Climate Feedback Phase Portrait

Forcing

CO₂ radiative forcing ΔF 3.7 W/m²

Feedback strengths (W/m²/K)

Water vapor + lapse rate 1.15

Ice–albedo 0.30

Cloud 0.45

Live readout

Global ΔT

0.00 °C

Model time

0 yr

Net feedback λ

1.75

Equilibrium ΔT_eq

2.11 °C

How it works

Same zero-dimensional energy-balance ODE as the 3D globe version, but plotted directly in its own state space instead of painted onto a sphere:

C · dT/dt = ΔF − λ·T
λ = λ_planck − (λ_wv + λ_ice + λ_cloud)
ΔT_eq = ΔF / λ   (the point where the line crosses dT/dt = 0)

The top panel is a phase portrait: the horizontal axis is the state T (global temperature anomaly), the vertical axis is its rate of change dT/dt. Because the ODE is linear, dT/dt vs T is a straight line of slope −λ/C. The bright dot is the live state; it always slides along this exact line toward wherever it crosses zero — that crossing *is* the equilibrium ΔT_eq.
Arrows along the T-axis show the flow direction at each T: pointing right (warming) where the line is above zero, left (cooling) where it's below. If sliders push λ ≤ 0, the entire visible line sits above zero — there's no crossing, so the state can only slide right forever (runaway).
λ_planck ≈ 3.2 W/m²/K — the fixed stabilizing blackbody response. Water vapor + lapse rate, ice–albedo and cloud are positive feedbacks that subtract from it.
The bottom strip scrolls T(t) itself in model-years, with a dashed line at the current ΔT_eq so you can see the trajectory close in on (or diverge from) it in real time — the same information the 3D globe encoded as cell color, here read directly off two 2D plots.

⚠ Feedbacks exceed the Planck response — no stable equilibrium (runaway regime)

dT/dt line · equilibrium at zero-crossing