Lorenz-96 model with PDAF

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.

Running the test case

Runnning a data assimilation experimnet 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 explained below.

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
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.