Heat Dome Lab (2D): Subsiding Ridge, Mixed Layer and Soil-Drying Feedback

Subsidence warming

A sinking air parcel is compressed adiabatically and keeps its potential temperature θ = T (1000/p)^κ, κ = R/c_p = 0.2857. At a fixed height the air warms at the rate w_s dθ/dz with large-scale subsidence w_s = D z (D = horizontal divergence, 10^-6 /s units here) and a free-atmosphere gradient of 4 K/km. At D = 4×10^-6 /s the air at 3 km sinks about 1 km per day. The θ isolines in the picture are carried down by this flow.

Surface energy balance

Available energy Q = 0.9 (0.78 S − L_net), S the half-sine diurnal solar flux, L_net = 95 + 5.5(θ_m − 290) W/m². It splits into latent heat LE = EF·Q and sensible heat H = (1 − EF) Q with evaporative fraction EF = 0.75 min(1, w/0.5): wet soil evaporates, dry soil heats the air. Soil water (150 mm capacity) loses LE/L_v and is not refilled (no rain).

Mixed layer (Tennekes / Stull slab)

dθ_m/dt = (H/(ρc_p) + w_e Δθ)/z_i, w_e = 0.2 H/(ρc_p Δθ), dz_i/dt = w_e − D z_i. Subsidence pushes the inversion down, so the same sunshine heats a shallower layer and every afternoon is hotter. The free-air profile relaxes to its climatology on 1.5 days (weakened under a block) and is cooled by 0.6 K/day radiation. At night the surface cools by the chosen amount below the residual layer.

Thickness

1000-500 hPa thickness Z = (R_d/g) T_mean ln 2, about 20 m per kelvin of layer-mean temperature.

Honest simplifications

• Single independent columns (no horizontal advection except the relaxation term); the ridge position is fixed.
• Radiation, relaxation time, entrainment constant and evaporative-fraction curve are textbook-style parameterisations tuned for plausible magnitudes (about 21-25 C normal, 35-45 C dome); they are not fitted to a real event, and no humidity, clouds, wind, urban surface or vegetation shading is modelled.

• Compare "Heat dome" with "Control": the dome layer stays about 1 km deep and each afternoon is hotter.
• Press "Parched soil" then "Wet, irrigated soil": same ridge, different Bowen ratio.
• Raise the speed to 8x and watch the daily-maximum graph climb for six days.
• Use "Hot nights": the minima stay high, the health-relevant part of a heat wave.
• Switch off the theta isolines to see only the mixed layer.