/[MITgcm]/manual/s_autodiff/text/doc_ad_2.tex

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-revision 1.6 by adcroft,
Thu Oct 11 19:37:39 2001 UTC
+revision 1.7 by cnh,
Thu Oct 25 18:36:55 2001 UTC
 Line 21 
 The MITGCM has been adapted for use with
  Tangent linear and Adjoint Model Compiler (TAMC) and its successor TAF
  (Transformation of Algorithms in Fortran), developed
  by Ralf Giering (\cite{gie-kam:98}, \cite{gie:99,gie:00}).
- The first application of the adjoint of the MITGCM for senistivity
+ The first application of the adjoint of the MITGCM for sensitivity
  studies has been published by \cite{maro-eta:99}.
  \cite{sta-eta:97,sta-eta:01} use the MITGCM and its adjoint
  for ocean state estimation studies.
 Line 52 
 $\vec{u}=(u_1,\ldots,u_m)$
  such as forcing functions) to the $n$-dimensional space
  $V \subset I\!\!R^n$ of
  model output variable $\vec{v}=(v_1,\ldots,v_n)$
- (model state, model diagnostcs, objective function, ...)
+ (model state, model diagnostics, objective function, ...)
  under consideration,
  %
  \begin{equation}
 Line 220 
 model integration,
  starting at step 0 and moving up to step $\Lambda$, with intermediate
  ${\cal M}_{\lambda} (\vec{u}) = \vec{v}^{(\lambda+1)}$ and final
  ${\cal M}_{\Lambda} (\vec{u}) = \vec{v}^{(\Lambda+1)} = \vec{v}$.
- Let ${\cal J}$ be a cost funciton which explicitly depends on the
+ Let ${\cal J}$ be a cost function which explicitly depends on the
  final state $\vec{v}$ only
  (this restriction is for clarity reasons only).
  %
 Line 301 
 We note in passing that that the $\delta
  are the Lagrange multipliers of the model equations which determine
  $ \vec{v}^{(\lambda)}$.
- In coponents, eq. (\ref{adjoint}) reads as follows.
+ In components, eq. (\ref{adjoint}) reads as follows.
  Let
  \[
  \begin{array}{rclcrcl}
 Line 322 
 Let
  \end{array}
  \]
  denote the perturbations in $\vec{u}$ and $\vec{v}$, respectively,
- and their adjoint varaiables;
+ and their adjoint variables;
  further
  \[
  M \, = \, \left(
 Line 468 
 variables $u$
  {\it all} intermediate states $ \vec{v}^{(\lambda)} $) are sought.
  In order to be able to solve for each component of the gradient
  $ \partial {\cal J} / \partial u_{i} $ in (\ref{forward})
- a forward calulation has to be performed for each component seperately,
+ a forward calculation has to be performed for each component separately,
  i.e. $ \delta \vec{u} = \delta u_{i} {\vec{e}_{i}} $
  for  the $i$-th forward calculation.
  Then, (\ref{forward}) represents the
 Line 487 
 M^T \left( \nabla_v {\cal J}^T \left(\de
  \nabla_u {\cal J}^T \cdot \delta \vec{J}
  \]
  where now $ \delta \vec{J} \in I\!\!R^l $ is a vector of
- dimenison $ l $.
+ dimension $ l $.
  In this case $ l $ reverse simulations have to be performed
  for each $ \delta J_{k}, \,\, k = 1, \ldots, l $.
  Then, the reverse mode is more efficient as long as
  $ l < n $, otherwise the forward mode is preferable.
- Stricly, the reverse mode is called adjoint mode only for
+ Strictly, the reverse mode is called adjoint mode only for
  $ l = 1 $.
  A detailed analysis of the underlying numerical operations
 Line 607 
 at every timestep
  [i.e. every hour $ i=0,...,5$ corresponding to
  $ k_{i}^{lev1} = 66, 67, \ldots, 71 $].
  Thus, the  final state $ v_n = v_{k_{n}^{lev1}} $ is reached
- and the model state of all peceeding timesteps along the last
+ and the model state of all  proceeding timesteps along the last
  sub-subsections are available, enabling integration backwards
  in time along the last sub-subsection.
  Thus, the adjoint can be computed along this last
 Line 683 
 The AD-relevant hooks in the code are sk
  \subsection{Overview of the experiment}
- We describe an adjoint sensitivity analysis of outgassing from
+ We describe an adjoint sensitivity analysis of out-gassing from
  the ocean into the atmosphere of a carbon-like tracer injected
  into the ocean interior (see \cite{hil-eta:01}).
 Line 691 
 into the ocean interior (see \cite{hil-e
  For this work the MITGCM was augmented with a thermodynamically
  inactive tracer, $C$. Tracer residing in the ocean
- model surface layer is outgassed according to a relaxation time scale,
+ model surface layer is out-gassed according to a relaxation time scale,
  $\mu$. Within the ocean interior, the tracer is passively advected
  by the ocean model currents. The full equation for the time evolution
  %
 Line 711 
 parameterized according to Gent/McWillia
  The convection function, $\Gamma$, mixes $C$ vertically wherever the
  fluid is locally statically unstable.
- The outgassing time scale, $\mu$, in eqn. (\ref{carbon_ddt})
+ The out-gassing time scale, $\mu$, in eqn. (\ref{carbon_ddt})
  is set so that \( 1/\mu \sim 1 \ \mathrm{year} \) for the surface
  ocean and $\mu=0$ elsewhere. With this value, eqn. (\ref{carbon_ddt})
  is valid as a prognostic equation for small perturbations in oceanic
  carbon concentrations. This configuration provides a
  powerful tool for examining the impact of large-scale ocean circulation
- on $ CO_2 $ outgassing due to interior injections.
+ on $ CO_2 $ out-gassing due to interior injections.
  As source we choose a constant in time injection of
  $ S = 1 \,\, {\rm mol / s}$.
 Line 728 
 $4^\circ \times 4^\circ$ resolution hori
  geography and bathymetry. Twenty vertical layers are used with
  vertical spacing ranging
  from 50 m near the surface to 815 m at depth.
- Driven to steady-state by climatalogical wind-stress, heat and
+ Driven to steady-state by climatological wind-stress, heat and
  fresh-water forcing the model reproduces well known large-scale
  features of the ocean general circulation.
- \subsubsection{Outgassing cost function}
+ \subsubsection{Out-gassing cost function}
- To quantify and understand outgassing due to injections of $C$
+ To quantify and understand out-gassing due to injections of $C$
  in eqn. (\ref{carbon_ddt}),
  we define a cost function $ {\cal J} $ that measures the total amount of
- tracer outgassed at each timestep:
+ tracer out-gassed at each timestep:
  %
  \begin{equation}
  \label{cost_tracer}
  {\cal J}(t=T)=\int_{t=0}^{t=T}\int_{A} \mu C \, dA \, dt
  \end{equation}
  %
- Equation(\ref{cost_tracer}) integrates the outgassing term, $\mu C$,
+ Equation(\ref{cost_tracer}) integrates the out-gassing term, $\mu C$,
  from (\ref{carbon_ddt})
  over the entire ocean surface area, $A$, and accumulates it
  up to time $T$.
  Physically, ${\cal J}$ can be thought of as representing the amount of
- $CO_2$ that our model predicts would be outgassed following an
+ $CO_2$ that our model predicts would be out-gassed following an
  injection at rate $S$.
  The sensitivity of ${\cal J}$ to the spatial location of $S$,
  $\frac{\partial {\cal J}}{\partial S}$,
  can be used to identify regions from which circulation
- would cause $CO_2$ to rapidly outgas following injection
+ would cause $CO_2$ to rapidly out-gas following injection
  and regions in which $CO_2$ injections would remain effectively
- sequesterd within the ocean.
+ sequestered within the ocean.
  \subsection{Code configuration}
  The model configuration for this experiment resides under the
  directory {\it verification/carbon/}.
- The code customisation routines are in {\it verification/carbon/code/}:
+ The code customization routines are in {\it verification/carbon/code/}:
  %
  \begin{itemize}
  %
 Line 830 
 $ adjoint/ $:
  \end{itemize}
  %
- Below we describe the customisations of this files which are
+ Below we describe the customizations of this files which are
  specific to this experiment.
  \subsubsection{File {\it .genmakerc}}
 Line 871 
 advection/diffusion of a passive tracer
  model integration. \\
  \hspace*{4ex} {\tt \#define ALLOW\_MIT\_ADJOINT\_RUN} \\
  This flag enables the inclusion of some AD-related fields
- concerning initialisation, link between control variables
+ concerning initialization, link between control variables
  and forward model variables, and the call to the top-level
  forward/adjoint subroutine {\it adthe\_main\_loop}
  instead of {\it the\_main\_loop}. \\
 Line 907 
 enables the checkpointing feature of TAM
  (see Section \ref{???}).
  In the present example a 3-level checkpointing is implemented.
  The code contains the relevant store directives, common block
- and tape initialisations, storing key computation,
+ and tape initializations, storing key computation,
  and loop index handling.
  The checkpointing length at each level is defined in
  file {\it tamc.h}, cf. below.
  %
  \item Cost function package: {\it pkg/cost/} \\
  This package contains all relevant routines for
- initialising, accumulating and finalizing the cost function
+ initializing, accumulating and finalizing the cost function
  (see Section \ref{???}). \\
  \hspace*{4ex} {\tt \#define ALLOW\_COST} \\
  enables all general aspects of the cost function handling,
- in particular the hooks in the foorward code for
+ in particular the hooks in the forward code for
- initialising, accumulating and finalizing the cost function. \\
+ initializing, accumulating and finalizing the cost function. \\
  \hspace*{4ex} {\tt \#define ALLOW\_COST\_TRACER} \\
  includes the call to the cost function for this
  particular experiment, eqn. (\ref{cost_tracer}).
 Line 958 
 model. It is identical to the {\it verif
  \hspace*{4ex} {\tt sNx = 90} \\
  \hspace*{4ex} {\tt sNy = 40} \\
  \hspace*{4ex} {\tt Nr = 20} \\
- It correpsponds to a single-tile/single-processor setup:
+ It corresponds to a single-tile/single-processor setup:
  {\tt nSx = nSy = 1, nPx = nPy = 1},
  with standard overlap dimensioning
  {\tt OLx = OLy = 3}.
 Line 1037 
 The following parameters may be worth de
  \subsubsection{File {\it makefile}}
- This file contains all relevant paramter flags and
+ This file contains all relevant parameter flags and
  lists to run TAMC or TAF.
  It is assumed that TAMC is available to you, either locally,
  being installed on your network, or remotely through the 'TAMC Utility'.
 Line 1078 
 the gradient vector $ \nabla_v J $.
  {\tt <file names>} refers to the list of files {\it .f} which are to be
  analyzed by TAMC. This list is generally smaller than the full list
  of code to be compiled. The files not contained are either
- above the top-level routine (some initialisations), or are
+ above the top-level routine (some initializations), or are
  deliberately hidden from TAMC, either because hand-written
  adjoint routines exist, or the routines must not (or don't have to)
  be differentiated. For each routine which is part of the flow tree
 Line 1211 
 TAMC or TAF info is written to file
  The multi-threading capability of the MITGCM requires a slight
  change in the parameter list of some routines that are related to
  to active file handling.
- This postprocessing invokes the sed script {\it adjoint\_ecco\_sed.com}
+ This post-processing invokes the sed script {\it adjoint\_ecco\_sed.com}
  to insert the threading counter {\bf myThId} into the parameter list
  of those subroutines.
  The resulting code is written to file {\it tamc\_code\_sed\_ad.f}
  and appended to the file {\it adjoint\_model.F}.
- This concludes the adjoint codel generation.
+ This concludes the adjoint code generation.
  %
  \item
  {\tt cd ../bin} \\
 Line 1296 
 $ {\cal J}(\vec{u}) \, = \, {\cal J}(M(\
  The input is referred to as the
  {\sf independent variables} or {\sf control variables}.
  All aspects relevant to the treatment of the cost function $ {\cal J} $
- (parameter setting, initialisation, accumulation,
+ (parameter setting, initialization, accumulation,
  final evaluation), are controlled by the package {\it pkg/cost}.
  \begin{figure}[h!]
 Line 1345 
 automatic differentiation, the CPP optio
  {\bf ALLOW\_ADJOINT\_RUN} should be defined
  (file {\it CPP\_OPTIONS.h}).
- \subsubsection{Initialisation}
+ \subsubsection{Initialization}
  %
- The initialisation of the {\it cost} package is readily enabled
+ The initialization of the {\it cost} package is readily enabled
  as soon as the CPP option {\bf ALLOW\_ADJOINT\_RUN} is defined.
  %
  \begin{itemize}
 Line 1378 
 Variables: {\it cost\_init}
  }
  \\
  This S/R
- initialises the different cost function contributions.
+ initializes the different cost function contributions.
- The contribtion for the present example is {\bf objf\_tracer}
+ The contribution for the present example is {\bf objf\_tracer}
  which is defined on each tile (bi,bj).
  %
  \end{itemize}
 Line 1455 
 as variable assignments. Therefore, file
  active variables are written and from which active variables
  are read are called {\sf active files}.
  All aspects relevant to the treatment of the control variables
- (parameter setting, initialisation, perturbation)
+ (parameter setting, initialization, perturbation)
- are controled by the package {\it pkg/ctrl}.
+ are controlled by the package {\it pkg/ctrl}.
  \begin{figure}[h!]
  \input{part5/doc_ctrl_flow}
 Line 1482 
 To enable the directory to be included t
  Each control variable is enabled via its own CPP option
  in {\it ECCO\_CPPOPTIONS.h}.
- \subsubsection{Initialisation}
+ \subsubsection{Initialization}
  %
  \begin{itemize}
  %
 Line 1522 
 Two important issues related to the hand
  variables in the MITGCM need to be addressed.
  First, in order to save memory, the control variable arrays
  are not kept in memory, but rather read from file and added
- to the initial fields during the model initialisation phase.
+ to the initial fields during the model initialization phase.
  Similarly, the corresponding adjoint fields which represent
  the gradient of the cost function w.r.t. the control variables
  are written to file at the end of the adjoint integration.
 Line 1602 
 dummy variable {\bf xx\_tr1\_dummy} is i
  and an 'active read' routine of the adjoint support
  package {\it pkg/autodiff} is invoked.
  The read-procedure is tagged with the variable
- {\bf xx\_tr1\_dummy} enabbling TAMC to recognize the
+ {\bf xx\_tr1\_dummy} enabling TAMC to recognize the
- initialisation of the perturbation.
+ initialization of the perturbation.
  The modified call of TAMC thus reads
  %
  \begin{verbatim}
 Line 1714 
 variables are written to {\bf adxx\_ ...
  \begin{itemize}
  %
  \item {\bf vector\_ctrl}: the control vector \\
- At the very beginning of the model initialisation,
+ At the very beginning of the model initialization,
  the updated compressed control vector is read (or initialised)
  and distributed to 2-dim. and 3-dim. control variable fields.
  %

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