Lorenz 05

Naming History

In earlier versions of DART, this collection of models was referred to as Lorenz 04. Edward Lorenz provided James A. Hansen these model formulations before they had been published, since both Lorenz and Hansen were faculty members at MIT at the time. Hansen developed the DART model interface and incorporated it into the DART codebase in 2004. Thus, within DART, it was named Lorenz 04.

The collection of models was published a year later in Lorenz (2005), [1] thus, within the wider community, the models are typically referred to as Lorenz 05. To reflect this fact, the collection of models was renamed within DART from Lorenz 04 to Lorenz 05 during the Manhattan release.

Overview

Lorenz (2005) provides a fascinating account of the difficulties involved in designing simple models that exhibit chaotic behavior and realistically simulate aspects of atmospheric flow. It presents three models of increasing complexity:

  • Model I is a single-scale model, similar to Lorenz (1996), [2] intended to represent the atmosphere at a specific height and latitude.

  • Model II is also a single-scale model, similar to Model I, but with spatial continuity in the waves.

  • Model III is a two-scale model. It is fundamentally different from the Lorenz 96 two-scale model because of the spatial continuity and the fact that both scales are projected onto a single variable of integration. The scale separation is achieved by a spatial filter and is therefore not perfect (i.e. there is leakage).

Model II and Model III are implemented in this DART model interface, and the user is free to choose Model II or III by editing the namelist. For users interested in Model I, please use Lorenz 96. The slow scale in Model III is Model II, and thus Model II is a deficient form of Model III.

The Lorenz 05 model has a work/workshop_setup.csh script that compiles and runs an example. This example may be used anywhere in the DART tutorial to explore multiscale dynamics and to provide insight into model/assimilation behavior. The example may or may not result in good (or even decent!) results!

Model Formulation

For Lorenz 05, DART to advances the model, gets the model state and metadata describing this state, finds state variables that are close to a given location, and does spatial interpolation for model state variables.

Namelist

The &model_nml namelist is read from the input.nml file. 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        = 960,
   forcing           = 15.00,
   delta_t           = 0.001,
   space_time_scale  = 10.00,
   coupling          = 3.00,
   K                 = 32,
   smooth_steps      = 12,
   time_step_days    = 0,
   time_step_seconds = 3600,
   model_number      = 3
/

Description of each namelist entry

Contents

Type

Description

model_size

integer

Number of variables in model

forcing

real(r8)

Forcing, F, for model

delta_t

real(r8)

Non-dimensional timestep

space_time_scale

real(r8)

Determines temporal and spatial relationship between fast and slow variables (model III)

coupling

real(r8)

Linear coupling between fast and slow variables (model III)

K

integer

Determines the wavenumber of the slow variables (K=1, smooth_steps=0 reduces model II to Lorenz 96)

smooth_steps

integer

Determines filter length to separate fast and slow scales

time_step_days

integer

Arbitrary real time step days

time_step_seconds

integer

Arbitrary real time step seconds (could choose this for proper scaling)

model_number

integer

2 = single-scale, 3 = 2-scale. (This follows the notation in the paper.)

References