Mountain Problem

Use functions from metpy.calc to perform calculations for a rising and sinking parcel.

The code below explores a common problem in meteorology where a parcel can be defined and lifted initiatlly dry adibatically until saturation is reached. It then ascends moist adiabatically to a desired level before descending back to the original level from which the parcel started.

import numpy as np

from metpy.calc import dry_lapse, lcl, moist_lapse
from metpy.units import units

To set up the classic mountain problem, let’s define that the parcel will start at 1000-hPa and ascend to 700-hPa with an initial temperature of 25 Celsius and a dewpoint of 10 Celsius

p = np.linspace(1000, 700, 301) * units.hPa
T = 25 * units.degC
Td = 10 * units.degC

We first need to determine the maximum level of dry ascent. For this we can use the LCL function and retain the pressure level and temperature of the parcel at the LCL

lclp, lclt = lcl(p[0], T, Td)
print('Initial dry ascent yields:')
print(f'  LCL Pressure: {lclp:.2f}')
print(f'  LCL Temperature: {lclt:.2f}')
print()

Initial dry ascent yields:
  LCL Pressure: 801.54 hectopascal
  LCL Temperature: 6.74 degree_Celsius

Knowing that the calculation of the dry ascent is accomplished by the LCL calculation, we know how to begin our moist ascent. Begin by subsetting the pressure to begin at levels less than or equal to the LCL pressure and use the moist_lapse to find the temperature at the top of our ascent (700-hPa in our case)

moist_ascent_p = p[p <= lclp]
moist_ascent_t = moist_lapse(moist_ascent_p, lclt)
print('After moist ascent:')
print(f'  Temperature at top of ascent: {moist_ascent_t[-1]:.2f}')
print()

After moist ascent:
  Temperature at top of ascent: 0.82 degree_Celsius

Now to come “down the mountain” our parcel will warm dry adiabatically, so we can use the dry_laspe function to descend from the lowest pressure (using [::-1] to reverse the order) and convert our solution to Celsius

dry_descent = dry_lapse(p[::-1], moist_ascent_t[-1]).to('degC')

Pulling it all together

print(f'Starting Temperature: {T:.2f}')
print(f'Starting Dewpoint: {Td:.2f}', end='\n\n')
print(f'Final Temperature: {dry_descent[-1]:.2f}')
print(f'Final Dewpoint: {moist_ascent_t[-1]:.2f}')

Starting Temperature: 25.00 degree_Celsius
Starting Dewpoint: 10.00 degree_Celsius

Final Temperature: 30.21 degree_Celsius
Final Dewpoint: 0.82 degree_Celsius

So as we expect the parcel has warmed and dried out through the combined dry and moist ascent due to the release of latent heat and subsequent precipitating out of moisture from the parcel