Ampt Approach Research Articles

Layered Green and Ampt Infiltration With Redistribution

AbstractNumerical solution of the one‐dimensional Richards equation (RE) accurately partitions precipitation into infiltration and runoff in capillary dominated soils. However, its application sometimes requires significant computational effort and presents reliability challenges. The Green and Ampt (G&A) approach represents a conservative and efficient method to calculate one‐dimensional infiltration but is limited to deep, well drained, uniform, non‐layered soils for a single rainfall event. The original G&A model and subsequent advancements represent wetting fronts as discrete objects, rather than discretizing the model domain in space, yielding a computationally simpler model than the RE. This paper describes an extension of the G&A method into layered soils on a continuous basis that we call Layered Green and Ampt with Redistribution (LGAR). Assumptions employed in the derivation include: uniform soil hydraulic properties within layers, single‐valued capillary head at the interface between soil layers, and no influence of groundwater table on soil moisture. Wetting fronts advance due to the combined effects of gravity and wetting front capillary drive in a layered soil profile. Results of multi‐month continuous LGAR simulations of infiltration using forcing and soil hydraulic data from USDA SCAN sites are compared against infiltration calculated using the HYDRUS‐1D RE solver using standard metrics. The assumptions employed in deriving the LGAR method limit its application to situations where cumulative potential evapotranspiration is greater than cumulative precipitation, typical of arid or semi‐arid conditions. LGAR is a mass‐conservative, computationally efficient, reliable and reasonably accurate method for simulating infiltration over extended time periods compared to the numerical solution of the RE in layered soils in arid and semi‐arid regions.

Modeling evapotranspiration for irrigation water management in a humid climate

Quantifying evapotranspiration (ET, consumptive crop water requirement) is critical to managing limited water resources for crop irrigations. Agricultural system simulation models that realistically simulate the ET processes are potential tools for integration, synthesis, and extrapolation of location-specific water management research data across soils and climates for limited-water management in agriculture. The objective of this investigation was to evaluate the accuracy of the Root Zone Water Quality Model v2.0 (RZWQM2) simulated ET against ET measured in corn, soybean, and cotton cropping systems in a predominantly clay soil under humid climate in the Lower Mississippi (MS) Delta, USA, in 2016, 2017, and 2018. Energy balance (EB) and eddy covariance (EC) methods were used for measuring ET. The RZWQM2 parameters calibrated in previous studies at the location were used in the simulations. Potential evapotranspiration (PET) in the model was simulated using an extended approach based on the Shuttleworth and Wallace (SW) model. Water infiltration into the soil was simulated using the Green and Ampt approach, and its further movement in soil layers and contributions to soil evaporation using Richard’s equation. Across the three crops and their crop-seasons, simulated daily ET deviated from EC and EB estimates with RMSEs between 0.09 and 0.14 cm and RRMSEs between 21 and 37%. On a weekly basis, accuracies in simulated ET (ETS) improved significantly with RRMSEs between 9 and 17%, and on a seasonal basis RRMSEs were between -9 and 11%. The imbalance in incoming and outgoing energies accounted in the EC system varied between 2 to 12%; taking this uncertainty in estimated ET into account, the accuracies in weekly and seasonal ET simulations were reasonable for their use in irrigation management at these time-scales.

Application of GUSED‐VBS 2 Model for Flow and Sediment Transport in Vegetated Strips to Improve Water Quality

AbstractVegetated buffer strips change flow hydrology and sediment transport by increasing resistance to the flow and intensifying infiltration. GUSED‐VBS 2 is a process‐based mathematical model developed to simulate flow characteristics and the fate and transport of sediment in the backwater region upstream of vegetated strips and within them. The model also predicts the concentration and delivery of different particle sizes leaving the vegetated strips and reaching open water bodies. GUSED‐VBS 2 assumes that entrainment and deposition processes occur simultaneously and uses the Green–Ampt approach to simulate infiltration and gradually varied flow and kinematic wave approximation to simulate the water profile in the backwater region and within the vegetated strip respectively. The modified GUEST model approach was used to model the fate and transport of sediment in vegetated strips. Field data were used to evaluate the model predictions of the efficiency of vegetated strips in reducing runoff, sediment concentration and sediment delivery, and the results showed that GUSED‐VBS 2 performed much better in controlled conditions compared to field conditions. The performance of the GUSED‐VBS 2 and WEPP models in simulating particle size distribution in the outflow was compared with different model evaluation criteria and GUSED‐VBS 2 showed better performance compared to WEPP. Copyright © 2017 John Wiley & Sons, Ltd.

An explicit, parsimonious, and accurate estimate for ponded infiltration into soils using the Green and Ampt approach

AbstractThe Green and Ampt solution for vertical ponded infiltration is implicit in time, which makes the result often cumbersome to apply. Here we present a simple explicit solution for the position of the wetting front in time based on approximating the term describing early time behavior by means of the sum of gravitational flow and the exact solution for capillary imbibition. The result is within 1% of the exact implicit solution of vertical Green and Ampt infiltration. We also check the overall accuracy of the Green and Ampt approach, and find it to be within 15% of numerical simulation results for the same soils obtained with the Richards equation. Hence, the proposed approximation adds essentially no error to the Green and Ampt approach, but greatly simplifies computation of infiltration. The approximation also makes explicit the role of the representation of capillarity, which can be adjusted in ways not possible with the implicit result. We find that predictions can be markedly improved by adjusting capillary versus gravitational drivers per soil texture, revealing both a limitation of the Green and Ampt approach, but also providing a potential refinement of Green and Ampt predictions per soil type (demonstrated for sandy and clayey soils). Further, the new approximation allows for simple computation of useful quantities such as flux and cumulative infiltration.

A Mesopore and Matrix infiltration model based on soil structure

After decades of research into the subject, preferential flow in soils still plagues those of us who hope to provide better solutions to society's natural resource management conundrums. To that end, simulation models that strike the balance between simplicity and robustness are a high priority. We present the two-domain, Mesopore and Matrix (M&M), water-infiltration module based on soil structure for the Precision Agricultural-Landscape Modeling System (PALMS), by combining laminar flow of water through inter-aggregate slits with water movement from slits into aggregates using Darcy's law. The M&M model is based on new assumptions using soil aggregate geometry that allow the model to be more easily parameterized for landscapes with varying soil properties. The vertical and horizontal arrangements of aggregates and the slit width (2 B ped( θ)) are based on cubic geometry, where the width of the cubes represents the width ( w ped( θ, z)) of soil structural units, which depends on soil water content ( θ) and depth ( z). The M&M module can be parameterized so that mesopore infiltration resembles that of the Richards equation as a starting point for the preferential-flow parameterization. Using field measurements of ped size and in situ mesopore volume to calculate B ped( θ) and w ped( θ, z), the parameters from the Richards equation starting point can be modified to capture mesopore effects. PALMS was run using this approach with and without M&M for the 1996 frost-free growing season (March 1 to Nov. 1). While both models slightly under-predicted 1.4 m depth drainage compared with independently measured field data from the same period, PALMS with the M&M module increased estimated drainage by 32% in response to the largest 1996 storm event (~ 100 mm in 2 days) and 11% seasonally (627 mm cumulative precipitation) over the original PALMS model using the Green and Ampt approach. For the 2008 growing season, a period of unusually high rainfall rates (820 mm annual precipitation), PALMS with M&M simulated a 57% increase in drainage response to the season's largest storm (~ 200 mm in 2 days) and a 20% increase in seasonal drainage compared to PALMS with the Green and Ampt equations. For both 1996 and 2008 seasons, the drainage response to large storms predicted by PALMS with M&M occurred much more rapidly (hours as opposed to days) than PALMS with the Green and Ampt approach.

On the estimation of antecedent wetness conditions in rainfall–runoff modelling

AbstractThe analysis of the physical processes involved in a conceptual model of soil water content balance is addressed with the objective of its application as a component of rainfall–runoff modelling. The model uses routinely measured meteorological variables (rainfall and air temperature) and incorporates a limited number of significant parameters. Its performance in estimating the soil moisture temporal pattern was tested through local measurements of volumetric water content carried out continuously on an experimental plot located in central Italy. The analysis was carried out for different periods in order to test both the representation of infiltration at the short time‐scale and drainage and evapotranspiration processes at the long time‐scale. A robust conceptual model was identified that incorporated the Green–Ampt approach for infiltration and a gravity‐driven approximation for drainage. A sensitivity analysis was performed for the selected model to assess the model robustness and to identify the more significant parameters involved in the principal processes that control the soil moisture temporal pattern.The usefulness of the selected model was tested for the estimation of the initial wetness conditions for rainfall–runoff modelling at the catchment scale. Specifically, the runoff characteristics (runoff depth and peak discharge) were found to be dependent on the pre‐event surface soil moisture. Both observed values and those estimated by the model gave good results. On the contrary, with the antecedent wetness conditions furnished by two versions of the antecedent precipitation index (API), large errors were obtained. Copyright © 2007 John Wiley & Sons, Ltd.

Determination of ponding condition and infiltration into layered soils under unsteady rainfall

Few infiltration models, based on the Green–Ampt approach, in current use are suitable for simulating infiltration into heterogeneous soils of variable initial moisture distributions during unsteady rainfall. An algorithm is proposed for determining the ponding condition, simulating infiltration into a layered soil profile of arbitrary initial water distributions under unsteady rainfall, and partitioning the rainfall input into infiltration and surface runoff. Two distinct periods, pre-ponding and post-ponding, are taken into account. The model tracks the movement of the wetting front along the soil profile, checks the ponding status, and in particular, handles the shift between ponding and non-ponding conditions. The modeling also covers a fully saturated flow condition when the wetting front reaches the bottom of the soil profile (water table). Detailed procedures that deal with the variability in both soil properties and rainfall intensity are presented. For the purpose of model testing, three different cases (homogeneous soil and unsteady rainfall; layered soils and steady rainfall; and layered soils and unsteady rainfall) were discussed. Comparisons of the developed model with other infiltration models (both modified Green–Ampt infiltration model and fully numerical model) and field measurements were conducted and good agreements were achieved.

Spatial averaging of land use and soil properties to develop the physically-based green and ampt parameters for HEC-1

The computer hydrologic model HEC-1, developed by the Hydrologic Engineering Center (HEC), has been used for many years by hydrologists and engineers to estimate surface water runoff caused by rainfall events. Besides the rainfall data itself, the most sensitive set of input parameters in a runoff model are the rainfall loss parameters. The SCS (NRCS) Curve Number approach is commonly used to compute rainfall losses. Another method available for computing rainfall losses in HEC-1 is the Green and Ampt approach. However, this method is used infrequently because of the difficulty in obtaining the soil data needed to derive the Green and Ampt parameters. The purpose of this study is to present an automated method of computing Green and Ampt parameters using digital soil and land use data. Studies were performed with data that compare this automated method with another non-automated method of computing Green and Ampt parameters. Parameters computed using the automated method were consistent with the parameters computed using the non-automated method. Furthermore, by taking advantage of Geographic Information System (GIS) overlay capabilities, significant time was saved in computing the Green and Ampt parameters.

Effects of the spatial organization of agricultural management on the hydrological behaviour of a farmed catchment during flood events

AbstractField limits, tillage practices and ditch networks constitute man‐made hydrological discontinuities in farmed catchments, and are expected to influence hydrological response during flood events. The purpose of this study is to assess the role of human impact, especially the existence of tillage practices and ditch network, on flood events. The study area is the farmed catchment of Roujan (0·91 km2) located in Southern France for which a spatially distributed hydrological model, MHYDAS, was developed and tested. The model considers the catchment as a series of interconnected field parts linked to the ditch network. Descriptions are provided for the main model procedures: computation of Hortonian excess rainfall on fields using the Green and Ampt approach, conversion of excess rainfall to surface runoff, interaction between ditch network and groundwater using a simple Darcian model and flood routing through the ditch network using the diffusive wave model. To analyse the role of both tillage practices and the ditch network, two sets of sensitivity analysis of the model were applied. The first set studied the role of tillage practices by comparing the actual spatial distribution of tillage practices on the catchment with three hypothetical scenarios. The second set studied the role of the ditch network by comparing the actual man‐made ditch network with a hypothetical drainage network automatically extracted from a digital elevation model. Results show the importance of the role of tillage and the ditch network on the form of the hydrograph, the lag time, the runoff volume and the peak discharge. This technique could also be applied to study the impact of land use change on the hydrological behaviour of the catchment. Copyright © 2002 John Wiley & Sons, Ltd.

Distributed sediment and phosporus transport modeling on a medium sized catchment in central germany

Current research suggests that strategies to control nitrogen as well as sediment and phosphorus loss from nonpoint sources should focus on different runoff components and their spatial and temporal variation within the catchment. Therefore nonpoint source models, especially in humid climatic regions, should consider variable hydrological active source areas. These models should also be able to consider runoff generation by saturated overland flow as well as Horton overland flow. A combination of the hydrologic model WaSiM-ETH and the erosion and P-transport model AGNPS Version 5 was chosen for this study. The models were run in the WaSiM-ETH runoff generation mode (Topmodel and Green a. Ampt approach) and the SCS curve number mode, modified by Lutz (1984), to assess these different runoff calculation procedures. A medium sized catchment in the lower Hessian uplands of Germany was selected for the present investigation. The results show that the combined Topmodel/Green and Ampt runoff approach produce reasonabe results for the simulation of runoff volume for single runoff events at the catchment outlet. The more physically based model approach computed a much more realistic distribution of runoff and P yield producing areas than the SCS curve number method, modified by Lutz (1984). Reasonable results were achieved for sediment yield calculations. Particulate P calculations showed larger deviations between measured and calculated values.

Green and Ampt infiltration into soils of variable pore size with depth

Most expressions for infiltration rely upon the assumption of vertical uniformity in soil texture and hydraulic properties. We present an extension of the results of Beven [1982, 1984] for infiltration and lateral flow in soils with decreasing permeability with depth. Unlike Beven, we base the derivations upon joint changes in soil properties based on an overall change in characteristic pore size via Miller scaling. A set of very simple expressions for the time rate of infiltration are obtained using a Green and Ampt approach for soils with permeability that decreases with depth following linear, power law, and exponential relationships.

Modeling of Infiltration from An Artificial Recharge Basin with a Decreasing Ponded Depth

The first important physical process in basin recharge is the infiltration of water from the basin's bed to the water table below. The Green and Ampt approach was applied to model infiltration from an artificial recharge basin with a decreasing ponded depth. Several field experiments were carried out. Results of one experiment were used to calibrate the model. The suggested approach was then used to predict infiltration for the other experiments and its results were compared to field values.

Green and Ampt analyses for rising water table and intermittent surface flux conditions

Equations developed for a Green and Ampt type analysis for moving water table conditions in an initially saturated homogeneous profile of porous material and used previously in a falling water table study are now applied to a falling‐rising water table sequence in a sand. The ability of the developed equations to be used in a system involving a directional change in water table movement relates to the inclusion in the equations of a term describing the initial saturated depth applicable to each new stage of the analysis. The predictive capability of the Green and Ampt approach for such a system is tested by comparing the results with those obtained from a computer‐based numerical analysis. The relevant subroutine in the computer program required certain restructuring to accommodate the rising water table component. An interpolative hysteresis model is used to describe the accompanying wetting process with the material in question wetting up along primary wetting scanning curves. In comparison with the complexity of the real system during rewetting, the simplicity of the Green and Ampt approach is very marked. Notwithstanding this, it is found that reasonable correspondence occurs, although care is necessary in specifying an appropriate value, applicable to the wetting process, for the characteristic pressure head at the sharp front. The Green and Ampt approach is also extended to include a falling water table system where an applied surface flux of constant magnitude is discontinued during the gravity drainage process. The analysis can be readily adapted to such intermittent inflow and, again, comparisons with a numerical simulation indicate that satisfactory accuracy is achievable.

Modeling Infiltration into Crusted Soils by the Green—Ampt Approach

AbstractThe study deals with infiltration of water through a stable surface crust, wherein the water content at the crust‐soil interface increases with time for a long period, and remains below the saturated value. An approximate Green‐Ampt‐type formulation derived from a physical basis, containing a time‐dependent capillary drive term and a profile shape factor, is evaluated by comparisons to a similarity solution and a finite‐difference numerical solution of the problem. The exact nature of the derived Green‐Ampt formulation is established for early to intermediate stages for certain reasonable conditions. Calculations of cumulative infiltration with time made by the above approach, with the profile shape factor set equal to unity, were within tolerable error from the numerical solution results for one soil and a set of experimental data for another. A previously reported piecewise application of the conventional form of the Green‐Ampt equation is also developed to enable its use from time zero, as an independent predictive method. This method, which includes some implicit correction for the profile shape, gave slightly better calculations of the cumulative infiltration. The above simple methods should also be applicable to related unsaturated flow problems, such as infiltration through a transient crust‐seal resistance and into a layered soil having a fine material overlying a coarse material.

Water Infiltration and Runoff under Rain Applications

AbstractExperiments to verify the validity and to evaluate the performance of rain infiltration models based on extending the Green and Ampt approach are lacking in the literature. There are severe gaps between theory, validity, and practicality of these models. In this study, a physically‐based model for describing infiltration into a homogeneous deep stable soil profile with uniform initial water content distribution is presented. The derivation of the model is based on the concept of mapping the actual wetted soil zone into an equivalent rectangular saturated zone with constant effective hydraulic conductivity and capillary pressure head at the abrupt wetting front. The model takes into account the intial water mobility in the soil profile and predicts the system response under any rainfall pattern. The proposed model is further simplified, for practical purposes, by grouping three basic input parameters into a single parameter, the Surface Saturation Index.The validity of the model was tested and strongly supported by the results of laboratory experiments conducted on samples of three soils, two silt loams and a silty clay loam, under five different (variable and constant) water application rate patterns. It was found that the amount of runoff from a nearly symmetrical convex variable rainfall pattern was very close to that which resulted from its equivalent average constant application rate pattern, regardless of the significant differences between the times at which runoff begins and the characteristics of infiltration rates thereafter.

Unsaturated Hydraulic Conductivity from Cumulative Inflow Data

AbstractA method of determining the wetting‐phase unsaturated hydraulic conductivity K(θ) from the data of cumulative inflow into a uniform soil core when water enters through a porous plate of high hydraulic resistance is described and evaluated. The method is based on piecewise application of the Green and Ampt (1911) approach to the above process of infiltration. The K(θ) determined by this technique from the numerical‐solution inflow data of Yolo light clay were within 20% of the K(θ) values actually used in obtaining the numerical solution in two different cases of hydraulic resistance. Similar analysis of the experimental inflow data of Salkum silty clay loam for four different hydraulic resistances yielded the K(θ) data which closely agreed with the K(θ) values determined by detailed analysis of the soil‐water content transients.