# 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 being 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_nmlinteger :: 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