Motion of wetting fronts moving into partially pre-wet soil

We study the motion of wetting fronts for vertical infiltration problems as modeled by Richards’ equation. Parlange and others have shown that wetting fronts in infiltration flows can be described by traveling wave solutions. If the soil layer is not initially dry, but has an initial distribution of water content then the motion of the wetting front will change due to the interaction of the infiltrating flow with the pre-existing soil conditions. Using traveling wave profiles, we construct simple approximate solutions of initial-boundary value problems for Richards’ equation that accurately describe the position and moisture distribution of the wetting front. We show that the influences of surface boundary conditions and initial conditions produce shifts to the position of the wetting front. The shifts can be calculated by examining the cumulative infiltration, and are validated numerically for several problems for Richards’ equation and the linear advection–diffusion equation.     

A new saturated/unsaturated model for stormwater infiltration systems

Infiltration systems are widely used as an effective urban stormwater control measure. Most design methods and models roughly approximate the complex physical flow processes in these systems using empirical equations and fixed infiltration rates to calculate emptying times from full. Sophisticated variably saturated flow models are available, but rarely applied owing to their complexity. This paper describes the development and testing of an integrated one‐dimensional model of flow through the porous storage of a typical infiltration system and surrounding soils. The model accounts for the depth in the storage, surrounding soil moisture conditions and the interaction between the storage and surrounding soil. It is a front‐tracking model that innovatively combines a soil‐moisture‐based solution of Richard's equation for unsaturated flow with piston flow through a saturated zone as well as a reservoir equation for flow through a porous storage. This allows the use of a simple non‐iterative numerical solution that can handle ponded infiltration into dry soils. The model is more rigorous than approximate stormwater infiltration system models and could therefore be valuable in everyday practice. A range of test cases commonly used to test soil water flow models for infiltration in unsaturated conditions, drainage from saturation and infiltration under ponded conditions were used to test the model along with an experiment with variable depth in a porous storage over saturated conditions. Results show that the model produces a good fit to the observed data, analytical solutions and Hydrus. Copyright © 2008 John Wiley & Sons, Ltd.     

Effects of surface characteristics on infiltration patterns in an arid shrub desert

Precipitation is often the sole source of water replenishment in arid and semi‐arid areas and, thus, plays a pertinent role in sustaining desert ecosystems. Revegetation over 40 years using mainly Artemisia ordosica and Caragana korshinskii at Shapotou Desert Experimental Research Station near Lanzhou, China, has established a dwarf‐shrub and microbiotic soil crust cover on the stabilized sand dunes. The redistribution of infiltrated moisture through percolation, root extraction, and evapotranspiration pathways was investigated. Three sets of time‐domain reflectometry (TDR) probes were inserted horizontally at 5, 10, 15, 20, 30 and 40 cm depths below the ground surface in a soil pit. The three sets of TDR probes were installed in dwarf‐shrub sites of A. ordosica and C. korshinskii community with and without a microbiotic soil crust cover, and an additional set was placed in a bare sand dune area that had neither vegetation nor a microbiotic soil crust present. Volumetric soil moisture content was recorded at hourly intervals and used in the assessment of infiltration for the different surface covers. Infiltration varied greatly, from 7·5 cm to more than 45 cm, depending upon rainfall quantity and soil surface conditions. In the shrub community area without microbiotic soil crust cover, infiltration increased due to preferential flow associated with root tunnels. The microbiotic soil crust cover had a significant negative influence on the infiltration for small rainfall events (～10 mm), restricting the infiltration depth to less than 20 cm and increasing soil moisture content just beneath the soil profile of 10 cm, whereas it was not as strong or clear for larger rainfall events (～60 mm). For small rainfall events, the wetting front depth for the three kinds of surface cover was as follows: shrub community without microbiotic soil crust > bare area > shrub community with microbiotic soil crust. In contrast, for large rainfall events, infiltration was similar in shrub communities with and without microbiotic soil crust cover, but significantly higher than measured in the bare area. Soil water extraction by roots associated with evapotranspiration restricted the wetting front penetration after 1 to 3 h of rainfall. Copyright © 2006 John Wiley & Sons, Ltd.     

A two‐dimensional model of hydraulic performance of stormwater infiltration systems

Stormwater infiltration systems are a popular method for urban stormwater control. They are often designed using an assumption of one‐dimensional saturated outflow, although this is not very accurate for many typical designs where two‐dimensional (2D) flows into unsaturated soils occur. Available 2D variably saturated flow models are not commonly used for design because of their complexity and difficulties with the required boundary conditions. A purpose‐built stormwater infiltration system model was thus developed for the simulation of 2D flow from a porous storage. The model combines a soil moisture–based model for unsaturated soils with a ponded storage model and uses a wetting front‐tracking approach for saturated flows. The model represents the main physical processes while minimizing input data requirements. The model was calibrated and validated using data from laboratory 2D stormwater infiltration trench experiments. Calibrations were undertaken using five different combinations of calibration data to examine calibration data requirements. It was found that storage water levels could be satisfactorily predicted using parameters calibrated with either data from laboratory soils tests or observed water level data, whereas the prediction of soil moistures was improved through the addition of observed soil moisture data to the calibration data set. Copyright © 2012 John Wiley & Sons, Ltd.     

Directions of preferential flow in a hillslope soil, 1. Quasi‐steady flow

Preferred infiltration is mainly perceived as vertically down whereas subsurface storm flow is thought to occur parallel to slopes. The transition from vertical to lateral flow in a layered hillslope soil is the focus of the contribution. Transient flow is assumed to move as a wetting front. Three time‐domain reflectometry (TDR) wave‐guides, each 0·15 m long, were mounted in the shape of a truncated tetrahedron with its peak pointing down. Each wave‐guide focuses the front velocity along its axis. The three front‐velocity vectors are decomposed into their x, y and z components, which are then assembled to the resultant velocity vector. The volume density flux of preferred flow is the product of the front velocity and the mobile water content. The latter is the amplitude of transient soil moisture measured with each wave‐guide. The resultant vector of the volume flux density is computed similarly to the velocity vector. The experimental approach allows for the rapid assessment of transient flows without relying on the variation of water potentials. The experiments indicate that the directions of the resultant vectors of velocity and volume flux density can be estimated if the moisture variations of the three TDR wave‐guides are strongly correlated during the passing of the wetting front. Copyright © 2004 John Wiley & Sons, Ltd.     

How soil texture,channel shape and cross-sectional area affect moisture dynamics and water loss in irrigation channels

To enhance the utilization efficiency of farmland irrigation water and reduce the leakage of water conveyance channels, the leakage process of channels was simulated dynamically. The simulated results were compared with data measured in laboratory experiments, and the performance of the model was evaluated. The results indicated that the simulated values of the model were consistent with the observation values, and the R² values varied between 0.91 and 0.99. In addition, based on the laboratory experiments, a water supply system (Mariotte bottles) and soil box were built using plexiglass. Three influencing factors, namely, the channel form, soil texture and channel cross-sectional area, were varied to observe and calculate the resulting cumulative infiltration amount, infiltration rate and wetting front migration distance. HYDRUS-3D software was used to solve the three-dimensional soil water movement equation under different initial conditions. The results demonstrated that the U-shaped channel was more effective than the trapezoidal channel in increasing the utilization efficiency of the water resources. A U-shaped channel with a small channel cross-sectional area should be adopted and the soil particle size should be prioritized in the construction of water conveyance channels for farmlands. The simulation results were in agreement with the observed results, which indicates that HYDRUS-3D is a reliable tool that can accurately simulate the soil moisture movement in water conveyance channels. The research results can provide a reference for the design and operation of farmland irrigation systems.     

Differences in soil moisture in two Middle Eastern oak forests: Comparing the effects of trees and soil composition

The incidence of large rain events in Mediterranean ecosystems vary among years. Summer aridity is interpreted as a resetting event, eliminating previous soil‐moisture dynamics. The dynamics of soil moisture and retention are critical to tree survival, particularly in dry regions. This study examines the long‐term soil water content (θ_V) dynamics in two distinct locations within the forest, under the canopy and forest clearing, within two diverse oak forests: subhumid mixed oak forests (MG) and semiarid monospecific oak woodlands (YE). Plots were established at small‐scale catchments and soil water contents were measured during 2010–2013, at three depths in the two different locations. Cumulative rainfall was used as an independent proxy for θ_V analysis. A novel bell‐bilogistic mathematical model of wetting, saturation, and drying arms was developed. We aimed to study the θ_V distribution differences between soil profiles giving the large climatic gradient between the two forested sub basins, the differences in vegetation traits along with soil attributes. We further aimed at determining the role of an individual tree in regulating soil‐moisture dynamics. We hypothesized the occurrence of distinct responses between sites in all soil‐moisture indices with higher θ_V at the wetter site. We tested the hypothesis that seasonal cumulative rainfall dictates the variations in soil‐moisture regimes throughout contiguous years. Annual rainfall was higher than long‐term average throughout the study. Soil profiles under the canopies at both sites were consistently wetter. Infiltration and depletion constants were higher at MG whereas maximum soil moisture was higher at YE. Homogenous recharge patterns were seen at MG although YE evinced more variation. Oaks had no effect on recharge at MG compared with the forest clearing. Soil properties primarily affected the wetting arm whereas vegetation composition regulated the drying arm. Mixed‐stands characterized by ever‐green and deciduous species may maintain favourable soil‐moisture conditions, in comparison with other mixed stand morphologies. The increasing role of slacking forces in infiltration process may alter the interaction between trees and herbaceous vegetation.     

Soil moisture response to rainfall on the Chinese Loess Plateau after a long‐term vegetation rehabilitation

The Chinese Loess Plateau (CLP) is a unique Critical Zone with deep loess deposits, where soil moisture is primarily replenished by seasonal monsoon rainfall. However, the role of vegetation, coupled with complex topography, on rainwater infiltration on the CLP, especially after long‐term revegetation for controlling erosion, is inadequately quantified. Over the growing season of 2016, we monitored soil moisture at the 30‐min interval at 5 depths (10, 20, 40, 60, and 100 cm) in an afforested catchment and a nearby catchment with natural regrowth of grasses. Two monitoring sites were established in each catchment, one in the downhill gully and the other in the uphill slope. We found that vegetation, topography, and rainfall attributes together determined rainwater infiltration and soil moisture replenishment. An accumulated rainfall amount of 9 mm was required to trigger soil moisture response at 10‐cm depth at the 2 grassland sites and the forestland uphill‐slope site whereas 14 mm of rainfall was required for the forestland gully site covered by dense undergrowth and trees. Rainfall events with larger sums and higher peak intensities permitted rainwater infiltration to deeper soil depths. However, no rain recharged soil moisture to 100‐cm depth during the monitoring period. The forestland uphill‐slope site showed the deepest wetting depth (up to 60‐cm depth), fastest wetting‐front velocity (up to 4 cm/hr below 10‐cm depth), and the most significant soil moisture increase (up to 15% cm ³ cm^?3 increase at 10‐cm depth) after rainfall in the growing season. The grassland gully site had the highest soil water storage, whereas soil moisture was depleted the most at the forestland gully site. Findings of this study reveal the transient dynamics of soil moisture after rainfall on the CLP, which signifies the role of revegetation on rainwater infiltration in the loess Critical Zone.     

Occurrence of water ponding on soil surfaces depending on infiltration rates on Mongolian rangeland

The occurrence of water ponding on soil surfaces during and after heavy rainfall produces surface run‐off or surface water accumulation in low‐lying areas, which might reduce the water supply to soils and result in a reduction of the soil water that plants can use, especially in arid climates. On Mongolian rangeland, we observed ponded water on the surface of a specific soil condition subjected to a heavy rainfall of 30 mm/hr. By contrast, ponded water was not observed for the same type of soil where livestock grazing had been removed for 6–8 years via a fence or for nearby soil containing less clay. We measured the infiltration rate (the saturated hydraulic conductivity of the surface soil, K_s) of the three sites by applying ponded water on the soil surface (an intake rate test). The results showed that K_s in the rangeland was lower than the rainfall intensity in the site where water ponded on the soil surface; however, K_s of the soil inside of the fence has recovered to 3 times that of the soil outside of the fence to exceed the rainfall intensity. Heavy rainfall that exceeds the infiltration rate occurs several times a year at the livestock grazing site where we observed ponded water. Slight water repellency of the soil reduces rain infiltration to increase the possibility of surface ponding for the soil.     

An analysis of infiltration with moisture content distribution in a two‐dimensional discretized water content domain

On the basis of unsaturated Darcy's law, the Talbot–Ogden method provides a fast unconditional mass conservative algorithm to simulate groundwater infiltration in various unsaturated soil textures. Unlike advanced reservoir modelling methods that compute unsaturated flow in space, it only discretizes the moisture content domain into a suitable number of bins so that the vertical water movement is estimated piecewise in each bin. The dimensionality of the moisture content domain is extended from one dimensional to two dimensional in this study, which allows us to distinguish pore shapes within the same moisture content range. The vertical movement of water in the extended model imitates the infiltration phase in the Talbot–Ogden method. However, the difference in this extension is the directional redistribution, which represents the horizontal inter‐bin flow and causes the water content distribution to have an effect on infiltration. Using this extension, we mathematically analyse the general relationship between infiltration and the moisture content distribution associated with wetting front depths in different bins. We show that a more negatively skewed moisture content distribution can produce a longer ponding time, whereas a higher overall flux cannot be guaranteed in this situation. It is proven on the basis of the water content probability distribution independent of soil textures. To illustrate this analysis, we also present numerical examples for both fine and coarse soil textures. Copyright © 2014 John Wiley & Sons, Ltd.     

Fire‐induced changes in soil water repellency increased fingered flow and runoff rates following the 2004 Huelva wildfire

Water repellency (WR) from fire‐affected soils can affect infiltration processes and increase runoff rates. We investigated the effects of fire‐induced changes in soil WR and the related soil hydrological response after one of the largest wildfires in Spain in recent years. The vertical distribution of WR in soil profiles was studied under oak and pine forests and the wetting pattern was analysed after rainfall simulations (85 mm h^?1 during 60 min). After burning, the persistence of WR in soils under oaks increased in the upper 0–5 cm of soil in comparison with pre‐fire WR, but no significant changes were observed under pines. After a fire, WR was stronger and the thickness of the water‐repellent layer increased in soils under pines in the upper 0–16 cm of soil. The hydrophobic layer was thinner under oaks, where no strong to extremely water‐repellent samples were observed below 12 (in burnt soils) and 8 cm (in unburnt soils). Uniform wetting was observed through soil depth in burnt and unburnt soils under oaks, as a consequence of the prevailing matrix flux infiltration. Water was mostly stored in the upper few centimetres and soil became rapidly saturated, favouring a continuous rise in the runoff rate during the experiments. Moisture profiles under pines showed a heterogeneous wetting pattern, with highly irregular wetting fronts, as a result of wettable and water‐repellent three‐dimensional soil patches. In this case, runoff rates on burnt plots increased in relation to unburnt plots, but runoff generation reached a steady state after 25–30 min of simulated rainfall at an intensity of 85 mm h^?1. Rainfall water infiltrated over a small part of the ponded area, where the vertical pressure of the water column overcame the WR. Copyright © 2010 John Wiley & Sons, Ltd.     

Factors affecting channel infiltration of floodwaters in Nahal Zin basin,Negev desert,Israel

Although floods in arid environments have been documented, considerable uncertainties still exist as to the floodwater and in‐channel infiltration relationships. In desert alluvial channels, the prime cause of flood discharge attenuation is water loss by infiltration into the alluvium. The present study documents flows in Nahal Zin, Israel, their infiltration into the channel bed, and the resultant change in the alluvium moisture content. The study uses a systematic combination of two experimental scales, the cross‐section scale and the reach scale. Direct measurements of moisture distribution in the active channel during floods were made using time domain reflectometry. Twelve flow events were recorded. Flow patterns and their respective alluvium moisture content were analysed. A trench was dug in the alluvium for the study of alluvium properties and time domain reflectometry sensor installation. The alluvium was characterized in terms of size distribution and sediment stratigraphy, structure, and composition. Two main alluvial structures (closed and open) affected the advance of the wetting front and water losses. Alluvial units with an open structure (clast‐supported) reached their maximum moisture content faster than closed structure units (matrix‐supported). Small‐sized particles and matrix‐supported layers reduced infiltration rate. The measured velocities of the wetting front were 0.33 and 2.88 m h^?1 for small and large floods respectively. The wetting front moved downward. Lateral movement was negligible. Copyright © 2016 John Wiley & Sons, Ltd.     

Remarks upon numerical solutions of infiltration into a soil profile

Abstract

A methodology of time-step estimation for numerically solving the Richards equation is discussed. Its importance in simulating water movement in unsaturated—saturated soils is shown for infiltration into a soil profile by applying various time-step estimations and boundary conditions for different soils. In order to test the results of the computations, infiltration theory was applied. According to infiltration theory, the pressure head in the initially unsaturated part will not take positive values as long as the moisture front has not reached the phreatic level, or, in the case of a profile with a free-draining lower boundary, it is not saturated at the base. In other cases, the appearance of positive values of the pressure head produces incorrect values for the inflow rate q.     

Modification and discussion of the Green-Ampt model for an evolving wetting profile

ABSTRACT

The Green-Ampt (GA) model has been widely used to evaluate soil water infiltration. While a simple piston profile is commonly used, the wetting profile of a soil changes during infiltration and a quarter-ellipse has been found to better describe its evolution. This study aims to improve the GA model and discuss the model parameters when the quarter-ellipse profile is utilized. The soil column is divided into three zones: saturated, transient and dry. The variable γ is introduced to express the ratio of the saturated zone depth to the wetting front depth. A modified GA model is derived via mathematical methods, but an exact solution is difficult to obtain. Therefore, a simplified (SGA) model is developed via a segmented method. Compared with the measured results, the SGA model is more accurate than the traditional model. Finally, the model parameters are discussed and a value of γ = 0.5 is recommended.     

Infiltration and runoff generation processes in fire‐affected soils

Post‐wildfire runoff was investigated by combining field measurements and modelling of infiltration into fire‐affected soils to predict time‐to‐start of runoff and peak runoff rate at the plot scale (1 m²). Time series of soil‐water content, rainfall and runoff were measured on a hillslope burned by the 2010 Fourmile Canyon Fire west of Boulder, Colorado during cyclonic and convective rainstorms in the spring and summer of 2011. Some of the field measurements and measured soil physical properties were used to calibrate a one‐dimensional post‐wildfire numerical model, which was then used as a ‘virtual instrument’ to provide estimates of the saturated hydraulic conductivity and high‐resolution (1 mm) estimates of the soil‐water profile and water fluxes within the unsaturated zone. Field and model estimates of the wetting‐front depth indicated that post‐wildfire infiltration was on average confined to shallow depths less than 30 mm. Model estimates of the effective saturated hydraulic conductivity, K_s, near the soil surface ranged from 0.1 to 5.2 mm h^?1. Because of the relatively small values of K_s, the time‐to‐start of runoff (measured from the start of rainfall), t_p, was found to depend only on the initial soil‐water saturation deficit (predicted by the model) and a measured characteristic of the rainfall profile (referred to as the average rainfall acceleration, equal to the initial rate of change in rainfall intensity). An analytical model was developed from the combined results and explained 92–97% of the variance of t_p, and the numerical infiltration model explained 74–91% of the variance of the peak runoff rates. These results are from one burned site, but they strongly suggest that t_p in fire‐affected soils (which often have low values of K_s) is probably controlled more by the storm profile and the initial soil‐water saturation deficit than by soil hydraulic properties. Published 2013. This article is a U.S. Government work and is in the public domain in the USA.     

Groundwater recharge estimation from ephemeral streams. Case study: Wadi Tabalah,Saudi Arabia

Estimation of groundwater recharge to an unconfined aquifer is studied using analytical and numerical techniques and results are compared with field observations. There is an acute need for such estimation in water balance studies in arid climates, and the case study in this paper is for such a region. The wetting front movement in the unsaturated zone depends on antecedent soil moisture, the ponded water depth and its duration, and on the position of the water table and the hydraulic properties of the unsaturated zone. A hydraulic connection between the recharge basin and the aquifer is not immediately established because the wetting front is unsaturated. A numerical model is applied to estimate recharge in an arid-zone wadi, and its validity is tested by comparing it with an analytical solution of the equations. The calculated recharge values matched the piezometric levels observed at a well site at the edge of the wadi channel. The total recharge depths found by integration in the time domain provided a good estimate of the transmitted volume of water per unit length of wadi channel. The findings were confirmed by runoff volume measurements at gauging stations located in the basin. © 1997 John Wiley & Sons, Ltd.     

Improving the representation of soil moisture by using a semi‐analytical infiltration model

Soil moisture is widely recognized as a fundamental variable governing the mass and energy fluxes between the land surface and the atmosphere. In this study, the soil moisture modelling at sub‐daily timescale is addressed by using an accurate representation of the infiltration component. For that, the semi‐analytical infiltration model proposed by Corradini et al. (1997) has been incorporated into a soil water balance model to simulate the evolution in time of surface and profile soil moisture. The performances of this new soil moisture model [soil water balance module‐semi‐analytical (SWBM‐SA)] are compared with those of a precedent version [SWBM‐Green–Ampt (GA)] where the GA approach was employed. Their capability to reproduce in situ soil moisture observations at three sites in Italy, Spain and France is analysed. Hourly observations of quality‐checked rainfall, temperature and soil moisture data for a 2‐year period are used for testing the modelling approaches. Specifically, different configurations for the calibration and validation of the models are adopted by varying a single parameter, that is, the saturated hydraulic conductivity. Results indicate that both SWBMs are able to reproduce satisfactorily the hourly soil moisture temporal pattern for the three sites with root mean square errors lower than 0.024 m³/m³ both in the calibration and validation periods. For all sites, the SWBM‐SA model outperforms the SWBM‐GA with an average reduction of the root mean square error of ~20%. Specifically, the higher improvement is observed for the French site for which in situ observations are measured at 30 cm depth, and this is attributed to the capability of the SA infiltration model to simulate the time evolution of the whole soil moisture profile. The reasonable models performance coupled with the need to calibrate only a single parameter makes them useful tools for soil moisture simulation in different regions worldwide, also in scarcely gauged areas. Copyright © 2013 John Wiley & Sons, Ltd.     

Soil water content vertical profiles under natural conditions: matching of experiments and simulations by a conceptual model

The prediction of soil moisture content, θ, as a function of depth, z, and time, t, is of fundamental importance for applications in many hydrological processes. The main objective of this paper is to provide an approach to solve this problem at a local scale in soils with vegetation. The matching of soil moisture vertical profiles observed under natural conditions in grassy plots and their simulations by a conceptual model is presented. Experimental measurements were performed in a plot located in Central Italy, complete with hydrometeorological sensors specifically set up and equipped with a time domain reflectometry system providing the water content, θ_e(z, t). A conceptual model framework earlier proposed for two‐layered soil vertical profiles was modified and adopted for simulations. The changes concern the incorporation of evapotranspiration, the reduction of the original model for applications also to homogeneous soil vertical profiles, and a correction for the differences existing between assumed and observed initial moisture contents. In the model calibration, it was found that the effects of vegetation could be represented adequately by a fictitious soil vertical profile with a more permeable upper layer of saturated hydraulic conductivity, K_s, independent of time. Then, for the validation events, the model simulations in the stages of both infiltration and redistribution/evapotranspiration reproduced appropriately θ_e(z, t) with typical values of root mean square error in the range 0.0017–0.0657. Similar results were obtained by applying the modified two‐layered model for simulations of experimental data observed in three other plots located in Northern Italy and Germany. For all four vegetated sites, the two‐layer profile better matched the experimental data than the assumption of a homogeneous profile. Thus, the conceptual approach based on a two‐layered scheme for representing θ(z, t) in soils with vegetation appears to be appropriate for many hydrological applications. Copyright © 2013 John Wiley & Sons, Ltd.     

The effect of biological soil crusts on soil moisture dynamics under different rainfall conditions in the Tengger Desert,China

Rainfall is considered as the dominant water replenishment in desert ecosystems, and the conversion of rainfall into soil water availability plays a central role in sustaining the ecosystem function. In this study, the role of biological soil crusts (BSCs), typically formed in the revegetated desert ecosystem in the Tengger Desert of China, in converting rainfall into soil water, especially for the underlying soil moisture dynamics, was clarified by taking into account the synthetic effects of BSCs, rainfall characteristics, and antecedent soil water content on natural rainfall conditions at point scale. Our results showed that BSCs retard the infiltration process due to its higher water holding capacity during the initial stage of infiltration, such negative effect could be offset by the initial wet condition of BSCs. The influence of BSCs on infiltration amount was dependent on rainfall regime and soil depth. BSCs promoted a higher infiltration through the way of prolonged water containing duration in the ground surface and exhibited a lower infiltration at deep soil layer, which were much more obvious under small and medium rainfall events for the BSCs area compared with the sand area. Generally, the higher infiltration at top soil layer only increased soil moisture at 0.03 m depth; in consequence, there was no water recharge for the deep soil, and thus, BSCs had a negative effect on soil water effectiveness, which may be a potential challenge for the sustainability of the local deep‐rooted vegetation under the site specific rainfall conditions in northwestern China.     

On a fractional derivative form of the Green-Ampt infiltration model

The Green-Ampt model for infiltration into homogeneous soils predicts a monotonically decreasing infiltration rate and a wetting front that initially advances as the square root of time. Infiltration in heterogeneous soils, however, can exhibit non-monotonic infiltration rates and wetting front advances that differ from the square root of time (“anomalous diffusion”).Here it is postulated, that if the length scales of the heterogeneities can be assumed to be power law distributed, it may be appropriate to model infiltration in heterogeneous soils in terms of fractional derivatives. Then, by expressing the hydraulic flux as a Caputo fractional derivative (order 0 < α ? 1) of the head, a fractional Green-Ampt infiltration model is obtained. It is shown that solutions of this model predict non-monotonic and anomalous diffusion behaviors consistent with observations in field infiltration trials; a finding that indicates that a non-local moisture flux model, based on fractional derivatives, is a plausible model for describing infiltration into heterogeneous soils.