Once the top of a soil has dried, water can only leave as vapour creeping up through the dry layer. Watch that layer thicken day by day, see why the wind soon stops mattering, and test what a gravel mulch does.
Runs 20 days with the current weather for 0, 2, 5 and 10 cm of gravel and lists the water lost and the final dry-layer depth.
Wind from 0.5 to 8 m/s. Prediction: once even a thin dry layer exists, wind barely changes the water lost through the air resistance; its larger effect in the full model is that it cools the ground.
The science
Why a dry layer. Liquid water in a soil can follow the drying surface only while capillary flow is fast enough. Once the top layer has dried, evaporation moves below it to a front at depth zf, and water leaves only as vapour diffusion through the air-filled pores above the front.
Vapour flux. Resistances in series, as for an electric circuit: E = (ρv,sat(Tf) − RH · ρv,sat(Tair)) / (ra + rg + rs) with the soil term rs = zf / Deff, the gravel term rg = hg / Deff,g and the air term ra = ln²(2/0.01)/(0.41² u) (neutral wind profile, roughness 1 cm). Saturation vapour density uses the Tetens vapour pressure and the ideal-gas law. The effective diffusivity in a dry porous layer follows Millington and Quirk, Deff = Dv ε10/3 / φ2 with Dv = 2.12×10-5 (T/273.15)1.75 m²/s.
Front growth. Each kilogram of vapour that escapes empties the soil just below the dry layer: dzf/dt = E / (ρw Δθ). With constant forcing this integrates to zf² = z0² + 2 Deff Δρ t / (ρw Δθ), the square-root-of-time law that is tested below. Because rs grows with zf, the evaporation rate falls as 1/zf, and the wind, which only changes ra (and cools the ground a little), matters less and less.
Heat. The sunlight is S(t) = Smax sin(π(h−6)/12) between 06:00 and 18:00. The ground-surface temperature is the air temperature plus (1−albedo) S / hc with hc = 10 + 4u W/m²/K (a linearised mix of long-wave and convective exchange), minus 2 K on clear nights. Its first four daily harmonics are propagated downward by heat conduction: T(z,t) = T̄ + Σn An e−z√n/d cos(nωt − φn − z√n/d) with damping depth d = √(2κ/ω) (here about 12 cm for κ = 5×10-7 m²/s). The front therefore sees a smaller and later temperature wave the deeper it sinks, and a deep layer evaporates mostly in the evening.
Potential rate for the comparison line is Priestley-Taylor, 1.26 Δ/(Δ+γ) Rn / λ, with net radiation taken as 0.75(1−albedo)S − 50 W/m².
Honest simplifications: the surface temperature is a skin approximation, not a full energy balance; only the first four daily harmonics are propagated into the soil; liquid water flow below the front, adsorption of night-time vapour and dew, rain, plants, cracks and salts are not modelled; the dry-layer porosity, the 2 K night cooling, the heat-exchange coefficient and the thermal diffusivity are typical illustrative values, not measurements of a particular soil. The vertical scale of the picture is stretched 2x. Models built with Blender and Three.js.
Educational model; no affiliation.