DART “pre_guam release” Documentation¶
Overview of DART¶
The Data Assimilation Research Testbed (DART) is designed to facilitate the combination of assimilation algorithms, models, and observation sets to allow increased understanding of all three. The DART programs have been compiled with the Intel 7.1 Fortran compiler and run on a linux compute-server. If your system is different, you will definitely need to read the Customizations section.
The latest software release – “pre_guam”[22 Mb – .tar.gz]
DART programs can require three different types of input. First, some of the DART programs, those for creating synthetic
observational datasets, require interactive input from the keyboard. For simple cases, this interactive input can be
made directly from the keyboard. In more complicated cases, a file containing the appropriate keyboard input can be
created and this file can be directed to the standard input of the DART program. Second, many DART programs expect one
or more input files in DART specific formats to be available. For instance, perfect_model_obs creates a synthetic
observation set given a particular model and a description of a sequence of observations requires an input file that
describes this observation sequence. At present, the observation files for DART are inefficient but human-readable ascii
files in a custom format. Third, many DART modules (including main programs) make use of the Fortan90 namelist facility
to obtain values of certain parameters at run-time. All programs look for a namelist input file called input.nml in
the directory in which the program is executed. The input.nml file can contain a sequence of individual Fortran90
namelists which specify values of particular parameters for modules that compose the executable program. Unfortunately,
the Fortran90 namelist interface is poorly defined in the language standard, leaving considerable leeway to compiler
developers in implementing the facility. The Intel 7.1 compiler has some particularly unpleasant behavior when a
namelist file contains an entry that is NOT defined in the program reading the namelist. Error behavior is
unpredictable, but often results in read errors for other input files opened by DART programs. If you encounter run-time
read errors, the first course of action should be to ensure the components of the namelist are actual components.
Changing the names of the namelist components will create unpleasantries. DART provides a mechanism that
automatically generates namelists with the default values for each program to be run.
DART uses the netCDF self-describing data format with a particular
metadata convention to describe output that is used to analyze the results of assimilation experiments. These files have
the extension .nc and can be read by a number of standard data analysis tools. A set of
Matlab scripts, designed to produce graphical diagnostics from DART netCDF output files
are available. DART users have also used ncview to create
rudimentary graphical displays of output data fields. The NCO tools, produced by UCAR’s
Unidata group, are available to do operations like concatenating, slicing, and dicing of netCDF files.
Requirements: an F90 compiler¶
The DART software has been successfully built on several Linux/x86 platforms with the Intel Fortran Compiler 7.1 for Linux, which is free for individual scientific use. It has also been built and successfully run with the Portland Group Fortran Compiler (5.02), and again with the Intel 8.0.034 compiler. Since recompiling the code is a necessity to experiment with different models, there are no binaries to distribute.
DART uses the netCDF self-describing data format for the results of
assimilation experiments. These files have the extension .nc and can be read by a number of standard data analysis
tools. In particular, DART also makes use of the F90 interface to the library which is available through the
netcdf.mod and typesizes.mod modules. IMPORTANT: different compilers create these modules with different
“case” filenames, and sometimes they are not both installed into the expected directory. It is required that both
modules be present. The normal place would be in the netcdf/include directory, as opposed to the netcdf/lib
directory.
If the netCDF library does not exist on your system, you must build it (as well as the F90 interface modules). The library and instructions for building the library or installing from an RPM may be found at the netCDF home page: http://www.unidata.ucar.edu/packages/netcdf/ Pay particular attention to the compiler-specific patches that must be applied for the Intel Fortran Compiler. (Or the PG compiler, for that matter.)
The location of the netCDF library, libnetcdf.a, and the locations of both netcdf.mod and typesizes.mod will
be needed by the makefile template, as described in the compiling section.
DART also uses the very common udunits library for manipulating units of physical quantities. If, somehow, it is not installed on your system, you will need to install it (instructions are available from Unidata’s Downloads page).
The location of the udunits library, libudunits.a, will be needed by the makefile template, as described in the
compiling section.
Unpacking the distribution¶
The DART source code is distributed as a compressed tar file. DART_fiji.tar.gz [22347692 bytes].
When untarred, the source tree will begin with a directory named DART and will be approximately 105 Mb. Compiling
the code in this tree (as is usually the case) will necessitate much more space.
gunzip DART_fiji.tar.gz
tar -xvf DART_fiji.tar
The code tree is very “bushy”; there are many directories of support routines, etc. but only a few directories involved
with the customization and installation of the DART software. If you can compile and run ONE of the low-order models,
you should be able to compile and run ANY of the low-order models. For this reason, we can focus on the Lorenz `63
model. Subsequently, the only directories with files to be modified to check the installation are: DART/mkmf,
DART/models/lorenz_63/work, and DART/matlab (but only for analysis).
Customizing the build scripts – overview¶
DART executable programs are constructed using two tools: make and mkmf. The make utility is a relatively
common piece of software that requires a user-defined input file that records dependencies between different source
files. make then performs a hierarchy of actions when one or more of the source files is modified. The mkmf
utility is a custom preprocessor that generates a make input file (named Makefile) and an example namelist
input.nml.mkmf with the default values. The Makefile is designed specifically to work with object-oriented
Fortran90 (and other languages) for systems like DART.
mkmf requires two separate input files. The first is a `template’ file which specifies details of the commands
required for a specific Fortran90 compiler and may also contain pointers to directories containing pre-compiled
utilities required by the DART system. This template file will need to be modified to reflect your system. The
second input file is a `path_names’ file which includes a complete list of the locations (either relative or absolute)
of all Fortran90 source files that are required to produce a particular DART program. Each ‘path_names’ file must
contain a path for exactly one Fortran90 file containing a main program, but may contain any number of additional paths
pointing to files containing Fortran90 modules. An mkmf command is executed which uses the ‘path_names’ file and the
mkmf template file to produce a Makefile which is subsequently used by the standard make utility.
mkmf see the FMS mkmf
description.mkmf is that it also creates an example namelist file for each program. The example
namelist is called input.nml.mkmf, so as not to clash with any exising input.nml that may exist in that
directory.Building and customizing the ‘mkmf.template’ file¶
A series of templates for different compilers/architectures exists in the DART/mkmf/ directory and have names with
extensions that identify either the compiler, the architecture, or both. This is how you inform the build process of the
specifics of your system. Our intent is that you copy one that is similar to your system into mkmf.template and
customize it. For the discussion that follows, knowledge of the contents of one of these templates (i.e.
mkmf.template.pgi) is needed: (note that only the first few lines are shown here)
# Makefile template for PGI f90 FC = pgf90 CPPFLAGS = FFLAGS = -r8 -Ktrap=fp -pc 64 -I/usr/local/netcdf/include LD = pgf90 LDFLAGS = $(LIBS) LIBS = -L/usr/local/netcdf/lib -lnetcdf -L/usr/local/udunits-1.11.7/lib -ludunits LIST = -Mlist # you should never need to change any lines below. …
Essentially, each of the lines defines some part of the resulting Makefile. Since make is particularly good at
sorting out dependencies, the order of these lines really doesn’t make any difference. The FC = pgf90 line
ultimately defines the Fortran90 compiler to use, etc. The lines which are most likely to need site-specific changes
start with FFLAGS and LIBS, which indicate where to look for the netCDF F90 modules and the location of the
netCDF and udunits libraries.
` <fflags>`__
FFLAGS¶
Each compiler has different compile flags, so there is really no way to exhaustively cover this other than to say the
templates as we supply them should work – depending on the location of the netCDF modules netcdf.mod and
typesizes.mod. Change the /usr/local/netcdf/include string to reflect the location of your modules. The
low-order models can be compiled without the -r8 switch, but the bgrid_solo model cannot.
` <libs>`__
Libs¶
LIBS value should be relatively straightforward./usr/local/netcdf/lib string to reflect the location of your libnetcdf.a./usr/local/udunits-1.11.7/lib string to reflect the location of your libudunits.a.Customizing the ‘path_names_*’ file¶
Several path_names_* files are provided in the work directory for each specific model, in this case:
DART/models/lorenz_63/work.
path_names_create_obs_set_defpath_names_create_obs_sequencepath_names_perfect_model_obspath_names_filter
Since each model comes with its own set of files, no further customization is needed.
Building the Lorenz_63 DART project¶
Currently, DART executables are constructed in a work subdirectory under the directory containing code for the given
model. In the top-level DART directory, change to the L63 work directory and list the contents:
cd DART/models/lorenz_63/work ls -1
With the result:
filter_ics
mkmf_create_obs_sequence
mkmf_create_obs_set_def
mkmf_filter
mkmf_perfect_model_obs
path_names_create_obs_sequence
path_names_create_obs_set_def
path_names_filter
path_names_perfect_model_obs
perfect_ics
There are four mkmf_xxxxxx files for the programs create_obs_set_def, create_obs_sequence,
perfect_model_obs, and filter along with the corresponding path_names_xxxxxx files. You can examine the
contents of one of the path_names_xxxxxx files, for instance path_names_filter, to see a list of the
relative paths of all files that contain Fortran90 modules required for the program filter for the L63 model. All of
these paths are relative to your DART directory. The first path is the main program (filter.f90) and is followed
by all the Fortran90 modules used by this program.
The mkmf_xxxxxx scripts are cryptic but should not need to be modified – as long as you do not restructure the
code tree (by moving directories, for example). The only function of the mkmf_xxxxxx script is to generate a
Makefile and an input.nml.mkmf file. It is not supposed to compile anything:
csh mkmf_create_obs_set_def mv input.nml.mkmf input.nml.create_obs_set_def make
The first command generates an appropriate Makefile and the input.nml.mkmf file. The second saves the example
namelist to a unique name (the next DART release will do this automatically – no harm is done by omitting this step)
and the last command results in the compilation of a series of Fortran90 modules which ultimately produces an executable
file: create_obs_set_def. Should you need to make any changes to the DART/mkmf/mkmf.template, you will need to
regenerate the Makefile. A series of object files for each module compiled will also be left in the work directory,
as some of these are undoubtedly needed by the build of the other DART components. You can proceed to create the other
three programs needed to work with L63 in DART as follows:
csh mkmf_create_obs_sequence mv input.nml.mkmf input.nml.create_obs_sequence make csh mkmf_perfect_model_obs mv input.nml.mkmf input.nml.perfect_model_obs make csh mkmf_filter mv input.nml.mkmf input.nml.filter make
typesizes.mod) are not found. Edit the
DART/mkmf/mkmf.template, recreate the Makefile, and try again.program |
purpose |
|---|---|
|
specify a (set) of observation characteristics taken by a particular (set of) instruments |
|
specify the temporal attributes of the observation sets |
|
spinup, generate “true state” for synthetic observation experiments, … |
|
perform experiments |
Running Lorenz_63¶
This initial sequence of exercises includes detailed instructions on how to work with the DART code and allows investigation of the basic features of one of the most famous dynamical systems, the 3-variable Lorenz-63 model. The remarkable complexity of this simple model will also be used as a case study to introduce a number of features of a simple ensemble filter data assimilation system. To perform a synthetic observation assimilation experiment for the L63 model, the following steps must be performed (an overview of the process is given first, followed by detailed procedures for each step):
Experiment overview¶
Integrate the L63 model for a long time starting from arbitrary initial conditions to generate a model state that lies on the attractor. The ergodic nature of the L63 system means a ‘lengthy’ integration always converges to some point on the computer’s finite precision representation of the model’s attractor.
Generate a set of ensemble initial conditions from which to start an assimilation. Since L63 is ergodic, the ensemble members can be designed to look like random samples from the model’s ‘climatological distribution’. To generate an ensemble member, very small perturbations can be introduced to the state on the attractor generated by step 1. This perturbed state can then be integrated for a very long time until all memory of its initial condition can be viewed as forgotten. Any number of ensemble initial conditions can be generated by repeating this procedure.
Simulate a particular observing system by first creating an ‘observation set definition’ and then creating an ‘observation sequence’. The ‘observation set definition’ describes the instrumental characteristics of the observations and the ‘observation sequence’ defines the temporal sequence of the observations.
Populate the ‘observation sequence’ with ‘perfect’ observations by integrating the model and using the information in the ‘observation sequence’ file to create simulated observations. This entails operating on the model state at the time of the observation with an appropriate forward operator (a function that operates on the model state vector to produce the expected value of the particular observation) and then adding a random sample from the observation error distribution specified in the observation set definition. At the same time, diagnostic output about the ‘true’ state trajectory can be created.
Assimilate the synthetic observations by running the filter; diagnostic output is generated.
1. Integrate the L63 model for a ‘long’ time¶
perfect_model_obs integrates the model for all the times specified in the ‘observation sequence definition’ file. To
this end, begin by creating an ‘observation sequence definition’ file that spans a long time. Creating an ‘observation
sequence definition’ file is a two-step procedure involving create_obs_sequence followed by
create_fixed_network_seq. After they are both run, it is necessary to integrate the model with
perfect_model_obs.
1.1 Create an observation set definition¶
create_obs_sequence creates an observation set definition, the time-independent part of an observation sequence.
An observation set definition file only contains the location, type, and observational error characteristics
(normally just the diagonal observational error variance) for a related set of observations. There are no actual
observations, nor are there any times associated with the definition. For spin-up, we are only interested in
integrating the L63 model, not in generating any particular synthetic observations. Begin by creating a minimal
observation set definition.set_def.out)
that defines the single identity observation of the first state variable of the L63 model. The following is a
screenshot (much of the verbose logging has been left off for clarity), the user input looks like this.[unixprompt]$ ./create_obs_set_def
Initializing the utilities module.
Registering module :
$source$
$revision: 3169 $
$date: 2007-12-07 16:40:53 -0700 (Fri, 07 Dec 2007) $
Registration complete.
&UTILITIES_NML
TERMLEVEL = 2,
LOGFILENAME = dart_log.out
/
Registering module :
$source$
$revision: 3169 $
$date: 2007-12-07 16:40:53 -0700 (Fri, 07 Dec 2007) $
Registration complete.
Input the filename for output of observation set_def_list? [set_def.out]
set_def.out
{ ... }
Input the number of unique observation sets you might define
1
How many observations in set 1
1
Defining observation 1
Input error variance for this observation definition
1000000
Input an integer index if this is identity observation, else -1
1
Registering module :
$source$
$revision: 3169 $
$date: 2007-12-07 16:40:53 -0700 (Fri, 07 Dec 2007) $
Registration complete.
set_def.out successfully created.
Terminating normally.
1.2 Create an observation sequence definition¶
create_obs_sequence creates an ‘observation sequence definition’ by extending the ‘observation set definition’
with the temporal attributes of the observations.perfect_model_obs program.[thoar@ghotiol work]$ ./create_obs_sequence
Registering module :
$source$
$revision: 3169 $
$date: 2007-12-07 16:40:53 -0700 (Fri, 07 Dec 2007) $
Registration complete.
&UTILITIES_NML
TERMLEVEL = 2,
LOGFILENAME = dart_log.out
/
Registering module :
$source$
$revision: 3169 $
$date: 2007-12-07 16:40:53 -0700 (Fri, 07 Dec 2007) $
Registration complete.
What is name of set_def_list? [set_def.out]
set_def.out
{ ... }
Setting times for obs_def 1
To input a regularly repeating time sequence enter 1
To enter an irregular list of times enter 2
1
Input number of observations in sequence
1000
Input time of initial ob in sequence in days and seconds
1, 0
Input period of obs in days and seconds
1, 0
time 1 is 0 1
time 2 is 0 2
time 3 is 0 3
...
time 998 is 0 998
time 999 is 0 999
time 1000 is 0 1000
Input file name for output of obs_sequence? [obs_seq.in]
obs_seq.in
1.3 Initialize the model onto the attractor¶
perfect_model_obs can now advance the arbitrary initial state for 24,000 timesteps to move it onto the attractor.perfect_model_obs uses the Fortran90 namelist input mechanism instead of (admittedly gory, but temporary)
interactive input. All of the DART software expects the namelists to found in a file called input.nml. When you
built the executable, an example namelist was created input.nml.mkmf that contains all of the namelist input for
the executable. If you followed the example, each namelist was saved to a unique name. We must now rename and edit the
namelist file for perfect_model_obs. Copy input.nml.perfect_model_obs to input.nml and edit it to look
like the following:&perfect_model_obs_nml async = 0, obs_seq_in_file_name = “obs_seq.in”, obs_seq_out_file_name = “obs_seq.out”, start_from_restart = .false., output_restart = .true., restart_in_file_name = “perfect_ics”, restart_out_file_name = “perfect_restart”, init_time_days = 0, init_time_seconds = 0, output_interval = 1 &end &assim_tools_nml prior_spread_correction = .false., filter_kind = 1, slope_threshold = 1.0 &end &cov_cutoff_nml select_localization = 1 &end &assim_model_nml binary_restart_files = .true. &end &model_nml sigma = 10.0, r = 28.0, b = 2.6666666666667, deltat = 0.01 &end &utilities_nml TERMLEVEL = 1 logfilename = ‘dart_log.out’ &end
perfect_model_obs_nml¶
namelist variable |
description |
|---|---|
|
For the lorenz_63, simply ignore this. Leave it set to ‘0’ |
|
specifies the file name that results from running |
|
specifies the output file name containing the ‘observation sequence’, finally populated with (perfect?) ‘observations’. |
|
When set to ‘false’, |
|
When set to ‘true’, |
|
is ignored when ‘start_from_restart’ is ‘false’. |
|
if |
|
the start time of the integration. |
|
interval at which to save the model state. |
utilities_nml¶
namelist variable |
description |
|---|---|
|
When set to ‘1’ the programs terminate when a ‘warning’ is generated. When set to ‘2’ the programs terminate only with ‘fatal’ errors. |
|
Run-time diagnostics are saved to this file. This namelist is used by all programs, so the file is opened in APPEND mode. Subsequent executions cause this file to grow. |
Executing perfect_model_obs will integrate the model 24,000 steps and output the resulting state in the file
perfect_restart. Interested parties can check the spinup in the True_State.nc file.
perfect_model_obs
2. Generate a set of ensemble initial conditions¶
perfect_restart), running perfect_model_obs to generate the ‘true state’ of the experiment and a
corresponding set of observations, and then feeding the same initial spun-up state and resulting observations into
filter.perfect_restart to perfect_ics, and rerunning perfect_model_obs. This execution of perfect_model_obs
will advance the model state from the end of the first 24,000 steps to the end of an additional 24,000 steps and place
the final state in perfect_restart. The rest of the namelists in input.nml should remain unchanged.&perfect_model_obs_nml async = 0, obs_seq_in_file_name = “obs_seq.in”, obs_seq_out_file_name = “obs_seq.out”, start_from_restart = .true., output_restart = .true., restart_in_file_name = “perfect_ics”, restart_out_file_name = “perfect_restart”, init_time_days = 0, init_time_seconds = 0, output_interval = 1 &end
cp perfect_restart perfect_ics perfect_model_obs
A True_State.nc file is also created. It contains the ‘true’ state of the integration.
Generating the ensemble¶
is done with the program filter, which also uses the Fortran90 namelist mechanism for input. It is now necessary to
copy the input.nml.filter namelist to input.nml or you may simply insert the filter_nml namelist into the
existing input.nml. Having the perfect_model_obs namelist in the input.nml does not hurt anything. In fact, I
generally create a single input.nml that has all the namelist blocks in it.
&perfect_model_obs_nml async = 0, obs_seq_in_file_name = “obs_seq.in”, obs_seq_out_file_name = “obs_seq.out”, start_from_restart = .true., output_restart = .true., restart_in_file_name = “perfect_ics”, restart_out_file_name = “perfect_restart”, init_time_days = 0, init_time_seconds = 0, output_interval = 1 &end &assim_tools_nml prior_spread_correction = .false., filter_kind = 1, slope_threshold = 1.0 &end &cov_cutoff_nml select_localization = 1 &end &assim_model_nml binary_restart_files = .true. &end &model_nml sigma = 10.0, r = 28.0, b = 2.6666666666667 deltat = 0.01 &end &utilities_nml TERMLEVEL = 1 logfilename = ‘dart_log.out’ &end ®_factor_nml select_regression = 1, input_reg_file = “time_mean_reg” &end &filter_nml async = 0, ens_size = 20, cutoff = 0.20, cov_inflate = 1.00, start_from_restart = .false., output_restart = .true., obs_sequence_file_name = “obs_seq.out”, restart_in_file_name = “perfect_ics”, restart_out_file_name = “filter_restart”, init_time_days = 0, init_time_seconds = 0, output_state_ens_mean = .true., output_state_ens_spread = .true., num_output_ens_members = 20, output_interval = 1, num_groups = 1, confidence_slope = 0.0, output_obs_diagnostics = .false., get_mean_reg = .false., get_median_reg = .false. &end
Only the non-obvious(?) entries for filter_nml will be discussed.
namelist variable |
description |
|---|---|
|
Number of ensemble members. 20 is sufficient for most of the L63 exercises. |
|
to limit the impact of an observation, set to 0.0 (i.e. spin-up) |
|
A value of 1.0 results in no inflation.(spin-up) |
|
when ‘.false.’, |
|
may be a value from 0 to |
|
when ‘.true.’ the mean of all ensemble members is output. |
|
when ‘.true.’ the spread of all ensemble members is output. |
|
Jeff - units for interval? |
The filter is told to generate its own ensemble initial conditions since start_from_restart is ‘.false.’. However,
it is important to note that the filter still makes use of perfect_ics which is set to be the
restart_in_file_name. This is the model state generated from the first 24,000 step model integration by
perfect_model_obs. Filter generates its ensemble initial conditions by randomly perturbing the state variables
of this state.
The arguments output_state_ens_mean and output_state_ens_spread are ‘.true.’ so that these quantities are output
at every time for which there are observations (once a day here) and num_output_ens_members means that the same
diagnostic files, Posterior_Diag.nc and Prior_Diag.nc also contain values for all 20 ensemble members once a
day. Once the namelist is set, execute filter to integrate the ensemble forward for 24,000 steps with the final
ensemble state written to the filter_restart. Copy the perfect_model_obs restart file perfect_restart (the
`true state’) to perfect_ics, and the filter restart file filter_restart to filter_ics so that future
assimilation experiments can be initialized from these spun-up states.
filter cp perfect_restart perfect_ics cp filter_restart filter_ics
The spin-up of the ensemble can be viewed by examining the output in the netCDF files True_State.nc generated by
perfect_model_obs and Posterior_Diag.nc and Prior_Diag.nc generated by filter. To do this, see the
detailed discussion of matlab diagnostics in Appendix I.
3. Simulate a particular observing system¶
Begin by using create_obs_set_def to generate an observation set in which each of the 3 state variables of L63 is
observed with an observational error variance of 1.0 for each observation. To do this, use the following input sequence
(the text including and after # is a comment and does not need to be entered):
set_def.out |
# Output file name |
1 |
# Number of sets |
3 |
# Number of observations in set (x, y, and z) |
1.0 |
# Variance of first observation |
1 |
# First ob is identity observation of state variable 1 (x) |
1.0 |
# Variance of second observation |
2 |
# Second is identity observation of state variable 2 (y) |
1.0 |
# Variance of third ob |
3 |
# Identity ob of third state variable (z) |
Now, generate an observation sequence definition by running create_obs_sequence with the following input sequence:
set_def.out |
# Input observation set definition file |
1 |
# Regular spaced observation interval in time |
1000 |
# 1000 observation times |
0, 43200 |
# First observation after 12 hours (0 days, 3600 * 12 seconds) |
0, 43200 |
# Observations every 12 hours |
obs_seq.in |
# Output file for observation sequence definition |
4. Generate a particular observing system and true state¶
An observation sequence file is now generated by running perfect_model_obs with the namelist values (unchanged from
step 2):
&perfect_model_obs_nml async = 0, obs_seq_in_file_name = “obs_seq.in”, obs_seq_out_file_name = “obs_seq.out”, start_from_restart = .true., output_restart = .true., restart_in_file_name = “perfect_ics”, restart_out_file_name = “perfect_restart”, init_time_days = 0, init_time_seconds = 0, output_interval = 1 &end
This integrates the model starting from the state in perfect_ics for 1000 12-hour intervals outputting synthetic
observations of the three state variables every 12 hours and producing a netCDF diagnostic file, True_State.nc.
5. Filtering¶
Finally, filter can be run with its namelist set to:
&filter_nml async = 0, ens_size = 20, cutoff = 22222222.0, cov_inflate = 1.00, start_from_restart = .true., output_restart = .true., obs_sequence_file_name = “obs_seq.out”, restart_in_file_name = “filter_ics”, restart_out_file_name = “filter_restart”, init_time_days = 0, init_time_seconds = 0, output_state_ens_mean = .true., output_state_ens_spread = .true., num_output_ens_members = 20, output_interval = 1, num_groups = 1, confidence_slope = 0.0, output_obs_diagnostics = .false., get_mean_reg = .false., get_median_reg = .false. &end
The large value for the cutoff allows each observation to impact all other state variables (see Appendix V for
localization). filter produces two output diagnostic files, Prior_Diag.nc which contains values of the ensemble
members, ensemble mean and ensemble spread for 12- hour lead forecasts before assimilation is applied and
Posterior_Diag.nc which contains similar data for after the assimilation is applied (sometimes referred to as
analysis values).
Now try applying all of the matlab diagnostic functions described in the Matlab Diagnostics section.
Matlab® diagnostics¶
The output files are netCDF files, and may be examined with many different software packages. We happen to use Matlab®, and provide our diagnostic scripts in the hopes that they are useful.
The Matlab diagnostic scripts and underlying functions reside in the DART/matlab directory. They are reliant on the
public-domain netcdf toolbox from
http://woodshole.er.usgs.gov/staffpages/cdenham/public_html/MexCDF/nc4ml5.html as well as the public-domain CSIRO
matlab/netCDF interface from
http://www.marine.csiro.au/sw/matlab-netcdf.html. If you do not have them installed on your system and want to use
Matlab to peruse netCDF, you must follow their installation instructions.
Once you can access the getnc function from within Matlab, you can use our diagnostic scripts. It is necessary to
prepend the location of the DART/matlab scripts to the matlabpath. Keep in mind the location of the netcdf operators on
your system WILL be different from ours … and that’s OK.
0[269]0 ghotiol:/<5>models/lorenz_63/work]$ matlab -nojvm
< M A T L A B >
Copyright 1984-2002 The MathWorks, Inc.
Version 6.5.0.180913a Release 13
Jun 18 2002
Using Toolbox Path Cache. Type "help toolbox_path_cache" for more info.
To get started, type one of these: helpwin, helpdesk, or demo.
For product information, visit www.mathworks.com.
>> which getnc
/contrib/matlab/matlab_netcdf_5_0/getnc.m
>>ls *.nc
ans =
Posterior_Diag.nc Prior_Diag.nc True_State.nc
>>path('../../../matlab',path)
>>which plot_ens_err_spread
../../../matlab/plot_ens_err_spread.m
>>help plot_ens_err_spread
DART : Plots summary plots of the ensemble error and ensemble spread.
Interactively queries for the needed information.
Since different models potentially need different
pieces of information ... the model types are
determined and additional user input may be queried.
Ultimately, plot_ens_err_spread will be replaced by a GUI.
All the heavy lifting is done by PlotEnsErrSpread.
Example 1 (for low-order models)
truth_file = 'True_State.nc';
diagn_file = 'Prior_Diag.nc';
plot_ens_err_spread
>>plot_ens_err_spread
And the matlab graphics window will display the spread of the ensemble error for each state variable. The scripts are
designed to do the “obvious” thing for the low-order models and will prompt for additional information if needed. The
philosophy of these is that anything that starts with a lower-case plot_some_specific_task is intended to be
user-callable and should handle any of the models. All the other routines in DART/matlab are called BY the
high-level routines.
Matlab script |
description |
|---|---|
|
plots ensemble rank histograms |
|
Plots space-time series of correlation between a given variable at a given time and other variables at all times in a n ensemble time sequence. |
|
Plots summary plots of the ensemble error and ensemble spread. Interactively queries for the needed information. Since different models potentially need different pieces of information … the model types are determined and additional user input may be queried. |
|
Queries for the state variables to plot. |
|
Queries for the state variables to plot. |
|
Plots a 3D trajectory of (3 state variables of) a single ensemble member. Additional trajectories may be superimposed. |
|
Summary plots of global error and spread. |
|
Plots time series of correlation between a given variable at a given time and another variable at all times in an ensemble time sequence. |
Bias, filter divergence and covariance inflation (with the l63 model)¶
One of the common problems with ensemble filters is filter divergence, which can also be an issue with a variety of
other flavors of filters including the classical Kalman filter. In filter divergence, the prior estimate of the model
state becomes too confident, either by chance or because of errors in the forecast model, the observational error
characteristics, or approximations in the filter itself. If the filter is inappropriately confident that its prior
estimate is correct, it will then tend to give less weight to observations than they should be given. The result can be
enhanced overconfidence in the model’s state estimate. In severe cases, this can spiral out of control and the ensemble
can wander entirely away from the truth, confident that it is correct in its estimate. In less severe cases, the
ensemble estimates may not diverge entirely from the truth but may still be too confident in their estimate. The result
is that the truth ends up being farther away from the filter estimates than the spread of the filter ensemble would
estimate. This type of behavior is commonly detected using rank histograms (also known as Talagrand diagrams). You can
see the rank histograms for the L63 initial assimilation by using the matlab script plot_bins.
A simple, but surprisingly effective way of dealing with filter divergence is known as covariance inflation. In this
method, the prior ensemble estimate of the state is expanded around its mean by a constant factor, effectively
increasing the prior estimate of uncertainty while leaving the prior mean estimate unchanged. The program filter has
a namelist parameter that controls the application of covariance inflation, cov_inflate. Up to this point,
cov_inflate has been set to 1.0 indicating that the prior ensemble is left unchanged. Increasing cov_inflate to
values greater than 1.0 inflates the ensemble before assimilating observations at each time they are available. Values
smaller than 1.0 contract (reduce the spread) of prior ensembles before assimilating.
You can do this by modifying the value of cov_inflate in the namelist, (try 1.05 and 1.10 and other values at your
discretion) and run the filter as above. In each case, use the diagnostic matlab tools to examine the resulting changes
to the error, the ensemble spread (via rank histogram bins, too), etc. What kind of relation between spread and error is
seen in this model?
Synthetic observations¶
Synthetic observations are generated from a `perfect’ model integration, which is often referred to as the `truth’ or a `nature run’. A model is integrated forward from some set of initial conditions and observations are generated as y = H(x) + e where H is an operator on the model state vector, x, that gives the expected value of a set of observations, y, and e is a random variable with a distribution describing the error characteristics of the observing instrument(s) being simulated. Using synthetic observations in this way allows students to learn about assimilation algorithms while being isolated from the additional (extreme) complexity associated with model error and unknown observational error characteristics. In other words, for the real-world assimilation problem, the model has (often substantial) differences from what happens in the real system and the observational error distribution may be very complicated and is certainly not well known. Be careful to keep these issues in mind while exploring the capabilities of the ensemble filters with synthetic observations.