Water flux and sediment transport within a forested landscape: the role of connectivity,subsurface flow,and slope length scale on transport mechanism

The connectivity and upscaling of overland runoff and sediment transport are important issues in hillslope hydrology to identify water flux and sediment transport within landscape. These processes are highly variable in time and space with regard to their interactions with vegetation and soil surface conditions. The generation of overland runoff and its spatial connectivity were examined along a slope to determine the variations in the transport mechanism of runoff and soil particles by rain splash and overland runoff. Field experiments were conducted by erosion plots on a steep hillslope at lengths of 5, 10, and 15 m. The overland runoff connectivity and flow transport distance decreased with the slope length, while spatial variability of infiltration increased significantly with the slope length. Observation of subsurface flow revealed that surface soil and litter layer could have important role in water transport. However, the surface soil water content and water flux transport along the slope was highly variable for different storm events; the variability was related to the complexity of the system, mainly by way of the initial wetness conditions and infiltration characteristics. Only net rain‐splashed soil was measurable, but examination of the water flux, overland runoff and sediment transport connectivity, characteristics of sheetwash, and the variability in spatial infiltration indicated an increase in the contribution of the rain splash transport mechanism along the slope. Copyright © 2013 John Wiley & Sons, Ltd.     

ERRORS OF KINEMATIC-WAVE AND DIFFUSION-WAVE APPROXIMATIONS FOR SPACE-INDEPENDENT FLOWS ON INFILTRATING SURFACES

Error equations for the kinematic-wave and diffusion-wave approximations were derived under simplified conditions for space-independent flows occurring on infiltrating planes or channels. These equations specify error as a function of time in the flow hydrograph. The kinematic-wave, diffusion wave and dynamic-wave solutions were parameterized through a dimensionless parameter γ which is dependent on the initial conditions. This parameter reflects the effect of initial flow depth, channel-bed slope, lateral inflow and channel roughness when the initial condition is non-vanishing; and it reflects the effect of bed slope, channel roughness, lateral inflow and infiltration when the initial condition is vanishing. The error equations were found to be the Riccati equation.     

Do not only connect: a model of infiltration‐excess overland flow based on simulation

The paper focusses on connectivity in the context of infiltration‐excess overland flow and its integrated response as slope‐base overland flow hydrographs. Overland flow is simulated on a sloping surface with some minor topographic expression and spatially differing infiltration rates. In each cell of a 128 × 128 grid, water from upslope is combined with incident rainfall to generate local overland flow, which is stochastically routed downslope, partitioning the flow between downslope neighbours. Simulations show the evolution of connectivity during simple storms. As a first approximation, total storm runoff is similar everywhere, discharge increasing proportionally with drainage area. Moderate differences in plan topography appear to have only a second‐order impact on hydrograph form and runoff amount. Total storm response is expressed as total runoff, runoff coefficient or total volume infiltrated; each plotted against total storm rainfall, and allowing variations in average gradient, overland flow roughness, infiltration rate and storm duration. A one‐parameter algebraic expression is proposed that fits simulation results for total runoff, has appropriate asymptotic behaviour and responds rationally to the variables tested. Slope length is seen to influence connectivity, expressed as a scale distance that increases with storm magnitude and can be explicitly incorporated into the expression to indicate runoff response to simple events as a function of storm size, storm duration, slope length and gradient. The model has also been applied to a 10‐year rainfall record, using both hourly and daily time steps, and the implications explored for coarser scale models. Initial trails incorporating erosion continuously update topography and suggest that successive storms produce an initial increase in erosion as rilling develops, while runoff totals are only slightly modified. Other factors not yet considered include the dynamics of soil crusting and vegetation growth. Copyright © 2014 John Wiley & Sons, Ltd.     

Testing a theoretical resistance law for overland flow on a stony hillslope

Overland flow, sediments, and nutrients transported in runoff are important processes involved in soil erosion and water pollution. Modelling transport of sediments and chemicals requires accurate estimates of hydraulic resistance, which is one of the key variables characterizing runoff water depth and velocity. In this paper, a new theoretical power–velocity profile, originally deduced neglecting the impact effect of rainfall, was initially modified for taking into account the effect of rainfall intensity. Then a theoretical flow resistance law was obtained by integration of the new flow velocity distribution. This flow resistance law was tested using field measurements by Nearing for the condition of overland flow under simulated rainfall. Measurements of the Darcy–Weisbach friction factor, corresponding to flow Reynolds number ranging from 48 to 194, were obtained for simulated rainfall with two different rainfall intensity values (59 and 178 mm hr⁻¹). The database, including measurements of flow velocity, water depth, cross-sectional area, wetted perimeter, and bed slope, allowed for calibration of the relationship between the velocity profile parameter Γ, the slope steepness s, and the flow Froude number F, taking also into account the influence of rainfall intensity i. Results yielded the following conclusions: (a) The proposed theoretical flow resistance equation accurately estimated the Darcy–Weisbach friction factor for overland flow under simulated rainfall, (b) the flow resistance increased with rainfall intensity for laminar overland flow, and (c) the mean flow velocity was quasi-independent of the slope gradient.     

Hydrological simulation of a conservation bench terrace system in a subhumid climate

Abstract

A finite element model to simulate runoff and soil erosion from agricultural lands has been developed. The sequential solutions of the governing differential equations were found: Richards' equation with a sink term for infiltration and soil water dynamics under cropped conditions; St Venant equation with kinematic wave approximation for overland and channel flow; and sediment continuity equation, for soil erosion. The model developed earlier has been improved to simulate erosion/deposition in impoundments and predicted and observed soil loss values were in reasonably good agreement when the model was tested for a conservation bench terrace (CBT) system. The finite element model was extensively applied to study the hydrological behaviour of a CBT system vis-à-vis the conventional system of sloping borders. The model estimates runoff and soil loss reasonably well, under varying conditions of rainfall and at different crop growth stages. The probable reasons for discrepancies between observation and simulation are reported and discussed. Sensitivity analysis was carried out to study the effect of various hydrological, soil and topographical parameters, such as ratio of contributing to receiving areas, weir length, depth of impoundment, slope of contributing area, etc. on the flow behaviour in a CBT system.     

Scale effects of Hortonian overland flow and rainfall‐runoff dynamics: laboratory validation of a process‐based model

Hortonian runoff was measured in the laboratory from uniform slopes of lengths of 1·5, 3·0, and 6·0 m for steady, high‐intensity rainstorms with durations of 1·0 to 7·5 min. A clear reduction in runoff per unit slope length was found as slope lengths were increased. This effect becomes more pronounced with decreasing storm duration. The runoff data were used to validate a simple process‐based model that combines the Philip‐two‐term infiltration equation with the kinematic wave overland flow principle. The predicted and experimental results agreed well. Laboratory findings were extrapolated with the aid of the model to slopes and rainfall durations similar to those found under West African conditions. The calculated reduction of runoff per unit length is similar to reported observations. Thus, this process‐based model can largely explain the phenomenon of runoff reduction with increasing slope length. Copyright © 2002 John Wiley & Sons, Ltd.     

Terrestrial laser scanning soil surfaces: a field methodology to examine soil surface roughness and overland flow hydraulics

Conventional roughness–resistance relationships developed for pipe and open‐channel flows cannot accurately describe shallow overland flows over natural rough surfaces. This paper develops a new field methodology combining terrestrial laser scanning (TLS) and overland flow simulation to provide a high‐resolution dataset of surface roughness and overland flow hydraulics as simulated on natural bare soil surfaces. This method permits a close examination of the factors controlling flow velocity and a re‐evaluation of the relationship between surface roughness and flow resistance. The aggregate effect of flow dynamics, infiltration and depression storage on retarding the passage of water over a surface is important where runoff‐generating areas are distant from well‐defined channels. Experiments to separate these effects show that this ‘effective resistance’ is dominated by surface roughness. Eight measurements of surface roughness are found to be related to flow resistance: standard deviation of elevations, inundation ratio, pit density (measured both perpendicular and parallel to the flow direction), slope, median depth, skewness of the depth distribution and frontal area. Hillslope position is found to affect the significant roughness measures. In contrast, infiltration rate has little effect on the velocity of water fronts advancing over the soil surfaces examined here and the effect of depression storage is limited. Overland flow resistance is depth dependent where complex microtopographic structures are progressively inundated. Copyright © 2010 John Wiley & Sons, Ltd.     

An accurate time integration method for simplified overland flow models

An accurate time integration method for the diffusion-wave and kinematic-wave approximated models for the overland flow is proposed. The discretization of the first- and second-order spatial derivatives in the basic equation is obtained by using the second-order Lax–Wendroff and the three-point centred finite difference schemes, respectively. For the solution in time, the system of ordinary differential equations, obtained by the linearization of the celerity and of the hydraulic diffusivity by Taylor series expansions, is integrated analytically. The stability and the numerical dissipation and dispersion are investigated by the Fourier analysis. A proper Courant number, and the corresponding time step for the numerical simulations can be established. In addition, the proposed diffusion-wave and kinematic-wave models are straightforwardly extended to the two-dimensional flow. Test cases for both one- and two-dimensional problems, compare the solutions of the diffusion-wave and kinematic-wave models with analytical solutions, with experimental results and with numerical solutions obtained by the Saint–Venant equations. These simulations show that the proposed numerical–analytical models accurately predict the overland flow for several situations, in particular for unsteady rainfall rate and for spatial variations of the surface roughness.     

Study on effect of surface roughness on overland flow from different geometric surfaces through numerical simulation

Effect of variability in surface roughness on overland flow from different geometric surfaces is investigated using numerical solution of diffusion wave equation. Three geometric surfaces rectangular plane, converging and diverging plane at slopes 1 to 3% are used. Overland flow is generated by applying rainfall at constant intensity of 10 mm/h for period 30 min and 100 min. Three scenarios of spatial roughness conditions viz. roughness increasing in downstream direction, roughness decreasing in downstream direction and roughness distributed at random are considered. Effect of variability of roughness on overland flow in terms of depth, velocity of flow and discharge along the distance from upstream to downstream for different geometric surfaces are discussed in detail. Results from the study indicate that roughness distribution has significant effect on peak, time to peak and overall shape of the overland flow hydrograph. The peak occurs earlier for the scenario when roughness increases in downstream direction as compared to scenario when roughness is decreasing in downstream for all three geometric surfaces due to very low friction factor and more velocity at the top of the domain. The converging plane attains equilibrium state early as compared to rectangular and diverging plane. Different set of random values result in different time to peak and shape of hydrograph for rectangular and diverging plane. However, in case of converging plane, the shape of computed hydrographs remains almost similar for different sets of random roughness values indicating stronger influence of converging geometry than effect due to variation of roughness sequence on computed runoff hydrograph. Hierarchically, the influence of geometry on overland flow is stronger than the influence of slope and the influence of slope is stronger than the influence of roughness. Copyright © 2013 John Wiley & Sons, Ltd.     

Depth distribution of interrill overland flow and the formation of rills

A Gumbel distribution for maxima is proposed as a model for the depths of interrill overland flow. The model is tested against three sets of field measurements of interrill overland flow depths obtained on shrubland and grassland hillslopes at Walnut Gulch Experimental Watershed, southern Arizona. The model is found to be a satisfactory fit to 81 of the 90 measured distributions. The shape δ and location λ parameters of all fitted distributions are strongly correlated with discharge. However, whereas a common relationship exists between discharge and δ for all depth distributions, the relationships with λ vary systematically downslope. Using the Gumbel distribution as a model for the distribution of overland flow depths, a probabilistic model for the initiation of rills is developed, drawing upon the previous work of Nearing. As an illustration of this approach, we apply this model to the shrubland and grassland hillslopes at Walnut Gulch. It is concluded that the presence of rills on the shrubland, but not on the grassland, is due to the greater runoff coefficient for the shrubland and/or the greater propensity of the shrubland for soil disturbance compared with the grassland. Finally, a generalized conceptual model for rill initiation is proposed. This model takes account of the depth distribution of overland flow, the probability of flow shear stress in excess of local soil shear strength, the spatial variability in soil shear strength and the diffusive effect of soil detachment by raindrops. Copyright © 2005 John Wiley & Sons, Ltd.     

Prediction of siderophile element metal-silicate partition coefficients to 20 GPa and 2800°C: the effects of pressure, temperature, oxygen fugacity, and silicate and metallic melt compositions

We report new metal-silicate partition coefficients for Ni, Co and P at 7.0 GPa (1650–1750°C), and Ni, Co, Mo, W and P at 0.8, 1.0 and 1.5 GPa (1300–1400°C). Guided by thermodynamics, all available metal-silicate partition coefficients, D(i), where i is Ni, Co, P, Mo and W, are regressed against 1/T, P/T, lnf(O₂), ln(1 − X_s) (X_S is mole fraction of S in metallic liquid) and nbo/t (non-bridging oxygen/tetrahedral cation ratio, a silicate melt compositional-structural parameter) to derive equations of the following form: ln D(i) = aln f(O₂) + (b/T) + (cP/T) + d(nbo/t) + eln(1 − X_S) + f. Expressions for solid metal-liquid silicate and liquid metal-liquid silicate partition coefficients are derived for S-free and S-bearing systems.

We investigate whether Earth's upper-mantle siderophile element abundances can be reconciled with simple metal-silicate equilibrium. Sulfur-free metallic compositions do not allow a good fit. However, Ni, Co, Mo, W and P abundances in the upper mantle are consistent with simple metal-silicate equilibrium at mantle pressures and temperatures (27 GPa, 2200 K, ΔIW(iron-wüstite) = −0.15, nbo/t = 2.7; X_S = 0.15). Although these conditions are near the anhydrous peridotite solidus, they are well above the hydrous solidus and probably closer to the liquidus. A hydrous magma ocean and early mantle are consistent with predicted planetary accretion models. These results suggest that siderophile element abundances in Earth's upper mantle were established by liquid metal-liquid silicate equilibrium near the upper-mantle-lower-mantle boundary.     

An experimental investigation of the effects of thawed soil depth on rill flow velocity

Water flow velocity is an important hydraulic variable in hydrological and soil erosion models, and is greatly affected by freezing and thawing of the surface soil layer in cold high-altitude regions. The accurate measurement of rill flow velocity when impacted by the thawing process is critical to simulate runoff and sediment transport processes. In this study, an electrolyte tracer modelling method was used to measure rill flow velocity along a meadow soil slope at different thaw depths under simulated rainfall. Rill flow velocity was measured using four thawed soil depths (0, 1, 2 and 10 cm), four slope gradients (5°, 10°, 15° and 20°) and four rainfall intensities (30, 60, 90 and 120 mm·h⁻¹). The results showed that the increase in thawed soil depth caused a decrease in rill flow velocity, whereby the rate of this decrease was also diminishing. Whilst the rill flow velocity was positively correlated with slope gradient and rainfall intensity, the response of rill flow velocity to these influencing factors varied with thawed soil depth. The mechanism by which thawed soil depth influenced rill flow velocity was attributed to the consumption of runoff energy, slope surface roughness, and the headcut effect. Rill flow velocity was modelled by thawed soil depth, slope gradient and rainfall intensity using an empirical function. This function predicted values that were in good agreement with the measured data. These results provide the foundation for a better understanding of the effect of thawed soil depth on slope hydrology, erosion and the parameterization scheme for hydrological and soil erosion models.     

Infiltration,runoff and sediment production in blanket peat catchments: implications of field rainfall simulation experiments

Blanket peat covers the headwaters of many major European rivers. Runoff production in upland blanket peat catchments is flashy with large flood peaks and short lag times; there is minimal baseflow. Little is known about the exact processes of infiltration and runoff generation within these upland headwaters. This paper presents results from a set of rainfall simulation experiments performed on the blanket peat moorland of the North Pennines, UK. Rainfall was simulated at low intensities (3–12 mm h^?1), typical of natural rainfall, on bare and vegetated peat surfaces. Runoff response shows that infiltration rate increases with rainfall intensity; the use of low‐intensity rainfall therefore allows a more realistic evaluation of infiltration rates and flow processes than previous studies. Overland flow is shown to be common on both vegetated and bare peat surfaces although surface cover does exert some control. Most runoff is produced within the top few centimetres of the peat and runoff response decreases rapidly with depth. Little vertical percolation takes place to depths greater than 10 cm owing to the saturation of the peat mass. This study provides evidence that the quickflow response of upland blanket peat catchments is a result of saturation‐excess overland flow generation. Rainfall–runoff response from small plots varies with season. Following warm, dry weather, rainfall tends to infiltrate more readily into blanket peat, not just initially but to the extent that steady‐state surface runoff rates are reduced and more flow takes place within the peat, albeit at shallow depth. Sediment erosion from bare peat plots tends to be supply limited. Seasonal weather conditions may affect this in that after a warm, dry spell, surface desiccation allows sediment erosion to become transport limited. Copyright © 2002 John Wiley & Sons, Ltd.     

Generalized conceptual modeling of dimensionless overland flow hydrographs

The rising and recession limbs of conceptual dimensionless overland flow hydrographs are calculated for specific values of the rating exponent in the range 1 ≤ m ≤ 3, including a linear reservoir (m = 1); 100% turbulent Chezy friction (m = 3/2); 100% turbulent Manning friction (m = 5/3); 67% turbulent Chezy (or 75% turbulent Manning) (m = 2); and 100% laminar flow (m = 3). These conceptual overland flow hydrographs show finite amounts of diffusion, increasing with decreasing rating exponent, unlike the kinematic wave hydrograph, which is nondiffusive.     

Mathematical expressions used in amino acid racemisation geochronology—A review

A variety of mathematical expressions that describe changes over time (t) in the extent of amino acid racemisation (AAR, expressed as the ratio of d- to l-amino acid isomers or epimers) have been used in Quaternary geochronology. The integrated rate equation was first used to estimate fossil age from D/L but its geochronological utility is disadvantaged by uncertainties regarding the conformity of AAR in fossil protein to apparent reversible first-order kinetics for the entire reaction history. ‘Non-linear’ models have subsequently been used to relate D/L to t. The logarithmic equation successfully applied to Atlantic Coastal Plain research has not achieved widespread application, perhaps due to the regional calibration required if sensitivity to temperature is to be modelled, or the difficulties encountered when extending the model to include fossils with D/L<0.1. Success producing a linear correlation between D/L transformed with a power function and t has seen this approach emerge as one of the most commonly applied in AAR geochronology in recent years. Like parabola curve fitting, which has been applied to trends in D/L versus t in a variety of fossils and geographic settings, power transformations may not be suitable for geochronological modelling during the latter stages of amino acid diagenesis. Several studies have demonstrated the utility of simple and contingent linear equations for relating D/L to t. Future research should aim to reduce reliance on independent calibration and explore the geochronological benefits of AAR in pools other than the total hydrolysable amino acids.     

Processes of accelerated pluvial erosion on desert hillslopes modified by vehicular traffic

Accelerated pluvial erosion on hillslopes modified by off-road vehicles (ORVs) is analysed using results from 50 rainfall simulation experiments conducted in the Mojave Desert, California. Sediment yield from 1 m² hillslope plots subjected to intense, 20-minute rainfalls is typically increased 10 to 20-fold following ORV use. Salient effects of vehicle traffic, which reduce infiltration, increase runoff sediment transport efficiency, and enhance gully formation, are further studied by combining simple theoretical relations with experimental data. This analysis helps identify factors controlling erosion on natural desert hillslopes, as well as those used by ORVs. Erosion of natural or vehicle-used desert surfaces is heavily influenced by runoff hydraulics. Calculated Darcy-Weisbach friction factors decrease by an average of 13-fold following vehicular slope modification, whereas runoff Reynolds numbers increase by an average of 5 1/2-fold. The capacity of overland flow to transport sediment is related to runoff power and its degree of localization, which usually increase considerably following ORV activity; however, the ability of overland flow to move large grains (competency) is related to a combination of factors not always systematically influenced by ORV use. Kinematic runoff routing, which is used to extrapolate experimental results to longer slope lengths, leads to the suggestion that the hydraulic roughness of desert hillslopes strongly influences their erosional behaviour.     

The effect of storm movement on infiltration,runoff and soil erosion in a semi-arid catchment

Rainfall characteristics are key factors influencing infiltration and runoff generation in catchment hydrology, particularly for arid and semiarid catchments. Although the effect of storm movement on rainfall-runoff processes has been evaluated and emphasized since the 1960s, the effect on the infiltration process has barely been considered. In this study, a physically based distributed hydrological model (InHM) was applied to a typical semi-arid catchment (Shejiagou, 4.26 km²) located in the Loess Plateau, China, to investigate the effect of storm movement on infiltration, runoff and soil erosion at the catchment scale. Simulations of 84 scenarios of storm movement were conducted, including storms moving across the catchment in both the upstream and downstream directions along the main channel, while in each direction considering four storm moving speeds, three rainfall depths and two storm ranges. The simulation results showed that, on both the hillslopes facing downstream (facing south) and in the main channel, the duration of the overland flow process under the upstream-moving storms was longer than that under the downstream-moving storms. Thus, the duration and volume of infiltration under upstream-moving storms were larger in these areas. For the Shejiagou catchment, as there are more hillslopes facing downstream, more infiltration occurred under the upstream-moving storms than the downstream-moving storms. Therefore, downstream-moving storms generated up to 69% larger total runoff and up to 351% more soil loss in the catchment than upstream-moving storms. The difference in infiltration between the storms moving upstream and downstream decreased as the storm moving speed increased. The relative difference in total runoff and sediment yield between the storms moving upstream and downstream decreased with increasing rainfall depth and storm speed. The results of this study revealed that the infiltration differences under moving storms largely influenced the total runoff and sediment yield at the catchment scale, which is of importance in runoff prediction and flood management. The infiltration differences may be a potential factor leading to different groundwater, vegetation cover and ecology conditions for the different sides of the hillslopes.     

Modelling overland flow based on Saint‐Venant equations for a discretized hillslope system

Mathematical modelling of overland flow is a critical task in simulating transport of water, sediment and other pollutants from land surfaces to receiving waters. In this paper, an overland flow routing method is developed based on the Saint‐Venant equations using a discretized hillslope system for areas with high roughness and steep slope. Under these conditions, the momentum equation reduces to a unique relationship between the flow depth and discharge. A hillslope is treated as a system divided into several subplanes. A set of first‐order non‐linear differential equations for subsequent subplanes are solved analytically using Chezy's formula in lieu of the momentum equation. Comparison of the analytical solution of the first‐order non‐linear ordinary differential equations and a numerical solution using the Runge‐Kutta method shows a relative error of 0·3%. Using runoff data reported in the literature, comparison between the new approach and a numerical solution of the full Saint‐Venant equations showed a close agreement. Copyright © 2002 John Wiley & Sons, Ltd.     

A new approach for measuring surface hydrological connectivity

The development of surface hydrological connectivity is a key determinant of flood magnitude in drylands. Thresholds in runoff response may be reached when isolated runoff-generating areas connect with each other to form continuous links to river channels, enabling these areas to contribute to flood hydrographs. Such threshold behaviour explains observed nonlinearities and scale dependencies of dryland rainfall–runoff relationships and complicates attempts at flood prediction. However, field methods for measuring the propensity of a surface to transmit water downslope are lacking, and conventional techniques of infiltration measurement are often inappropriate for use on non-agricultural drylands. Here, we argue for a reconceptualization of the dryland surface runoff process, suggesting that the downslope transfer of water should be considered alongside surface infiltration; that is, there is a need for the “aggregated” measurement of infiltration and overland flow hydraulics. Surface application of a set volume of water at a standardized rate generates runoff that travels downslope; the distance it travels downslope is determined by infiltration along the flow, integration of flow paths, and flow resistance. We demonstrate the potential of such a combined measurement system coupled with structure-from-motion photogrammetry to identify surface controls on runoff generation and transfer on dryland hillslopes, with vegetation, slope, surface stone cover, and surface roughness all having a significant effect. The measurement system has been used on slopes up to 37° compared with the flat surface typically required for infiltration methods. On average, the field workflow takes ~10–15 min, considerably quicker than rainfall simulation. A wider variety of surfaces can be sampled with relative ease, as the method is not restricted to stone and vegetation-free land. We argue that this aggregated measurement represents surface connectivity and dryland runoff response better than standard hydrological approaches and can be applied on a much greater variety of dryland surfaces.     

Steady state analysis of unsaturated flow above a shallow water-table aquifer drained by ditches

The one-dimensional pressure head profile above a fixed water-table was studied for different steady infiltration rates. As shown in previous studies, when the infiltration rate (q_in) is less than the soil saturated hydraulic conductivity (Ks), this profile can be divided into two parts: (1) from the water-table surface (z₀) to an elevation z_γ, the pressure head varies from 0 to a value h_γ such as K(h_γ)=−q_in; (2) above the elevation z_γ the pressure head is constant and equal to h_γ. Above the water-table the zone where the pressure head is variable has been called ‘transition zone’. Its height is shown to be highly variable and to depend on soil properties as well as on the infiltration rate. This transition zone is not the ‘capillary fringe’ as defined by Gillham (Gillham R.W., 1984. The capillary fringe and its effect on water-table response. J. Hydrol. 67, 307–324). Numerical experiments performed with HYDRUS-2D^® for the case of a water-table drained by parallel ditches have shown that the height of the transition zone is similar in the one-dimensional profile and in the two-dimensional system as long as the local slope of the water-table is small. This result is important since in a two-dimensional system, the transition zone is the place where all the horizontal component of the unsaturated flow occurs. The ratio of the horizontal component of the unsaturated flow vs the total horizontal flow in both the unsaturated and saturated zones has been computed. For a given soil, this ratio decreases as the infiltration rate increases; for a given infiltration rate, the soil with the thinnest transition zone transfers the largest amount of water above the water-table.