Atmospheric Physics

Atmospheric Radiation

The atmosphere interacts with electromagnetic radiation through absorption, emission, and scattering. Understanding these processes is fundamental to climate modeling.

Stefan-Boltzmann Law

The total energy radiated by a black body:

Where .

Planck Function

The spectral radiance of a black body:

Wien's Displacement Law

The wavelength of peak emission:

Where .

Atmospheric Windows

The atmosphere is transparent in certain wavelength regions:

• Visible light (0.4-0.7 micrometers)
• Microwave region
• Parts of the infrared

Absorption by Greenhouse Gases

Beer-Lambert Law for absorption:

Where is the mass absorption coefficient, is density, and is path length.

Python Example: Black Body Spectrum

import numpy as np
import matplotlib.pyplot as plt

def planck(wavelength, T):
    """Planck function in SI units."""
    h = 6.626e-34  # Planck constant
    c = 3e8        # Speed of light
    kb = 1.381e-23 # Boltzmann constant
    lam = wavelength * 1e-6  # Convert um to m
    return (2 * h * c**2 / lam**5) / (np.exp(h * c / (lam * kb * T)) - 1)

wavelengths = np.linspace(0.1, 30, 1000)
T_earth = 288
T_sun = 5778

plt.figure(figsize=(10, 6))
plt.plot(wavelengths, planck(wavelengths, T_sun), label='Sun (5778 K)')
plt.plot(wavelengths, planck(wavelengths, T_earth) * 100, label='Earth (288 K) x100')
plt.xlabel('Wavelength (um)')
plt.ylabel('Spectral Radiance')
plt.legend()
plt.title('Black Body Spectra')
plt.show()

Convection Processes

Dry adiabatic lapse rate:

Moist adiabatic lapse rate:

Where is latent heat of vaporization, is saturation mixing ratio.

Cloud Physics

Cloud formation requires:

1. Supersaturation (relative humidity > 100%)
2. Cloud condensation nuclei (CCN)
3. Updrafts to lift air parcels

Boundary Layer

The atmospheric boundary layer (ABL) has characteristic depths:

• Stable boundary layer: 0.1-0.3 km
• Convective boundary layer: 1-3 km
• Neutral boundary layer: 0.3-1 km

Turbulent Fluxes

Sensible heat flux:

Latent heat flux:

Geostrophic Wind

Balance between pressure gradient and Coriolis force:

Where is the Coriolis parameter.

Key Dimensionless Numbers

Exercises

1. Calculate the peak emission wavelength for the Sun and Earth
2. Derive the dry adiabatic lapse rate from first principles
3. Compute the net radiation at the top of atmosphere for different CO2 levels