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 :doc:`DART_tutorial <../../../theory/readme>` 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. .. code-block:: fortran &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 2.0.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 2.0.CO;2>`__ .. [3] Holton, James R., and Gregory J. Hakim, 2013: *An Introduction to Dynamic Meteorology -- Fifth Edition.* Academic Press, 532 pp.