= Lorenz-96 model with PDAF = 

[[PageOutline(2-3,Contents of this page)]]

The implementation of the Lorenz-96 model coupled to PDAF is in the directory `testsuite/src/lorenz96/` of the PDAF package.
Provided is a full implementation of PDAF with the nonlinear Lorenz96 model (E. N. Lorenz (1996) Predictability - a problem partly 
solved. Proceedings Seminar on Predictability, ECMWF, READING, UK) providing various filter and smoother methods. We used this implementation for different publications in which we studied the behavior of different data assimilation methods.

Next to the implementation of Lorenz-96 with PDAF, the test case provides tool programs and scripts that
allow to run a test case and to display the outputs. Note, that this implementation runs without parallelization.


== Running the test case  ==

Runnning a data assimilation experiment with the Lorenz-96 model is a two step process: First one runs the model without PDAF to generate a file holding the trajectory of a forward run. Then one generates files with observations and a covariance matrix for the initialization of the initial ensemble. In the second step, one compiles the Lorenz-96 with activated coupling to PDAF and runs the experiments. 

=== 1. Compile and run the forward model without assimilation ===

First change in the file `make.arch/linux_gfortran.h` the line
{{{
CPP_DEFS = -DUSE_PDAF
}}}
to 
{{{
CPP_DEFS = #-DUSE_PDAF
}}}
to deactivate the coupling to PDAF in the model code. Now build the forward model program with
{{{
  cd testsuite/src
  make lorenz_96 PDAF_ARCH=linux_gfortran
}}}
in the directory `testsuite/src/` of the PDAF package. You have to ensure
that in the machine-specific make include file `linux_gfortran.h` `-DUSE_PDAF` is not defined
for CPP_DEFS (such that calls to PDAF are not active). The executable
is generated in `testsuite/bin/`.

'''Note''': The implementation uses the NetCDF library for file outputs. If the compilation above fails, please ensure the netcdf-library ist installed. On computers running Linux, it is usually available as a package of the operating system. 

To run the forward model use
{{{
  cd ../bin
  ./lorenz_96 -total_steps 10000
}}}
This runs Lorenz-96 model for 10000 time steps and the trajectory is written into a file `state.nc`. 

=== 2. Generate observations and a covariance matrix ===

To build the executables for the tool programs use
{{{
  cd ../src/lorenz96/tools
  make all PDAF_ARCH=linux_gfortran
}}}

Now run
{{{
  ./generate_obs
}}}
and
{{{
  ./generate_covar
}}}
to generate a file holding observations (`obs.nc` in testsuite/bin/) and
a file holding the covariance matrix information (`covar.nc` in
testsuite/bin/), which is used to generate an initial ensemble for
the data assimilation experiments.


=== 3. Build and run the assimilation program ===

Change in the `make.arch/linux_gfortran.h` the line
{{{
CPP_DEFS = #-DUSE_PDAF
}}}
back to 
{{{
CPP_DEFS = -DUSE_PDAF
}}}
to activate the coupling to PDAF in the model code. 

Now compile the Lorenz-96 model with activated
PDAF. First clean the directories for the main driver and the Lorenz-96 model using
{{{
  cd ../../
  make cleandriver PDAF_ARCH=linux_gfortran
  make cleanlorenz_96 PDAF_ARCH=linux_gfortran
}}}
(This removes object files that were compiled without support for PDAF)
Then build the executable using
{{{
  make pdaf_lorenz_96 PDAF_ARCH=linux_gfortran
}}} 
The program `pdaf_lorenz_96` is generated in testsuite/bin.


To run the assimilation program, do
{{{
  cd ../bin
  ../src/lorenz96/tools/runasml.sh 
}}}
The script runsasml.sh runs 11 experiments with a fixed ensemble size, but
different covariance inflations (forgetting factors). The execution can 
take about 2 minutes.

=== 4. Plot output from the assimilation experiments ===

To display the output of the assimilation experiments we provide several plotting scripts for Matlab and Octave. To use them do
{{{
cd ../src/lorenz96/plotting/
}}}
and see the file README there for a description of the available plotting scripts. 

For example, `plot_example.m`
plots the true and estimated mean RMS errors as a function of the
forgetting factor. For the usage of the other functions, use 'help'
in Matlab.


== Run options ==

The implementation for the Lorenz-96 model has a wide range of options. For the full set, we reommend to check the list in the file init_pdaf.F90. Essentiall all of the options can be specified on the command line in the format '-VARIABLE VALUE', where VARIABLE is the name of the variable in the program and VALUE is its value. The experiments in `runasml.sh` are executed like
{{{
./pdaf_lorenz_96 -total_steps 5000 -step_null 1000 -dim_ens 30 -filtertype 1 -forget 0.99 -file_asml t1_N30_f0.99.nc
}}}
The meaning of the different options is the following:

||= Variable =||= Description =||= Default value =||
|| dim_ens || ensemble size || 30
|| file_asml || the name of the output file || assimilation.nc ||
|| filtertype || Specifies the filter to use; 1 sets the SEIK filter || 1 || 
|| forget  || value of the forgetting factor for multiplicative variance inflation || 1.0 ||
|| step_null || initial time step of experiment. This specifies the offset of the observations which are generated from a model forward run. A value 1000 avoids the spin-up phase of the model || none - always set it ||
|| total_steps || number of time step in the experiment || none - always set it ||

Some further options:

||= Variable =||= Description =||= Default value =||
|| delt_obs  || time interval between observation, i.e. for forecast length || 1 ||
|| dim_lag   || set the time lag for the smoother (the smoother is actiave for dim_lag>0) || 0 ||
|| dim_state || set state dimension (if changed, the true state trajectory, observations, and covariance matrix file need to be re-generated) || 40 ||
|| dx_obs    || distance between observation on the grid; let's you specify an incompletely observated state (only used when use_obs_mask=.true.) || 1 ||
|| local_range || localization radius in grid points || 5 ||
|| locweight || choose localiztion weight function, e.g. 4 is the 5th-order polynomial mimicking a Gaussian (see Gaspari and Cohn 1999) || 0 || 
|| model_error || a logical variable activiting model error noise || .false. ||
|| model_err_amp || amplitude of the model error || 0.1 ||
|| numobs || number of observed grid points; the points 1 to numobs are observed (can be combined with dx_obs; only used when use_obs_mask=.true.) || dim_state ||
|| use_obs_mask || whether to use incomplete observations (need to be .true. for any other settings on the observation density to be used) || .false. ||

For the full set of options, please see init_pdaf.F90. There, also the possible setting e..g for `filtertype` are described.