4.1 Air Masses

An air mass is a large body of air with relatively uniform temperature and humidity characteristics, acquired from its source region. Air masses are classified by their source and modification.

Air Mass Classification

Continental Polar (cP)

Cold, dry. Source: Siberia, Canada

Winter: T ~ -30°C, Td ~ -35°C

Maritime Polar (mP)

Cool, moist. Source: N. Pacific, N. Atlantic

T ~ 5°C, Td ~ 2°C

Continental Tropical (cT)

Hot, dry. Source: Sahara, SW deserts

T ~ 40°C, Td ~ 5°C

Maritime Tropical (mT)

Warm, humid. Source: Gulf of Mexico, tropics

T ~ 25°C, Td ~ 22°C

Thermodynamic Classification Parameters

Air masses are quantitatively classified using conserved thermodynamic variables. The equivalent potential temperature $\theta_e$ is conserved during both dry and moist adiabatic processes, making it ideal for identifying air mass types:

$$\theta_e = \theta \exp\!\left(\frac{L_v \, w_s}{c_p \, T}\right)$$

where $\theta$ is potential temperature, $L_v$ is latent heat of vaporisation,$w_s$ is saturation mixing ratio, $c_p$ is specific heat, and $T$ is temperature

The mixing ratio, which measures moisture content, is given by:

$$w = \varepsilon \frac{e}{p - e}, \qquad \varepsilon = \frac{M_v}{M_d} \approx 0.622$$

where $e$ is vapour pressure, $p$ is total pressure, and $M_v/M_d$ is the ratio of molar masses of water vapour and dry air

The wet-bulb potential temperature $\theta_w$ is also widely used — it is the temperature a parcel reaches when lifted moist-adiabatically to low pressure and then brought back dry-adiabatically to 1000 hPa. Tropical maritime air typically has $\theta_w \approx 20\text{--}24\,°\text{C}$, while polar air has $\theta_w < 10\,°\text{C}$.

Source Region Requirements

• Large, uniform surface (ocean or flat land)
• Light winds (stagnant high pressure)
• Several days of residence time
• Clear distinction from surrounding air

Static Stability of Source Regions

Source regions are characterised by weak flow and high static stability. The static stability parameter in pressure coordinates is:

$$\sigma = -\frac{T}{\theta}\frac{\partial \theta}{\partial p}$$

Large positive $\sigma$ indicates strong static stability — air resists vertical displacement, allowing uniform properties to develop

Air Mass Modification

When an air mass moves away from its source region, it is modified by the underlying surface. The rate of temperature change can be approximated empirically by a Newtonian relaxation:

$$\frac{dT}{dt} \approx \frac{T_s - T}{\tau}$$

where $T_s$ is the surface temperature, $T$ is the air mass temperature, and $\tau$ is the adjustment time scale (typically 1--3 days over ocean, longer over land)

Interactive Simulation: Air Mass Classification Diagram

Python

Plots temperature vs dew point for major air mass types (cA, cP, mP, cT, mT, mE) with relative humidity contours, clustered data points for each type, and a bar chart showing temperature, dew point, and dew point depression as a stability indicator.

air_mass_classification.py93 lines

import numpy as np
import matplotlib.pyplot as plt

def sat_vp(T):
    """Saturation vapour pressure (hPa) via Tetens formula."""
    return 6.11 * np.exp(17.27 * T / (T + 237.3))

def relative_humidity(T, Td):
    return 100 * sat_vp(Td) / sat_vp(T)

# Air mass properties: (T, Td, name, source region, color, marker)
air_masses = {
    'cA':  (-50, -55, 'Continental Arctic', 'Arctic basin', '#60a5fa', 's'),
    'cP':  (-20, -30, 'Continental Polar', 'Siberia/Canada', '#38bdf8', 'D'),
    'mP':  (5,   2,   'Maritime Polar', 'N. Pacific/Atlantic', '#2dd4bf', 'o'),
    'cT':  (40,  5,   'Continental Tropical', 'Sahara/SW deserts', '#f87171', '^'),
    'mT':  (25,  22,  'Maritime Tropical', 'Gulf of Mexico', '#fb923c', 'p'),
    'mE':  (27,  25,  'Maritime Equatorial', 'Equatorial oceans', '#a3e635', '*'),
}

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 6))
fig.patch.set_facecolor('#0f172a')
for ax in (ax1, ax2):
    ax.set_facecolor('#1e293b')
    ax.tick_params(colors='#cbd5e1')
    for spine in ax.spines.values():
        spine.set_color('#334155')
    ax.grid(True, color='#334155', alpha=0.4)

# Left: T vs Td scatter with RH lines and stability annotation
T_range = np.linspace(-55, 45, 300)
for rh in [20, 40, 60, 80, 100]:
    es = sat_vp(T_range)
    e_target = rh / 100.0 * es
    # Invert Tetens: Td = 237.3 * ln(e/6.11) / (17.27 - ln(e/6.11))
    with np.errstate(invalid='ignore', divide='ignore'):
        ratio = np.log(e_target / 6.11)
        Td_line = 237.3 * ratio / (17.27 - ratio)
    valid = np.isfinite(Td_line) & (Td_line <= T_range) & (Td_line > -60)
    ax1.plot(T_range[valid], Td_line[valid], '--', color='#475569', alpha=0.5, linewidth=0.8)
    mid = len(T_range[valid]) // 3
    if np.any(valid) and mid < len(T_range[valid]):
        ax1.text(T_range[valid][mid], Td_line[valid][mid] - 2, f'{rh}%',
                 fontsize=7, color='#64748b')

for key, (T, Td, name, source, color, marker) in air_masses.items():
    # Random cluster around mean
    np.random.seed(hash(key) % 2**31)
    Tc = T + np.random.randn(15) * 2
    Tdc = Td + np.random.randn(15) * 1.5
    ax1.scatter(Tc, Tdc, s=40, c=color, alpha=0.35, marker=marker)
    ax1.scatter(T, Td, s=200, c=color, edgecolors='white', linewidths=1.5,
                marker=marker, zorder=5, label=f'{key}: {name}')
    ax1.annotate(key, (T + 1.5, Td + 1.5), fontsize=9, fontweight='bold', color=color)

ax1.plot([-60, 50], [-60, 50], ':', color='#475569', linewidth=0.7)
ax1.set_xlabel('Temperature (C)', color='#cbd5e1')
ax1.set_ylabel('Dew Point (C)', color='#cbd5e1')
ax1.set_title('Air Mass Classification (T vs Td)', color='#cbd5e1', fontsize=12)
ax1.legend(fontsize=7, facecolor='#1e293b', edgecolor='#334155', labelcolor='#cbd5e1', loc='upper left')
ax1.set_xlim(-58, 48)
ax1.set_ylim(-62, 32)

# Right: bar chart with stability indicator (T - Td = dew point depression)
keys = list(air_masses.keys())
T_vals = [air_masses[k][0] for k in keys]
Td_vals = [air_masses[k][1] for k in keys]
dd = [T - Td for T, Td in zip(T_vals, Td_vals)]
colors_bar = [air_masses[k][4] for k in keys]

x = np.arange(len(keys))
width = 0.28
ax2.bar(x - width, T_vals, width, color=colors_bar, alpha=0.85, label='Temperature')
ax2.bar(x, Td_vals, width, color=colors_bar, alpha=0.45, label='Dew Point', hatch='//')
ax2.bar(x + width, dd, width, color='#a78bfa', alpha=0.7, label='Dew Pt Depression')
ax2.set_xticks(x)
ax2.set_xticklabels(keys, color='#cbd5e1')
ax2.set_xlabel('Air Mass Type', color='#cbd5e1')
ax2.set_ylabel('Temperature (C) / Depression (K)', color='#cbd5e1')
ax2.set_title('Air Mass Properties & Stability', color='#cbd5e1', fontsize=12)
ax2.legend(fontsize=8, facecolor='#1e293b', edgecolor='#334155', labelcolor='#cbd5e1')
ax2.axhline(y=0, color='#cbd5e1', linewidth=0.8)

plt.tight_layout()
plt.savefig('output.png', dpi=150, bbox_inches='tight', facecolor=fig.get_facecolor())

print("=== Air Mass Classification Diagram ===")
print(f"{'Type':<5} {'T(C)':>6} {'Td(C)':>6} {'RH(%)':>6} {'DD(K)':>6}  Source Region")
print("-" * 65)
for key, (T, Td, name, source, c, m) in air_masses.items():
    rh = relative_humidity(T, Td)
    print(f"{key:<5} {T:6.0f} {Td:6.0f} {rh:6.0f} {T-Td:6.0f}  {source}")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

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