def blbr_jord8(q: sd, al: sd, bl: sd, br: sd, dm: sd):
with computation(PARALLEL), interval(...):
xt = 2.0 * dm
aldiff = al - q
aldiffj = al[0, 1, 0] - q
bl = -1.0 * sign(min(abs(xt), abs(aldiff)), xt)
br = sign(min(abs(xt), abs(aldiffj)), xt)
def compute_pkz_tempadjust(
delp: sd, delz: sd, cappa: sd, heat_source: sd, delt: sd, pt: sd, pkz: sd
):
with computation(PARALLEL), interval(...):
pkz = exp(cappa / (1.0 - cappa) * log(constants.RDG * delp / delz * pt))
pkz = (constants.RDG * delp / delz * pt) ** (cappa / (1.0 - cappa))
dtmp = heat_source / (constants.CV_AIR * delp)
deltmin = sign(min(delt, abs(dtmp)), dtmp)
pt = pt + deltmin / pkz
def compute_pkz_tempadjust(
delp: FloatField,
delz: FloatField,
cappa: FloatField,
heat_source: FloatField,
pt: FloatField,
pkz: FloatField,
delt_time_factor: float,
):
"""
Adjust air temperature from heating due to vorticity damping.
Heating is limited by deltmax times the length of a timestep, with the
highest levels limited further.
Args:
delp: Pressure thickness of atmosphere layers (in)
delz: Vertical thickness of atmosphere layers (in)
cappa: Power to raise pressure to (in)
heat_source: heat source from vorticity damping implied by
energy conservation (in)
pt: Air potential temperature (inout)
pkz: Layer mean pressure raised to the power of Kappa (in)
delta_time_factor: scaled time step (in)
"""
with computation(PARALLEL), interval(...):
pkz = exp(cappa / (1.0 - cappa) *
log(constants.RDG * delp / delz * pt))
pkz = (constants.RDG * delp / delz * pt)**(cappa / (1.0 - cappa))
dtmp = heat_source / (constants.CV_AIR * delp)
with computation(PARALLEL):
with interval(0, 1):
deltmin = sign(min(delt_time_factor * 0.1, abs(dtmp)), dtmp)
pt = pt + deltmin / pkz
with interval(1, 2):
deltmin = sign(min(delt_time_factor * 0.5, abs(dtmp)), dtmp)
pt = pt + deltmin / pkz
with interval(2, None):
deltmin = sign(min(delt_time_factor, abs(dtmp)), dtmp)
pt = pt + deltmin / pkz
def blbr_iord8(q: FloatField, al: FloatField, dm: FloatField):
xt = 2.0 * dm
bl = -1.0 * sign(min(abs(xt), abs(al - q)), xt)
br = sign(min(abs(xt), abs(al[1, 0, 0] - q)), xt)
return bl, br
def dm_iord8plus(q: FloatField):
xt = 0.25 * (q[1, 0, 0] - q[-1, 0, 0])
dqr = max(max(q, q[-1, 0, 0]), q[1, 0, 0]) - q
dql = q - min(min(q, q[-1, 0, 0]), q[1, 0, 0])
return sign(min(min(abs(xt), dqr), dql), xt)
def bl_br_edges(bl, br, q, dxa, al, dm):
from __externals__ import i_end, i_start
# TODO(eddied): This temporary prevents race conditions in regions
al_ip1 = al[1, 0, 0]
with horizontal(region[i_start - 1, :]):
# TODO(rheag) when possible
# dm_left = dm_iord8plus(q[-1, 0, 0])
xt = 0.25 * (q - q[-2, 0, 0])
dqr = max(max(q[-1, 0, 0], q[-2, 0, 0]), q) - q[-1, 0, 0]
dql = q[-1, 0, 0] - min(min(q[-1, 0, 0], q[-2, 0, 0]), q)
dm_left = sign(min(min(abs(xt), dqr), dql), xt)
xt_bl = ppm.s14 * dm_left + ppm.s11 * (q[-1, 0, 0] - q) + q
xt_br = xt_dxa_edge_0(q, dxa)
with horizontal(region[i_start, :]):
# TODO(rheag) when possible
# dm_right = dm_iord8plus(q[1, 0, 0])
xt = 0.25 * (q[2, 0, 0] - q)
dqr = max(max(q[1, 0, 0], q), q[2, 0, 0]) - q[1, 0, 0]
dql = q[1, 0, 0] - min(min(q[1, 0, 0], q), q[2, 0, 0])
dm_right = sign(min(min(abs(xt), dqr), dql), xt)
xt_bl = ppm.s14 * dm_left + ppm.s11 * (q[-1, 0, 0] - q) + q
xt_bl = xt_dxa_edge_1(q, dxa)
xt_br = ppm.s15 * q + ppm.s11 * q[1, 0, 0] - ppm.s14 * dm_right
with horizontal(region[i_start + 1, :]):
xt_bl = ppm.s15 * q[-1, 0, 0] + ppm.s11 * q - ppm.s14 * dm
xt_br = al_ip1
with horizontal(region[i_end - 1, :]):
xt_bl = al
xt_br = ppm.s15 * q[1, 0, 0] + ppm.s11 * q + ppm.s14 * dm
with horizontal(region[i_end, :]):
# TODO(rheag) when possible
# dm_left_end = dm_iord8plus(q[-1, 0, 0])
xt = 0.25 * (q - q[-2, 0, 0])
dqr = max(max(q[-1, 0, 0], q[-2, 0, 0]), q) - q[-1, 0, 0]
dql = q[-1, 0, 0] - min(min(q[-1, 0, 0], q[-2, 0, 0]), q)
dm_left_end = sign(min(min(abs(xt), dqr), dql), xt)
xt_bl = ppm.s15 * q + ppm.s11 * q[-1, 0, 0] + ppm.s14 * dm_left_end
xt_br = xt_dxa_edge_0(q, dxa)
with horizontal(region[i_end + 1, :]):
# TODO(rheag) when possible
# dm_right_end = dm_iord8plus(q[1, 0, 0])
xt = 0.25 * (q[2, 0, 0] - q)
dqr = max(max(q[1, 0, 0], q), q[2, 0, 0]) - q[1, 0, 0]
dql = q[1, 0, 0] - min(min(q[1, 0, 0], q), q[2, 0, 0])
dm_right_end = sign(min(min(abs(xt), dqr), dql), xt)
xt_bl = xt_dxa_edge_1(q, dxa)
xt_br = ppm.s11 * (q[1, 0, 0] - q) - ppm.s14 * dm_right_end + q
with horizontal(region[i_start - 1:i_start + 2, :],
region[i_end - 1:i_end + 2, :]):
bl = xt_bl - q
br = xt_br - q
return bl, br
def dm_jord8plus(q: sd, al: sd, dm: sd):
with computation(PARALLEL), interval(...):
xt = 0.25 * (q[0, 1, 0] - q[0, -1, 0])
dqr = max(max(q, q[0, -1, 0]), q[0, 1, 0]) - q
dql = q - min(min(q, q[0, -1, 0]), q[0, 1, 0])
dm = sign(min(min(abs(xt), dqr), dql), xt)
def blbr_jord8(q: FloatField, al: FloatField, dm: FloatField):
yt = 2.0 * dm
bl = -1.0 * sign(min(abs(yt), abs(al - q)), yt)
br = sign(min(abs(yt), abs(al[0, 1, 0] - q)), yt)
return bl, br
def dm_jord8plus(q: FloatField):
yt = 0.25 * (q[0, 1, 0] - q[0, -1, 0])
dqr = max(max(q, q[0, -1, 0]), q[0, 1, 0]) - q
dql = q - min(min(q, q[0, -1, 0]), q[0, 1, 0])
return sign(min(min(abs(yt), dqr), dql), yt)
def bl_br_edges(bl, br, q, dya, al, dm):
from __externals__ import j_end, j_start
# TODO(eddied): This temporary prevents race conditions in regions
al_ip1 = al[0, 1, 0]
with horizontal(region[:, j_start - 1]):
# TODO(rheag) when possible
# dm_left = dm_jord8plus(q[0, -1, 0])
yt = 0.25 * (q - q[0, -2, 0])
dqr = max(max(q[0, -1, 0], q[0, -2, 0]), q) - q[0, -1, 0]
dql = q[0, -1, 0] - min(min(q[0, -1, 0], q[0, -2, 0]), q)
dm_left = sign(min(min(abs(yt), dqr), dql), yt)
yt_bl = ppm.s14 * dm_left + ppm.s11 * (q[0, -1, 0] - q) + q
yt_br = yt_dya_edge_0(q, dya)
with horizontal(region[:, j_start]):
# TODO(rheag) when possible
# dm_right = dm_jord8plus(q[0, 1, 0])
yt = 0.25 * (q[0, 2, 0] - q)
dqr = max(max(q[0, 1, 0], q), q[0, 2, 0]) - q[0, 1, 0]
dql = q[0, 1, 0] - min(min(q[0, 1, 0], q), q[0, 2, 0])
dm_right = sign(min(min(abs(yt), dqr), dql), yt)
yt_bl = ppm.s14 * dm_left + ppm.s11 * (q[0, -1, 0] - q) + q
yt_bl = yt_dya_edge_1(q, dya)
yt_br = ppm.s15 * q + ppm.s11 * q[0, 1, 0] - ppm.s14 * dm_right
with horizontal(region[:, j_start + 1]):
yt_bl = ppm.s15 * q[0, -1, 0] + ppm.s11 * q - ppm.s14 * dm
yt_br = al_ip1
with horizontal(region[:, j_end - 1]):
yt_bl = al
yt_br = ppm.s15 * q[0, 1, 0] + ppm.s11 * q + ppm.s14 * dm
with horizontal(region[:, j_end]):
# TODO(rheag) when possible
# dm_left_end = dm_jord8plus(q[0, -1, 0])
yt = 0.25 * (q - q[0, -2, 0])
dqr = max(max(q[0, -1, 0], q[0, -2, 0]), q) - q[0, -1, 0]
dql = q[0, -1, 0] - min(min(q[0, -1, 0], q[0, -2, 0]), q)
dm_left_end = sign(min(min(abs(yt), dqr), dql), yt)
yt_bl = ppm.s15 * q + ppm.s11 * q[0, -1, 0] + ppm.s14 * dm_left_end
yt_br = yt_dya_edge_0(q, dya)
with horizontal(region[:, j_end + 1]):
# TODO(rheag) when possible
# dm_right_end = dm_jord8plus(q[0, 1, 0])
yt = 0.25 * (q[0, 2, 0] - q)
dqr = max(max(q[0, 1, 0], q), q[0, 2, 0]) - q[0, 1, 0]
dql = q[0, 1, 0] - min(min(q[0, 1, 0], q), q[0, 2, 0])
dm_right_end = sign(min(min(abs(yt), dqr), dql), yt)
yt_bl = yt_dya_edge_1(q, dya)
yt_br = ppm.s11 * (q[0, 1, 0] - q) - ppm.s14 * dm_right_end + q
with horizontal(region[:, j_start - 1:j_start + 2],
region[:, j_end - 1:j_end + 2]):
bl = yt_bl - q
br = yt_br - q
return bl, br
def blbr_iord8(q: sd, al: sd, bl: sd, br: sd, dm: sd):
with computation(PARALLEL), interval(...):
# al, dm = al_iord8plus_fn(q, al, dm, r3)
xt = 2.0 * dm
bl = -1.0 * sign(min(abs(xt), abs(al - q)), xt)
br = sign(min(abs(xt), abs(al[1, 0, 0] - q)), xt)
