This is a height–time (Hovmöller) cross-section of the polar stratospheric column, solved as a 1-D finite-difference PDE on 26 vertical levels from the ground to ~50 km — a genuinely different numerical model from a single-level scalar simulation. At every level i the zonal wind U and polar-cap temperature anomaly T evolve as:
dU_i/dt = -k·A_i(t)·max(0,U_i) + γ·(U0_i - U_i) + D∇²U_i
dT_i/dt = β·max(0,-dU_i/dt) - α·(T_i - T0) + D∇²T_i
U0_i is the climatological jet profile (peaking near 10 hPa). A_i(t) is the local wave-forcing amplitude, which is NOT the surface value you set instantaneously — it lags behind it, integrated as its own first-order relaxation with a level-dependent time constant τ_i = z_i / c_g. That reproduces the finite vertical group velocity c_g at which planetary waves actually carry momentum upward, so forcing set at the surface only reaches 10 hPa (~32 km) after several simulated days — watch the color front tilt upward-and-rightward across the strip below.
- Wave amplitude — sets the surface-injected forcing; stronger and more sustained forcing decelerates U at every level it reaches, and can push it through zero at 60°N/10 hPa (the formal SSW criterion, shown by the wind panel flipping from blue to red).
- m = 1 vs m = 2 — real planetary wavenumber-1 disturbances are less strongly refracted with height and penetrate deep into the stratosphere with a slower, sustained deceleration (matching displacement-type SSWs); wavenumber-2 forcing dissipates faster with altitude, producing a shallower but quicker deceleration (matching split-type SSWs) — modeled here via a wavenumber-dependent vertical attenuation e^(-κ·z).
- Downward temperature descent — once a level warms from forced subsidence, vertical diffusion D∇²T spreads that anomaly toward neighboring levels over subsequent days, reproducing the well-documented downward propagation of the SSW temperature/circulation signal toward the troposphere.
Real-world relevance: SSWs are the strongest documented case of stratosphere–troposphere coupling — the weakened-vortex signal shown descending in the right-hand profile panel foreshadows a shift in the surface jet stream and storm track 4–8 weeks later, a key source of sub-seasonal cold-air-outbreak predictability.