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5.4 Tropical Cyclones

Tropical cyclones -- hurricanes, typhoons, and cyclones -- are the most powerful weather systems on Earth. These warm-core axisymmetric vortices operate as natural Carnot heat engines sustained by the thermodynamic disequilibrium between the warm ocean surface and the cold upper troposphere, achieving efficiencies of 30-35%. Understanding their structure, intensification mechanisms, and hazards is critical for coastal protection.

Emanuel's Potential Intensity Theory

Emanuel (1986, 1988) modeled a tropical cyclone as a Carnot heat engine. Air spirals inward at low levels, acquiring enthalpy from the warm ocean (isothermal expansion), rises in the eyewall (adiabatic expansion), flows outward at the tropopause, and radiatively cools (isothermal compression) before subsiding (adiabatic compression).

Carnot Efficiency

$$\eta = \frac{T_s - T_o}{T_o}$$

With T_s ~ 300 K (SST) and T_o ~ 200 K (outflow temperature), η ≈ 0.50. This sets the fraction of ocean heat convertible to kinetic energy.

Emanuel's Maximum Potential Intensity

$$V_{\max}^2 = \frac{C_k}{C_d} \cdot \frac{T_s - T_o}{T_o} \cdot (k_s^* - k)$$

C_k is the enthalpy exchange coefficient (~1.2 × 10³), C_d is the drag coefficient (~1.5 × 10³), k_s* is saturation moist enthalpy at the ocean surface, and k is boundary layer inflow enthalpy. The ratio C_k/C_d ≈ 0.8 is critical; observed range is 0.5-1.5.

WISHE Feedback

Wind-Induced Surface Heat Exchange (WISHE) is the positive feedback that amplifies disturbances into tropical cyclones: (1) stronger winds enhance ocean evaporation, (2) greater enthalpy flux fuels deeper convection, (3) convection lowers surface pressure, (4) increased pressure gradient accelerates winds -- returning to step (1). This feedback becomes self-sustaining above a critical wind speed threshold (~15 m/s).

Vortex Dynamics and Wind Structure

Gradient Wind Balance

$$\frac{v^2}{r} + fv = \frac{1}{\rho}\frac{\partial p}{\partial r}$$

Centrifugal + Coriolis = pressure gradient force. This balance holds above the frictional boundary layer and determines the primary tangential circulation.

Rankine Vortex Model

$$v(r) = \begin{cases} V_{\max}\dfrac{r}{R_{\max}} & r \leq R_{\max} \\ V_{\max}\left(\dfrac{R_{\max}}{r}\right)^{\alpha} & r > R_{\max} \end{cases}$$

V_max is maximum tangential wind, R_max is radius of maximum wind (20-60 km), α is the decay exponent (0.4-0.6 for real TCs). Inside R_max: solid body rotation.

Angular Momentum Conservation

$$M = rv + \frac{1}{2}fr^2$$

M is conserved above the boundary layer. A parcel at r = 500 km with v = 5 m/s achieves v = 125 m/s at r = 20 km without friction -- demonstrating how the vortex spins up.

Eye Formation and Warm Core Structure

The eye is a calm, cloud-free region at the center (20-60 km diameter) where air subsides, warming adiabatically by 5-10°C relative to the environment at 300 hPa. This warm core is the defining feature that distinguishes tropical from extratropical cyclones.

Subsidence Warming

Air detrained from the eyewall at upper levels descends in the eye. Adiabatic compression warms this air by ~7°C/km. The resulting warm core reduces surface pressure hydrostatically, maintaining the TC circulation.

Eyewall Replacement Cycles

In intense TCs, an outer eyewall forms and contracts inward, choking off the inner eyewall. During this process, the storm weakens temporarily (20-30 kt) before re-intensifying as the new eyewall contracts. Cycle duration: 12-48 hours.

Hydrostatic Warm Core Pressure Reduction

$$\Delta p_s \approx -\frac{p_s}{R_d} \int_0^{z_t} \frac{\Delta T(z)}{T^2(z)} g \, dz$$

The surface pressure deficit is proportional to the vertically-integrated warm anomaly. A 10°C anomaly over 10 km depth gives Δp ≈ 50-80 hPa.

Track, Rapid Intensification, and Storm Surge

Beta Drift

The beta effect (β = df/dy) causes asymmetric Rossby wave dispersion in the vortex outer circulation. Beta gyres develop that propel the TC poleward and westward at 1-3 m/s, superimposed on the large-scale steering flow:

$$\frac{\partial \zeta}{\partial t} + \beta v = 0 \quad \Rightarrow \quad c_\beta \sim -\frac{\beta \, L^2}{2}$$

where L is the vortex scale. Beta drift is most important for TCs in weak steering flow.

Rapid Intensification

RI is defined as ≥ 30 kt increase in 24 hours. It is favored by: warm SST (> 28.5°C), deep ocean heat content (> 50 kJ/cm²), low vertical shear (< 5 m/s), high mid-level humidity, and efficient upper-level outflow. The ventilation index $V_I = \text{shear} \times \text{dry\_air} / \text{MPI}$ quantifies the tendency for environmental factors to inhibit intensification. Low $V_I$ favors RI.

Genesis Potential Index

$$\text{GPI} = |10^5 \eta|^{3/2} \left(\frac{H}{50}\right)^3 \left(\frac{V_{\text{pot}}}{70}\right)^3 (1 + 0.1 V_s)^{-2}$$

η is absolute vorticity, H is 600 hPa relative humidity (%), V_pot is potential intensity (m/s), and V_s is 200-850 hPa wind shear (m/s). GPI captures the climatological TC genesis distribution.

Storm Surge Physics

Storm Surge Components

$$\eta \approx \underbrace{\frac{\Delta p}{\rho_w g}}_{\text{inverse barometer}} + \underbrace{\frac{\tau_s L}{\rho_w g h}}_{\text{wind setup}}$$

Inverse barometer: 1 hPa drop ≈ 1 cm rise (~1 m for Cat 5). Wind setup dominates in shallow water, producing 3-8 m of surge. Amplified by shallow bathymetry, concave coastlines, and slow storm motion.

TC Rainfall: Lilly-Emanuel Efficiency

TC precipitation efficiency is the fraction of vapor inflow that precipitates. The axisymmetric rainfall peaks in the eyewall (50-100 mm/hr) and decreases outward. Total accumulation depends primarily on storm size and translation speed, not peak intensity. Hurricane Harvey (2017) produced 1,539 mm near Houston over 5 days due to near-stationary motion.

Fortran + Python: Gradient Wind Solver with Visualization

Python

Compiles and runs a Fortran program (gfortran) that solves the gradient wind equation for a Rankine vortex. Python captures the Fortran output and generates matplotlib plots of wind profiles, pressure fields, forward vs inverse solutions, and MPI vs SST.

tc_fortran_plot.py269 lines

import subprocess, tempfile, os, re
import numpy as np
import matplotlib.pyplot as plt

# ---- Fortran source code (written to file, compiled, and executed) ----
fortran_src = r"""program tc_gradient_wind
  implicit none
  integer, parameter :: nr = 1000
  real(8), parameter :: pi = 3.14159265358979d0
  real(8), parameter :: rho = 1.15d0, f = 5.0d-5
  real(8), parameter :: p_env = 101300.0d0, g_acc = 9.81d0
  real(8), parameter :: rho_w = 1025.0d0
  real(8) :: Vmax, Rmax, alpha, dr_m
  real(8) :: r(nr), v(nr), p_fwd(nr), v_inv(nr)
  real(8) :: v_avg, r_avg, dpdr, A_q, B_q, disc
  real(8) :: p_central, delta_p, ang_mom
  integer :: i, j
  integer, parameter :: ns = 3
  real(8) :: Vm(ns), Rm(ns)
  Vm = (/35.0d0, 55.0d0, 80.0d0/)
  Rm = (/50.0d3, 35.0d3, 20.0d3/)
  alpha = 0.5d0

write(*,'(A)') '=== TC Gradient Wind Balance ==='
  do j = 1, ns
    Vmax = Vm(j); Rmax = Rm(j)
    dr_m = (500.0d3 - 500.0d0) / dble(nr - 1)
    do i = 1, nr
      r(i) = 500.0d0 + dble(i-1) * dr_m
    end do
    do i = 1, nr
      if (r(i) <= Rmax) then
        v(i) = Vmax * r(i) / Rmax
      else
        v(i) = Vmax * (Rmax / r(i))**alpha
      end if
    end do
    p_fwd(nr) = p_env
    do i = nr-1, 1, -1
      v_avg = 0.5d0 * (v(i) + v(i+1))
      r_avg = 0.5d0 * (r(i) + r(i+1))
      dpdr = rho * (v_avg**2 / r_avg + f * v_avg)
      p_fwd(i) = p_fwd(i+1) - dpdr * dr_m
    end do
    p_central = p_fwd(1) / 100.0d0
    delta_p = (p_env - p_fwd(1)) / 100.0d0
    v_inv(1) = 0.0d0
    do i = 2, nr-1
      dpdr = (p_fwd(i+1) - p_fwd(i-1)) / (2.0d0 * dr_m)
      A_q = 1.0d0 / r(i)
      B_q = f
      disc = B_q**2 + 4.0d0 * A_q * dpdr / rho
      if (disc >= 0.0d0) then
        v_inv(i) = (-B_q + sqrt(disc)) / (2.0d0 * A_q)
      else
        v_inv(i) = 0.0d0
      end if
    end do
    v_inv(nr) = v_inv(nr-1)
    ang_mom = Rmax * Vmax + 0.5d0 * f * Rmax**2

write(*,'(A,F5.0,A,F5.0,A)') 'STORM Vmax=', Vmax, ' Rmax=', Rmax/1d3, ' km'
    write(*,'(A,F8.1,A,F8.1)') '  pc=', p_central, ' dp=', delta_p

block
      real(8) :: ib, ws, tau, Cd, h_shelf, L_fetch
      Cd = 2.0d-3; h_shelf = 20.0d0; L_fetch = 200.0d3
      ib = delta_p * 100.0d0 / (rho_w * g_acc)
      tau = Cd * rho * Vmax**2
      ws = tau * L_fetch / (rho_w * g_acc * h_shelf)
      write(*,'(A,F6.2,A,F6.2,A,F6.2)') '  surge_ib=', ib, ' surge_ws=', ws, ' total=', ib+ws
    end block

! Output radial profile data as CSV for Python parsing
    write(*,'(A,I1)') 'PROFILE_START ', j
    do i = 1, nr, 5
      write(*,'(F10.3,A,F10.3,A,F10.1,A,F10.3)') &
        r(i)/1d3, ',', v(i), ',', p_fwd(i)/100d0, ',', v_inv(i)
    end do
    write(*,'(A)') 'PROFILE_END'
  end do

! MPI vs SST
  write(*,'(A)') 'MPI_START'
  block
    real(8) :: SST_C, SST_K, T_out, eta, es, dk, V_mpi
    T_out = 200.0d0
    do i = 26, 33
      SST_C = dble(i); SST_K = SST_C + 273.15d0
      eta = (SST_K - T_out) / T_out
      es = 611.2d0 * exp(17.67d0 * SST_C / (SST_C + 243.5d0))
      dk = 0.7d0 * 2.501d6 * 0.622d0 * es / 101325.0d0
      V_mpi = sqrt(0.8d0 * eta * dk)
      write(*,'(F6.1,A,F8.3,A,F8.1,A,F8.0)') SST_C, ',', eta, ',', V_mpi, ',', V_mpi*1.944d0
    end do
  end block
  write(*,'(A)') 'MPI_END'

end program tc_gradient_wind
"""

# ---- Step 1: Compile and run Fortran ----
src_file = 'tc_gradient_wind.f90'
bin_file = './tc_gradient_wind'
with open(src_file, 'w') as f:
    f.write(fortran_src)

comp = subprocess.run(['gfortran', '-o', bin_file, src_file],
                      capture_output=True, text=True)
if comp.returncode != 0:
    print("COMPILATION ERROR:")
    print(comp.stderr)
    raise SystemExit(1)
print("Fortran compiled successfully with gfortran")

result = subprocess.run([bin_file], capture_output=True, text=True, timeout=30)
output = result.stdout
print("Fortran execution complete\n")

# ---- Step 2: Parse Fortran output ----
storms = []
profiles = {}
mpi_data = []
current_profile = None

for line in output.split('\n'):
    line = line.strip()
    if line.startswith('STORM'):
        m = re.search(r'Vmax=\s*([\d.]+)\s*Rmax=\s*([\d.]+)', line)
        if m:
            storms.append({'Vmax': float(m.group(1)), 'Rmax': float(m.group(2))})
    elif line.startswith('  pc='):
        m = re.search(r'pc=\s*([\d.]+)\s*dp=\s*([\d.]+)', line)
        if m and storms:
            storms[-1]['pc'] = float(m.group(1))
            storms[-1]['dp'] = float(m.group(2))
    elif line.startswith('  surge_ib='):
        m = re.search(r'surge_ib=\s*([\d.]+)\s*surge_ws=\s*([\d.]+)\s*total=\s*([\d.]+)', line)
        if m and storms:
            storms[-1]['surge_ib'] = float(m.group(1))
            storms[-1]['surge_ws'] = float(m.group(2))
            storms[-1]['surge_total'] = float(m.group(3))
    elif line.startswith('PROFILE_START'):
        idx = int(line.split()[-1])
        current_profile = idx
        profiles[idx] = {'r': [], 'v': [], 'p': [], 'v_inv': []}
    elif line == 'PROFILE_END':
        current_profile = None
    elif current_profile is not None and ',' in line:
        parts = line.split(',')
        if len(parts) == 4:
            profiles[current_profile]['r'].append(float(parts[0]))
            profiles[current_profile]['v'].append(float(parts[1]))
            profiles[current_profile]['p'].append(float(parts[2]))
            profiles[current_profile]['v_inv'].append(float(parts[3]))
    elif line.startswith('MPI_START'):
        pass
    elif line == 'MPI_END':
        pass
    elif mpi_data is not None and ',' in line and not line.startswith('='):
        parts = line.split(',')
        if len(parts) == 4:
            try:
                mpi_data.append([float(x) for x in parts])
            except ValueError:
                pass

# ---- Step 3: Print summary from Fortran ----
print("=" * 62)
print("  TC Gradient Wind Balance Analysis (Fortran output)")
print("=" * 62)
labels = ['Cat 1', 'Cat 3', 'Cat 5']
print(f"{'Storm':<8} {'Vmax(m/s)':>9} {'Rmax(km)':>9} {'Pc(hPa)':>9} {'dP(hPa)':>9} {'Surge(m)':>9}")
print("-" * 62)
for s, lab in zip(storms, labels):
    print(f"{lab:<8} {s['Vmax']:>9.0f} {s['Rmax']:>9.0f} {s['pc']:>9.1f} {s['dp']:>9.1f} {s['surge_total']:>9.2f}")

if mpi_data:
    mpi_arr = np.array(mpi_data)
    print(f"\n{'SST(C)':>8} {'eta':>8} {'Vmax(m/s)':>10} {'Vmax(kt)':>10}")
    print("-" * 40)
    for row in mpi_arr:
        print(f"{row[0]:>8.1f} {row[1]:>8.3f} {row[2]:>10.1f} {row[3]:>10.0f}")

# ---- Step 4: Plot with matplotlib ----
fig, axes = plt.subplots(2, 2, figsize=(14, 10))
fig.patch.set_facecolor('#0f172a')
colors = ['#22d3ee', '#a78bfa', '#f87171']

for ax in axes.flat:
    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)

# Panel 1: Wind profiles
ax = axes[0, 0]
for idx, (j, lab, col) in enumerate(zip([1, 2, 3], labels, colors)):
    if j in profiles:
        r_arr = np.array(profiles[j]['r'])
        v_arr = np.array(profiles[j]['v'])
        ax.plot(r_arr, v_arr, color=col, lw=2.5, label=f"{lab} (Vmax={storms[idx]['Vmax']:.0f} m/s)")
        ax.plot(storms[idx]['Rmax'], storms[idx]['Vmax'], 'o', color=col, ms=8, zorder=5)
ax.axhline(y=33, color='#475569', ls=':', alpha=0.5)
ax.text(350, 34, 'Hurricane (33 m/s)', color='#94a3b8', fontsize=8)
ax.axvspan(0, 15, alpha=0.15, color='#94a3b8', label='Eye')
ax.set_xlabel('Radius (km)', color='#cbd5e1', fontsize=11)
ax.set_ylabel('Wind Speed (m/s)', color='#cbd5e1', fontsize=11)
ax.set_title('Rankine Vortex Wind Profile (Fortran)', color='#cbd5e1', fontsize=12)
ax.legend(fontsize=8, facecolor='#1e293b', edgecolor='#334155', labelcolor='#cbd5e1')
ax.set_xlim(0, 400)

# Panel 2: Pressure profiles
ax = axes[0, 1]
for idx, (j, lab, col) in enumerate(zip([1, 2, 3], labels, colors)):
    if j in profiles:
        r_arr = np.array(profiles[j]['r'])
        p_arr = np.array(profiles[j]['p'])
        ax.plot(r_arr, p_arr, color=col, lw=2.5, label=f"{lab} (Pc={storms[idx]['pc']:.0f} hPa)")
ax.axhline(y=1013, color='#475569', ls='--', alpha=0.5)
ax.text(300, 1015, 'Ambient 1013 hPa', color='#94a3b8', fontsize=8)
ax.set_xlabel('Radius (km)', color='#cbd5e1', fontsize=11)
ax.set_ylabel('Pressure (hPa)', color='#cbd5e1', fontsize=11)
ax.set_title('Radial Pressure Profile (Fortran)', color='#cbd5e1', fontsize=12)
ax.legend(fontsize=8, facecolor='#1e293b', edgecolor='#334155', labelcolor='#cbd5e1')
ax.set_xlim(0, 400)

# Panel 3: Forward vs Inverse wind (Cat 3)
ax = axes[1, 0]
if 2 in profiles:
    r_arr = np.array(profiles[2]['r'])
    v_fwd = np.array(profiles[2]['v'])
    v_inv = np.array(profiles[2]['v_inv'])
    ax.plot(r_arr, v_fwd, color='#a78bfa', lw=2.5, label='Forward (Rankine)')
    ax.plot(r_arr, v_inv, color='#fbbf24', lw=2, ls='--', label='Inverse (from pressure)')
    ax.set_xlabel('Radius (km)', color='#cbd5e1', fontsize=11)
    ax.set_ylabel('Wind Speed (m/s)', color='#cbd5e1', fontsize=11)
    ax.set_title('Cat 3: Forward vs Inverse Solution', color='#cbd5e1', fontsize=12)
    ax.legend(fontsize=9, facecolor='#1e293b', edgecolor='#334155', labelcolor='#cbd5e1')
    ax.set_xlim(0, 400)

# Panel 4: MPI vs SST
ax = axes[1, 1]
if mpi_data:
    mpi_arr = np.array(mpi_data)
    ax.plot(mpi_arr[:, 0], mpi_arr[:, 2], 'o-', color='#f97316', lw=2.5, ms=8, label='MPI (m/s)')
    ax2 = ax.twinx()
    ax2.plot(mpi_arr[:, 0], mpi_arr[:, 3], 's--', color='#22d3ee', lw=2, ms=6, label='MPI (kt)')
    ax2.set_ylabel('MPI (knots)', color='#22d3ee', fontsize=11)
    ax2.tick_params(colors='#22d3ee')
    ax2.spines['right'].set_color('#22d3ee')
    ax.set_xlabel('SST (°C)', color='#cbd5e1', fontsize=11)
    ax.set_ylabel('MPI (m/s)', color='#f97316', fontsize=11)
    ax.set_title('Maximum Potential Intensity vs SST', color='#cbd5e1', fontsize=12)
    lines1, labels1 = ax.get_legend_handles_labels()
    lines2, labels2 = ax2.get_legend_handles_labels()
    ax.legend(lines1+lines2, labels1+labels2, fontsize=9, facecolor='#1e293b', edgecolor='#334155', labelcolor='#cbd5e1')

# Storm surge bar inset
fig.text(0.5, 0.01, 'Storm Surge: ' + ' | '.join(
    f"{lab}: {s['surge_total']:.1f}m (IB={s['surge_ib']:.1f}+WS={s['surge_ws']:.1f})"
    for s, lab in zip(storms, labels)
), ha='center', color='#94a3b8', fontsize=9)

plt.tight_layout(rect=[0, 0.03, 1, 1])
plt.savefig('output.png', dpi=150, bbox_inches='tight', facecolor=fig.get_facecolor())
print("\nPlots generated from Fortran output.")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

Interactive Simulation: Holland Wind Profile Model

Python

Plot tangential wind and pressure profiles for Category 1-5 tropical cyclones using the Holland (1980) parametric model. Marks the radius of maximum wind and eye wall for each storm category.

holland_wind_profile.py87 lines

import numpy as np
import matplotlib.pyplot as plt

# Holland (1980) parametric wind profile model
rho_a = 1.15   # Air density (kg/m^3)
f = 5.0e-5     # Coriolis parameter (1/s)

def holland_wind(r_km, Vmax, Rmax_km, Pc, Pn=1013.0):
    """Holland wind profile. r_km: radius (km), returns V (m/s)."""
    r = r_km * 1000.0     # Convert to meters
    Rm = Rmax_km * 1000.0
    dP = (Pn - Pc) * 100.0  # Pressure deficit in Pa
    # Holland B parameter
    B = Vmax**2 * np.e * rho_a / dP
    B = np.clip(B, 1.0, 2.5)
    x = (Rm / r)**B
    V = np.sqrt(B * dP * np.exp(-x) * x / rho_a + (r * f / 2)**2) - r * f / 2
    return np.maximum(V, 0)

# Saffir-Simpson category storms
storms = [
    {'name': 'Cat 1 (Vmax=35 m/s)', 'Vmax': 35, 'Rmax': 50, 'Pc': 980, 'color': '#22d3ee'},
    {'name': 'Cat 2 (Vmax=45 m/s)', 'Vmax': 45, 'Rmax': 40, 'Pc': 968, 'color': '#38bdf8'},
    {'name': 'Cat 3 (Vmax=55 m/s)', 'Vmax': 55, 'Rmax': 35, 'Pc': 950, 'color': '#a78bfa'},
    {'name': 'Cat 4 (Vmax=67 m/s)', 'Vmax': 67, 'Rmax': 25, 'Pc': 935, 'color': '#f97316'},
    {'name': 'Cat 5 (Vmax=80 m/s)', 'Vmax': 80, 'Rmax': 20, 'Pc': 910, 'color': '#f87171'},
]

r = np.linspace(1, 400, 1000)

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)

print("Holland Wind Profile Model - Tropical Cyclone Analysis")
print("=" * 60)
print(f"{'Category':<25} {'Vmax(m/s)':>10} {'Rmax(km)':>10} {'Pc(hPa)':>10} {'B':>6}")
print("-" * 60)

# Panel 1: Wind profiles
for s in storms:
    v = holland_wind(r, s['Vmax'], s['Rmax'], s['Pc'])
    ax1.plot(r, v, color=s['color'], lw=2.5, label=s['name'])
    # Mark Rmax and Vmax
    ax1.plot(s['Rmax'], s['Vmax'], 'o', color=s['color'], ms=8, zorder=5)
    B = s['Vmax']**2 * np.e * rho_a / ((1013 - s['Pc']) * 100)
    B = np.clip(B, 1.0, 2.5)
    print(f"{s['name']:<25} {s['Vmax']:>10} {s['Rmax']:>10} {s['Pc']:>10} {B:>6.2f}")

# Mark eye region
ax1.axvspan(0, 15, alpha=0.15, color='#94a3b8', label='Eye region')
ax1.axhline(y=33, color='#475569', ls=':', alpha=0.5)
ax1.text(350, 34, 'Hurricane (33 m/s)', color='#94a3b8', fontsize=8)
ax1.set_xlabel('Radius (km)', color='#cbd5e1', fontsize=12)
ax1.set_ylabel('Tangential Wind (m/s)', color='#cbd5e1', fontsize=12)
ax1.set_title('Holland Wind Profile Model', color='#cbd5e1', fontsize=13)
ax1.legend(fontsize=8, facecolor='#1e293b', edgecolor='#334155', labelcolor='#cbd5e1')
ax1.set_xlim(0, 400)

# Panel 2: Pressure profiles
for s in storms:
    v = holland_wind(r, s['Vmax'], s['Rmax'], s['Pc'])
    Rm = s['Rmax'] * 1000.0
    dP = (1013 - s['Pc']) * 100.0
    B = np.clip(s['Vmax']**2 * np.e * rho_a / dP, 1.0, 2.5)
    p = s['Pc'] + (1013 - s['Pc']) * np.exp(-(Rm / (r * 1000))**B)
    ax2.plot(r, p, color=s['color'], lw=2.5, label=s['name'])

ax2.axhline(y=1013, color='#475569', ls='--', alpha=0.5)
ax2.text(300, 1015, 'Ambient (1013 hPa)', color='#94a3b8', fontsize=8)
ax2.set_xlabel('Radius (km)', color='#cbd5e1', fontsize=12)
ax2.set_ylabel('Pressure (hPa)', color='#cbd5e1', fontsize=12)
ax2.set_title('Radial Pressure Profile', color='#cbd5e1', fontsize=13)
ax2.legend(fontsize=8, facecolor='#1e293b', edgecolor='#334155', labelcolor='#cbd5e1')
ax2.set_xlim(0, 400)

plt.tight_layout()
plt.savefig('output.png', dpi=150, bbox_inches='tight', facecolor=fig.get_facecolor())
print()
print("Dots mark the radius of maximum wind (Rmax) for each storm.")
print("The Holland B parameter controls the shape of the wind profile.")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

← 5.3 Severe Weather Part 6: Radiation & Climate →