from veros import VerosSetup, veros_routine
from veros.variables import allocate, Variable
from veros.distributed import global_min, global_max
from veros.core.operators import numpy as npx, update, at
import veros.tools
[docs]class ACCSectorSetup(VerosSetup):
"""A model using spherical coordinates with a partially closed domain representing the narrow sector of Atlantic and ACC.
The bathymetry of the model is idealized to a flat-bottom (with depth of 4000 m) over the majority of the domain,
except a half depth appended within the confines of the circumpolar channel at the inflow and outflow regions.
The horizontal grid has resolution of :math:`2 \\times 2` degrees, and the vertical one has 40 levels.
Wind forcing over the sector part and buoyancy relaxation drive a large-scale meridional overturning circulation.
This setup demonstrates:
- setting up an idealized geometry after `(Munday et al., 2013) <https://doi.org/10.1175/JPO-D-12-095.1>`_.
- modifing surface forcings over selected regions of the domain
- sensitivity of circumpolar transport and meridional overturning
to changes in Southern Ocean wind stress and buoyancy anomalies
- basic usage of diagnostics
:doc:`Adapted from ACC channel model </reference/setups/acc>`.
Reference:
Laurits S. Andreasen. (2019). Time scales of the Bipolar seesaw: The role of oceanic cross-hemisphere signals,
Southern Ocean eddies and wind changes, MSc Thesis, 42p.
`<https://sid.erda.dk/share_redirect/CVvcrowL22/Thesis/Laurits_Andreasen_MSc_thesis.pdf>`_.
"""
max_depth = 4000.0
@veros_routine
def set_parameter(self, state):
settings = state.settings
settings.identifier = "acc_sector"
settings.nx, settings.ny, settings.nz = 15, 62, 40
settings.dt_mom = 3600.0
settings.dt_tracer = 3600.0
settings.runlen = 86400 * 365
settings.x_origin = 0.0
settings.y_origin = -60.0
settings.coord_degree = True
settings.enable_cyclic_x = True
settings.enable_neutral_diffusion = True
settings.K_iso_0 = 1000.0
settings.K_iso_steep = 500.0
settings.iso_dslope = 0.005
settings.iso_slopec = 0.01
settings.enable_skew_diffusion = True
settings.enable_hor_friction = True
settings.A_h = 5e4 * 2
settings.enable_hor_friction_cos_scaling = True
settings.hor_friction_cosPower = 1
settings.enable_bottom_friction = True
settings.r_bot = 1e-5
settings.enable_implicit_vert_friction = True
settings.enable_tke = True
settings.c_k = 0.1
settings.c_eps = 0.7
settings.alpha_tke = 30.0
settings.mxl_min = 1e-8
settings.tke_mxl_choice = 2
settings.kappaM_min = 2e-4
settings.kappaH_min = 2e-5
settings.enable_Prandtl_tke = False
settings.enable_kappaH_profile = True
settings.K_gm_0 = 1300.0
settings.enable_eke = False
settings.eke_k_max = 1e4
settings.eke_c_k = 0.4
settings.eke_c_eps = 0.5
settings.eke_cross = 2.0
settings.eke_crhin = 1.0
settings.eke_lmin = 100.0
settings.enable_eke_superbee_advection = False
settings.enable_eke_isopycnal_diffusion = False
settings.enable_idemix = False
settings.enable_idemix_hor_diffusion = False
settings.enable_eke_diss_surfbot = False
settings.eke_diss_surfbot_frac = 0.2
settings.enable_idemix_superbee_advection = False
settings.eq_of_state_type = 3
var_meta = state.var_meta
var_meta.update(
t_star=Variable("t_star", ("yt",), "deg C", "Reference surface temperature"),
t_rest=Variable("t_rest", ("xt", "yt"), "1/s", "Surface temperature restoring time scale"),
)
@veros_routine
def set_grid(self, state):
vs = state.variables
settings = state.settings
# keep total domain size constant when nx or ny changes
vs.dxt = update(vs.dxt, at[...], 2.0 * 15 / settings.nx)
vs.dyt = update(vs.dyt, at[...], 2.0 * 62 / settings.ny)
vs.dzt = veros.tools.get_vinokur_grid_steps(settings.nz, self.max_depth, 10.0, refine_towards="lower")
@veros_routine
def set_coriolis(self, state):
vs = state.variables
settings = state.settings
vs.coriolis_t = update(
vs.coriolis_t, at[:, :], 2 * settings.omega * npx.sin(vs.yt[None, :] / 180.0 * settings.pi)
)
@veros_routine
def set_topography(self, state):
vs = state.variables
x, y = npx.meshgrid(vs.xt, vs.yt, indexing="ij")
vs.kbot = npx.logical_or((x > 1.0) & (x < 27), y < -40).astype("int")
# A half depth (ridge) is appended to the domain within the confines
# of the circumpolar channel at the inflow and outflow regions
bathymetry = npx.logical_or(((x <= 1.0) & (y < -40)), ((x >= 27) & (y < -40)))
kzt2000 = npx.sum((vs.zt < -2000.0).astype("int"))
vs.kbot = npx.where(bathymetry, kzt2000, vs.kbot)
@veros_routine
def set_initial_conditions(self, state):
vs = state.variables
settings = state.settings
# initial conditions
vs.temp = update(vs.temp, at[...], ((1 - vs.zt[None, None, :] / vs.zw[0]) * 15 * vs.maskT)[..., None])
vs.salt = update(vs.salt, at[...], 35.0 * vs.maskT[..., None])
# wind stress forcing
yt_min = global_min(vs.yt.min())
yu_min = global_min(vs.yu.min())
yt_max = global_max(vs.yt.max())
yu_max = global_max(vs.yu.max())
taux = allocate(state.dimensions, ("yt",))
north = vs.yt > 30
subequatorial_north_n = (vs.yt >= 15) & (vs.yt < 30)
subequatorial_north_s = (vs.yt > 0) & (vs.yt < 15)
equator = (vs.yt > -5) & (vs.yt < 5)
subequatorial_south_n = (vs.yt > -15) & (vs.yt < 0)
subequatorial_south_s = (vs.yt <= -15) & (vs.yt > -30)
south = vs.yt < -30
taux = npx.where(north, -5e-2 * npx.sin(settings.pi * (vs.yu - yu_max) / (yt_max - 30.0)), taux)
taux = npx.where(subequatorial_north_s, 5e-2 * npx.sin(settings.pi * (vs.yu - 30.0) / 30.0), taux)
taux = npx.where(subequatorial_north_n, 5e-2 * npx.sin(settings.pi * (vs.yt - 30.0) / 30.0), taux)
taux = npx.where(subequatorial_south_n, -5e-2 * npx.sin(settings.pi * (vs.yu - 30.0) / 30.0), taux)
taux = npx.where(subequatorial_south_s, -5e-2 * npx.sin(settings.pi * (vs.yt - 30.0) / 30.0), taux)
taux = npx.where(equator, -1.5e-2 * npx.cos(settings.pi * (vs.yu - 10.0) / 10.0) - 2.5e-2, taux)
taux = npx.where(south, 15e-2 * npx.sin(settings.pi * (vs.yu - yu_min) / (-30.0 - yt_min)), taux)
vs.surface_taux = taux * vs.maskU[:, :, -1]
# surface heatflux forcing
delta_t, ts, tn = 25.0, 0.0, 5.0
vs.t_star = allocate(state.dimensions, ("yt",), fill=delta_t)
vs.t_star = npx.where(
vs.yt < 0, ts + delta_t * npx.sin(settings.pi * (vs.yt + 60.0) / npx.abs(2 * settings.y_origin)), vs.t_star
)
vs.t_star = npx.where(
vs.yt > 0,
tn + (delta_t + ts - tn) * npx.sin(settings.pi * (vs.yt + 60.0) / npx.abs(2 * settings.y_origin)),
vs.t_star,
)
vs.t_rest = vs.dzt[-1] / (10.0 * 86400.0) * vs.maskT[:, :, -1]
if settings.enable_tke:
vs.forc_tke_surface = update(
vs.forc_tke_surface,
at[2:-2, 2:-2],
npx.sqrt(
(0.5 * (vs.surface_taux[2:-2, 2:-2] + vs.surface_taux[1:-3, 2:-2]) / settings.rho_0) ** 2
+ (0.5 * (vs.surface_tauy[2:-2, 2:-2] + vs.surface_tauy[2:-2, 1:-3]) / settings.rho_0) ** 2
)
** (1.5),
)
if settings.enable_idemix:
vs.forc_iw_bottom = 1e-6 * vs.maskW[:, :, -1]
vs.forc_iw_surface = 1e-7 * vs.maskW[:, :, -1]
@veros_routine
def set_forcing(self, state):
vs = state.variables
vs.forc_temp_surface = vs.t_rest * (vs.t_star - vs.temp[:, :, -1, vs.tau])
@veros_routine
def set_diagnostics(self, state):
settings = state.settings
state.diagnostics["snapshot"].output_frequency = 86400 * 10
state.diagnostics["averages"].output_variables = (
"salt",
"temp",
"u",
"v",
"w",
"psi",
"rho",
"surface_taux",
"surface_tauy",
)
state.diagnostics["averages"].output_frequency = 365 * 86400.0
state.diagnostics["averages"].sampling_frequency = settings.dt_tracer * 10
state.diagnostics["overturning"].output_frequency = 365 * 86400.0 / 48.0
state.diagnostics["overturning"].sampling_frequency = settings.dt_tracer * 10
state.diagnostics["tracer_monitor"].output_frequency = 365 * 86400.0 / 12.0
state.diagnostics["energy"].output_frequency = 365 * 86400.0 / 48
state.diagnostics["energy"].sampling_frequency = settings.dt_tracer * 10
@veros_routine
def after_timestep(self, state):
pass