Changeset 3101 for branches/2011/dev_NOC_UKMO_MERGE/DOC

Timestamp:

2011-11-14T18:39:45+01:00 (13 years ago)

Author:

acc

Message:

Branch dev_NOC_UKMO_MERGE #890. Resolved conflicts (most arising from the tracer sub-timestepping)

Location:

branches/2011/dev_NOC_UKMO_MERGE/DOC/TexFiles

Files:

• Biblio/Biblio.bib (modified) (1 diff)
• Chapters/Chap_DYN.tex (modified) (2 diffs)
• Chapters/Chap_MISC.tex (modified) (1 diff)
• Chapters/Chap_ZDF.tex (modified) (6 diffs)
• Namelist/nambfr (modified) (1 diff)
• Namelist/namdyn_hpg (modified) (1 diff)
• Namelist/namdyn_nept (copied) (copied from branches/2011/dev_NOC_2011_MERGE/DOC/TexFiles/Namelist/namdyn_nept)
• Namelist/namtra_ldf (modified) (1 diff)

branches/2011/dev_NOC_UKMO_MERGE/DOC/TexFiles/Biblio/Biblio.bib

@@ -1275 +1275 @@
   url = {http://dx.doi.org/10.1016/j.ocemod.2009.12.003},
   issn = {1463-5003},
+}
+
+@ARTICLE{HollowayOM86,
+  author = {Greg Holloway},
+  title = {A Shelf Wave/Topographic Pump Drives Mean Coastal Circulation (part I)},
+  journal = OM,
+  year = {1986},
+  volume = {68},  
+}
+
+@ARTICLE{HollowayJPO92,
+  author = {Greg Holloway},
+  title = {Representing Topographic Stress for Large-Scale Ocean Models},
+  journal = JPO,
+  year = {1992},
+  volume = {22},  
+  pages = {1033--1046},
+}
+
+@ARTICLE{HollowayJPO94,
+  author = {Michael Eby and Greg Holloway},
+  title = {Sensitivity of a Large-Scale Ocean Model to a Parameterization of Topographic Stress},
+  journal = JPO,
+  year = {1994},
+  volume = {24},  
+  pages = {2577--2587},
+}
+
+@ARTICLE{HollowayJGR09,
+  author = {Greg Holloway and Zeliang Wang},
+  title = {Representing eddy stress in an Arctic Ocean model},
+  journal = JGR,
+  year = {2009},
+  doi = {10.1029/2008JC005169},  
+}
+
+@ARTICLE{HollowayOM08,
+  author = {Mathew Maltrud and Greg Holloway},
+  title = {Implementing biharmonic neptune in a global eddying ocean model},
+  journal = OM,
+  year = {2008},
+  volume = {21},  
+  pages = {22--34},
 }
 

branches/2011/dev_NOC_UKMO_MERGE/DOC/TexFiles/Chapters/Chap_DYN.tex

@@ -633 +633 @@
 $\bullet$ Rotated axes scheme (rot) \citep{Thiem_Berntsen_OM06} (\np{ln\_dynhpg\_rot}=true)
 
-Note that expression \eqref{Eq_dynhpg_sco} is used when the variable volume 
+$\bullet$ Pressure Jacobian scheme (prj) \citep{Thiem_Berntsen_OM06} (\np{ln\_dynhpg\_prj}=true)
+
+Note that expression \eqref{Eq_dynhpg_sco} is commonly used when the variable volume 
 formulation is activated (\key{vvl}) because in that case, even with a flat bottom, 
 the coordinate surfaces are not horizontal but follow the free surface 
-\citep{Levier2007}. The other pressure gradient options are not yet available.
+\citep{Levier2007}. Only the pressure jacobian scheme (\np{ln\_dynhpg\_prj}=true) is available as an 
+alternative to the default \np{ln\_dynhpg\_sco}=true when \key{vvl} is active.  The pressure Jacobian scheme uses 
+a constrained cubic spline to reconstruct the density profile across the water column. This method
+maintains the monotonicity between the density nodes and is of a higher order than the linear
+interpolation method. The pressure can be calculated by analytical integration of the density profile and
+a pressure Jacobian method is used to solve the horizontal pressure gradient. This method should
+provide a more accurate calculation of the horizontal pressure gradient than the standard scheme.
 
 %--------------------------------------------------------------------------------------------------------------
@@ -1162 +1170 @@
 
 % ================================================================
+% Neptune effect 
+% ================================================================
+\section  [Neptune effect (\textit{dynnept})]
+                {Neptune effect (\mdl{dynnept})}
+\label{DYN_nept}
+
+The "Neptune effect" (thus named in \citep{HollowayOM86}) is a
+parameterisation of the potentially large effect of topographic form stress
+(caused by eddies) in driving the ocean circulation. Originally developed for
+low-resolution models, in which it was applied via a Laplacian (second-order)
+diffusion-like term in the momentum equation, it can also be applied in eddy
+permitting or resolving models, in which a more scale-selective bilaplacian
+(fourth-order) implementation is preferred. This mechanism has a
+significant effect on boundary currents (including undercurrents), and the
+upwelling of deep water near continental shelves.
+
+The theoretical basis for the method can be found in 
+\citep{HollowayJPO92}, including the explanation of why form stress is not
+necessarily a drag force, but may actually drive the flow. 
+\citep{HollowayJPO94} demonstrate the effects of the parameterisation in
+the GFDL-MOM model, at a horizontal resolution of about 1.8 degrees. 
+\citep{HollowayOM08} demonstrate the biharmonic version of the
+parameterisation in a global run of the POP model, with an average horizontal
+grid spacing of about 32km.
+
+The NEMO implementation is a simplified form of that supplied by
+Greg Holloway, the testing of which was described in \citep{HollowayJGR09}.
+The major simplification is that a time invariant Neptune velocity
+field is assumed.  This is computed only once, during start-up, and
+made available to the rest of the code via a module.  Vertical
+diffusive terms are also ignored, and the model topography itself
+is used, rather than a separate topographic dataset as in
+\citep{HollowayOM08}.  This implementation is only in the iso-level
+formulation, as is the case anyway for the bilaplacian operator.
+
+The velocity field is derived from a transport stream function given by:
+
+\begin{equation} \label{Eq_dynnept_sf}
+\psi = -fL^2H
+\end{equation}
+
+where $L$ is a latitude-dependant length scale given by:
+
+\begin{equation} \label{Eq_dynnept_ls}
+L = l_1 + (l_2 -l_1)\left ( {1 + \cos 2\phi \over 2 } \right )
+\end{equation}
+
+where $\phi$ is latitude and $l_1$ and $l_2$ are polar and equatorial length scales respectively.
+Neptune velocity components, $u^*$, $v^*$ are derived from the stremfunction as:
+
+\begin{equation} \label{Eq_dynnept_vel}
+u^* = -{1\over H} {\partial \psi \over \partial y}\ \ \  ,\ \ \ v^* = {1\over H} {\partial \psi \over \partial x}
+\end{equation}
+
+\smallskip
+%----------------------------------------------namdom----------------------------------------------------
+\namdisplay{namdyn_nept}
+%--------------------------------------------------------------------------------------------------------
+\smallskip
+
+The Neptune effect is enabled when \np{ln\_neptsimp}=true (default=false).
+\np{ln\_smooth\_neptvel} controls whether a scale-selective smoothing is applied
+to the Neptune effect flow field (default=false) (this smoothing method is as
+used by Holloway).  \np{rn\_tslse} and \np{rn\_tslsp} are the equatorial and
+polar values respectively of the length-scale parameter $L$ used in determining
+the Neptune stream function \eqref{Eq_dynnept_sf} and \eqref{Eq_dynnept_ls}.
+Values at intermediate latitudes are given by a cosine fit, mimicking the
+variation of the deformation radius with latitude.  The default values of 12km
+and 3km are those given in \citep{HollowayJPO94}, appropriate for a coarse
+resolution model. The finer resolution study of \citep{HollowayOM08} increased
+the values of L by a factor of $\sqrt 2$ to 17km and 4.2km, thus doubling the
+stream function for a given topography.
+
+The simple formulation for ($u^*$, $v^*$) can give unacceptably large velocities
+in shallow water, and \citep{HollowayOM08} add an offset to the depth in the
+denominator to control this problem. In this implementation we offer instead (at
+the suggestion of G. Madec) the option of ramping down the Neptune flow field to
+zero over a finite depth range. The switch \np{ln\_neptramp} activates this
+option (default=false), in which case velocities at depths greater than
+\np{rn\_htrmax} are unaltered, but ramp down linearly with depth to zero at a
+depth of \np{rn\_htrmin} (and shallower).
+
+% ================================================================

branches/2011/dev_NOC_UKMO_MERGE/DOC/TexFiles/Chapters/Chap_MISC.tex

@@ -253 +253 @@
 Note this implementation may be sensitive to the optimization level. 
 
+\subsection{MPP scalability}
+\label{MISC_mppsca}
+
+The default method of communicating values across the north-fold in distributed memory applications
+(\key{mpp\_mpi}) uses a \textsc{MPI\_ALLGATHER} function to exchange values from each processing
+region in the northern row with every other processing region in the northern row. This enables a
+global width array containing the top 4 rows to be collated on every northern row processor and then
+folded with a simple algorithm. Although conceptually simple, this "All to All" communication will
+hamper performance scalability for large numbers of northern row processors. From version 3.4
+onwards an alternative method is available which only performs direct "Peer to Peer" communications
+between each processor and its immediate "neighbours" across the fold line. This is achieved by
+using the default \textsc{MPI\_ALLGATHER} method during initialisation to help identify the "active"
+neighbours. Stored lists of these neighbours are then used in all subsequent north-fold exchanges to
+restrict exchanges to those between associated regions. The collated global width array for each
+region is thus only partially filled but is guaranteed to be set at all the locations actually
+required by each individual for the fold operation. This alternative method should give identical
+results to the default \textsc{ALLGATHER} method and is recommended for large values of \np{jpni}.
+The new method is activated by setting \np{ln\_nnogather} to be true ({\bf nammpp}). The
+reproducibility of results using the two methods should be confirmed for each new, non-reference
+configuration.
 
 % ================================================================

branches/2011/dev_NOC_UKMO_MERGE/DOC/TexFiles/Chapters/Chap_ZDF.tex

@@ -1 +1 @@
 % ================================================================
-% Chapter Ñ Vertical Ocean Physics (ZDF)
+% Chapter  Vertical Ocean Physics (ZDF)
 % ================================================================
 \chapter{Vertical Ocean Physics (ZDF)}
@@ -539 +539 @@
 the clipping factor is of crucial importance for the entrainment depth predicted in 
 stably stratified situations, and that its value has to be chosen in accordance 
-with the algebraic model for the turbulent ßuxes. The clipping is only activated 
+with the algebraic model for the turbulent fluxes. The clipping is only activated 
 if \np{ln\_length\_lim}=true, and the $c_{lim}$ is set to the \np{rn\_clim\_galp} value.
 
@@ -981 +981 @@
 reduced as necessary to ensure stability; these changes are not reported.
 
+Limits on the bottom friction coefficient are not imposed if the user has elected to
+handle the bottom friction implicitly (see \S\ref{ZDF_bfr_imp}). The number of potential
+breaches of the explicit stability criterion are still reported for information purposes.
+
+% -------------------------------------------------------------------------------------------------------------
+%       Implicit Bottom Friction
+% -------------------------------------------------------------------------------------------------------------
+\subsection{Implicit Bottom Friction (\np{ln\_bfrimp}$=$\textit{T})}
+\label{ZDF_bfr_imp}
+
+An optional implicit form of bottom friction has been implemented to improve
+model stability. We recommend this option for shelf sea and coastal ocean applications, especially 
+for split-explicit time splitting. This option can be invoked by setting \np{ln\_bfrimp} 
+to \textit{true} in the \textit{nambfr} namelist. This option requires \np{ln\_zdfexp} to be \textit{false} 
+in the \textit{namzdf} namelist. 
+
+This implementation is realised in \mdl{dynzdf\_imp} and \mdl{dynspg\_ts}. In \mdl{dynzdf\_imp}, the 
+bottom boundary condition is implemented implicitly.
+
+\begin{equation} \label{Eq_dynzdf_bfr}
+\left.{\left( {\frac{A^{vm} }{e_3 }\ \frac{\partial \textbf{U}_h}{\partial k}} \right)} \right|_{mbk}
+    = \binom{c_{b}^{u}u^{n+1}_{mbk}}{c_{b}^{v}v^{n+1}_{mbk}}
+\end{equation}
+
+where $mbk$ is the layer number of the bottom wet layer. superscript $n+1$ means the velocity used in the
+friction formula is to be calculated, so, it is implicit.
+
+If split-explicit time splitting is used, care must be taken to avoid the double counting of
+the bottom friction in the 2-D barotropic momentum equations. As NEMO only updates the barotropic 
+pressure gradient and Coriolis' forcing terms in the 2-D barotropic calculation, we need to remove
+the bottom friction induced by these two terms which has been included in the 3-D momentum trend 
+and update it with the latest value. On the other hand, the bottom friction contributed by the
+other terms (e.g. the advection term, viscosity term) has been included in the 3-D momentum equations
+and should not be added in the 2-D barotropic mode.
+
+The implementation of the implicit bottom friction in \mdl{dynspg\_ts} is done in two steps as the
+following:
+
+\begin{equation} \label{Eq_dynspg_ts_bfr1}
+\frac{\textbf{U}_{med}-\textbf{U}^{m-1}}{2\Delta t}=-g\nabla\eta-f\textbf{k}\times\textbf{U}^{m}+c_{b}
+\left(\textbf{U}_{med}-\textbf{U}^{m-1}\right)
+\end{equation}
+\begin{equation} \label{Eq_dynspg_ts_bfr2}
+\frac{\textbf{U}^{m+1}-\textbf{U}_{med}}{2\Delta t}=\textbf{T}+
+\left(g\nabla\eta^{'}+f\textbf{k}\times\textbf{U}^{'}\right)-
+2\Delta t_{bc}c_{b}\left(g\nabla\eta^{'}+f\textbf{k}\times\textbf{u}_{b}\right)
+\end{equation}
+
+where $\textbf{T}$ is the vertical integrated 3-D momentum trend. We assume the leap-frog time-stepping
+is used here. $\Delta t$ is the barotropic mode time step and $\Delta t_{bc}$ is the baroclinic mode time step.
+ $c_{b}$ is the friction coefficient. $\eta$ is the sea surface level calculated in the barotropic loops
+while $\eta^{'}$ is the sea surface level used in the 3-D baroclinic mode. $\textbf{u}_{b}$ is the bottom
+layer horizontal velocity.
+
+
+
+
 % -------------------------------------------------------------------------------------------------------------
 %       Bottom Friction with split-explicit time splitting
 % -------------------------------------------------------------------------------------------------------------
-\subsection{Bottom Friction with split-explicit time splitting}
+\subsection{Bottom Friction with split-explicit time splitting (\np{ln\_bfrimp}$=$\textit{F})}
 \label{ZDF_bfr_ts}
 
@@ -993 +1050 @@
 {\key{dynspg\_flt}). Extra attention is required, however, when using 
 split-explicit time stepping (\key{dynspg\_ts}). In this case the free surface 
-equation is solved with a small time step \np{nn\_baro}*\np{rn\_rdt}, while the three 
-dimensional prognostic variables are solved with a longer time step that is a 
-multiple of \np{rn\_rdt}. The trend in the barotropic momentum due to bottom 
+equation is solved with a small time step \np{rn\_rdt}/\np{nn\_baro}, while the three 
+dimensional prognostic variables are solved with the longer time step 
+of \np{rn\_rdt} seconds. The trend in the barotropic momentum due to bottom 
 friction appropriate to this method is that given by the selected parameterisation 
 ($i.e.$ linear or non-linear bottom friction) computed with the evolving velocities 
@@ -1018 +1075 @@
 \end{enumerate}
 
-Note that the use of an implicit formulation
+Note that the use of an implicit formulation within the barotropic loop
 for the bottom friction trend means that any limiting of the bottom friction coefficient 
 in \mdl{dynbfr} does not adversely affect the solution when using split-explicit time 
 splitting. This is because the major contribution to bottom friction is likely to come from 
-the barotropic component which uses the unrestricted value of the coefficient.
-
-The implicit formulation takes the form:
+the barotropic component which uses the unrestricted value of the coefficient. However, if the
+limiting is thought to be having a major effect (a more likely prospect in coastal and shelf seas
+applications) then the fully implicit form of the bottom friction should be used (see \S\ref{ZDF_bfr_imp} ) 
+which can be selected by setting \np{ln\_bfrimp} $=$ \textit{true}.
+
+Otherwise, the implicit formulation takes the form:
 \begin{equation} \label{Eq_zdfbfr_implicitts}
  \bar{U}^{t+ \rdt} = \; \left [ \bar{U}^{t-\rdt}\; + 2 \rdt\;RHS \right ] / \left [ 1 - 2 \rdt \;c_b^{u} / H_e \right ]  
@@ -1091 +1151 @@
 The essential goal of the parameterization is to represent the momentum 
 exchange between the barotropic tides and the unrepresented internal waves 
-induced by the tidal ßow over rough topography in a stratified ocean. 
+induced by the tidal flow over rough topography in a stratified ocean. 
 In the current version of \NEMO, the map is built from the output of 
 the barotropic global ocean tide model MOG2D-G \citep{Carrere_Lyard_GRL03}.

branches/2011/dev_NOC_UKMO_MERGE/DOC/TexFiles/Namelist/nambfr

@@ -9 +9 @@
    ln_bfr2d    = .false.   !  horizontal variation of the bottom friction coef (read a 2D mask file )
    rn_bfrien   =    50.    !  local multiplying factor of bfr (ln_bfr2d=T)
+   ln_bfrimp   = .false.   !  implicit bottom friction (requires ln_zdfexp = .false. if true)
 /

branches/2011/dev_NOC_UKMO_MERGE/DOC/TexFiles/Namelist/namdyn_hpg

@@ -9 +9 @@
    ln_hpg_djc  = .false.   !  s-coordinate (Density Jacobian with Cubic polynomial)
    ln_hpg_rot  = .false.   !  s-coordinate (ROTated axes scheme)
+   ln_hpg_prj  = .false.   !  s-coordinate (Pressure Jacobian scheme)
    rn_gamma    = 0.e0      !  weighting coefficient (wdj scheme)
    ln_dynhpg_imp = .false. !  time stepping: semi-implicit time scheme  (T)

branches/2011/dev_NOC_UKMO_MERGE/DOC/TexFiles/Namelist/namtra_ldf

@@ -9 +9 @@
    ln_traldf_hor    =  .false.  !  horizontal (geopotential)            (require "key_ldfslp" when ln_sco=T)
    ln_traldf_iso    =  .true.   !  iso-neutral                          (require "key_ldfslp")
-   ln_traldf_grif   =  .false.  !  griffies skew flux formulation       (require "key_ldfslp")  ! UNDER TEST, DO NOT USE
-   ln_traldf_gdia   =  .false.  !  griffies operator strfn diagnostics  (require "key_ldfslp")  ! UNDER TEST, DO NOT USE
+   ln_traldf_grif   =  .false.  !  griffies skew flux formulation       (require "key_ldfslp")
+   ln_traldf_gdia   =  .false.  !  griffies operator strfn diagnostics  (require "key_ldfslp")
+   ln_triad_iso     =  .false.  !  griffies operator calculates triads twice => pure lateral mixing in ML (require "key_ldfslp")
+   ln_botmix_grif   =  .false.  !  griffies operator with lateral mixing on bottom (require "key_ldfslp")
    !                       !  Coefficient
    rn_aht_0         =  2000.    !  horizontal eddy diffusivity for tracers [m2/s]