Simulating the motion of a downdraft parcel

Copyright (c) 2021 Thomas Schanzer.

Distributed under the terms of the BSD 3-Clause License.

In this notebook, we illustrate the use of the dparcel package to simulate the motion of descending parcels.

import numpy as np
import matplotlib.pyplot as plt
import sys

from metpy.units import units
from metpy.plots import SkewT

from dparcel.thermo import saturation_specific_humidity
from dparcel.parcel import IdealisedParcel

First create the downdraft parcel associated with an idealised sounding with 50% relative humidity above the boundary layer:

parcel = IdealisedParcel(0.5)

This is what the sounding looks like:

fig = plt.figure(figsize=(6,6))
skew = SkewT(fig, rotation=45)
skew.plot(parcel._pressure_raw, parcel._temperature_raw,
          label='Temperature')
skew.plot(parcel._pressure_raw, parcel._dewpoint_raw, label='Dew point')
lgd = skew.ax.legend()
skew.ax.set_xlim(-30, 30)
skew.ax.set_ylim(top=160)
skew.ax.set(
    xlabel='Temperature ($^\circ$C)',
    ylabel='Pressure (mbar)')
plt.show()

Now set the initial conditions. We use several different entrainment rates, with everything else fixed.

z_initial = 5*units.km
w_initial = 0*units.meter/units.second
p_initial = parcel.pressure(z_initial)
t_initial = parcel.wetbulb_temperature(z_initial)
q_initial = saturation_specific_humidity(p_initial, t_initial)
time = np.arange(0, 10.1, 0.1)*units.minute
rates = np.arange(0, 2.1, 0.1)/units.km
l_initial = 2e-3*units.dimensionless

Using the parcel.motion method, simulate the parcel’s motion for each set of initial conditions:

%%time
sols = []
for i, rate in enumerate(rates):
    sys.stdout.write('\rCalculation {} of {}    '.format(i+1, rates.size))
    sol = parcel.motion(
        time, z_initial, w_initial, t_initial, q_initial, l_initial, rate,
        kind='reversible')
    sols.append(sol)
sys.stdout.write('\n')

Calculation 21 of 21
CPU times: user 35.2 s, sys: 250 ms, total: 35.5 s
Wall time: 35.4 s

1

Now plot the results:

fig = plt.figure(figsize=(12,10))
ax = fig.add_subplot(221)
for sol, rate in zip(sols[::4], rates[::4]):
    ax.plot(time, sol.height)
ax.grid()
ax.set(
    xlabel='Time (min)',
    ylabel='Height (m)')

ax = fig.add_subplot(222)
for sol, rate in zip(sols[::4], rates[::4]):
    ax.plot(time, sol.velocity, label='{:.1f}'.format(rate.m))
lgd = ax.legend(loc=[1.05, 0.15])
lgd.set_title('Entr. rate\n(/km)')
ax.grid()
ax.set(
    xlabel='Time (min)',
    ylabel='Velocity (m/s)')

ax = fig.add_subplot(223)
ax.plot(rates, [sol.min_height.m for sol in sols])
ax.grid()
ax.set(
    xlabel='Entrainment rate (/km)',
    ylabel='Minimum height (m)')

ax = fig.add_subplot(224)
ax.plot(rates, [np.nanmin(sol.velocity.m) for sol in sols])
ax.grid()
ax.set(
    xlabel='Entrainment rate (/km)',
    ylabel='Maximum velocity (m/s)')

fig.tight_layout()
plt.show()

We see that entrainment impedes the parcel’s descent; mixing it with the environment causes it to come into equilibrium faster.

These calculations are not restricted to idealised soundings; see the “Supplying your own atmospheric sounding” for instructions to supply your own real sounding data.