Move a barometer over a mountain-and-sea coast, deepen a low-pressure centre and read what pressure, wind, cloud and boiling point do.
The science
Pressure falls with height. Hydrostatic balance dp/dz = −ρ g with the ideal gas law and a constant lapse rate Γ = 6.5 K/km gives p(z) = pSL (1 − Γ z / T0)^(g/(R Γ)) (exponent 5.2559). Station pressure over a 4 km summit is therefore about 60 % of the sea-level value, and a weather map reduces every station to sea level (QFF) with the inverse formula before drawing isobars.
Mercury barometer. h = p / (ρHg g), ρHg = 13 595 kg/m³: 760 mm at 101 325 Pa.
Boiling point. Water boils when its vapour pressure equals the air pressure; the Antoine fit log₁₀ P[mmHg] = 8.07131 − 1730.63/(233.426 + T[°C]) gives 100 °C at sea level and about 90 °C near 3 km.
Pressure gradient force and wind. Per unit mass the force is −∇p/ρ. Away from the equator the Coriolis parameter f = 2 Ω sin φ turns the flow until the two balance: geostrophic wind Vg = |∇p| / (ρ f) blowing along the isobars with low pressure on the left (northern hemisphere). Around a curved low the gradient-wind balance V²/r + f V = (1/ρ) ∂p/∂r applies, with solution V = (−f r + √(f² r² + 4 r (1/ρ)∂p/∂r))/2; it is slower than the geostrophic wind. The low here has a Gaussian profile p = p∞ − Δp e^(−r²/2s²).
Surface friction. Near the ground the wind is slowed (×0.75 over sea, ×0.55 over land, ×0.4 over high mountains) and turned toward low pressure by 15° / 28°, which is why surface air spirals inward around a low.
Mountains and cloud. Wind blowing uphill is forced to rise at w = V·∇h. Rising air cools at about 9.8 K/km; the lifting condensation level is zLCL ≈ 125 (T − Td) metres, and cloud puffs are drawn where forced ascent is positive and the terrain is high enough.
Simplifications. A 300 km domain with one synthetic coast; the cyclone is a stationary Gaussian vortex added to a uniform background gradient (a linear superposition, not a full weather model); gradient wind uses the sea-level density; friction is a fixed factor and angle; northern hemisphere only; the cloud spiral and rain towers are schematic. Not a forecasting tool. Models built with Blender, scene by Three.js.