9-variable

Overview

The 9-variable model is described in Lorenz (1980). 1 Lorenz developed this primitive-equation model using shallow-water equations as a starting point and manipulating the divergence equations so that the model exhibits quasi-geostrophic behavior and transient gravity waves that dissipate with time. Gent and McWilliams (1982) 2 explore the behavior of this model extensively. For an introduction to shallow-water equations, we recommend consulting the relevant section of a meteorology textbook such as section 4.5 of Holton and Hakim (2013). 3

The model’s three X variables are at 0, 1/9, and 2/9, three Y variables are at 3/9, 4/9 and 5/9, and three Z variables are at 6/9, 7/9, and 8/9 on a cyclic [0, 1] domain.

In the 9-variable model, DART advances the model, gets the model state and metadata describing this state. The model can be configured by altering the &model_nml namelist in the input.nml file. The details of the &model_nml namelist are always model-specific (there are no generic namelist values). The model time step defaults to 1 hour (3600 seconds) but is settable by altering the namelist.

The 9-variable model has a work/workshop_setup.csh script that compiles and runs an example. This example is referenced in Sections 7 and 10 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!

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
   g                 = 8.0,
   deltat            = 0.0833333333333333,
   time_step_days    = 0,
   time_step_seconds = 3600
/

Description of each namelist entry

Item	Type	Description
g	real(r8)	Model parameter, see comp_dt in code for equations.
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	real(r8)	Number of days for dimensional timestep, mapped to delta_t.
time_step_seconds	real(r8)	Number of seconds for dimensional timestep, mapped to delta_t.

References

1

Lorenz, Edward N., 1980: Attractor Sets and Quasi-Geostrophic Equilibrium. Journal of the Atmospheric Sciences, 37, 1685-1699. doi:10.1175/1520-0469(1980)037<1685:ASAQGE>2.0.CO;2

2

Gent, Peter R., and James C. McWilliams, 1982: Intermediate Model Solutions to the Lorenz Equations: Strange Attractors and Other Phenomena. Journal of the Atmospheric Sciences, 39, 3-13. doi:10.1175/1520-0469(1982)039<0003:IMSTTL>2.0.CO;2

3

Holton, James R., and Gregory J. Hakim, 2013: An Introduction to Dynamic Meteorology – Fifth Edition. Academic Press, 532 pp.