def __call__(self, atmosphere):
if self._lapse_cache is not None:
return self._lapse_cache
T = atmosphere['T'][0, :]
p = atmosphere['plev'][:]
phlev = atmosphere['phlev'][:]
# Use short formula symbols for physical constants.
g = constants.earth_standard_gravity
L = constants.heat_of_vaporization
Rd = constants.specific_gas_constant_dry_air
Rv = constants.specific_gas_constant_water_vapor
Cp = constants.isobaric_mass_heat_capacity_dry_air
gamma_d = g / Cp # dry lapse rate
w_saturated = vmr2mixing_ratio(saturation_pressure(T) / p)
gamma_m = (gamma_d * ((1 + (L * w_saturated) / (Rd * T)) /
(1 + (L**2 * w_saturated) / (Cp * Rv * T**2))
)
)
lapse = interp1d(np.log(p), gamma_m, fill_value='extrapolate')(
np.log(phlev[:-1]))
if self.fixed:
self._lapse_cache = lapse
return lapse
def calc_lapse_rate(self, p, T):
# Use short formula symbols for physical constants.
g = constants.earth_standard_gravity
L = constants.heat_of_vaporization
Rd = constants.specific_gas_constant_dry_air
Rv = constants.specific_gas_constant_water_vapor
Cp = constants.isobaric_mass_heat_capacity_dry_air
gamma_d = g / Cp # dry lapse rate
w_saturated = vmr2mixing_ratio(saturation_pressure(T) / p)
gamma_m = gamma_d * ((1 + (L * w_saturated) / (Rd * T)) /
(1 + (L**2 * w_saturated) / (Cp * Rv * T**2)))
return _to_p_coordinates(gamma_m, p, T)
def entrain(self, T_con_adiabat, atmosphere):
# Physical constants.
L = constants.heat_of_vaporization
Rv = constants.specific_gas_constant_water_vapor
Cp = constants.isobaric_mass_heat_capacity_dry_air
# Abbreviated variables references.
T_rad = atmosphere["T"][0, :]
p = atmosphere["plev"][:]
phlev = atmosphere["phlev"][:]
# Zero-buoyancy plume entrainment.
k_ttl = np.max(np.where(T_con_adiabat >= T_rad))
r_saturated = np.ones_like(p) * 0.0
r_saturated[: k_ttl + 1] = vmr2mixing_ratio(
saturation_pressure(T_con_adiabat[: k_ttl + 1]) / p[: k_ttl + 1]
)
q_saturated = r_saturated / (1 + r_saturated)
q_saturated_hlev = interp1d(np.log(p), q_saturated, fill_value="extrapolate")(
np.log(phlev[:-1])
)
z = atmosphere["z"][0, :]
zhlev = interp1d(np.log(p), z, fill_value="extrapolate")(np.log(phlev[:-1]))
dz_lapse = np.hstack((np.array([z[0] - zhlev[0]]), np.diff(z)))
RH = vmr2relative_humidity(atmosphere["H2O"][0, :], p, atmosphere["T"][0, :])
RH = np.where(RH > 1, 1, RH)
RH_hlev = interp1d(np.log(p), RH, fill_value="extrapolate")(np.log(phlev[:-1]))
entr = self.entr
deltaT = np.ones_like(p) * 0.0
k_cb = np.max(np.where(p >= 96000.0))
# First calculate temperature deviation based on Eq. (4) in Singh&O'Gorman (2013)
deltaT[k_cb:] = (
1
/ (1 + L / (Rv * T_con_adiabat[k_cb:] ** 2) * L * q_saturated[k_cb:] / Cp)
* np.cumsum(
entr
/ zhlev[k_cb:]
* (1 - RH_hlev[k_cb:])
* L
/ Cp
* q_saturated_hlev[k_cb:]
* dz_lapse[k_cb:]
)
)
# Second weight deltaT obtained from above by a height-dependent coefficient,
# as described in Eq. (4) in Bao et al. (submitted).
if np.any(T_con_adiabat > T_rad):
k_ttl = np.max(np.where(T_con_adiabat > T_rad))
z_ttl = z[k_ttl]
z_cb = z[k_cb]
f = lambda x: x ** (2.0 / 3.0)
weight = f((z[k_cb : k_ttl + 1] - z_ttl) / (z_cb - z_ttl))
deltaT[k_cb : k_ttl + 1] = deltaT[k_cb : k_ttl + 1] * weight
deltaT[k_ttl + 1 :] = 0
self.create_variable(
name="entrainment_cooling",
dims=("time", "plev"),
data=deltaT.reshape(1, -1),
)
return T_con_adiabat - deltaT