"""
von Bezold's potential temperature (1888)
=========================================

Wilhelm von Bezold named the temperature a sample of air would have if
brought adiabatically to a standard pressure. Unlike temperature it does not
change when dry air rises or sinks, so it labels air masses. In a sounding
whose temperature falls more slowly than 9.8 K/km, potential temperature
increases with height and the column is stable. The conversion back to
temperature recovers the sounding exactly.
"""

import matplotlib.pyplot as plt
import numpy as np

from earthsciencekit.atmosphere import barometric_pressure, potential_temperature, temperature_from_potential
from earthsciencekit.constants import GRAVITY

height = np.linspace(0, 10e3, 101)
temperature = 288.15 - 0.0065 * height
pressure = barometric_pressure(101325, height, 255, GRAVITY)
theta = potential_temperature(temperature, pressure, 1e5)
np.testing.assert_allclose(temperature_from_potential(theta, pressure, 1e5), temperature)
assert np.all(np.diff(theta) > 0)

fig, ax = plt.subplots()
ax.plot(temperature, height / 1000, label="temperature")
ax.plot(theta, height / 1000, ls="--", label="potential temperature (1000 hPa)")
ax.set(xlabel="[K]", ylabel="height [km]", title="A stable sounding")
ax.legend()

plt.show()