← Back to Part 1: Atmosphere Fundamentals

1.2 Atmospheric Composition

The atmosphere is a mixture of gases, aerosols, and water vapor. While nitrogen and oxygen dominate by volume, trace gases like CO₂, CH₄, and O₃ play crucial roles in climate and chemistry.

Major Atmospheric Gases

Nitrogen (N₂)

78.08%

Chemically inert in lower atmosphere. Essential for life via nitrogen cycle.

Oxygen (O₂)

20.95%

Essential for respiration. Product of photosynthesis. Absorbs UV in stratosphere.

Argon (Ar)

0.93%

Noble gas, completely inert. Third most abundant atmospheric constituent.

Water Vapor (H₂O)

0-4%

Highly variable. Most important greenhouse gas. Source of clouds and precipitation.

Mixing Ratio Definitions

Atmospheric composition is commonly expressed using mixing ratios:

$$w = \frac{m_v}{m_d} \quad \text{(mass mixing ratio)}, \qquad \chi = \frac{n_v}{n_{\text{total}}} \quad \text{(volume mixing ratio)}$$

where $m_v$ is the mass of the trace species, $m_d$ is the mass of dry air, and $n_v / n_{\text{total}}$ is the number fraction

Partial Pressure (Dalton's Law)

Each gas in the mixture contributes a partial pressure proportional to its volume fraction:

$$p_i = x_i \, p$$

where $x_i$ is the mole fraction of species $i$ and $p$ is total pressure. For example, $p_{\text{O}_2} = 0.2095 \times 1013.25 \approx 212$ hPa.

Trace Gases & Climate

Carbon Dioxide (CO₂)

~420 ppm

Primary anthropogenic greenhouse gas. Risen from 280 ppm pre-industrial to 420 ppm today.

Methane (CH₄)

~1.9 ppm

25× more potent GHG than CO₂ over 100 years. Sources: wetlands, agriculture, fossil fuels.

Ozone (O₃)

~0.3 ppm

Stratospheric: protects from UV. Tropospheric: pollutant and greenhouse gas.

Nitrous Oxide (N₂O)

~0.33 ppm

Potent GHG (298× CO₂). Sources: agriculture, combustion, industrial processes.

Radiative Absorption & Atmospheric Lifetimes

Beer-Lambert Law

Radiation is attenuated exponentially as it passes through an absorbing medium:

$$I = I_0 \, e^{-\tau}$$

where $I_0$ is the incident intensity and $\tau$ is the optical depth along the path

Optical Depth

The optical depth is the integrated absorption along a vertical column:

$$\tau = \int_0^{\infty} k_\lambda \, \rho \, dz$$

where $k_\lambda$ is the mass absorption coefficient (m²/kg) and $\rho$ is the absorber density

Residence Time

The average time a molecule remains in the atmosphere before being removed:

$$\tau_{\text{res}} = \frac{M_{\text{burden}}}{S} = \frac{M_{\text{burden}}}{L}$$

where $M_{\text{burden}}$ is the total atmospheric burden, $S$ is the source rate, and $L$ is the loss rate (at steady state $S = L$)

Mean Molecular Weight

$$\bar{M} = \sum_i x_i M_i = 28.97 \text{ g/mol}$$

For dry air (dominated by N₂ at 28 and O₂ at 32)

The ideal gas law for air: $p = \rho R_d T$ where R_d = R*/M̄ = 287 J/(kg·K) is the gas constant for dry air.

Expanding for the major constituents:

$$\bar{M} = x_{\text{N}_2} M_{\text{N}_2} + x_{\text{O}_2} M_{\text{O}_2} + x_{\text{Ar}} M_{\text{Ar}} + \cdots = 0.7808(28.01) + 0.2095(32.00) + 0.0093(39.95) + \cdots$$

Interactive Simulation: Beer-Lambert Atmospheric Absorption

Python

Simulates how solar radiation is absorbed by O3, H2O, CO2, and O2 as it passes through the atmosphere. Shows individual gas transmittance and the combined atmospheric transmission spectrum.

beer_lambert_absorption.py58 lines

import numpy as np
import matplotlib.pyplot as plt

wav = np.linspace(0.2, 15.0, 2000)  # wavelength in microns

def gauss_abs(wav, center, width, strength):
    return strength * np.exp(-0.5 * ((wav - center) / width) ** 2)

# Absorption profiles for each gas (simplified Gaussian bands)
tau_o3 = gauss_abs(wav, 0.25, 0.03, 8) + gauss_abs(wav, 0.32, 0.02, 3) + gauss_abs(wav, 9.6, 0.8, 2.5)
tau_h2o = (gauss_abs(wav, 0.94, 0.05, 1.5) + gauss_abs(wav, 1.14, 0.06, 1.8) +
           gauss_abs(wav, 1.38, 0.08, 3.0) + gauss_abs(wav, 1.87, 0.1, 2.5) +
           gauss_abs(wav, 2.7, 0.2, 4.0) + gauss_abs(wav, 6.3, 0.8, 5.0))
tau_co2 = gauss_abs(wav, 2.7, 0.15, 3.0) + gauss_abs(wav, 4.3, 0.3, 5.0) + gauss_abs(wav, 15.0, 2.0, 3.5)
tau_o2 = gauss_abs(wav, 0.76, 0.01, 2.0) + gauss_abs(wav, 0.69, 0.008, 1.0)

tau_total = tau_o3 + tau_h2o + tau_co2 + tau_o2
trans_total = np.exp(-tau_total)
trans_o3 = np.exp(-tau_o3); trans_h2o = np.exp(-tau_h2o)
trans_co2 = np.exp(-tau_co2); trans_o2 = np.exp(-tau_o2)

fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(12, 8), sharex=True)
fig.patch.set_facecolor('#0f172a')
for ax in (ax1, ax2):
    ax.set_facecolor('#1e293b'); ax.tick_params(colors='#cbd5e1')
    ax.xaxis.label.set_color('#cbd5e1'); ax.yaxis.label.set_color('#cbd5e1')
    ax.title.set_color('#cbd5e1'); ax.grid(True, color='#334155', alpha=0.5)
    for sp in ax.spines.values(): sp.set_color('#334155')

ax1.fill_between(wav, trans_o3, 1, alpha=0.35, color='#c084fc', label='O\u2083')
ax1.fill_between(wav, trans_h2o, 1, alpha=0.35, color='#38bdf8', label='H\u2082O')
ax1.fill_between(wav, trans_co2, 1, alpha=0.35, color='#f97316', label='CO\u2082')
ax1.fill_between(wav, trans_o2, 1, alpha=0.35, color='#4ade80', label='O\u2082')
ax1.plot(wav, trans_o3, color='#c084fc', lw=1); ax1.plot(wav, trans_h2o, color='#38bdf8', lw=1)
ax1.plot(wav, trans_co2, color='#f97316', lw=1); ax1.plot(wav, trans_o2, color='#4ade80', lw=1)
ax1.set_ylabel('Individual Transmittance', fontsize=11)
ax1.set_title('Atmospheric Absorption by Gas Species (Beer-Lambert)', fontsize=13, fontweight='bold')
ax1.set_ylim(0, 1.05); ax1.legend(loc='lower right', facecolor='#1e293b', edgecolor='#334155', labelcolor='#cbd5e1')
ax1.axvspan(0.4, 0.7, alpha=0.15, color='yellow', label='Visible')

ax2.fill_between(wav, trans_total, 1, alpha=0.4, color='#ef4444')
ax2.plot(wav, trans_total, color='#fbbf24', lw=2)
ax2.set_xlabel('Wavelength (\u03bcm)', fontsize=11); ax2.set_ylabel('Total Transmittance', fontsize=11)
ax2.set_title('Combined Atmospheric Transmittance', fontsize=13, fontweight='bold')
ax2.set_ylim(0, 1.05); ax2.set_xlim(0.2, 15)
ax2.axvspan(0.4, 0.7, alpha=0.15, color='yellow')
ax2.text(0.55, 0.05, 'Visible', color='#fde047', fontsize=9, ha='center')
ax2.text(3.5, 0.05, '8-13 \u03bcm\nWindow', color='#fbbf24', fontsize=9, ha='center')

plt.tight_layout()
plt.savefig('output.png', dpi=150, bbox_inches='tight', facecolor=fig.get_facecolor())
print("=== Beer-Lambert Atmospheric Absorption ===")
print("Key absorption bands:")
print("  O3:  UV (0.25 \u03bcm), Hartley band (0.32 \u03bcm), IR (9.6 \u03bcm)")
print("  H2O: Near-IR (0.94, 1.14, 1.38, 1.87, 2.7 \u03bcm), Far-IR (6.3 \u03bcm)")
print("  CO2: 2.7 \u03bcm, 4.3 \u03bcm, 15 \u03bcm (major greenhouse band)")
print("  O2:  0.69 \u03bcm, 0.76 \u03bcm (A-band)")
print("\nAtmospheric windows: visible (0.4-0.7 \u03bcm), thermal IR (8-13 \u03bcm)")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

← 1.1 Atmosphere Structure 1.3 Solar Radiation →