Desert Sandstorm

What is modelled

A desert oasis with a 10 m weather mast. When the storm front arrives the wind rises; once the friction velocity passes the threshold, sand grains start to hop (saltation), their impacts kick up fine dust, turbulence lifts the dust, and the dust cuts the visibility. The page follows that chain of cause and effect with standard aeolian-science formulas, and the grains you see are integrated with real drag.

Equations

• Wind profile near the ground: u(z) = (u*/κ) ln(z/z0) with κ = 0.4 and u* = κ U10 / ln(10/z0).
• Threshold for moving sand (Bagnold): u*t = A √((ρp − ρa) g d / ρa), A = 0.1, multiplied by the Fecan moisture factor √(1 + 1.21 (w − w')0.68) for wet soil (w' set by 5 % clay).
• Saltation flux per metre of width: q = 2.61 (ρa/g) u*3 (1 − u*t/u*)(1 + u*t/u*)2 √(d / 250 µm).
• Dust emission by sandblasting: F = α q, α of order 10⁻⁵ per metre. Dust falls at the Stokes speed ws = (ρp − ρa) g d2 / (18 μ).
• Steady suspension (Rouse): turbulent diffusion K = κ u* z against settling gives C(z) = Cref (z/zref)−b, b = ws/(κ u*), Cref = F / ws.
• Visibility: extinction σ = σbg + 3 Q C / (4 ρp r) with Q = 2, and Koschmieder's V = 3.912 / σ (2 % contrast threshold). The fog in the 3D view uses exactly this V.
• The dust level follows the equilibrium with a response time of fetch / wind speed, and decays by settling when the wind drops.

Checks run in the page

• Stokes settling speed against a numerical integration of nonlinear drag.
• The log wind law against a numerical integral of the shear.
• The Rouse exponent against a finite-volume solution of the diffusion-settling balance.
• Koschmieder visibility against marching a beam through haze, and the textbook visibilities for 1 mg/m3 and 1 g/m3 of 5 µm dust.

Honest simplifications

• Neutral atmosphere, flat terrain for the physics; the dunes are only scenery. The dust wall is drawn at a reduced scale (a real haboob wall is a kilometre high) and its arrival time is fixed at 90 s of simulation time.
• The dust emission efficiency α, the saltation prefactor and the mass-extinction assumptions (Q = 2, one particle size) are representative values; measured dust emission varies by orders of magnitude between soils.
• Saltating grains are a visual sample whose number follows q; their rebound and splash rules are simplified, and their count is not a measurement.
• Sun dimming uses the column optical depth of the equilibrium profile up to a 300 m mixing height.

• Press Summon the storm front: first the wind rises, then grains start hopping once u* passes the threshold, then fine dust is lifted and the distant objects fade.
• Pick Wet soil after rain: the Fecan moisture factor raises the threshold, the grains stay put and the air stays clear at the same wind speed.
• Compare Coarse sand, fine dust with Fine silt, big dust: bigger grains need more wind, bigger dust settles faster so visibility recovers sooner.