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. / | .. container:: +---------------------+----------+-----------------------------------------------------------------------------------+ | 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]*. | .. container:: routine *model_size = get_model_size( )* :: integer :: get_model_size .. container:: indent1 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. ============== ===================================== | .. container:: routine *call adv_1step(x, time)* :: real(r8), dimension(:), intent(inout) :: x type(time_type), intent(in) :: time .. container:: indent1 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. ======== ================================== | .. container:: routine *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 .. container:: indent1 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. | +--------------+------------------------------------------------------------------------------------------------------+ | .. container:: routine *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 .. container:: indent1 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. | +--------------+------------------------------------------------------------------------------------------------------+ | .. container:: routine *var = get_model_time_step()* :: type(time_type) :: get_model_time_step .. container:: indent1 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. ======= ============================ | .. container:: routine *call static_init_model()* .. container:: indent1 Reads the namelist, defines the 2 initial locations of the state variables, and sets the timestep. | .. container:: routine *call end_model()* .. container:: indent1 A NULL INTERFACE in this model. | .. container:: routine *call init_time(time)* :: type(time_type), intent(out) :: time .. container:: indent1 Returns a time of 0. ======== =================== ``time`` Initial model time. ======== =================== | .. container:: routine *call init_conditions(x)* :: real(r8), dimension(:), intent(out) :: x .. container:: indent1 Sets 2 initial locations close to the attractor. ===== ==================================== ``x`` Initial conditions for state vector. ===== ==================================== | .. container:: routine *ierr = nc_write_model_atts(ncFileID)* :: integer :: nc_write_model_atts integer, intent(in) :: ncFileID .. container:: indent1 Uses the default template code. ============ ========================================================= ``ncFileID`` Integer file descriptor to previously-opened netCDF file. ``ierr`` Returns a 0 for successful completion. ============ ========================================================= | .. container:: routine *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 .. container:: indent1 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. ============= ================================================= | .. container:: routine *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 .. container:: indent1 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. =================== ============================================= | .. container:: routine *call get_close_maxdist_init(gc, maxdist)* :: type(get_close_type), intent(inout) :: gc real(r8), intent(in) :: maxdist .. container:: indent1 Pass-through to the 1-D locations module. See :doc:`get_close_maxdist_init() <../../assimilation_code/location/oned/location_mod>` for the documentation of this subroutine. | .. container:: routine *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) .. container:: indent1 Pass-through to the 1-D locations module. See :doc:`get_close_obs_init() <../../assimilation_code/location/oned/location_mod>` for the documentation of this subroutine. | .. container:: routine *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(:) .. container:: indent1 Pass-through to the 1-D locations module. See `get_close_obs() <../../location/oned/location_mod.html#get_close_obs>`__ for the documentation of this subroutine. | .. container:: routine *call ens_mean_for_model(ens_mean)* :: real(r8), dimension(:), intent(in) :: ens_mean .. container:: indent1 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