5.4 Tropical Cyclones
Tropical cyclones (hurricanes, typhoons) are intense low-pressure systems fueled by warm ocean water. They are among the most destructive weather phenomena on Earth.
Formation Requirements
- • SST > 26.5°C (warm water for evaporation)
- • Distance from equator (f ≠ 0 for Coriolis)
- • Low vertical wind shear
- • Pre-existing disturbance (tropical wave)
- • Moist mid-troposphere
Saffir-Simpson Scale
| Category | Wind (kt) | Pressure (hPa) |
|---|---|---|
| 1 | 64-82 | >980 |
| 2 | 83-95 | 965-979 |
| 3 (Major) | 96-112 | 945-964 |
| 4 | 113-136 | 920-944 |
| 5 | >137 | <920 |
Python: Maximum Potential Intensity
#!/usr/bin/env python3
"""tropical_cyclones.py - Hurricane intensity potential"""
import numpy as np
import matplotlib.pyplot as plt
def max_potential_intensity(SST, T_outflow=200):
"""Emanuel's MPI theory (simplified)"""
# SST in Kelvin, returns max wind in m/s
Ts = SST
To = T_outflow # Outflow temperature ~200K
Ck = 1.5e-3 # Exchange coefficient
Cd = 1.5e-3 # Drag coefficient
# Thermodynamic efficiency
eta = (Ts - To) / Ts
# Enthalpy disequilibrium (simplified)
delta_k = 1500 # J/kg typical value
V_max = np.sqrt(Ck/Cd * eta * delta_k)
return V_max * 2 # Empirical factor
SST_range = np.linspace(298, 305, 50) # 25-32°C
V_max = [max_potential_intensity(T) for T in SST_range]
plt.figure(figsize=(10, 6))
plt.plot(SST_range - 273.15, V_max, 'r-', linewidth=2)
plt.xlabel('Sea Surface Temperature (°C)')
plt.ylabel('Maximum Potential Intensity (m/s)')
plt.title('Hurricane Intensity vs SST')
plt.axhline(y=33, color='orange', linestyle='--', label='Cat 1')
plt.axhline(y=50, color='red', linestyle='--', label='Cat 3')
plt.legend()
plt.grid(True, alpha=0.3)
plt.savefig('tropical_cyclones.png', dpi=150)
plt.show()