# MODULE model_mod (Lorenz_96)

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## Overview

DART interface module for the Lorenz-96 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.

Quoting from the Lorenz 1998 paper:

... the authors introduce a model consisting of 40 ordinary differential equations, with the dependent variables representing values of some atmospheric quantity at 40 sites spaced equally about a latitude circle. The equations contain quadratic, linear, and constant terms representing advection, dissipation, and external forcing. Numerical integration indicates that small errors (differences between solutions) tend to double in about 2 days. Localized errors tend to spread eastward as they grow, encircling the globe after about 14 days.
...
We have chosen a model with J variables, denoted by X1, ..., XJ; in most of our experiments we have let J = 40. The governing equations are:
```dXj/dt = (Xj+1 - Xj-2)Xj-1 - Xj + F         (1)
```
for j = 1, ..., J. To make Eq. (1) meaningful for all values of j we define X-1 = XJ-1, X0 = XJ, and XJ+1 = X1, so that the variables form a cyclic chain, and may be looked at as values of some unspecified scalar meteorological quantity, perhaps vorticity or temperature, at J equally spaced sites extending around a latitude circle. Nothing will simulate the atmosphere's latitudinal or vertical extent.

See the references section for more details.

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## 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
model_size        = 40,
forcing           = 8.00,
delta_t           = 0.05,
time_step_days    = 0,
time_step_seconds = 3600
/
```

Item Type Description
model_size integer Number of variables in model.
forcing real(r8) Forcing, F, for model.
delta_t real(r8) Non-dimensional timestep. This is mapped to the dimensional timestep specified by time_step_days and time_step_seconds.
time_step_days integer Number of days for dimensional timestep, mapped to delta_t.
time_step_seconds integer Number of seconds for dimensional timestep, mapped to delta_t.

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## OTHER MODULES USED

```types_mod
time_manager_mod
oned/location_mod
utilities_mod
```
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## 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, which is settable by namelist and defaults to 40.

 model_size The length of the model state vector.

```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 Specifies time of the initial model state.

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 metadata about a given element, indexed by index_in, in the model state vector. The location defines where the state variable is located For lorenz-96, variable 1 is at 0.0, variable 2 is at 1/40., variable 3 is at 2/40., etc. on a cyclic [0, 1] domain. The variable type is always returned as 1.

 index_in Index of state vector element about which information is requested. location The location of state variable element. var_type Returns the type (always 1) 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
```

Given model state, returns the value interpolated to a given location in [0, 1] by linear interpolation. The type variable is not used here and istatus is always returned as 0 (successful interpolation).

 x A model state vector. location Location to which to interpolate. itype Not used. obs_val The interpolated value from the model. istatus Quality control information, always returned 0.

var = get_model_time_step()
```type(time_type) :: get_model_time_step
```

Returns the time step (forecast length) of the model; The time step defaults to 1 hour but is settable by namelist.

 var Smallest time step of model.

call static_init_model()

Used for runtime initialization of model; reads namelist, initializes model parameters, etc. This is the first call made to the model by any DART-compliant assimilation routine.

call end_model()

A stub since lorenz 96 requires no cleanup.

call init_time(time)
```type(time_type), intent(out) :: time
```

Returns the time at which the model will start if no input initial conditions are to be used. This is used to spin-up the model from rest. Sets time to 0 in this model.

 time Initial model time.

call init_conditions(x)
```real(r8), dimension(:), intent(out) :: x
```

Returns default initial conditions for the model; generally used for spinning up initial model states. Values chosen here are 0.1 for all nine state variables.

 x Initial conditions for state vector.

ierr = nc_write_model_atts(ncFileID)
```integer             :: nc_write_model_atts
integer, intent(in) :: ncFileID
```

Function to write model specific attributes to a netCDF file. At present, DART is using the NetCDF format to output diagnostic information. This is not a requirement, and models could choose to provide output in other formats. This function writes the metadata associated with the model to a NetCDF file opened to a file identified by ncFileID.

 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
```

Writes a copy of the state variables to a netCDF file. Multiple copies of the state for a given time are supported, allowing, for instance, a single file to include multiple ensemble estimates of the state.

 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.

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## 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
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## REFERENCES

Lorenz, E. N., 1995: Predictability: A Problem Partly Solved.  Proc. Seminar on Predictability. 1, ECMWF, Reading, Berkshire, UK, 1-18.

Lorenz, E. N., and K. A. Emanuel, 1998: Optimal sites for supplementary weather observations: Simulations with a small model.  J. Atmos. Sci., 55, 399-414.

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## ERROR CODES and CONDITIONS

Routine Message Comment
nc_write_model_atts
nc_write_model_vars
Various netCDF-f90 interface error messages From one of the netCDF calls in the named routine

## KNOWN BUGS

none at this time

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## FUTURE PLANS

none at this time

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N/A

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