GFDL - Geophysical Fluid Dynamics Laboratory

module shallow_dynamics_mod

Contact: Isaac Held

Reviewers: Peter Phillipps

OVERVIEW

The dynamical core of the spectral transform model for the shallow water equations on the sphere.

DESCRIPTION

Integrates the shallow water equation for hydrostatic flow of a homgeoneous, incompressible fluid on the sphere using the spectral transform technique. Also allows for the inclusion of a passive tracer advected by the the spectral advection algorithm, and a gridpoint tracer advected with a finite volume algorithm on the transform grid. Thinking of the model as one of the upper tropopsheric flow, the default experiment involves relaxation of the geopotential to an “equilibrium value” with maxima (whose amplitude and shape are controlled from the namelist) along the equator and in the subtropicals.
For a full description of the model and algorithms used, see shallow.pdf For higher level routines for running
this barotropic spectral model, see atmosphere_mod

OTHER MODULES USED

  • fms_mod
  • constants_mod
  • time_manager_mod
  • transforms_mod
  • spectral_damping_mod
  • leapfrog_mod
  • fv_advection_mod

PUBLIC INTERFACE

  use shallow_dynamics_mod [,only: shallow_dynamics_init,       
                                      shallow_dynamics,
                          shallow_dynamics_end,
                                      dynamics_type,
                      grid_type,
                      spectral_type,
                      tendency_type]

PUBLIC DATA


type grid_type
   real, pointer, dimension(:,:,:) :: u, v, vor, div, h, trs, tr
   real, pointer, dimension(:,:)   :: stream, pv
end type

   allocated space for grid fields

   (:,:,:) => (lon, lat, time_level)
   (:,:)   => (lon, lat)
      (lon, lat) on local computational domain
      time_level stores the two time levels needed for the
          leapfrog step
   
   u      -- eastward velocity (m/s)
   v      -- northward velocity (m/s)
   vor    -- vorticity (1/s)
   trs    -- tracer advected spectrally
   tr     -- tracer advected on grid
   pv     -- absolute vorticity, f + vor, where f = 2*omega*sin(lat) (1/s)
   stream -- streamfunction (m^2/s) at current time

type spectral_type
   complex, pointer, dimension(:,:,:) :: vor, trs
end type

   allocated space for spectral fields
   
      (:,:,:) => (zonal, meridional, time_level)

   vor -- spectral vorticity
   trs -- spectral tracer
  

type tendency_type
    real, pointer, dimension(:,:) :: u, v, trs, tr
end type

   allocated space for accumulating tendencies, d/dt, in grid space, 
           for prognostic variables
   
      (:,:,:) => (lon, lat)

type dynamics_type
   type(grid_type)     :: grid
   type(spectral_type) :: spec
   type(tendency_type) :: tend
   integer             :: num_lon, num_lat  ! size of global domain
   logical             :: grid_tracer, spec_tracer 
end type

   grid_tracer = .true. => tracer with gridpoint advection is beign integrated
   similarly for spec_tracer

PUBLIC ROUTINES

subroutine  barotropic_dynamics_init





subroutine barotropic _dynamics





subroutine barotropic_dynamics_end





type (grid_type)





type (spectral_type)





type (tendency_type)





type (dynamics_type)











 subroutine barotropic_dynamics_init(Dyn,  Time, Time_init)
 
   type(dynamics_type), intent(inout)  :: Dyn
         type containing all dynamical fields and related information
     (see type (dynamics_type))











type(time_type) , intent(in) :: Time, Time_init











current time and time at which integeration began











time_type defined by time_manager_mod











Initializes the module;











Reads restart from 'INPUT/barotropic_dynamics.res' if Time = Time_init;











otherwise uses default initial conditions






  subroutine barotropic_dynamics &
     (Time, Time_init, Dyn, previous, current, future, delta_t)
 
     type(time_type)    , intent(inout)  :: Time, Time_init
     type(dynamics_type), intent(inout)  :: Dyn
     integer            , intent(in   )  :: previous, current, future
     real               , intent(in   )  :: delta_t
      
     previous, current and future = 1 or 2
       these integers refer to the third dimension of the 
         three-dimensional fields in Dyn
       the fields at time t - delta_t are assumed to be in (:,:,previous)
       the fields at time t           are assumed to be in (:,:,current)
       the fields at time t + delta_t are placed        in (:,:,future)
          overwriting whatever is already there

     delta_t = time step in seconds
     
     updates dynamical fields by one time step

   subroutine barotropic_dynamics_end(Dyn, previous, current)
   
     type(dynamics_type), intent(inout)  :: Dyn
     integer, intent(in) :: previous, current
   
      
    Terminates module; 
     writes restart file to 'RESTART/barotropic_dynamics.res'

NAMELIST

&barotropic_dynamics_nml











integer :: num_lat = 128











number of latitudes in global grid











integer :: num_lon = 256











number of longitudes in global grid











should equal 2*num_lat for Triangular truncation











integer :: num_fourier = 85











the retained fourier wavenumber are n*fourier_inc, where











n ranges from 0 to num_fourier











integer :: num_spherical = 86











the maximum number of meridional modes for any zonal wavenumber











for triangular truncation, set num_spherical = num_fourier +1











integer :: fourier_inc = 1











creates a "sector" model if fourier_inc > 1; integration domain is











(360 degrees longitude)/fourier_inc











(the default values listed above define a standard T85 model)











logical :: check_fourier_imag = .false.











if true, checks to see if fields to be transformed to grid











domain have zero imaginary part to their zonally symmetric











modes; useful for debugging











logical :: south_to_north = .true.











true => grid runs from south to north











false => grid runs from north to south











logical :: triangular_trunc = .true.











true => shape of truncation is triangular











false => shape of truncation is rhomboidal











real :: robert_coeff = 0.04











x(current) => (1-2r)*x(current) + r*(x(future)+x(previous))











where r = robert_coeff (non-dimensional)

















real :: longitude_origin = 0.0











longitude of first longitude, in degrees











(if you want the westgern boundary of first grid boc to be at











0.0, set longitude_origin = 0.5*360./float(num_lon))











character :: damping_option = 'resolution_dependent'











integer :: damping_order = 4











real :: damping_coeff = 1.e-04

















damping = nu*(del^2)^n where n = damping order











damping_option = 'resolution_dependent' or 'resolution_independent'











= 'resolution_dependent' => nu is set so that the damping rate for the











mode (m=0,n=num_spherical-1) equals damping_coeff (in 1/s)











For triangular truncation, damping_coeff is then the











rate of damping of the highest retained mode

















= 'resolution_independent' => nu = damping_coef

















real :: zeta_0 = 8.e-05











integer :: m_0 = 4











real :: eddy_width = 15.0











real :: eddy_lat = 45.0

















eddy component of the initial condition is sinusoidal with











wavenumber m_0 and with a gaussian distribution of











vorticity in latitude, centered at eddy_lat with half-width











eddy_width











zeta_0 ( 1/s)











eddy_width and eddy_lat (degrees)











logical :: spec_tracer = .true.











logical :: grid_tracer = .true.











spec_tracer = true => a passive tracer is carried that is advected











spectrally, with the same algorithm as the vorticity











grid_tracer = true => a passive tracer is carried that is advected











on the spectral transform grid by a finite-volume algorithm











Both tracers can be carried simultaeneously











The vorticity and the tracers are initialized within subroutine











barotropic_dynamics_init











real, dimension(2) :: valid_range_v = -1000., 1000.











A valid range for meridional wind. Model terminates if meridional wind











goes outside the valid range. Allows model to terminate gracefully when,











for example, the model becomes numerically unstable.











character :: initial_zonal_wind = 'two_jets'











initial_zonal_wind = 'two_jets' => A jet in each hemisphere centered near 30 deg latitude











initial_zonal_wind = 'zero' => Zero zonal wind






ERROR MESSAGES

   "Dynamics has not been initialized"
      -- barotropic_dynamics_init must be called before any other
         routines in the module are called
     
   "restart does not exist" 
      -- Time is not equal to Time_init at initalization, but the file
          'INPUT/barotropic_dynamics.res' does not exit