DART “pre_j release” Documentation¶
Overview of DART¶
Prior_Diag.nc
and just after the adjustment Posterior_Diag.nc as well as a file obs_seq.final with the model estimates of
the observations. There is a suite of Matlab® functions that facilitate exploration of the results.The pre_j release provides several new models and has a greatly expanded capability for real observations which required a fundamentally different implementation of the low-level routines. It is now required to run a preprocessor on several of the program units to construct the source code files which will be compiled by the remaining units. Due to the potentially large number of observations types possible and for portability reasons, the preprocessor is actually a F90 program that uses the namelist mechanism for specifying the observation types to be included. This also prevents having a gory set of compile flags that is different for every compiler. One very clever colleague also ‘built a better mousetrap’ and figured out how to effectively and robustly read namelists, detect errors, and generate meaningful error messages. HURRAY!
The pre_j release has also been tested with more compilers in an attempt to determine non-portable code elements. It is
my experience that the largest impediment to portable code is the reliance on the compiler to autopromote real
variables to one flavor or another. Using the F90 “kind” allows for much more flexible
code, in that the use of interface procedures is possible only when two routines do not have identical sets of input
arguments – something that happens when the compiler autopromotes 32bit reals to 64bit reals, for example.
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, which 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 in a custom format in
either human-readable ascii or more compact machine-specific binary. 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. 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 several versions of the Intel Fortran Compiler for Linux, which (at one point) is/was free for individual scientific use. It has also been built and successfully run with several versions of each of the following: Portland Group Fortran Compiler, Lahey Fortran Compiler, Pathscale Fortran Compiler, Absoft Fortran 90/95 Compiler (Mac OSX). 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.
Unpacking the distribution¶
The DART source code is distributed as a compressed tar file from our download site.
When gunzip’ed and untarred, the source tree will begin with a directory named DART and will be approximately 189
Mb. Compiling the code in this tree (as is usually the case) will necessitate much more space.
gunzip DART_pre_j.tar.gz
tar -xvf DART_pre_j.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.program_default 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.program_default, 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.pgf90.ghotiol) is needed: (note that only the LAST lines are shown here, the head of the file is just
a big comment)
# Makefile template for PGI f90
FC = pgf90
LD = pgf90
CPPFLAGS =
LIST = -Mlist
NETCDF = /contrib/netcdf-3.5.1-cc-c++-pgif90.5.2-4
FFLAGS = -O0 -Ktrap=fp -pc 64 -I$(NETCDF)/include
LIBS = -L$(NETCDF)/lib -lnetcdf
LDFLAGS = $(LIBS)
...
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 NETCDF, which indicate where to look for the netCDF F90 modules and the location of the
netCDF library and modules.
Netcdf¶
NETCDF value should be relatively straightforward.netcdf.mod and typesizes.mod.
The value of the NETCDF variable will be used by the FFLAGS, LIBS, and LDFLAGS variables.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 your netCDF. The low-order models can be
compiled without a -r8 switch, but the bgrid_solo model cannot.
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_preprocesspath_names_create_obs_sequencepath_names_create_fixed_network_seqpath_names_perfect_model_obspath_names_filterpath_names_obs_diag
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
filter_restart
input.nml
mkmf_create_fixed_network_seq
mkmf_create_obs_sequence
mkmf_filter
mkmf_obs_diag
mkmf_perfect_model_obs
mkmf_preprocess
obs_seq.final
obs_seq.in
obs_seq.out
obs_seq.out.average
obs_seq.out.x
obs_seq.out.xy
obs_seq.out.xyz
obs_seq.out.z
path_names_create_fixed_network_seq
path_names_create_obs_sequence
path_names_filter
path_names_obs_diag
path_names_perfect_model_obs
path_names_preprocess
perfect_ics
perfect_restart
Posterior_Diag.nc
Prior_Diag.nc
set_def.out
True_State.nc
workshop_setup.csh
There are six mkmf_xxxxxx files for the programs preprocess, create_obs_sequence,
create_fixed_network_seq, perfect_model_obs, filter, and obs_diag 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 (after
preprocessing).
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.program_default file. It is not supposed to compile anything:
csh mkmf_preprocess make
Makefile and the input.nml.preprocess_default file. The second
command results in the compilation of a series of Fortran90 modules which ultimately produces an executable file:
preprocess. Should you need to make any changes to the DART/mkmf/mkmf.template, you will need to regenerate
the Makefile.preprocess program actually builds source code to be used by all the remaining modules. It is imperative
to actually run preprocess before building the remaining executables. This is how the same code can assimilate
state vector ‘observations’ for the Lorenz_63 model and real radar reflectivities for WRF without needing to specify a
set of radar operators for the Lorenz_63 model!preprocess reads the &preprocess_nml namelist to determine what observations and operators to incorporate. For
this exercise, we will use the values in input.nml. preprocess is designed to abort if the files it is
supposed to build already exist. For this reason, it is necessary to remove a couple files (if they exist) before you
run the preprocessor. It is just a good habit to develop.\rm -f ../../../obs_def/obs_def_mod.f90
\rm -f ../../../obs_kind/obs_kind_mod.f90
./preprocess
ls -l ../../../obs_def/obs_def_mod.f90
ls -l ../../../obs_kind/obs_kind_mod.f90
../../../obs_def/obs_def_mod.f90 from ../../../obs_kind/DEFAULT_obs_kind_mod.F90 and several
other modules. ../../../obs_kind/obs_kind_mod.f90 was created similarly. Now we can build the rest of the project.csh mkmf_create_obs_sequence
make
csh mkmf_create_fixed_network_seq
make
csh mkmf_perfect_model_obs
make
csh mkmf_filter
make
csh mkmf_obs_diag
make
The result (hopefully) is that six executables now reside in your work directory. The most common problem is that the
netCDF libraries and include files (particularly typesizes.mod) are not found. Edit the DART/mkmf/mkmf.template,
recreate the Makefile, and try again.
program |
purpose |
|---|---|
|
creates custom source code for just the observations of interest |
|
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 |
|
creates observation-space diagnostic files to be explored by the Matlab® scripts. |
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_sequence
Initializing the utilities module.
Trying to read from unit 10
Trying to open file dart_log.out
Registering module :
$source: /home/dart/CVS.REPOS/DART/utilities/utilities_mod.f90,v $
$revision: 1.18 $
$date: 2004/06/29 15:16:40 $
Registration complete.
&UTILITIES_NML
TERMLEVEL= 2,LOGFILENAME=dart_log.out
/
Registering module :
$source: /home/dart/CVS.REPOS/DART/obs_sequence/create_obs_sequence.f90,v $
$revision: 1.18 $
$date: 2004/05/24 15:41:46 $
Registration complete.
{ ... }
Input upper bound on number of observations in sequence
10
Input number of copies of data (0 for just a definition)
0
Input number of quality control values per field (0 or greater)
0
Input a -1 if there are no more obs
0
Registering module :
$source$
$revision: 3169 $
$date: 2007-12-07 16:40:53 -0700 (Fri, 07 Dec 2007) $
Registration complete.
Registering module :
$source$
$revision: 3169 $
$date: 2007-12-07 16:40:53 -0700 (Fri, 07 Dec 2007) $
Registration complete.
initialize_module obs_kind_nml values are
-------------- ASSIMILATE_THESE_OBS_TYPES --------------
RAW_STATE_VARIABLE
-------------- EVALUATE_THESE_OBS_TYPES --------------
------------------------------------------------------
Input -1 * state variable index for identity observations
OR input the name of the observation kind from table below:
OR input the integer index, BUT see documentation...
1 RAW_STATE_VARIABLE
-1
Input time in days and seconds
1 0
Input error variance for this observation definition
1000000
Input a -1 if there are no more obs
-1
Input filename for sequence ( set_def.out usually works well)
set_def.out
write_obs_seq opening formatted file set_def.out
write_obs_seq closed file set_def.out
1.2 Create an observation sequence definition¶
create_fixed_network_seq creates an ‘observation sequence definition’ by extending the ‘observation set
definition’ with the temporal attributes of the observations.perfect_model_obs program.[unixprompt]$ ./create_fixed_network_seq
...
Registering module :
$source: /home/dart/CVS.REPOS/DART/obs_sequence/obs_sequence_mod.f90,v $
$revision: 1.31 $
$date: 2004/06/29 15:04:37 $
Registration complete.
Input filename for network definition sequence (usually set_def.out )
set_def.out
...
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
1
2
3
...
997
998
999
1000
What is output file name for sequence ( obs_seq.in is recommended )
obs_seq.in
write_obs_seq opening formatted file obs_seq.in
write_obs_seq closed file [blah blah blah]/work/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.perfect_model_obs_default 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_default to
input.nml and edit it to look like the following: (just worry about the highlighted stuff)&perfect_model_obs_nml
async = 0,
adv_ens_command = "./advance_ens.csh",
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 /
&ensemble_manager_nml
in_core = .true.,
single_restart_file_in = .true.,
single_restart_file_out = .true. /
&assim_tools_nml
filter_kind = 1,
cutoff = 0.2,
sort_obs_inc = .false.,
cov_inflate = -1.0,
cov_inflate_sd = 0.05,
sd_lower_bound = 0.05,
deterministic_cov_inflate = .true.,
start_from_assim_restart = .false.,
assim_restart_in_file_name =
'assim_tools_ics',
assim_restart_out_file_name =
'assim_tools_restart',
do_parallel = 0,
num_domains = 1
parallel_command = "./assim_filter.csh",
spread_restoration = .false.,
cov_inflate_upper_bound = 10000000.0,
internal_outlier_threshold = -1.0 /
&cov_cutoff_nml
select_localization = 1 /
®_factor_nml
select_regression = 1,
input_reg_file = "time_mean_reg"
save_reg_diagnostics = .false.,
reg_diagnostics_file = 'reg_diagnostics' /
&obs_sequence_nml
write_binary_obs_sequence = .false. /
&obs_kind_nml
assimilate_these_obs_types = 'RAW_STATE_VARIABLE' /
&assim_model_nml
write_binary_restart_files = .true. /
&model_nml
sigma = 10.0,
r = 28.0,
b = 2.6666666666667,
deltat = 0.01,
time_step_days = 0,
time_step_seconds = 3600 /
&utilities_nml
TERMLEVEL = 1
logfilename = 'dart_log.out' /
perfect_model_obs_nml¶
namelist variable |
description |
|---|---|
|
For the lorenz_63, simply ignore this. Leave it set to ‘0’ |
|
specifies the shell commands or script to execute when async /= 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), run perfect_model_obs to generate the ‘true state’
of the experiment and a corresponding set of observations. 2) Feed 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,
adv_ens_command = "./advance_ens.csh",
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
/
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¶
This step (#2 from above) 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_default namelist to input.nml or you may simply insert
the filter_nml namelist block 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. I simply copied the filter namelist block from input.nml.filter_default and inserted it into our input.nml
for the following example.
&perfect_model_obs_nml
async = 0,
adv_ens_command = "./advance_ens.csh",
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 /
&filter_nml
async = 0,
adv_ens_command = "./advance_ens.csh",
ens_size = 100,
cov_inflate = 1.0,
start_from_restart = .false.,
output_restart = .true.,
obs_sequence_in_name = "obs_seq.out",
obs_sequence_out_name = "obs_seq.final",
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.,
output_obs_ens_mean = .true.,
output_obs_ens_spread = .true.,
num_output_state_members = 20,
num_output_obs_members = 20,
output_interval = 1,
num_groups = 1,
outlier_threshold = -1.0 /
&ensemble_manager_nml
in_core = .true.,
single_restart_file_in = .true.,
single_restart_file_out = .true. /
&assim_tools_nml
filter_kind = 1,
cutoff = 0.2,
sort_obs_inc = .false.,
cov_inflate = -1.0,
cov_inflate_sd = 0.05,
sd_lower_bound = 0.05,
deterministic_cov_inflate = .true.,
start_from_assim_restart = .false.,
assim_restart_in_file_name =
'assim_tools_ics',
assim_restart_out_file_name =
'assim_tools_restart',
do_parallel = 0,
num_domains = 1
parallel_command = "./assim_filter.csh",
spread_restoration = .false.,
cov_inflate_upper_bound = 10000000.0,
internal_outlier_threshold = -1.0 /
&cov_cutoff_nml
select_localization = 1 /
®_factor_nml
select_regression = 1,
input_reg_file = "time_mean_reg"
save_reg_diagnostics = .false.,
reg_diagnostics_file = 'reg_diagnostics' /
&obs_sequence_nml
write_binary_obs_sequence = .false. /
&obs_kind_nml
assimilate_these_obs_types = 'RAW_STATE_VARIABLE'
/
&assim_model_nml
write_binary_restart_files = .true. /
&model_nml
sigma = 10.0,
r = 28.0,
b = 2.6666666666667,
deltat = 0.01,
time_step_days = 0,
time_step_seconds = 3600 /
&utilities_nml
TERMLEVEL = 1
logfilename = 'dart_log.out' /
Only the non-obvious(?) entries for filter_nml will be discussed.
namelist variable |
description |
|---|---|
|
Number of ensemble members. 100 is sufficient for most of the L63 exercises. |
|
A value of 1.0 results in no inflation.(spin-up) |
|
when ‘.false.’, |
|
when ‘.true.’ the mean of all ensemble members is output. |
|
when ‘.true.’ the spread of all ensemble members is output. |
|
may be a value from 0 to |
|
when ‘.true.’ Output ensemble mean in observation output file. |
|
when ‘.true.’ Output ensemble spread in observation output file. |
|
may be a value from 0 to |
|
The frequency with which output state diagnostics are written. Units are in assimilation times. Default value is 1 meaning output is written at every observation time |
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 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_sequence 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):
4 |
# upper bound on num of observations in sequence |
0 |
# number of copies of data (0 for just a definition) |
0 |
# number of quality control values per field (0 or greater) |
0 |
# -1 to exit/end observation definitions |
-1 |
# observe state variable 1 |
0 0 |
# time – days, seconds |
1.0 |
# observational variance |
0 |
# -1 to exit/end observation definitions |
-2 |
# observe state variable 2 |
0 0 |
# time – days, seconds |
1.0 |
# observational variance |
0 |
# -1 to exit/end observation definitions |
-3 |
# observe state variable 3 |
0 0 |
# time – days, seconds |
1.0 |
# observational variance |
-1 |
# -1 to exit/end observation definitions |
set_def.out |
# Output file name |
Now, generate an observation sequence definition by running create_fixed_network_seq 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, 12 * 3600 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,
adv_ens_command = "./advance_ens.csh",
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 /
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,
adv_ens_command = "./advance_ens.csh",
ens_size = 100,
cov_inflate = 1.0,
start_from_restart = .true.,
output_restart = .true.,
obs_sequence_in_name = "obs_seq.out",
obs_sequence_out_name = "obs_seq.final",
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.,
output_obs_ens_mean = .true.,
output_obs_ens_spread = .true.,
num_output_state_members = 20,
num_output_obs_members = 20,
output_interval = 1,
num_groups = 1,
outlier_threshold = -1.0 /
filter produces two output diagnostic files, Prior_Diag.nc which contains values of the ensemble mean, ensemble
spread, and ensemble members 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 diagnostic scripts and underlying functions reside in two places: DART/diagnostics/matlab and DART/matlab.
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. The ‘interested reader’ may want to look at
the DART/matlab/startup.m file I use on my system. If you put it in your $HOME/matlab directory, it is invoked
every time you start up Matlab.
getnc function from within Matlab, you can use our diagnostic scripts. It is necessary to
prepend the location of the DART/matlab scripts to the matlabpath. Keep in mind the location of the netcdf
operators on your system WILL be different from ours … and that’s OK.0[269]0 ghotiol:/<5>models/lorenz_63/work]$ 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)
>>path('../../../diagnostics/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.