--- manual/s_phys_pkgs/text/gridalt.tex	2005/08/02 21:15:00	1.5
+++ manual/s_phys_pkgs/text/gridalt.tex	2010/08/27 13:15:37	1.13
@@ -6,7 +6,8 @@
 
 \subsubsection {Introduction} 
 
-The gridalt package is designed to allow different components of the MITgcm to
+The gridalt package \citep{mol:09} 
+is designed to allow different components of MITgcm to
 be run using horizontal and/or vertical grids which are different from the main 
 model grid. The gridalt routines handle the definition of the all the various
 alternative grid(s) and the mappings between them and the MITgcm grid.
@@ -43,11 +44,10 @@
 \begin{figure}[htbp]
 \vspace*{-0.4in}
 \begin{center}
-\includegraphics[height=2.4in]{part6/vertical.eps}
-\caption{Vertical discretization for the MITgcm (dark grey lines) and for the
+\includegraphics[height=2.4in]{s_phys_pkgs/figs/vertical.eps}
+\caption{Vertical discretization for MITgcm (dark grey lines) and for the
 atmospheric physics (light grey lines). In this implementation, all MITgcm level
 interfaces must coincide with atmospheric physics level interfaces.}
-must be entirely
 \end{center}
 \end{figure}
 
@@ -97,7 +97,7 @@
 
 \item{Compute the tendency due to physics processes.}
 
-\item{Advance the physics state: ${T^{n+1}^{**}}_{phys}(l) = {T^n}_{phys}(l) + \delta T_{phys}$.}
+\item{Advance the physics state: ${{T^{n+1}}^{**}}_{phys}(l) = {T^n}_{phys}(l) + \delta T_{phys}$.}
 
 \item{Interpolate the physics tendency to the dynamics grid, and advance the dynamics
 state by physics and dynamics tendencies:
@@ -105,10 +105,10 @@
 
 \item{Interpolate the dynamics tendency to the physics grid, and update the physics
 grid due to dynamics tendencies: 
-${T^{n+1}^*}_{phys}(l)$ = ${T^{n+1}^{**}}_{phys}(l) + {\delta T_{dyn}(L)}(l)$.}
+${{T^{n+1}}^*}_{phys}(l)$ = ${{T^{n+1}}^{**}}_{phys}(l) + {\delta T_{dyn}(L)}(l)$.}
 
 \item{Apply correction term to physics state to account for divergence from dynamics state:
-${T^{n+1}}_{phys}(l)$ = ${T^{n+1}^*}_{phys}(l) + \gamma \{  T_{dyn}(L) - [T_{phys}(l)](L) \}(l)$.} \\
+${T^{n+1}}_{phys}(l)$ = ${{T^{n+1}}^*}_{phys}(l) + \gamma \{  T_{dyn}(L) - [T_{phys}(l)](L) \}(l)$.} \\
 Where $\gamma=1$ here. 
 
 \end{enumerate}
@@ -117,19 +117,148 @@
 In order to minimize the correction terms for the state variables on the alternative,
 higher resolution grid, the vertical interpolation scheme must be constructed so that
 a dynamics-to-physics interpolation can be exactly reversed with a physics-to-dynamics mapping.
-The simple scheme employed to achieve this is:
+The simple scheme employed to achieve this is:\\
 
 Coarse to fine:\
 For all physics layers l in dynamics layer L, $ T_{phys}(l) = \{T_{dyn}(L)\} = T_{dyn}(L) $.
 
 Fine to coarse:\
-For all physics layers l in dynamics layer L, $T_{dyn}(L) = [T_{phys}(l)] = \int{T_{phys} dp } $.
+For all physics layers l in dynamics layer L, $T_{dyn}(L) = [T_{phys}(l)] = \int{T_{phys} dp } $.\\
 
 Where $\{\}$ is defined as the dynamics-to-physics operator and $[ ]$ is the physics-to-dynamics operator, $T$ stands for any state variable, and the subscripts $phys$ and $dyn$ stand for variables on
 the physics and dynamics grids, respectively.
 
 \subsubsection {Key subroutines, parameters and files } 
 
+\noindent
+One of the central elements of the gridalt package is the routine which 
+is called from subroutine gridalt\_initialise to define the grid to be
+used for the high end physics calculations. Routine make\_phys\_grid
+passes back the parameters which define the grid, ultimately stored 
+in the common block gridalt\_mapping.
+
+\begin{verbatim}
+       subroutine make_phys_grid(drF,hfacC,im1,im2,jm1,jm2,Nr,
+     . Nsx,Nsy,i1,i2,j1,j2,bi,bj,Nrphys,Lbot,dpphys,numlevphys,nlperdyn)
+c***********************************************************************
+c Purpose: Define the grid that the will be used to run the high-end
+c          atmospheric physics.
+c
+c Algorithm: Fit additional levels of some (~) known thickness in
+c          between existing levels of the grid used for the dynamics
+c
+c Need:    Information about the dynamics grid vertical spacing
+c
+c Input:   drF         - delta r (p*) edge-to-edge
+c          hfacC       - fraction of grid box above topography
+c          im1, im2    - beginning and ending i - dimensions
+c          jm1, jm2    - beginning and ending j - dimensions
+c          Nr          - number of levels in dynamics grid
+c          Nsx,Nsy     - number of processes in x and y direction
+c          i1, i2      - beginning and ending i - index to fill
+c          j1, j2      - beginning and ending j - index to fill
+c          bi, bj      - x-dir and y-dir index of process
+c          Nrphys      - number of levels in physics grid
+c
+c Output:  dpphys      - delta r (p*) edge-to-edge of physics grid
+c          numlevphys  - number of levels used in the physics
+c          nlperdyn    - physics level number atop each dynamics layer
+c
+c NOTES: 1) Pressure levs are built up from bottom, using p0, ps and dp:
+c              p(i,j,k)=p(i,j,k-1) + dp(k)*ps(i,j)/p0(i,j)
+c        2) Output dp's are aligned to fit EXACTLY between existing
+c           levels of the dynamics vertical grid
+c        3) IMPORTANT! This routine assumes the levels are numbered
+c           from the bottom up, ie, level 1 is the surface.
+c           IT WILL NOT WORK OTHERWISE!!!
+c        4) This routine does NOT work for surface pressures less
+c           (ie, above in the atmosphere) than about 350 mb
+c***********************************************************************
+\end{verbatim}
+
+\noindent In the case of the grid used to compute the atmospheric physical
+forcing (fizhi package), the locations of the grid points move in time with 
+the MITgcm $p^*$ coordinate, and subroutine gridalt\_update is called during 
+the run to update the locations of the grid points:
+
+\begin{verbatim}
+       subroutine gridalt_update(myThid)
+c***********************************************************************
+c Purpose: Update the pressure thicknesses of the layers of the
+c          alternative vertical grid (used now for atmospheric physics).
+c
+c Calculate: dpphys    - new delta r (p*) edge-to-edge of physics grid
+c                        using dpphys0 (initial value) and rstarfacC
+c***********************************************************************
+\end{verbatim}
+
+\noindent The gridalt package also supplies utility routines which perform
+the mappings from one grid to the other. These routines are called from the 
+code which computes the fields on the alternative (fizhi) grid.
+
+\begin{verbatim}
+      subroutine dyn2phys(qdyn,pedyn,im1,im2,jm1,jm2,lmdyn,Nsx,Nsy,
+     . idim1,idim2,jdim1,jdim2,bi,bj,windphy,pephy,Lbot,lmphy,nlperdyn,
+     . flg,qphy)
+C***********************************************************************
+C Purpose:
+C   To interpolate an arbitrary quantity from the 'dynamics' eta (pstar)
+C               grid to the higher resolution physics grid
+C Algorithm:
+C   Routine works one layer (edge to edge pressure) at a time.
+C   Dynamics -> Physics retains the dynamics layer mean value,
+C   weights the field either with the profile of the physics grid
+C   wind speed (for U and V fields), or uniformly (T and Q)
+C
+C Input:
+C   qdyn..... [im,jm,lmdyn] Arbitrary Quantity on Input Grid
+C   pedyn.... [im,jm,lmdyn+1] Pressures at bottom edges of input levels
+C   im1,2 ... Limits for Longitude Dimension of Input
+C   jm1,2 ... Limits for Latitude  Dimension of Input
+C   lmdyn.... Vertical  Dimension of Input
+C   Nsx...... Number of processes in x-direction
+C   Nsy...... Number of processes in y-direction
+C   idim1,2.. Beginning and ending i-values to calculate
+C   jdim1,2.. Beginning and ending j-values to calculate
+C   bi....... Index of process number in x-direction
+C   bj....... Index of process number in x-direction
+C   windphy.. [im,jm,lmphy] Magnitude of the wind on the output levels
+C   pephy.... [im,jm,lmphy+1] Pressures at bottom edges of output levels
+C   lmphy.... Vertical  Dimension of Output
+C   nlperdyn. [im,jm,lmdyn] Highest Physics level in each dynamics level
+C   flg...... Flag to indicate field type (0 for T or Q, 1 for U or V)
+C
+C Output:
+C   qphy..... [im,jm,lmphy] Quantity at output grid (physics grid)
+C
+C Notes:
+C   1) This algorithm assumes that the output (physics) grid levels
+C      fit exactly into the input (dynamics) grid levels
+C***********************************************************************
+\end{verbatim}
+
+\noindent And similarly, gridalt contains subroutine phys2dyn.
+
+\subsubsection {Gridalt Diagnostics}
+\label{sec:pkg:gridalt:diagnostics}
+
+{\footnotesize
+\begin{verbatim}
+
+------------------------------------------------------------------------
+<-Name->|Levs|<-parsing code->|<--  Units   -->|<- Tile (max=80c) 
+------------------------------------------------------------------------
+DPPHYS  | 20 |SM      ML      |Pascal          |Pressure Thickness of Layers on Fizhi Grid
+\end{verbatim}
+}
+
 \subsubsection {Dos and donts}
 
 \subsubsection {Gridalt Reference} 
+
+\subsubsection{Experiments and tutorials that use gridalt}
+\label{sec:pkg:gridalt:experiments}
+
+\begin{itemize}
+\item{Fizhi experiment, in fizhi-cs-32x32x10 verification directory }
+\end{itemize}
