5.1 Cloud Physics
Cloud physics studies how cloud droplets and ice crystals form, grow, and interact. Understanding these microphysical processes is essential for precipitation and climate modeling.
Cloud Formation
Nucleation
Cloud condensation nuclei (CCN) allow water vapor to condense at RH < 100%.
Köhler Equation
$$S = \frac{e}{e_s} = \exp\left(\frac{2\sigma}{\rho_w R_v T r} - \frac{i m_s M_w}{\frac{4}{3}\pi r^3 \rho_w M_s}\right)$$
Droplet Growth
Diffusion Growth
Slow, produces narrow size distribution (10-20 μm)
Collision-Coalescence
Rapid growth when drops exceed ~20 μm, produces rain
Python: Droplet Growth
#!/usr/bin/env python3
"""cloud_physics.py - Model cloud droplet growth"""
import numpy as np
import matplotlib.pyplot as plt
# Diffusional growth rate
def diffusion_growth(r, S, T=273):
"""dr/dt for diffusional growth (m/s)"""
D_v = 2.2e-5 # m²/s diffusivity
K = 0.024 # W/(m·K) thermal conductivity
L_v = 2.5e6 # J/kg latent heat
rho_w = 1000 # kg/m³
R_v = 461 # J/(kg·K)
e_s = 611 * np.exp(17.27 * (T-273) / (T-35.85))
G = 1 / ((L_v/(R_v*T) - 1) * L_v*rho_w/(K*T) + rho_w*R_v*T/(D_v*e_s))
return G * (S - 1) / r
# Time evolution
t = np.linspace(0, 3600, 1000) # 1 hour
r = np.zeros_like(t)
r[0] = 1e-6 # 1 μm initial radius
S = 1.005 # 0.5% supersaturation
for i in range(1, len(t)):
dt = t[i] - t[i-1]
r[i] = r[i-1] + diffusion_growth(r[i-1], S) * dt
if r[i] < 1e-7: r[i] = 1e-7
plt.figure(figsize=(10, 6))
plt.plot(t/60, r*1e6, 'b-', linewidth=2)
plt.xlabel('Time (minutes)')
plt.ylabel('Droplet Radius (μm)')
plt.title('Cloud Droplet Growth by Diffusion')
plt.grid(True, alpha=0.3)
plt.savefig('cloud_physics.png', dpi=150)
plt.show()