Ikeda

Overview

DART interface module for the Ikeda model. The 16 public interfaces are standardized for all DART compliant models. These interfaces allow DART to advance the model, get the model state and metadata describing this state, find state variables that are close to a given location, and do spatial interpolation for model state variables.

The Ikeda model is a 2D chaotic map useful for visualization data assimilation updating directly in state space. There are three parameters: a, b, and mu. The state is 2D, x = [X Y]. The equations are:

X(i+1) = 1 + mu * ( X(i) * cos( t ) - Y(i) * sin( t ) )
Y(i+1) =     mu * ( X(i) * sin( t ) + Y(i) * cos( t ) ),

where

t = a - b / ( X(i)**2 + Y(i)**2 + 1 )

Note the system is time-discrete already, meaning there is no delta_t. The system stems from nonlinear optics (Ikeda 1979, Optics Communications). Interface written by Greg Lawson, CalTech. Thanks Greg!

“The initial conditions were generated by observing state variable 1 with an enormous (~1,000,000.0) observation error variance. The observation was defined to be taken at day=0, seconds = 0. create_fixed_network_sequence was run to create a sequence with 3000 hourly observations starting at day=0, seconds =0. The initial conditions for filter can accomodate 100 ensemble members.”

Namelist

This namelist is read from the file input.nml. Namelists start with an ampersand ‘&’ and terminate with a slash ‘/’. Character strings that contain a ‘/’ must be enclosed in quotes to prevent them from prematurely terminating the namelist.

&model_nml
   a  = 0.40,
   b  = 6.00,
   mu = 0.83,
   time_step_days      = 0,
   time_step_seconds   = 3600,
   output_state_vector = .true.
/

Item	Type	Description
a	real(r8)	Model parameter.
b	real(r8)	Model parameter.
mu	real(r8)	Model parameter.
time_step_days	integer	Model advance time in days.
time_step_seconds	integer	Model advance time in seconds.
output_state_vector	logical	If true, output the state vector data to the diagnostic files as a single 1D array. If false, break up output data into logical model variables.

Other modules used

types_mod
time_manager_mod
oned/location_mod
utilities_mod

Public interfaces

use model_mod, only :	get_model_size
	adv_1step
	get_state_meta_data
	model_interpolate
	get_model_time_step
	static_init_model
	end_model
	init_time
	init_conditions
	nc_write_model_atts
	nc_write_model_vars
	pert_model_state
	get_close_maxdist_init
	get_close_obs_init
	get_close_obs
	ens_mean_for_model

A note about documentation style. Optional arguments are enclosed in brackets [like this].

model_size = get_model_size( )

integer :: get_model_size

Returns the length of the model state vector as an integer. This is fixed at 2 for this model.

model_size

The length of the model state vector.

call adv_1step(x, time)

real(r8), dimension(:), intent(inout) :: x
type(time_type),        intent(in)    :: time

Advances the model for a single time step. The time associated with the initial model state is also input although it is not used for the computation.

`x`	State vector of length model_size.
`time`	Unused in this model.

call get_state_meta_data (index_in, location, [, var_type] )

integer,             intent(in)  :: index_in
type(location_type), intent(out) :: location
integer, optional,   intent(out) ::  var_type

Returns the location of the given index, and a dummy integer as the var_type.

`index_in`	Index of state vector element about which information is requested.
`location`	Returns location of indexed state variable. The location should use a location_mod that is appropriate for the model domain. For realistic atmospheric models, for instance, a three-dimensional spherical location module that can represent height in a variety of ways is provided.
var_type	Returns the type of the indexed state variable as an optional argument.

call model_interpolate(x, location, itype, obs_val, istatus)

real(r8), dimension(:), intent(in)  :: x
type(location_type),    intent(in)  :: location
integer,                intent(in)  :: itype
real(r8),               intent(out) :: obs_val
integer,                intent(out) :: istatus

A NULL INTERFACE in this model. Always returns istatus = 0.

`x`	A model state vector.
`location`	Location to which to interpolate.
`itype`	Integer indexing which type of state variable is to be interpolated. Can be ignored for low order models with a single type of variable.
`obs_val`	The interpolated value from the model.
`istatus`	Quality control information about the observation of the model state.

var = get_model_time_step()

type(time_type) :: get_model_time_step

Returns the models base time step, or forecast length, as a time_type. This is settable in the namelist.

var

Smallest time step of model.

call static_init_model()

Reads the namelist, defines the 2 initial locations of the state variables, and sets the timestep.

call end_model()

A NULL INTERFACE in this model.

call init_time(time)

type(time_type), intent(out) :: time

Returns a time of 0.

time

Initial model time.

call init_conditions(x)

real(r8), dimension(:), intent(out) :: x

Sets 2 initial locations close to the attractor.

`x`	Initial conditions for state vector.

ierr = nc_write_model_atts(ncFileID)

integer             :: nc_write_model_atts
integer, intent(in) :: ncFileID

Uses the default template code.

`ncFileID`	Integer file descriptor to previously-opened netCDF file.
`ierr`	Returns a 0 for successful completion.

ierr = nc_write_model_vars(ncFileID, statevec, copyindex, timeindex)

integer                            :: nc_write_model_vars
integer,                intent(in) :: ncFileID
real(r8), dimension(:), intent(in) :: statevec
integer,                intent(in) :: copyindex
integer,                intent(in) :: timeindex

Uses the default template code.

`ncFileID`	file descriptor to previously-opened netCDF file.
`statevec`	A model state vector.
`copyindex`	Integer index of copy to be written.
`timeindex`	The timestep counter for the given state.
`ierr`	Returns 0 for normal completion.

call pert_model_state(state, pert_state, interf_provided)

real(r8), dimension(:), intent(in)  :: state
real(r8), dimension(:), intent(out) :: pert_state
logical,                intent(out) :: interf_provided

Given a model state, produces a perturbed model state. This particular model does not implement an interface for this and so returns .false. for interf_provided.

`state`	State vector to be perturbed.
`pert_state`	Perturbed state vector: NOT returned.
`interf_provided`	Returned false; interface is not implemented.

call get_close_maxdist_init(gc, maxdist)

type(get_close_type), intent(inout) :: gc
real(r8),             intent(in)    :: maxdist

Pass-through to the 1-D locations module. See get_close_maxdist_init() for the documentation of this subroutine.

call get_close_obs_init(gc, num, obs)

type(get_close_type), intent(inout) :: gc
integer,              intent(in)    :: num
type(location_type),  intent(in)    :: obs(num)

Pass-through to the 1-D locations module. See get_close_obs_init() for the documentation of this subroutine.

call get_close_obs(gc, base_obs_loc, base_obs_kind, obs, obs_kind, num_close, close_ind [, dist])

type(get_close_type), intent(in)  :: gc
type(location_type),  intent(in)  :: base_obs_loc
integer,              intent(in)  :: base_obs_kind
type(location_type),  intent(in)  :: obs(:)
integer,              intent(in)  :: obs_kind(:)
integer,              intent(out) :: num_close
integer,              intent(out) :: close_ind(:)
real(r8), optional,   intent(out) :: dist(:)

Pass-through to the 1-D locations module. See get_close_obs() for the documentation of this subroutine.

call ens_mean_for_model(ens_mean)

real(r8), dimension(:), intent(in) :: ens_mean

A NULL INTERFACE in this model.

ens_mean

State vector containing the ensemble mean.

Files

filename	purpose
input.nml	to read the model_mod namelist
preassim.nc	the time-history of the model state before assimilation
analysis.nc	the time-history of the model state after assimilation
dart_log.out [default name]	the run-time diagnostic output
dart_log.nml [default name]	the record of all the namelists actually USED - contains the default values

References

Ikeda 1979, Optics Communications

Private components

N/A