Soil Evaporation Lysimeter 2D

Why a soil dries in two stages

Water leaves a wet soil surface at the rate the atmosphere can take it. Stage 1 (energy-limited) lasts while capillary flow from deeper layers can resupply the surface faster than the air removes water: the rate equals the evaporative demand Ep. When the surface layer dries out, the unsaturated hydraulic conductivity there collapses by orders of magnitude and the soil can no longer keep up. In stage 2 (soil-limited) the rate falls with time, because water must now reach the surface through an ever thicker dry layer. A sandy soil has a high conductivity but small capillary lift, so its stage 1 ends early; a clay loam conducts slowly, so it also runs out of supply, but it holds more water in the pores that stay connected.

The model: the Richards equation

Water flow in the unsaturated column is solved in one dimension, with pressure head h (cm, negative in unsaturated soil) and height z above the bottom: C(h) ∂h/∂t = ∂/∂z [ K(h) (∂h/∂z + 1) ], where C = dθ/dh is the specific capacity. Retention and conductivity follow van Genuchten (1980) and Mualem (1976): Se = [1 + (α|h|)n]−m, m = 1 − 1/n, θ = θr + (θs − θr) Se, K = Ks √Se [1 − (1 − Se1/m)m]2, with Carsel and Parrish parameters for the four soils. The 60 cells are integrated implicitly with the mass-conservative modified Picard iteration of Celia et al. (1990) and an adaptive time step.

The atmosphere

The demand is the FAO-56 Penman-Monteith reference evaporation ET0 = [0.408 Δ (Rn − G) + γ (900/(T + 273)) u2 (es − ea)] / [Δ + γ (1 + 0.34 u2)] with the lamp as net radiation Rn, the fan as wind speed u2, and the vapour deficit from temperature and humidity (soil heat flux G neglected). The surface flux is the smaller of this demand and what the soil can deliver with the surface at the air-dry head hair = −105 cm: q = K [ (h1 − hair)/(Δz/2) − 1 ]. Mulch is modelled as a demand reduction (1 − 0.75 c).

Honest simplifications

Isothermal liquid flow only: no vapour diffusion in the dry layer (which dominates real stage 2 in very dry soil), no heating of the surface, no hysteresis or soil heterogeneity, and the Penman-Monteith grass formula stands in for a bare-soil energy balance. The qualitative two-stage behaviour and the soil ranking are robust; absolute rates are not predictions for a field.

• Run the Loam preset for 10 days: the rate stays at the demand for about a day, then falls. The orange line marks the start of stage 2.
• Compare Sand and Clay loam on the cumulative graph: which loses more water in 20 days, and why?
• Switch the bottom boundary to Water table: after the surface dries the rate settles at a steady value fed by capillary rise.
• Cover the soil with mulch (90 %): stage 1 is stretched, and the total loss over 20 days drops.
• Turn the fan up in dry air versus humid air: the wind matters only when there is a vapour deficit.