GFDL - Geophysical Fluid Dynamics Laboratory

module barotropic_dynamics_mod

Contact: Isaac Held

Reviewers: Peter Phillipps

OVERVIEW

The dynamical core of the spectral transform model for two-dimensional, non-divergent
flow on the surface of the sphere.

DESCRIPTION

Integrates the barotropic vorticity equation for nondivergent flow on the sphere
using the spectral transform technique. Also allows for the inclusion of a passive
tracer advected by the same spectral advection algorithm as the vorticity, and a
gridpoint tracer advected with a finite volume algorithm on the transform grid.
The default initial condition provided as an example is a zonal flow resembling
that in the Northern winter, plus a sinusoidal disturbance localized in midlatitudes.
For a full description of the model and algorithms used, see
barotropic.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 barotropic_dynamics_mod [,only: barotropic_dynamics_init,       
                                      barotropic_dynamics,
                          barotropic_dynamics_end,
                                      dynamics_type,
                      grid_type,
                      spectral_type,
                      tendency_type]

PUBLIC DATA


type grid_type
   real, pointer, dimension(:,:,:) :: u, v, vor, trs, tr, pv
   real, pointer, dimension(:,:)   :: stream
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 for num_lat, num_lon, num_fourier and num_spherical define a standard T85 resolution)
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 western boundary of first grid box 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 (1/sec) integer :: m_0 = 4 real :: eddy_width = 15.0 (degrees longitude) real :: eddy_lat = 45.0 (degrees latitude) 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 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