Module 4: Extreme Weather & Ecology

Climate change amplifies the intensity, frequency, and duration of extreme weather events. This module derives the Clausius-Clapeyron scaling of precipitation, the exponential relationship between vapor pressure deficit and wildfire, hurricane potential intensity theory, and the ecological cascades that follow from drought, fire, and floods.

1. Clausius-Clapeyron & Extreme Precipitation

The Clausius-Clapeyron equation provides the thermodynamic foundation for understanding how atmospheric moisture content changes with temperature. As the atmosphere warms, it can hold more water vapor, directly increasing the intensity of precipitation events.

Derivation of the 7% Rule

Starting from the Clausius-Clapeyron equation for the saturation vapor pressure $e_s$:

$$\frac{de_s}{dT} = \frac{L_v \, e_s}{R_v \, T^2}$$

Integrating from a reference temperature $T_0$:

$$e_s(T) = e_s(T_0)\exp\!\left[\frac{L_v}{R_v}\left(\frac{1}{T_0} - \frac{1}{T}\right)\right]$$

Since specific humidity $q_s \approx 0.622\,e_s/p$, the fractional rate of change is:

$$\frac{1}{q_s}\frac{dq_s}{dT} = \frac{L_v}{R_v T^2} \approx \frac{2.5 \times 10^6}{461.5 \times 288^2} \approx 0.065 \text{ K}^{-1}$$

This is the “7% per °C” scaling: at 15°C, saturation humidity increases by ~6.5% per degree

Super-Clausius-Clapeyron Scaling

While daily precipitation extremes generally follow CC scaling (~7%/°C), sub-daily (hourly) extremes can exhibit “super-CC” scaling of up to 14%/°C (Lenderink & Meijgaard, 2008). This is attributed to convective invigoration: more latent heat release strengthens updrafts, creating a positive feedback:

$$\frac{\Delta P_{\text{extreme}}}{P_{\text{extreme}}} \approx \alpha \cdot \Delta T \quad \text{where} \quad \alpha \approx \begin{cases} 0.07 & \text{daily} \\ 0.14 & \text{hourly (convective)} \end{cases}$$

Clausius-Clapeyron: Atmospheric Moisture vs Temperature

2. Wildfire: Climate, Fuel, & Ecology

Wildfire activity is increasing globally, driven primarily by rising vapor pressure deficit (VPD), which desiccates vegetation fuels. Abatzoglou & Williams (2016) demonstrated that area burned in the western United States scales exponentially with VPD:

$$A_{\text{burned}} \propto \exp(\beta \cdot \text{VPD}) \quad \text{with} \quad \beta \approx 1.8$$

The Rothermel Fire Spread Model

The Rothermel (1972) model describes the rate of fire spread as a function of fuel properties, moisture, wind, and slope:

$$R = \frac{I_R \, \xi \, (1 + \phi_w + \phi_s)}{\rho_b \, \varepsilon \, Q_{ig}}$$

$I_R$ = reaction intensity, $\xi$ = propagation flux ratio, $\phi_w, \phi_s$ = wind/slope factors, $Q_{ig}$ = heat of ignition

The moisture damping coefficient $\eta_M$ reduces $I_R$ as fuel moisture increases:

$$\eta_M = 1 - 2.59\frac{M}{M_x} + 5.11\left(\frac{M}{M_x}\right)^2 - 3.52\left(\frac{M}{M_x}\right)^3$$

$M$ = fuel moisture content, $M_x$ = moisture of extinction (~25% for dead fine fuels)

Australian Black Summer 2019–20

The 2019–20 Australian bushfire season burned approximately 18.6 million hectares and affected an estimated 3 billion animals (van Eeden et al., 2020), including 143 million mammals, 2.46 billion reptiles, 180 million birds, and 51 million frogs. This was driven by unprecedented VPD values (~2.4 kPa), the result of compounding drought and heat (the Indian Ocean Dipole combined with long-term warming trends).

Wildfire-Climate Feedback Loop

3. Drought & Tree Mortality

Droughts are intensifying as warming increases evaporative demand. The water balance equation provides the framework for understanding drought development:

$$P - \text{ET} - R - \Delta S = 0$$

$P$ = precipitation, ET = evapotranspiration, $R$ = runoff, $\Delta S$ = change in soil moisture storage

As temperature rises, the Penman-Monteith equation predicts ET increases of approximately 5% per °C. When $\Delta S$ becomes persistently negative, drought develops. The Palmer Drought Severity Index (PDSI) quantifies this deficit:

$$\text{PDSI} \sim \sum_{i} \frac{P_i - \hat{P}_i}{\hat{P}_i} \quad \text{where} \quad \hat{P}_i = \text{climatological water demand}$$

PDSI < -2: moderate drought; PDSI < -4: extreme drought

Drought-Induced Tree Mortality

Trees die during drought through two interacting mechanisms (McDowell et al., 2008):

Hydraulic failure: When soil water potential drops below a critical threshold, cavitation (air embolism) in the xylem interrupts water transport. The vulnerability curve describes the percentage loss of conductivity (PLC) as:

$$\text{PLC} = \frac{100}{1 + \exp\!\left[a(\Psi - \Psi_{50})\right]}$$

$\Psi_{50}$ = water potential at 50% conductivity loss; $a$ = slope parameter

Carbon starvation: Prolonged stomatal closure to conserve water prevents CO&sub2; uptake for photosynthesis. If the drought exceeds the tree’s carbohydrate reserves, metabolic functions fail. The time to carbon starvation depends on storage reserves and metabolic rate:

$$t_{\text{starv}} = \frac{C_{\text{storage}}}{R_{\text{maint}} \cdot Q_{10}^{(T-T_{\text{ref}})/10}}$$

Maintenance respiration increases exponentially with temperature (via $Q_{10} \approx 2$), shortening survival time during hot droughts

4. Hurricane Intensification

Tropical cyclones are heat engines that extract energy from warm ocean water. Emanuel (1986) derived the theoretical maximum intensity—the potential intensity (PI)—by treating the hurricane as a Carnot engine operating between the warm ocean surface and the cold tropopause.

Potential Intensity Theory

The maximum sustainable wind speed is:

$$V_{\max}^2 = \frac{C_k}{C_d} \cdot \frac{T_s - T_o}{T_o} \cdot (h_0^* - h)$$

$C_k/C_d$ = ratio of enthalpy to drag coefficients, $T_s$ = SST, $T_o$ = outflow temperature, $h_0^*$ = saturation enthalpy at SST

The Carnot efficiency factor $(T_s - T_o)/T_o$ explains why warmer SSTs produce stronger storms: more energy is available for conversion to kinetic energy. With $T_s = 303$ K (30°C) and $T_o = 200$ K, the efficiency is about 0.52.

The enthalpy disequilibrium term $(h_0^* - h)$ increases nonlinearly with SST because saturation humidity increases exponentially (Clausius-Clapeyron). This double effect—higher efficiency and more available energy—means PI increases rapidly with SST:

$$\frac{dV_{\max}}{dT_s} \approx 3\text{--}5 \text{ m/s per °C}$$

Rapid Intensification

Rapid intensification (RI), defined as a wind speed increase of ≥30 knots in 24 hours, has become more frequent (Bhatia et al., 2019). RI is most likely when SST exceeds ~28°C, wind shear is low, and mid-level humidity is high. The probability of RI follows an approximate logistic function of SST:

$$P(\text{RI}) = \frac{1}{1 + e^{-\beta(T_s - T_{\text{crit}})}} \quad \text{with} \quad T_{\text{crit}} \approx 28\text{°C}$$

Compound Events

The ecological impact of extreme weather is amplified when events compound. Drought followed by heatwave followed by wildfire creates cascading damage far exceeding the sum of individual impacts. The probability of compound events increases faster than individual events because the underlying drivers (temperature, moisture deficit) are correlated:

$$P(\text{drought} \cap \text{heat} \cap \text{fire}) \gg P(\text{drought}) \cdot P(\text{heat}) \cdot P(\text{fire})$$

Positive correlation means compound probability is much higher than assumed under independence

5. Ecological Impacts & Recovery

Extreme weather events reshape ecosystems through direct mortality, habitat destruction, and altered successional trajectories.

Post-Fire Succession

Many ecosystems have co-evolved with fire regimes. However, when fire frequency exceeds the recovery time for key species, ecosystems can undergo state shifts. For example, frequent severe fires in Australian eucalyptus forests can prevent canopy recovery, converting forest to shrubland. The recovery condition requires:

$$\tau_{\text{recovery}} < \tau_{\text{fire return}} \quad \Longrightarrow \quad \text{ecosystem persistence}$$

Drought Refugia

Topographic complexity creates microhabitats that buffer against drought—so-called “drought refugia.” North-facing slopes (in the Southern Hemisphere) and valley bottoms with deeper soils maintain higher water availability. Conservation prioritization increasingly targets these refugia as “climate-resilient” areas.

Flood Pulse Ecology

In floodplain ecosystems, periodic flooding is essential for nutrient distribution and spawning cues. Climate change alters flood timing, magnitude, and duration. The flood pulse concept (Junk et al., 1989) describes how floodplain productivity scales with the predictability of the flood regime. Increasing variability in flood timing disrupts fish breeding cycles and riparian vegetation establishment.

Simulation: Precipitation Intensity & Extremes

Clausius-Clapeyron moisture scaling, return period shifts for extreme rainfall, precipitation distribution tails under warming, and regional extreme precipitation projections.

Python

script.py144 lines

import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt

# Clausius-Clapeyron: Precipitation Intensity vs Warming
# The CC relation predicts ~7% increase in saturation vapor pressure per degree C
# dq_s/dT = L*q_s / (R_v * T^2)
# This sets a thermodynamic scaling for extreme precipitation

T_base = 288.15  # baseline temperature (15 C) in K
L_v = 2.5e6      # latent heat of vaporization (J/kg)
R_v = 461.5      # gas constant for water vapor (J/kg/K)

# Saturation vapor pressure (Clausius-Clapeyron)
def e_sat(T):
    """Saturation vapor pressure in hPa using CC equation"""
    e0 = 6.11  # hPa at 273.15 K
    return e0 * np.exp(L_v / R_v * (1/273.15 - 1/T))

# Temperature range
dT_range = np.linspace(0, 6, 100)
T_range = T_base + dT_range

# Saturation specific humidity q_s ~ 0.622 * e_s / p
p = 1013.25  # hPa
q_s = 0.622 * e_sat(T_range) / p
q_s_base = 0.622 * e_sat(T_base) / p
q_s_ratio = q_s / q_s_base

# CC scaling: ~7% per degree
cc_scaling = (1.07)**dT_range

# Observed extreme precip scaling (often exceeds CC: "super-CC")
# Lenderink & Meijgaard (2008): 14%/degree for hourly extremes
super_cc = (1.14)**dT_range

# Sub-daily vs daily scaling
daily_scaling = (1.065)**dT_range  # slightly below CC for daily
hourly_scaling = super_cc

fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2, figsize=(14, 11))
fig.patch.set_facecolor('#0a0a1a')

for ax in [ax1, ax2, ax3, ax4]:
    ax.set_facecolor('#0a0a1a')
    ax.tick_params(colors='#94a3b8')
    for spine in ax.spines.values():
        spine.set_color('#334155')
    ax.grid(True, color='#334155', alpha=0.4)

# Panel 1: CC scaling of moisture
ax1.plot(dT_range, (q_s_ratio - 1) * 100, '-', color='#22d3ee', linewidth=3,
         label='Exact CC calculation')
ax1.plot(dT_range, (cc_scaling - 1) * 100, '--', color='#4ade80', linewidth=2,
         label='7%/\u00b0C approximation')
ax1.plot(dT_range, (super_cc - 1) * 100, '-.', color='#f43f5e', linewidth=2,
         label='Super-CC (14%/\u00b0C, hourly)')
ax1.fill_between(dT_range, (daily_scaling - 1) * 100, (super_cc - 1) * 100,
                  alpha=0.1, color='#f43f5e', label='Observed range')

ax1.set_xlabel('Temperature increase (\u00b0C)', color='#94a3b8', fontsize=11)
ax1.set_ylabel('Increase in atmospheric moisture (%)', color='#94a3b8', fontsize=11)
ax1.set_title('Clausius-Clapeyron Moisture Scaling', color='#e2e8f0', fontsize=13, fontweight='bold')
ax1.legend(facecolor='#1e293b', edgecolor='#334155', labelcolor='#cbd5e1', fontsize=9)

# Panel 2: Return period shifts
# A 1-in-100 year event becomes more frequent with warming
# Using GEV distribution shift
return_periods = [2, 5, 10, 20, 50, 100]
warming_levels = [0, 1, 2, 3, 4]

# For a given warming, the return period of what was a 1-in-X event changes
# Approximate: new_return = old_return * scale_factor
for rp in [20, 50, 100]:
    new_rps = []
    for dT in warming_levels:
        # Intensity increases by CC, so frequency of exceeding old threshold increases
        scale = 1.07**dT
        # Approximate: new return period = old / scale^k where k depends on GEV shape
        k = 5  # typical for mid-latitude extremes
        new_rp = rp / scale**k
        new_rps.append(new_rp)
    color = {'20': '#4ade80', '50': '#facc15', '100': '#f43f5e'}[str(rp)]
    ax2.plot(warming_levels, new_rps, 'o-', color=color, linewidth=2, markersize=8,
             label=f'Current 1-in-{rp} yr event')

ax2.set_xlabel('Global warming (\u00b0C)', color='#94a3b8', fontsize=11)
ax2.set_ylabel('New return period (years)', color='#94a3b8', fontsize=11)
ax2.set_title('Extreme Rainfall Return Periods', color='#e2e8f0', fontsize=13, fontweight='bold')
ax2.legend(facecolor='#1e293b', edgecolor='#334155', labelcolor='#cbd5e1', fontsize=9)
ax2.set_yscale('log')
ax2.set_ylim(0.5, 200)

# Panel 3: Precipitation distribution shift
# Show how the tail of the distribution changes
np.random.seed(42)
n_events = 10000
precip_base = np.random.gamma(2, 15, n_events)  # baseline distribution
precip_2C = np.random.gamma(2, 15 * 1.14, n_events)  # +2C with CC scaling
precip_4C = np.random.gamma(2, 15 * 1.30, n_events)  # +4C

bins = np.linspace(0, 150, 60)
ax3.hist(precip_base, bins=bins, density=True, alpha=0.5, color='#22d3ee', label='Baseline')
ax3.hist(precip_2C, bins=bins, density=True, alpha=0.4, color='#facc15', label='+2\u00b0C')
ax3.hist(precip_4C, bins=bins, density=True, alpha=0.3, color='#f43f5e', label='+4\u00b0C')

# Mark extreme threshold
p99_base = np.percentile(precip_base, 99)
ax3.axvline(x=p99_base, color='white', linestyle='--', alpha=0.5, label=f'99th pctl baseline ({p99_base:.0f} mm)')

frac_above_2C = np.sum(precip_2C > p99_base) / n_events * 100
frac_above_4C = np.sum(precip_4C > p99_base) / n_events * 100

ax3.set_xlabel('Daily precipitation (mm)', color='#94a3b8', fontsize=11)
ax3.set_ylabel('Probability density', color='#94a3b8', fontsize=11)
ax3.set_title('Precipitation Distribution Shift', color='#e2e8f0', fontsize=13, fontweight='bold')
ax3.legend(facecolor='#1e293b', edgecolor='#334155', labelcolor='#cbd5e1', fontsize=9)

# Panel 4: Regional extreme precip changes
regions = ['Tropics', 'Mid-lat\nAsia', 'Europe', 'N.\nAmerica', 'S.E.\nAsia', 'Arctic']
scaling_2C = [14, 10, 8, 9, 16, 20]  # % increase at +2C
scaling_4C = [30, 22, 18, 20, 35, 45]  # % increase at +4C

x = np.arange(len(regions))
width = 0.35

bars1 = ax4.bar(x - width/2, scaling_2C, width, color='#facc15', alpha=0.8, label='+2\u00b0C')
bars2 = ax4.bar(x + width/2, scaling_4C, width, color='#f43f5e', alpha=0.8, label='+4\u00b0C')

ax4.axhline(y=14, color='#22d3ee', linestyle='--', alpha=0.5, label='CC scaling (+2\u00b0C)')
ax4.set_xticks(x)
ax4.set_xticklabels(regions, color='#94a3b8', fontsize=9)
ax4.set_ylabel('Extreme precip increase (%)', color='#94a3b8', fontsize=11)
ax4.set_title('Regional Extreme Precipitation Changes', color='#e2e8f0', fontsize=13, fontweight='bold')
ax4.legend(facecolor='#1e293b', edgecolor='#334155', labelcolor='#cbd5e1', fontsize=9)

plt.tight_layout()
plt.savefig('output.png', dpi=150, bbox_inches='tight', facecolor='#0a0a1a')
print("Precipitation intensity analysis complete.")
print(f"CC scaling at +2\u00b0C: {(1.07**2 - 1)*100:.1f}% more moisture")
print(f"CC scaling at +4\u00b0C: {(1.07**4 - 1)*100:.1f}% more moisture")
print(f"Events exceeding baseline 99th pctl: +2\u00b0C={frac_above_2C:.1f}%, +4\u00b0C={frac_above_4C:.1f}%")
print(f"(vs 1% in baseline)")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

Simulation: Wildfire Area & Fire Spread

Exponential VPD-fire relationship, Rothermel spread rate model, wildfire projections under emission scenarios, and fire-driven biodiversity impacts.

Python

script.py141 lines

import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt

# Wildfire: Area Burned vs Vapor Pressure Deficit (VPD)
# Abatzoglou & Williams (2016): Area burned ~ exp(beta * VPD)
# VPD increases with temperature: VPD ~ e_sat(T) * (1 - RH)
# Rothermel fire spread model: R = I_R * xi * (1+phi_w+phi_s) / (rho_b*epsilon*Q_ig)

# VPD-fire relationship
VPD_range = np.linspace(0.5, 3.0, 100)  # kPa
beta = 1.8  # empirical coefficient

# Normalized area burned (relative to VPD=1.0 kPa baseline)
area_burned_norm = np.exp(beta * (VPD_range - 1.0))

# Historical VPD trend (western US)
years = np.arange(1980, 2101)
# Observed: VPD increasing ~0.014 kPa/yr (Abatzoglou & Williams 2016)
VPD_hist = 1.0 + 0.014 * (years - 1980) * np.minimum((years - 1980) / 40, 1.0)
VPD_rcp45 = VPD_hist.copy()
VPD_rcp85 = VPD_hist.copy()
mask_proj = years >= 2024
VPD_rcp45[mask_proj] = VPD_hist[mask_proj] + 0.008 * (years[mask_proj] - 2024)
VPD_rcp85[mask_proj] = VPD_hist[mask_proj] + 0.020 * (years[mask_proj] - 2024)

# Area burned projections
AB_hist = np.exp(beta * (VPD_hist - 1.0))
AB_rcp45 = np.exp(beta * (VPD_rcp45 - 1.0))
AB_rcp85 = np.exp(beta * (VPD_rcp85 - 1.0))

# Rothermel spread rate model (simplified)
# R = (I_R * xi * (1 + phi_w)) / (rho_b * epsilon * Q_ig)
# Key insight: fuel moisture content decreases with VPD
fuel_moisture = np.linspace(0.30, 0.05, 100)  # fraction (dead fuel)
# Moisture damping coefficient
eta_M = 1 - 2.59 * fuel_moisture / 0.25 + 5.11 * (fuel_moisture / 0.25)**2 - 3.52 * (fuel_moisture / 0.25)**3
eta_M = np.maximum(eta_M, 0)

# Spread rate (relative units)
I_R_base = 1.0  # reaction intensity base
wind_factor = 1.5  # phi_w
spread_rate = I_R_base * eta_M * (1 + wind_factor)

# Australian 2019-20 Black Summer
# 3 billion animals affected, 46 million acres burned
aus_year = 2019
aus_area_burned = 18.6  # million hectares
aus_VPD = 2.4  # approximate VPD anomaly

fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2, figsize=(14, 11))
fig.patch.set_facecolor('#0a0a1a')

# Panel 1: Area burned vs VPD (exponential)
ax1.plot(VPD_range, area_burned_norm, '-', color='#f97316', linewidth=3,
         label=f'Area ~ exp({beta}*VPD)')
ax1.fill_between(VPD_range, area_burned_norm, alpha=0.15, color='#f97316')
ax1.axvline(x=1.0, color='#22d3ee', linestyle='--', alpha=0.5, label='Baseline VPD')
ax1.axvline(x=aus_VPD, color='#f43f5e', linestyle='--', alpha=0.7,
            label=f'Aus. 2019-20 (VPD={aus_VPD})')
ax1.set_xlabel('Vapor Pressure Deficit (kPa)', color='#94a3b8', fontsize=11)
ax1.set_ylabel('Relative area burned', color='#94a3b8', fontsize=11)
ax1.set_title('Wildfire Area vs Fuel Aridity', color='#e2e8f0', fontsize=13, fontweight='bold')
ax1.legend(facecolor='#1e293b', edgecolor='#334155', labelcolor='#cbd5e1', fontsize=9)
ax1.set_ylim(0, 15)

# Panel 2: VPD and area burned projections
ax2_twin = ax2.twinx()
ax2.plot(years, VPD_rcp45, '-', color='#facc15', linewidth=2, label='VPD (RCP 4.5)')
ax2.plot(years, VPD_rcp85, '-', color='#f43f5e', linewidth=2, label='VPD (RCP 8.5)')
ax2_twin.plot(years, AB_rcp45, '--', color='#facc15', linewidth=1.5, alpha=0.7, label='Area (RCP 4.5)')
ax2_twin.plot(years, AB_rcp85, '--', color='#f43f5e', linewidth=1.5, alpha=0.7, label='Area (RCP 8.5)')
ax2_twin.fill_between(years, AB_rcp45, AB_rcp85, alpha=0.1, color='#f97316')
ax2.axvline(x=2024, color='#94a3b8', linestyle=':', alpha=0.5)

ax2.set_xlabel('Year', color='#94a3b8', fontsize=11)
ax2.set_ylabel('VPD (kPa)', color='#facc15', fontsize=11)
ax2_twin.set_ylabel('Relative area burned', color='#f43f5e', fontsize=11)
ax2.set_title('Wildfire Projections (Western US)', color='#e2e8f0', fontsize=13, fontweight='bold')
ax2_twin.tick_params(colors='#f43f5e')
ax2.tick_params(axis='y', colors='#facc15')
lines1, labels1 = ax2.get_legend_handles_labels()
lines2, labels2 = ax2_twin.get_legend_handles_labels()
ax2.legend(lines1 + lines2, labels1 + labels2,
           facecolor='#1e293b', edgecolor='#334155', labelcolor='#cbd5e1', fontsize=8, loc='upper left')

# Panel 3: Rothermel fire spread rate vs fuel moisture
ax3.plot(fuel_moisture * 100, spread_rate, '-', color='#f97316', linewidth=3,
         label='Rothermel spread rate')
ax3.fill_between(fuel_moisture * 100, spread_rate, alpha=0.15, color='#f97316')
ax3.axvline(x=10, color='#f43f5e', linestyle='--', alpha=0.7, label='Critical moisture (10%)')
ax3.axvline(x=25, color='#4ade80', linestyle='--', alpha=0.7, label='Extinction moisture (25%)')

ax3.set_xlabel('Dead fuel moisture content (%)', color='#94a3b8', fontsize=11)
ax3.set_ylabel('Fire spread rate (relative)', color='#94a3b8', fontsize=11)
ax3.set_title('Rothermel Model: Spread Rate', color='#e2e8f0', fontsize=13, fontweight='bold')
ax3.legend(facecolor='#1e293b', edgecolor='#334155', labelcolor='#cbd5e1', fontsize=9)
ax3.invert_xaxis()

# Panel 4: Fire-biodiversity impacts
# Number of animals affected scales with area burned and habitat density
dT_range2 = np.linspace(0, 5, 100)
VPD_proj = 1.0 + 0.2 * dT_range2  # VPD scales ~0.2 kPa per degree
area_factor = np.exp(beta * (VPD_proj - 1.0))

# Habitat types and vulnerability
mammals = area_factor * 0.3  # relative impact
birds = area_factor * 0.5
reptiles = area_factor * 0.8  # most vulnerable (low mobility)
insects = area_factor * 1.0   # highest density

ax4.plot(dT_range2, mammals, '-', color='#f97316', linewidth=2, label='Mammals')
ax4.plot(dT_range2, birds, '-', color='#facc15', linewidth=2, label='Birds')
ax4.plot(dT_range2, reptiles, '-', color='#4ade80', linewidth=2, label='Reptiles/Amphibians')
ax4.plot(dT_range2, insects, '-', color='#a78bfa', linewidth=2, label='Invertebrates')
ax4.fill_between(dT_range2, mammals, insects, alpha=0.08, color='#f97316')

# Mark Australian Black Summer
ax4.axvline(x=1.5, color='#f43f5e', linestyle='--', alpha=0.7)
ax4.annotate('Aus. 2019-20\n3B animals', xy=(1.5, 3), fontsize=9, color='#f43f5e',
             ha='center', fontstyle='italic')

ax4.set_xlabel('Global warming (\u00b0C)', color='#94a3b8', fontsize=11)
ax4.set_ylabel('Relative wildlife impact', color='#94a3b8', fontsize=11)
ax4.set_title('Fire-Driven Biodiversity Impact', color='#e2e8f0', fontsize=13, fontweight='bold')
ax4.legend(facecolor='#1e293b', edgecolor='#334155', labelcolor='#cbd5e1', fontsize=9)

plt.tight_layout()
plt.savefig('output.png', dpi=150, bbox_inches='tight', facecolor='#0a0a1a')
print("Wildfire analysis complete.")
print(f"Area burned increase at VPD=2.0 kPa: {np.exp(beta*(2.0-1.0)):.1f}x baseline")
print(f"Area burned increase at VPD=2.5 kPa: {np.exp(beta*(2.5-1.0)):.1f}x baseline")
print(f"Australian Black Summer 2019-20: ~18.6 million ha, ~3 billion animals affected")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

Simulation: Hurricane PI & Drought Severity

Potential intensity vs SST, hurricane PI projections, rapid intensification probability, and regional drought severity under warming (PDSI).

Python

script.py149 lines

import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt

# Hurricane Potential Intensity (PI) vs SST
# Emanuel (1986, 2003): V_max = sqrt((Ck/Cd) * (SST - T_out)/T_out * (h* - h))
# Where: Ck = enthalpy exchange coefficient
#        Cd = drag coefficient
#        SST = sea surface temperature
#        T_out = outflow temperature (~200K)
#        h* = saturation enthalpy at SST
#        h = ambient boundary layer enthalpy

# Physical parameters
Ck_Cd = 0.9     # ratio of exchange coefficients (typical ocean)
T_out = 200.0   # outflow temperature (K) ~tropopause
c_p = 1004.0    # specific heat of air (J/kg/K)
L_v = 2.5e6     # latent heat of vaporization (J/kg)
R_v = 461.5     # gas constant for water vapor

# SST range
SST_C = np.linspace(22, 34, 100)
SST_K = SST_C + 273.15

# Saturation specific humidity at SST
def q_sat(T_K):
    e_s = 6.11 * np.exp(L_v / R_v * (1/273.15 - 1/T_K)) * 100  # Pa
    return 0.622 * e_s / 101325

# Boundary layer relative humidity (~80%)
RH = 0.80

# Enthalpy difference: h* - h ≈ L_v * (q_sat(SST) - RH*q_sat(SST)) + c_p*(SST - T_env)
# Simplified: delta_h ≈ L_v * q_sat(SST) * (1 - RH)
delta_h = L_v * q_sat(SST_K) * (1 - RH)

# Potential intensity
V_max = np.sqrt(Ck_Cd * (SST_K - T_out) / T_out * delta_h)

# Saffir-Simpson categories (m/s)
cat_thresholds = [33, 43, 50, 58, 70]  # Cat 1-5 lower bounds
cat_labels = ['Cat 1', 'Cat 2', 'Cat 3', 'Cat 4', 'Cat 5']
cat_colors = ['#4ade80', '#facc15', '#f97316', '#f43f5e', '#dc2626']

# SST trend
years = np.arange(1980, 2101)
SST_trend_base = 27.0  # tropical Atlantic baseline
SST_rcp45 = SST_trend_base + 0.015 * (years - 1980)
SST_rcp85 = SST_trend_base + 0.030 * (years - 1980)

# PI for each year
def calc_PI(SST_array):
    SST_K = SST_array + 273.15
    dh = L_v * q_sat(SST_K) * (1 - RH)
    return np.sqrt(Ck_Cd * (SST_K - T_out) / T_out * dh)

PI_rcp45 = calc_PI(SST_rcp45)
PI_rcp85 = calc_PI(SST_rcp85)

# Rapid intensification (RI) probability
# RI defined as >= 30 kt increase in 24 hours
# Kaplan & DeMaria (2003): RI probability increases with SST
RI_prob = 1 / (1 + np.exp(-0.8 * (SST_C - 28)))  # logistic function

fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2, figsize=(14, 11))
fig.patch.set_facecolor('#0a0a1a')

# Panel 1: PI vs SST
ax1.plot(SST_C, V_max, '-', color='#22d3ee', linewidth=3, label='Potential intensity')
for thresh, label, color in zip(cat_thresholds, cat_labels, cat_colors):
    ax1.axhline(y=thresh, color=color, linestyle='--', alpha=0.5, linewidth=1)
    ax1.text(22.5, thresh + 1, label, color=color, fontsize=9, alpha=0.8)

ax1.fill_between(SST_C, V_max, alpha=0.1, color='#22d3ee')
ax1.set_xlabel('Sea Surface Temperature (\u00b0C)', color='#94a3b8', fontsize=11)
ax1.set_ylabel('Maximum wind speed (m/s)', color='#94a3b8', fontsize=11)
ax1.set_title('Hurricane Potential Intensity vs SST', color='#e2e8f0', fontsize=13, fontweight='bold')
ax1.legend(facecolor='#1e293b', edgecolor='#334155', labelcolor='#cbd5e1', fontsize=9)

# Panel 2: PI evolution over time
ax2.plot(years, PI_rcp45, '-', color='#facc15', linewidth=2, label='RCP 4.5')
ax2.plot(years, PI_rcp85, '-', color='#f43f5e', linewidth=2, label='RCP 8.5')
ax2.fill_between(years, PI_rcp45, PI_rcp85, alpha=0.1, color='#f43f5e')
for thresh, label, color in zip(cat_thresholds[:3], cat_labels[:3], cat_colors[:3]):
    ax2.axhline(y=thresh, color=color, linestyle='--', alpha=0.3, linewidth=1)
    ax2.text(1982, thresh + 0.5, label, color=color, fontsize=8, alpha=0.7)

ax2.set_xlabel('Year', color='#94a3b8', fontsize=11)
ax2.set_ylabel('Potential intensity (m/s)', color='#94a3b8', fontsize=11)
ax2.set_title('Hurricane PI Projections', color='#e2e8f0', fontsize=13, fontweight='bold')
ax2.legend(facecolor='#1e293b', edgecolor='#334155', labelcolor='#cbd5e1', fontsize=9)

# Panel 3: Rapid intensification probability
ax3.plot(SST_C, RI_prob * 100, '-', color='#f97316', linewidth=3,
         label='RI probability')
ax3.fill_between(SST_C, RI_prob * 100, alpha=0.15, color='#f97316')
ax3.axvline(x=26.5, color='#22d3ee', linestyle='--', alpha=0.5, label='Hurricane threshold SST')
ax3.axvline(x=28.0, color='#facc15', linestyle='--', alpha=0.5, label='RI favorable SST')

ax3.set_xlabel('Sea Surface Temperature (\u00b0C)', color='#94a3b8', fontsize=11)
ax3.set_ylabel('RI probability (%)', color='#94a3b8', fontsize=11)
ax3.set_title('Rapid Intensification vs SST', color='#e2e8f0', fontsize=13, fontweight='bold')
ax3.legend(facecolor='#1e293b', edgecolor='#334155', labelcolor='#cbd5e1', fontsize=9)

# Panel 4: Drought severity projections (PDSI)
# Water balance: P - ET - R - delta_S = 0
# As T rises, ET increases (Penman-Monteith), drought intensifies
dT_drought = np.linspace(0, 5, 100)

# ET increase with temperature (~5% per degree via Penman-Monteith)
ET_increase = 1.05**dT_drought

# PDSI approximation (negative = drought)
# Baseline PDSI = 0 (normal)
# Each degree shifts PDSI by ~-0.5 in water-limited regions
PDSI_tropical = -0.3 * dT_drought
PDSI_subtrop = -0.8 * dT_drought  # most vulnerable
PDSI_temperate = -0.4 * dT_drought
PDSI_arid = -1.2 * dT_drought

ax4.plot(dT_drought, PDSI_tropical, '-', color='#4ade80', linewidth=2, label='Tropical')
ax4.plot(dT_drought, PDSI_temperate, '-', color='#22d3ee', linewidth=2, label='Temperate')
ax4.plot(dT_drought, PDSI_subtrop, '-', color='#facc15', linewidth=2, label='Subtropical')
ax4.plot(dT_drought, PDSI_arid, '-', color='#f43f5e', linewidth=2, label='Arid/Semi-arid')
ax4.axhline(y=-2, color='#f97316', linestyle='--', alpha=0.5, label='Moderate drought')
ax4.axhline(y=-4, color='#f43f5e', linestyle='--', alpha=0.5, label='Extreme drought')
ax4.fill_between(dT_drought, PDSI_subtrop, PDSI_arid, alpha=0.08, color='#f43f5e')

ax4.set_xlabel('Global warming (\u00b0C)', color='#94a3b8', fontsize=11)
ax4.set_ylabel('PDSI (Palmer Drought Index)', color='#94a3b8', fontsize=11)
ax4.set_title('Drought Severity Projections', color='#e2e8f0', fontsize=13, fontweight='bold')
ax4.legend(facecolor='#1e293b', edgecolor='#334155', labelcolor='#cbd5e1', fontsize=9)

plt.tight_layout()
plt.savefig('output.png', dpi=150, bbox_inches='tight', facecolor='#0a0a1a')
print("Hurricane and drought analysis complete.")
print(f"PI at SST=28\u00b0C: {calc_PI(np.array([28.0]))[0]:.1f} m/s")
print(f"PI at SST=32\u00b0C: {calc_PI(np.array([32.0]))[0]:.1f} m/s")
print(f"PI increase per \u00b0C SST: ~{(calc_PI(np.array([29.0]))[0]-calc_PI(np.array([28.0]))[0]):.1f} m/s")
print(f"RI probability at 28\u00b0C: {1/(1+np.exp(-0.8*(28-28)))*100:.0f}%")
print(f"RI probability at 30\u00b0C: {1/(1+np.exp(-0.8*(30-28)))*100:.0f}%")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

Key References

• Lenderink, G. & van Meijgaard, E. (2008). “Increase in hourly precipitation extremes beyond expectations from temperature changes.” Nature Geoscience, 1, 511–514.

• Abatzoglou, J. T. & Williams, A. P. (2016). “Impact of anthropogenic climate change on wildfire across western US forests.” Proceedings of the National Academy of Sciences, 113, 11770–11775.

• Rothermel, R. C. (1972). “A mathematical model for predicting fire spread in wildland fuels.” USDA Forest Service Research Paper INT-115.

• van Eeden, L. M. et al. (2020). “"; the number of animals killed and displaced by Australia’s 2019–20 bushfires.” Unpublished report, WWF-Australia.

• Emanuel, K. A. (1986). “An air-sea interaction theory for tropical cyclones.” Journal of the Atmospheric Sciences, 43, 585–604.

• Bhatia, K. T. et al. (2019). “Recent increases in tropical cyclone intensification rates.” Nature Communications, 10, 635.

• McDowell, N. et al. (2008). “Mechanisms of plant survival and mortality during drought.” New Phytologist, 178, 719–739.

• Junk, W. J. et al. (1989). “The flood pulse concept in river-floodplain systems.” Canadian Special Publication of Fisheries and Aquatic Sciences, 106, 110–127.

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