Alpine Pass Weather Explorer (2D)

Orographic lift and the lifting condensation level

Wind pushed up a mountain lifts air parcels. A rising parcel expands into lower pressure and cools without exchanging heat (adiabatic). While unsaturated it cools at the dry adiabatic lapse rate Gd = g / cp = 9.8 K/km. Its dew point falls more slowly, so the two meet at the lifting condensation level, z_LCL ~ 125 m per K of (T - Td) (here computed with Bolton's formula, T_LCL = 1/(1/(Td-56) + ln(T/Td)/800) + 56).

Moist adiabat and latent heat

Above the LCL condensation releases latent heat Lv, so the parcel cools more slowly: Gm = g (1 + Lv rs / (Rd T)) / (cp + Lv^2 rs eps / (Rd T^2)), about 6.5 K/km at 0 C and 4.3 K/km at 20 C near sea level. The simulator integrates this pseudo-adiabat in 12 m steps along the flow line with the saturation mixing ratio rs = eps es / (p - es) and es = 6.112 exp(17.67 T / (T + 243.5)) hPa.

Precipitation and the foehn effect

A fraction e (precipitation efficiency) of the condensate formed on the way up leaves the parcel as rain or snow; the rest stays as cloud water. Rain rate on a column is R = dp * rho * U * D / dx (condensate removed per step, air density, wind, lifted layer depth D, grid spacing). On the lee side the cloud water evaporates first (cooling on the moist adiabat), then the dry air sinks and warms at 9.8 K/km. Because it lost water vapour and latent heat is not given back, the air arrives in the lee valley warmer and drier than it started: the foehn (Fohn, chinook). With e = 0 the process is reversible and the parcel comes back to its start temperature.

Blocking and the Froude number

Stable air does not always climb the whole ridge. With buoyancy frequency N^2 = (g / T)(Gd - Genv) the Froude number is Fr = U / (N H). Following Sheppard's dividing-streamline idea, for Fr < 1 only air above z = H (1 - Fr) crosses the ridge, so the lift is reduced to Fr H (switchable). This is a one-line model, not a numerical weather prediction.

Snow line, snow cover and melt

The surface air temperature at each grid cell comes from the parcel temperature and the lapse rate to the actual ground height. Precipitation falls as snow when the temperature is below about 0 C (linear transition over 3 K), and a degree-day model melts M = ddf * max(0, T) mm of water equivalent per day. The day-night swing moves the 0 C level up and down. The snowline readouts are the lowest elevation along the selected line with more than 25 mm water equivalent.

Honest simplifications

The flow is terrain-following along x on a 250 m grid (no gravity waves, no turbulence, no valley winds, no Coriolis force); humidity above the start decays with a 2.5 km scale height; the precipitation layer depth is a tunable parameter; clouds, rain and snow particles are an illustration of the computed fields, props are drawn enlarged, and the terrain is an invented alpine pass (an analytic ridge plus a Blender-baked relief map), not a real place. The three checks in the panel recompute the physics on throw-away models.

• Press Guided tour and follow one air parcel from the valley, through the cloud base and over the crest to the warm lee valley.
• Set the efficiency to 0 (preset "Reversible"): the lee valley no longer warms. Raise it to 100 %: the foehn warming is largest.
• Drop the valley temperature to -2 C (preset "Cold snowy front") and watch the snow cover and the snowline move down.
• Slide the flow line y from the pass (0) to the ridge (about -4.5) and compare the lift, rain and foehn warming.
• Choose the "Blocked flow" preset or lower the wind below about 10 m/s: the Froude number drops under 1 and the lift shrinks.
• Use "Fast-forward 5 days", then change the melt factor or the day-night swing and watch the snow melt in the lee first.