Lorenz 84

Overview

This model was described in Lorenz (1984). [1] In Lorenz 84, DART advances the model, gets the model state and metadata describing this state, find states variables that are close to a given location, and does spatial interpolation for model state variables. The distinctive part of the model interfaces is the namelist.

The system of equations is:

\[\frac{dx}{dt} = -y^2-z^2-ax+aF \frac{dy}{dt} = xy-bxz-y+G \frac{dz}{dt} = bxy+xz-z\]

and, within DART, the model parameters have default values of:

\[a=\frac{1}{4}, b=4, F=8, G=\frac{5}{4}\]

that can be altered by editing the &model_nml namelist in the input.nml file.

The Lorenz 84 model has a work/workshop_setup.csh script that compiles and runs an example. This example is referenced specifically in Section 7 of the DART tutorial and is intended to provide insight into model/assimilation behavior. The example may or may not result in good (or even decent!) results!

The Lorenz 84 model may be used instead of the Lorenz 63 model in many sections of the Tutorial. It has a more complex attractor, is not as periodic as Lorenz 63 and may be more challenging for certain filter variants.

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
  a      = 0.25,
  b      = 4.00,
  f      = 8.00,
  g      = 1.25,
  deltat = 0.01,
  time_step_days    = 0,
  time_step_seconds = 3600
/

Description of each namelist entry

Item

Type

Description

a

real(r8)

Model parameter.

b

real(r8)

Model parameter.

f

real(r8)

Model parameter.

g

real(r8)

Model parameter.

deltat

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 deltat.

time_step_seconds

integer

Number of seconds for dimensional timestep, mapped to deltat.

References