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Climate Tipping Points & Sea Level Dynamics

1. Tipping Point Activation Condition

$$ \text{Risk} = \begin{cases} 1 & \text{if } \Delta T > T_{\text{threshold}} \\ 0 & \text{otherwise} \end{cases} $$

Thresholds may include:

• \(1.5^\circ C\) – permafrost thaw acceleration
• \(2.0^\circ C\) – Amazon forest dieback

2. Sea Level Rise Estimation

$$ SLR = \gamma \cdot \Delta T \cdot Y $$

Where:

• \(\gamma\): sensitivity factor (cm/°C/decade)
• \(Y\): number of decades into the future

3. Non-Linear Feedback Risk Potential

$$ R_f = \frac{1}{1 + e^{-k(\Delta T - T_c)}} $$

This sigmoid function estimates the probability of triggering irreversible feedbacks, where \(k\) determines slope and \(T_c\) is the critical temperature threshold.

These mathematical insights help track how close we stand to the precipice of profound planetary shifts.