Contact: Isaac Held
Reviewers: Peter Phillipps
The dynamical core of the spectral transform model for two-dimensional, non-divergent flow on the surface of the sphere.
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 disurbance localized in midlatitudes.
For a full description of the model and algorithms used, see
barotropic.ps
For higher level routines for running this barotropic spectral model,
see atmosphere_mod
fms_mod
constants_mod
time_manager_mod
transforms_mod
spectral_damping_mod
leapfrog_mod
fv_advection_mod
use barotropic_dynamics_mod [,only: barotropic_dynamics_init,
barotropic_dynamics,
barotropic_dynamics_end,
dynamics_type,
grid_type,
spectral_type,
tendency_type]
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
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'
&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))
integer :: 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 = ture => a passive tracer is carried that is advected
on the spectral transform grid by a finite-volume algorithm
(see barotropic.ps )
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.
"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