🪸 Coral Bleaching Simulator

AR(1) Process with Seasonal Forcing

T(t) = μ + trend·t + A·sin(2πt/365 + φ) + ε(t)
where ε(t) = ρ·ε(t-1) + σ√(1-ρ²)·η(t)

Parameters

• μ (mean): Baseline temperature
• A (amplitude): Strength of seasonal cycle (0 = no seasons)
• φ (phase): When the hot season occurs (peak day)
• trend: Climate change warming rate (°C/year)
• ρ (autocorrelation): Persistence of temperature anomalies
  • High ρ (0.9+) = sustained heat waves
  • Low ρ (0.3) = rapidly fluctuating temps
• σ (variability): Daily temperature noise

How It Works

The model combines three components:

1. Seasonal cycle: Regular annual variation (sine wave)
2. Long-term trend: Linear warming or cooling
3. AR(1) noise: Day-to-day variations with memory
   • Yesterday's anomaly influences today
   • Creates realistic "heat wave" events

What is Coral Bleaching?

Corals are animals that host millions of tiny algae (zooxanthellae) in their tissues. These algae photosynthesize and provide up to 90% of the coral's energy. When water gets too warm, the algae's photosynthesis malfunctions, producing harmful reactive oxygen species (ROS) instead of food. The coral expels the algae to protect itself, turning white ("bleaching"). Without their algae, corals can starve and die.

How This Simulator Works

Step 1: Generate Ocean Temperature

The simulator creates realistic multi-year sea surface temperature (SST) patterns that include:

• Seasonal cycles (summer/winter)
• Long-term warming trends (climate change)
• Heat waves and cold spells with realistic persistence

Step 2: Biological Response

The model tracks three key processes:

1. Symbiont Growth: Algae multiply fastest at their optimal temperature
2. ROS Production: When temperature exceeds the bleaching threshold, damaged photosynthesis creates harmful ROS
3. Expulsion: High ROS levels trigger the coral to expel algae

What You Can Explore

• Heat wave structure: Compare sustained vs. fluctuating warming
• Recovery dynamics: Can corals recover between bleaching events?
• Climate scenarios: How do different warming rates affect survival?
• Coral resilience: What makes some corals more tolerant than others?

Model Equations

State Variables:

• S(t): Symbiont density (cells/cm²)
• R(t): ROS concentration (arbitrary units)
• T(t): Sea surface temperature (°C)

Differential Equations:

Symbiont Growth (Logistic with Temperature Dependence):

Temperature effect f(T) is Gaussian-shaped, maximized at T_opt with width σ

Symbiont Loss:

Baseline loss has density-dependent protection (p = densityProtection parameter). ROS-driven expulsion follows Michaelis-Menten kinetics.

ROS Dynamics:

Baseline ROS production is proportional to symbiont density. Heat stress (T > threshold) causes exponential increase in ROS production.

Numerical Methods

The coupled ODEs are integrated using the 4th-order Runge-Kutta method (RK4) with a time step of Δt = 0.1 days. This explicit method provides good accuracy while remaining computationally efficient for multi-year simulations.

Mortality: Death occurs when symbiont density remains below the critical threshold (default 20% of K) for a specified number of consecutive days (default 30 days).

SST Model

Sea surface temperature is generated using an AR(1) process with seasonal forcing:

where η(t) ~ N(0,1) is white noise. The scaling factor √(1-ρ²) ensures constant variance regardless of autocorrelation.