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Rivulet Approach to Rates of Preferential Infiltration

Soil Science Section, Dep. of Geography, Univ. of Bern, Hallerstrasse 12, 3012 Bern, Switzerland

View larger version (43K): [in this window] [in a new window]   FIG. 1. Schematic representation of a rivulet during Stokes flow. F, thickness of the water film; f, thickness variable; df, thickness differential; l, length of contact between mobile soil moisture of the rivulet and the soil-water system at rest; H(t), vertical length of rivulet; G, weight of rivulet; v(f), velocity of the water at distance f from the parts at rest; , viscosity causing momentum dissipation toward the stationary parts.

View larger version (25K): [in this window] [in a new window]   FIG. 2. Properties of a rivulet in time and space (TI, ZI, and wR are scaling factors). (a) Characteristics of wetting and draining fronts and of four laminae. (b) w(Z,t) at four depths: z < ZI (twice), z = ZI, z > ZI. (c) w(Z,t) at four times: t < TS, TS < t < TI, t = TI, t > TI.

View larger version (30K): [in this window] [in a new window]   FIG. 3. Measured volumetric soil moisture, (Z,t), and capillary head, h(Z,t), at depths 0.1 m and 0.2 m due to infiltration at a rate of qS = 45.5 mm h–1 during TS = 1h for Run 10.

View larger version (27K): [in this window] [in a new window]   FIG. 4. Definitions of parameters and variables, shown for Run 7, depth 0.1 m. Times: thW, arrival of first pressure; thP, time of attaining pressure maximum; tW, arrival of first (measurable) moisture increase; tP, time of attaining steady soil moisture; TS, end of water input to the soil surface; tD, arrival of draining front; tF, end of measurements. Capillary heads: hinit, before infiltration; hmax, maximum. Volumetric soil moisture: in, initial; max, maximum; F, end of measurements; out, end of drainage or trailing wave; div (= out – in), divergence; wS (= max – out), amplitude of moisture wave.

View larger version (32K): [in this window] [in a new window]   FIG. 5. Superposition of three rivulet ensembles applied to the data of Run 6. sup(Z,t) declines faster than (Z,t) because div > 0 was ignored in the analysis.

View larger version (23K): [in this window] [in a new window]   FIG. 6. Ten rivulet ensembles applied to the data of Run 3, depth 0.1 m. Calibration: Approach applied to increasing limb of (Z,t). Validation: Superimposed trailing waves compared with data.

View larger version (29K): [in this window] [in a new window]   FIG. 7. Linear regressions of measured vs. modeled mobile soil moisture of trailing wave (upper plot) and of residuals of modeled data (lower plot) for Run 3. The respective differences are not significant.

View larger version (23K): [in this window] [in a new window]   FIG. 8. Film thicknesses of the rivulet ensembles vs. volumetric soil moisture for Runs 1–10. Input rates: 15.3 mm h–1; 28.8 mm h–1; 45.5 mm h–1 at depth (a) 0.1 m and (b) 0.2 m. * ± 1 SE indicates boundary between arriving-only and flow-through rivulets. F(D = ) represents the upper and lower limits of the film thickness where diffusivity equals kinematic viscosity (Germann et al., 1997).

View larger version (22K): [in this window] [in a new window]   FIG. 9. Sum of contact lengths of ensembles vs. volumetric soil moisture for Runs 1–10. Input rates: 15.3 mm h–1; 28.8 mm h–1; 45.5 mm h–1 at depth (a) 0.1 m and (b) 0.2 m. * ±1 SE indicates boundary between arriving-only and flow-through rivulets.

View larger version (31K): [in this window] [in a new window]   FIG. 10. Modeled and measured mobile soil moisture, w(Z,t) = [(Z,t) – out], and volumetric flux densities, q(Z,t). (a) Run 6, depth 0.1 m: typical evolution of soil moisture and flow; (b) Run 6, depth 0.2 m: typical evolution of soil moisture and flow; (c) Run 2, depth 0.1 m: qmax qS due to in > *; (d) Run 5, depth 0.2 m: q(Z,t) is much reduced compared with other runs due to max *.