Tropical Rainfall: Self-Organized Criticality

Power-law storm size distributions from atmospheric moisture dynamics

SOC in Rainfall

Tropical rainfall exhibits self-organized criticality: moisture accumulates locally until a threshold is crossed, triggering convection that spreads to neighbors — creating cascades.

Moisture dynamics: dwᵢ/dt = r - P(wᵢ) + Σⱼ fᵢⱼ Convective trigger: P > 0 when w > w_c Column Water Vapor (CWV): CWV_c ≈ 48 mm (tropics) Storm size distribution: P(S) ~ S^(-τ), τ ≈ 1.5-2.0 Power-law: scale-free storms (Neelin et al. 2009, Peters 2006)

The critical point w_c acts as an attractor: the atmosphere self-tunes to maintain moisture near threshold, producing storms at all scales from cells to MJO (Madden-Julian Oscillation).

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