reconstructed SWF at a given time step is the mean value 506 of the analytical cycle over this time step (Fig.\ref{Fig_SBC_diurnal}). 507 The use of diurnal cycle reconstruction requires the input SWF to be daily 508 ($i.e.$ a frequency of 24 and a time interpolation set to true in \np{sn\_qsr} namelist parameter). 509 Furthermore, it is recommended to have a least 8 surface module time step per day, 510 that is $\rdt \ \np{nn\_fsbc} < 10,800~s = 3~h$. An example of recontructed SWF 511 is given in Fig.\ref{Fig_SBC_dcy} for a 12 reconstructed diurnal cycle, one every 2~hours 512 (from 1am to 11pm). 513 514 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 515 \begin{figure}[!t] \label{Fig_SBC_dcy} \begin{center} 516 \includegraphics[width=0.7\textwidth]{./TexFiles/Figures/Fig_SBC_dcy.pdf} 517 \caption{Example of recontruction of the diurnal cycle variation of short wave flux 518 from daily mean values on an ORCA2 grid with a time sampling of 2~hours (from 1am to 11pm). 519 The display is on (i,j) plane. } 520 \end{center} \end{figure} 521 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 522 523 Note also that the setting a diurnal cycle in SWF is highly recommended when 524 the top layer thickness approach 1~m or less, otherwise large error in SST can 525 appear due to an inconsistency between the scale of the vertical resolution 526 and the forcing acting on that scale. 527 528 % ================================================================ 363 529 % Interpolation on the Fly 364 530 % ================================================================ … … 408 574 The symbolic algorithm used to calculate values on the model grid is now: 409 575 410 \begin{multline*} 411 f_{m}(i,j) = f_{m}(i,j) + \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))} 412 \\ 413 + \sum_{k=5}^{8} {wgt(k)\left.\frac{\partial f}{\partial i}\right| _{idx(src(k))} } 414 \\ 415 + \sum_{k=9}^{12} {wgt(k)\left.\frac{\partial f}{\partial j}\right| _{idx(src(k))} } 416 \\ 417 + \sum_{k=13}^{16} {wgt(k)\left.\frac{\partial ^2 f}{\partial i \partial j}\right| _{idx(src(k))} } 418 \end{multline*} 576 \begin{equation*} \begin{split} 577 f_{m}(i,j) = f_{m}(i,j) +& \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))} 578 + \sum_{k=5}^{8} {wgt(k)\left.\frac{\partial f}{\partial i}\right| _{idx(src(k))} } \\ 579 +& \sum_{k=9}^{12} {wgt(k)\left.\frac{\partial f}{\partial j}\right| _{idx(src(k))} } 580 + \sum_{k=13}^{16} {wgt(k)\left.\frac{\partial ^2 f}{\partial i \partial j}\right| _{idx(src(k))} } 581 \end{split} 582 \end{equation*} 419 583 The gradients here are taken with respect to the horizontal indices and not distances since the spatial dependency has been absorbed into the weights. 420 584 … … 515 679 516 680 \begin{equation} \label{Eq_sbc_dmp_emp} 517 EMP = EMP_o + \gamma_s^{-1} e_{3t} \frac{ \left(\left.S\right|_{k=1}-SSS_{Obs}\right)}681 \textit{emp} = \textit{emp}_o + \gamma_s^{-1} e_{3t} \frac{ \left(\left.S\right|_{k=1}-SSS_{Obs}\right)} 518 682 {\left.S\right|_{k=1}} 519 683 \end{equation} 520 684 521 where EMP$_{o }$ is a net surface fresh water flux (observed, climatological or an685 where $\textit{emp}_{o }$ is a net surface fresh water flux (observed, climatological or an 522 686 atmospheric model product), \textit{SSS}$_{Obs}$ is a sea surface salinity (usually a time 523 687 interpolation of the monthly mean Polar Hydrographic Climatology \citep{Steele2001}), … … 562 726 563 727 % ------------------------------------------------------------------------------------------------------------- 564 % Addition of river runoffs565 % -------------------------------------------------------------------------------------------------------------566 \subsection [Addition of river runoffs (\textit{sbcrnf})]567 {Addition of river runoffs (\mdl{sbcrnf})}568 \label{SBC_rnf}569 %------------------------------------------namsbc_rnf----------------------------------------------------570 \namdisplay{namsbc_rnf}571 %-------------------------------------------------------------------------------------------------------------572 573 The river runoffs574 575 It is convenient to introduce the river runoff in the model as a surface576 fresh water flux.577 578 579 %Griffies: River runoff generally enters the ocean at a nonzero depth rather than through the surface. Many global models, however, have traditionally inserted river runoff to the top model cell. Such can become problematic numerically and physically when the top grid cells are reÞned to levels common in coastal modelling. Hence, more applications are now considering the input of runoff throughout a nonzero depth. Likewise, sea ice can melt at depth, thus necessitating a mass transport to occur within the ocean between the liquid and solid water masses.580 581 \colorbox{yellow}{Nevertheless, Pb of vertical resolution and increase of Kz in vicinity of }582 583 \colorbox{yellow}{river mouths{\ldots}}584 585 %IF( ln_rnf ) THEN ! increase diffusivity at rivers mouths586 % DO jk = 2, nkrnf ; avt(:,:,jk) = avt(:,:,jk) + rn_avt_rnf * rnfmsk(:,:) ; END DO587 %ENDIF588 589 590 591 % -------------------------------------------------------------------------------------------------------------592 728 % Freshwater budget control 593 729 % ------------------------------------------------------------------------------------------------------------- … … 602 738 \item[\np{nn\_fwb}=0] no control at all. The mean sea level is free to drift, and will 603 739 certainly do so. 604 \item[\np{nn\_fwb}=1] global mean EMPset to zero at each model time step.740 \item[\np{nn\_fwb}=1] global mean \textit{emp} set to zero at each model time step. 605 741 %Note that with a sea-ice model, this technique only control the mean sea level with linear free surface (\key{vvl} not defined) and no mass flux between ocean and ice (as it is implemented in the current ice-ocean coupling). 606 742 \item[\np{nn\_fwb}=2] freshwater budget is adjusted from the previous year annual
Note: See TracChangeset
for help on using the changeset viewer.
