Green-Ampt Infiltration Model Research Articles

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.

Applicability of the Green-Ampt Infiltration Model with Shallow Boundary Conditions

The Green-Ampt model is an approximate analytical solution to Richards’ equation that is commonly used to simulate infiltration processes in hydrological models and land surface schemes. The Green-Ampt model assumes that neither a water table nor an impermeable layer (e.g., bedrock or a frost table) exist near the soil surface. In regional-scale applications these idealized conditions will often not be met, and it is presently unclear what implications this has for regional water resource models. This paper investigates the limiting conditions under which the Green-Ampt model is appropriate and how individual assumptions about lower boundary conditions affect the validity of the model. Guided by the comparison between the Green-Ampt model and numerical solutions to Richards’ equation, various simple revisions to the Green-Ampt model are suggested. Results demonstrate that even when the traditional assumptions are relaxed, the Green-Ampt model often still provides reasonable results for regional-scale anal...

Rainfall infiltration: infinite slope model for landslides triggering by rainstorm

Shallow slope failure due to heavy rainfall during rainstorm and typhoon is common in mountain areas. Among the models used for analyzing the slope stability, the rainwater infiltration model integrated with slope stability model can be an effective way to evaluate the stability of slopes during rainstorm. This paper will propose an integrated Green-Ampt infiltration model and infinite slope stability model for the analysis of shallow type slope failure. To verify the suitability of the proposed model, seven landslide cases occurred in Italy and Hong Kong are adopted in this paper. The results indicate that the proposed model can be used to distinguish failed and not-yet failed slopes. In addition, the proposed model can be used as the first approximation for estimating the occurrence time of a rainfall-induced shallow landslide and its depth of sliding.

Analysis of rainfall-induced infinite slope failure during typhoon using a hydrological–geotechnical model

Rainwater infiltration during typhoons tends to trigger slope instability. This paper presents the results of a study on slope response to rainwater infiltration during heavy rainfall in a mountain area of Taiwan. The Green-Ampt infiltration model is adopted here to study the behavior of rainwater infiltration on slopes. The failure mechanism of infinite slope is chosen to represent the rainfall-induced shallow slope failure. By combining rain infiltration model and infinite slope analysis, the proposed model can estimate the occurrence time of a slope failure. In general, if a slope failure is to happen on a slope covered with low permeability soil, failure tends to happen after the occurrence of the maximum rainfall intensity. In contrast, slope failure tends to occur prior to the occurrence of maximum rainfall intensity if a slope is covered with high-permeability soil. To predict the potential and timing of a landslide, a method is proposed here based on the normalized rainfall intensity (NRI) and normalized accumulated rainfall (NAR). If the actual NAR is higher than the NAR calculated by the proposed method, slope failure is very likely to happen. Otherwise, the slope is unlikely to fail. The applicability of the proposed model to occurrence time and the NAR–NRI relationship is evaluated using landslide cases obtained from the literature. The results of the proposed method are close to that of the selected cases. It verifies the applicability of the proposed method to slopes in different areas of the world.

Infiltration Characteristics of Tropical Soil Based on Water Retention Data

Water retention and hydraulic properties of undisturbed tropical soils collected from many regions of Indonesia were analyzed to estimate infiltration characteristics of the soils. Soil texture was classified based on International Society of Soil Science (ISSS) classification. The van-Genuchten model was used to estimate the relationship between water content and matrix potential at pF=1, pF=2, pF=2.54, pF=4.2. The 165 soil water retention data were used to optimize parameters of the model and to find the air entry value. Green-Ampt and Philip's infiltration models were applied to characterize soil infiltrability of each textural type. The Nash and Sutcliffe's efficiency was used to evaluate numerical simulation of cumulative infiltration of Green-Ampt's infiltration model compared to the results of laboratory experiments. The 165 soil samples were classified and were optimized into 10 ISSS textural types: heavy clay, sandy clay, sandy clay loam, sandy loam, sand, light clay, clay loam, loam, silty clay, and silty clay loam. The results of performance evaluation of Green-Ampt's infiltration model showed that Green-Ampt's infiltration model can describe infiltration characteristics by using soil water retention and hydraulic properties data. The tropical soils based on soil texture exhibit contrasting infiltration characteristics as indicated by infiltration rate, length of wetting front and sorptivity. The characteristics of soil infiltrability are mainly influenced by hydraulic conductivity, initial water content, and matrix potential at the wetting front.

Equação de green-ampt para a infiltração da água no solo aproximações numéricas para explicitação do volume infiltrado

The Green-Ampt infiltration model (1911), still used in Hydrology nowadays, does not allows to have an exact explicitation of the accumulated infiltration water versus time. The present work tries to solve this problem by presenting two solutions. The first equation is original and the second is the result of some improvements made in one of Li et al equations (1976).The relative errors proceeding from these equation were discussed and one example is presented in order to concretize these numerical applications.

A simple method to analyze infiltration into unsaturated soil slopes

Assessment of the stability of embankment and cut slopes over the life of a project are critical issues for railway and motorway infrastructure projects. Experience has shown that many slope failures occur during or shortly after rainfall. Analyses show that failure is initiated by the reduction in near surface suction over some critical depth in the slope. A simple method is proposed in this paper to estimate the time needed for a wetting front to develop. The method which is a modification of the traditional Green–Ampt infiltration model assumes that ponding of water cannot occur on soil slopes and as a consequence soil in the wetted zone remains partially saturated at the point of slope failure. It differentiates between cases where the initial suction in the slope is high and the rate of infiltration is controlled by the rainfall intensity (supply controlled) and, situations where the suction is low, and the rate of infiltration is controlled by the infiltration capacity of the soil (demand controlled). When applied to a case history where field measurements of infiltration into a slope were available the new method provided a reasonable approximation of the measured infiltration time.

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.

Derivation of a two-term infiltration equation from the Green–Ampt model

For a uniform and infinitely deep soil at constant initial volumetric soil water content θ n , the soil surface is subjected instantaneously to a ponded-water head that increases with the square root of time t 1/2 after the initial ponding of water. An integration procedure is used in a rigorous derivation of the one-dimensional Green–Ampt flux equation. The resulting ordinary differential equation is solved exactly to yield the two-term infiltration equation wherein the coefficient of t is the sated hydraulic conductivity, but the ponded-head t 1/2 function must be the same as the one found earlier by a different but exact mathematical derivation. The present findings reveal and describe this previously unknown kinship between the Green–Ampt infiltration model and the two-term infiltration equation, and underscore in still another way the serious limitations of the two-term equation.

A COMPARISON OF THE GREEN-AMPT AND A SPATIALLY VARIABLE INFILTRATION MODEL FOR NATURAL STORM EVENTS

Rainfall-runoff data collected from bare plots (20-216 m2) at 1-min intervals were used to compare theperformance of the Green-Ampt infiltration model and a spatially variable infiltration model (SVIM). The two modelshave the same number of parameters. For 60 natural storm events from six sites in Australia and South-East Asiancountries, the average Nash-Sutcliffe model efficiency was 0.77 for the Green-Ampt model and 0.83 for the SVIM. At allsites, the SVIM consistently outperformed the Green-Ampt model when compared to runoff data at a range of timeintervals and storm events, including events of very long duration. A larger hydrologic lag is needed for the Green-Amptmodel to fit the measured hydrographs in comparison to the SVIM, suggesting that the Green-Ampt model tends tounderestimate the infiltration rate when rainfall intensity is high. Measured rainfall and runoff rates show a positiverelationship between rainfall intensity and infiltration rate. Considerable spatial variability in the infiltration capacity atthe plot scale is implied by this positive relationship. This spatial variability clearly needs to be accommodated ininfiltration models, and the SVIM represents a simple formulation of the infiltration rate as a function of rainfall intensityto address this spatial variability. SVIM parameters can be related to the Green-Ampt parameters, and they couldtherefore be estimated directly using soil properties.

PLOT-SCALE RAINFALL-RUNOFF CHARACTERISTICS AND MODELING AT SIX SITES IN AUSTRALIA AND SOUTHEAST ASIA

During major runoff events when most soil loss occurs, runoff is likely to dominate the rainfall-driven erosionprocesses. Thus accurate estimation of the runoff rate is critical to soil loss predictions. At plot scale, the Green-Amptinfiltration model is commonly assumed to be able to describe the temporal variation of the infiltration rate over a stormevent. Field measurements of both rainfall intensity and runoff rate at 1-min intervals at six sites in the tropical and subtropicalregions of Australia and Southeast Asia, however, strongly suggest that the apparent infiltration rate is closelyrelated to the rainfall intensity and it is essentially independent of the cumulative infiltration amount, features not accordwith the Green-Ampt infiltration equation. Furthermore, the storage effect and runoff rate attenuation are not negligibleat the plot scale. With an initial infiltration amount to determine when runoff begins, an exponential distribution todescribe the spatial variation in the maximum infiltration rate and a linear storage formulation to model the lag betweenrunoff and rainfall, we were able to develop a satisfactory three-parameter model for the runoff rate at 1-min intervalswithin a storm event.

LISEM: A SINGLE-EVENT PHYSICALLY BASED HYDROLOGICAL AND SOIL EROSION MODEL FOR DRAINAGE BASINS. I: THEORY, INPUT AND OUTPUT

A new physically based hydrological and soil erosion model has been developed, which can be used for planning and conservation purposes: the LImburg Soil Erosion Model (LISEM). The LISEM model is one of the first examples of a physically based model that is completely incorporated in a raster Geographical Information System. This incorporation facilitates easy application in larger catchments, improves the user friendliness by avoiding conversion routines and allows remotely sensed data to be used. Processes incorporated in the model are rainfall, interception, surface storage in micro-depressions, infiltration and vertical movement of water in the soil, overland flow, channel flow, detachment by rainfall and throughfall, detachment by overland flow and transport capacity of the flow. Special attention has been given to the influence of tractor wheelings, small roads and surface sealing. Vertical movement of water in the soil is simulated using the Richard's equation. Optionally, the user can choose the Holtan or the Green–Ampt infiltration model. For the distribution flow routing, a four-point finite-difference solution of the kinematic wave is used together with Manning's equation.

Distributed parameter hydrology model (ANSWERS) applied to a range of catchment scales using rainfall simulator data I: Infiltration modelling and parameter measurement

A multi-layer, transient conductivity Green-Ampt infiltration model was evaluated and parameterised for a layered soil, using rainfall simulator data. The model simulates transient surface sealing and subsoil restrictions on infiltration under rainfall. Rainfall simulator plots (1 m2) were run on four soil conditions/layers of a cultivated clay soil and infiltration parameters were derived for each layer: (a) surface (freshly tilled), (b) surface seal (precrusted), (c) tilled layer and (d) subsoil. For this soil, runoff was generated by restricted infiltration into the subsoil when surface sealing was prevented and by surface sealing alone when there was a crust created by prior rain (even though this crust was dried and cracked). For freshly tilled bare soil, surface sealing controlled initiation of surface ponding and subsequent infiltration, but at longer times infiltration was controlled by the subsoil. For freshly tilled soil, a single, consistent set of parameters were obtained for the layered soil system. These parameters gave good predictions of infiltration curves for all plots, including calibration and independent test plots, for a range of tillage depth, antecedent moisture and rainfall intensity. Surface seals reformed rapidly on the pre-crusted plots; infiltration curves were predicted well using a constant low or rapidly declining conductivity. Further research is needed on crusts formed by prior rain and their effect on infiltration parameters, as such crusts are common on bare clay soils except immediately after tillage. A large number of rainfall simulator studies are conducted for a range of purposes. These data should not be ignored as a source of parameters for hydrologic modelling.

AN ANALYTICAL SOLUTION FOR PREDICTING SOLUTE TRANSPORT DURING PONDED INFILTRATION

An analytical solution is presented for one-dimensional solute transport in soil during ponded infiltration. The pore-water velocity υ = q/θ in the convection-dispersion transport equation was obtained by assuming that the water flux density q in the soil can be calculated with the Green-Ampt infiltration model, q = a + b/I, in which a and b are constants and I is the cumulative infiltration rate evaluated using Philip's twoterm infiltration equation. The water content θ was approximated by the saturated water content, θ s . Through an appropriate transformation, the solute transport equation for transient unsaturated flow conditions was linearized and solved analytically for a general initial concentration profile given by an arbitrary number of straight line segments. The solution compared well with more complete numerical solutions of the transport problem, as well as with several experimental data sets

Technical Notes: Effect of Initial Water Content on Green-Ampt Parameters

The relationship between initial water content and Green-Ampt parameters was established explicitly using the Brooks-Corey representation of the soil-water retention curve. Such a relationship enhanced the versatility of Green-Ampt infiltration model. The parametric values measured at a given initial water content can be adjusted to obtain the parametric values at other initial water content conditions.

Optimum Operation of Recharge Basins

Mathematical models based on nonlinear programming are developed for operating recharge-basin systems (also referred to as soil-aquifer treatment systems). The objective of these optimization models is to determine the operation policy (loading schedules) that maximizes the infiltration volume subject to constraints for continuity, infiltration, ground-water flow, and the physical constraints describing the recharge basins. Two basic physical processes that are involved in the recharge-basin systems are the infiltration process and the soil-moisture–redistribution process. The infiltration process is modeled using both the Philip’s and the Green-Ampt infiltration models, and the soil-moisture redistribution process is modeled using Darcy’s equation as well as a kinematic-wave model. An improvement on the developed models is to consider the final moisture content at the end of each cycle time as a decision variable; which also allows the total cycle time to become a decision variable. In the modified applications, the objective is changed to maximizing the infiltration rate instead of maximizing the infiltration volume. Several hypothetical applications are presented to illustrate the modeling procedure.

Field Evaluation of Layered Green-Ampt Infiltration Model Considering Temporal Variation of Physical Properties

A layered Green-Ampt infiltration model considering temporal variation of tilled soil was evaluated with a field experiment on a freshly tilled soil and a soil planted in soybeans under natural rainfalls. Field tests were conducted on a sandy loam soil for two years (1989 to 1990). Temporal variation due to rainfall since last tillage of porosity, hydraulic conductivity and capillary pressure on tilled soil was investigated in 1989 and incorporated into the model as a function of cumulative rainfall energy and porosity. Field data from 1989 were used for model calibration and data from 1990 were used for model verification. A parameter optimization technique was used to calibrate three model parameters, surface roughness, rainfall kinetic energy and final crust conductivity. Using the calibrated parameters from 1989, the model was partially verified with six rainfall events in 1990. The simulated results of the layered model were in good agreement with measured data.

Runoff and Peak Discharges Using Green‐Ampt Infiltration Model

The Green-Ampt infiltration model is used to predict runoff from 12 rangeland and cropland watersheds in Montana and Wyoming. Soil parameters derived from data in standard USDA soil surveys are used, and 99 rainfall events are modeled. The runoff distributions obtained from the model are then used with a hydrograph model to predict the peak discharge from the watershed. Procedures are applied that adjusted the Green-Ampt infiltration parameters for various cover and condition classes. The model is applied to areas of up to 54 sq mi with a wide variety of soil and cover conditions. The runoff volumes and peak discharges are compared with the measured values and with those predicted by the Soil Conservation Service (SCS) curve-number procedure. The Green-Ampt model predicted both the runoff volume and peak discharge better than the curve-number model. The standard error of estimate was less for the Green-Ampt model in nine of 12 watersheds for runoff volumes and in 11 of 12 watersheds for peak discharges.

DEVELOPMENT OF A CRUST FACTOR FOR A GREEN AMPT MODEL

ABSTRACT The formation of a soil crust has been shown to cause a major decrease in infiltration and needs to be accounted for in infiltration models. In response to this need, a procedure based on such properties and wetted front depth was developed for incorporating the steady state crust conductivity into the hydraulic conductivity term of the Green-Ampt infiltration model. This effective hydraulic conductivity is calculated as a harmonic mean of the crust and subcrust hydraulic conductivity. Tests on a range of soils verified that the procedure gives an acceptable first approximation of the crust effects.

Explicit infiltration equations based on the Green–Ampt model

The Green–Ampt infiltration equations are based on physical parameters of the soil that can be either measured or calculated reasonably easily. However, neither the infiltration rate equation nor the cumulative depth of infiltration equation is in a form that can be used easily in hydrologic modeling, as both equations are in an implicit form when time is the independent variable. Therefore iterative procedures must be used to find either the infiltration rate or cumulative depth at a specific time.Explicit infiltration equations have been developed, based on the Green–Ampt infiltration model. These equations describe the infiltration rate and the cumulative depth of infiltration with a maximum deviation from the Green–Ampt equations of 2.5% for any time. The derived equations have been put in dimensionless form by choosing appropriate length and time scales. Approximate values for the length and time scales for 11 different soil textures, ranging from sand to clay, are given. Key words: infiltration, Green–Ampt explicit equations, hydrology, hydrologic models, surface irrigation, surface irrigation models.