Green-Ampt Model Research Articles

Modeling water balance components and irrigation efficiencies in relation to water requirements for double-cropping systems

This paper describes the estimation of total water requirements as well as reservoir releases required to replenish the water deficit for double cropping of rice. A water balance equation is derived and the performance of a project is analyzed. The water balance components were modeled without calibration, and compared with measured data whenever possible. The potential evapotranspiration ET p were modeled for monthly time series using Penman–Monteith model [Monteith, J.L.,1965. Symp. Soc. Exp. Biol. 19, 205–234]. To estimate surface runoff, the proportion of elementary areas that are saturated were described by a spatial distribution function, considering the average total existing water (TEW) of both cropping seasons from 1991 to 1997. The monthly rainfalls (1971–1997) of 53 uniformly distributed rainfall stations were averaged and the rainfall considered uniform over the whole area. The effective meteorological input M e was considered positive to produce runoff. The variation of the soil suction head and hydraulic conductivity with moisture content, studied by Brooks and Corey [Brooks, R.H., Corey, A.T., 1964. Hydraulic properties of porous media. Hydrology Paper No. 3, Colorado State University, Fort Collins, CO] was applied in the Green–Ampt model [Green, W.H., Ampt, G.A., 1911. J. Agric. Sci. 4 (1), 1–24] to estimate infiltration. The performance of a farm irrigation system is, in general, evaluated by the efficiency of the system. The nonlinear Muskingum–Cunge method [Cunge, J.A., 1969. J. Hydraulics Res., Int. Assoc. Hydraulics Res. 7 (2), 205–230] was applied as a distributed channel routing technique to calculate the conveyance losses from the study reservoir (Pedu Reservoir) to the end of the main canal, a total reach of about 108 km. The mean conveyance efficiency from the Pedu dam to the Pelubang barrage (67 km reach) was found to be 66%, while the same from the Pedu dam to the end of the main canals was found to be 59%. Using Central Canal Right Bank Drain (CCRBD) A1 block data as reported by Batumalai and Nassir [Batumalai, R., Nassir, M.A.,1986. Effective water utilization with on farm terminal infrastructure. Northern Regional Water Seminar, Alor Setar, Malaysia], the distribution efficiency was determined to be 94%. The water use efficiency was estimated using MADA’s field water supply data. The overall project efficiency for the main and off-seasons were calculated separately and found to be 18 and 32%, respectively. The total water requirements for rice in the main and off-seasons were determined and the amounts of water needed to release from the reservoir to meet the crop water deficit for double cropping were estimated to be 1385 million cubic meters (MCM).

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.

Watertable dynamics under capillary fringes: experiments and modelling

Watertable heights and total moisture content were measured in a sand column where the piezometric head at the base (“the driving head”) varied as a simple harmonic with periods in the range from 14.5 min to 6.5 h. The watertable height h( t) responded very closely to the driving head compared with the predictions of previous analytical and numerical models. The total moisture quantified as an equivalent, saturated height h tot( t) varied very little compared with the watertable height. Neither h( t) nor h tot( t) deviated significantly from simple harmonics when the driving head was simple harmonic. This indicates that non-linear effects are weak and hence that analysis based on linear solutions have fairly broad applicability. When h( t) and h tot( t) are simple harmonic, the ratio n d=[d h tot/d t]/[d h/d t] is a constant in the complex formalism. Its magnitude | n d| is the usual effective porosity while its argument accounts for the phase shift which is always observed between h( t) and h tot( t). Within the current range of experiments this dynamic, effective porosity n d appears to be almost independent of the forcing frequency, i.e., it is a function of the soil and its compaction only. Introducing the complex n d enables analytical solution for the watertable height in the column which is simpler and more consistently accurate over a range of frequencies than previous models including Richard’s equation with van Genuchten parameters corresponding to the measured water retention curve. The complex n d can be immediately adopted into linear watertable problems in 1 or 2 horizontal dimensions. Compared with “no fringe solutions”, this leads to modification of the watertable behaviour which is in agreement with experiments and previous models. The use of a complex n d to account for the capillary fringe in watertable models has the advantage, compared with previous models, e.g., [Parlange J-Y, Brutsaert W. A capillary correction for free surface flow of groundwater. Water Resour Res 1987; 23(5):805–8.] that the order of the differential equations is lower. For example, the linearised Boussinesq equation with complex n d is still of second order while the Parlange and Brutsaert equation is of third order. The extra work of calculating the imaginary part of the initially complex solution is insignificant compared to dealing with higher order equations. On the basis of the presently available data it also seems that the “complex n d approach” is more accurate. This is to be expected since the complex n d accounts implicitly for hysteresis while the Green–Ampt model does not. With respect to linear watertable waves, accounting for the capillary fringe through the complex n d is a very simple extension since the determination of wave numbers already involves complex numbers.

A numerical method for simulating discontinuous shallow flow over an infiltrating surface

A numerical method based on the MacCormack finite difference scheme is presented. The method was developed for simulating two-dimensional overland flow with spatially variable infiltration and microtopography using the hydrodynamic flow equations. The basic MacCormack scheme is enhanced by using the method of fractional steps to simplify application; treating the friction slope, a stiff source term, point-implicitly, plus, for numerical oscillation control and stability, upwinding the convective acceleration term. A higher-order smoothing operator is added to aid oscillation control when simulating flow over highly variable surfaces. Infiltration is simulated with the Green–Ampt model coupled to the surface water component in a manner that allows dynamic interaction. The developed method will also be useful for simulating irrigation, tidal flat and wetland circulation, and floods. Copyright © 2000 John Wiley & Sons, Ltd.

A numerical method for simulating discontinuous shallow flow over an infiltrating surface

A numerical method based on the MacCormack finite difference scheme is presented. The method was developed for simulating two-dimensional overland flow with spatially variable infiltration and microtopography using the hydrodynamic flow equations. The basic MacCormack scheme is enhanced by using the method of fractional steps to simplify application; treating the friction slope, a stiff source term, point-implicitly, plus, for numerical oscillation control and stability, upwinding the convective acceleration term. A higher-order smoothing operator is added to aid oscillation control when simulating flow over highly variable surfaces. Infiltration is simulated with the Green–Ampt model coupled to the surface water component in a manner that allows dynamic interaction. The developed method will also be useful for simulating irrigation, tidal flat and wetland circulation, and floods. Copyright © 2000 John Wiley & Sons, Ltd.

MODIFIED GREEN AND AMPT MODELS FOR LAYERED SOIL INFILTRATION AND MUDDY WATER INFILTRATION

Soil water infiltration is an important hydrological process at the earth's surface. It is connected with both soil water recharge and surface runoff and erosion. While most soil water infiltration models are designed for clean water entering uniform soil profiles, many actual soil profiles consist of layers. Existing models do not account for surface deposition during muddy water infiltration. The objectives of this study are to measure soil water infiltration into layered soil columns, to measure infiltration with various muddied waters, and to develop simple models describing layered soil infiltration and muddy water infiltration. Experimental results show clear effects of layering and muddy water on soil water infiltration. Layered soil infiltration can be divided into two time frames: (i) when infiltration is controlled by the top soil layer and (ii) when infiltration is controlled by a subsurface layer. A simple modification to the Green-Ampt model is shown to provide a good description of two-layer infiltration. Muddy water infiltration is related to the sediment concentration of the infiltrating water. The larger the sediment concentration, the slower the infiltration. A modified Green-Ampt model is also shown to be useful for describing muddy water infiltration.

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.

WATER AND HEAT BALANCES IN THE MIDDLEREACH CATCHMENT OF TAMA RIVER AND SENSITIVITY ANALYSIS

A distributed model of water and heat transfers is described at first. The subgrid heterogeneity of land use is considered by using a nesting method. Evapotranspiration and latent heat flux are computed by the Penman-Monteith equation, infiltration excess during heavy rains is simulated by a generalized Green-Ampt model whereas saturation excess during the remaining periods is obtained by balance analysis in unsaturated soil layers. Surface temperatures are solved by the Force-Restore method. Two dimensional groundwater flow is simulated to consider the interactions between grid cells. The river flowrouting is conducted by using the kinematic wave method. The model is applied to the middle-reach catchment of Tama river and it is verified by the observed discharges at the catchment outlet in the threeyears from 1992 to 1994. Finally, sensitivity analysis shows the effects of input data and model parameters on annual water and heat balances.

Integrated Analysis of Water and Heat Balances in Tokyo Metropolis with a Distributed Model.

Integrated analysis of water and heat balances in Tokyo metropolis is conducted by applying a distributed model. The subgrid heterogeneity of land covers is considered by using a nesting method. Evapotranspiration is computed by the Penman-Monteith equation and sensible heat flux by the aerodynamic method. Surface temperature is solved by the Force-Restore method. Infiltration excess during heavy rains is simulated by a generalized Green-Ampt model which considers soil stratification and rain unsteadiness. Saturation excess during the left periods is obtained by balance analysis in unsaturated soil layers. Two dimensional groundwater flow is simulated to consider the inter-actions between grid cells and the impact of groundwater table on surface runoff generation and heat flux partition. The simulated water and heat balances are dually verified both in the whole study area and in a catchment inside it. It is shown that both urbanization and weather variation have big impacts on water and heat balances in Tokyo me-tropolis.

Modeling Infiltration into a Multi-layered Soil during an Unsteady Rain

The Green-Ampt model is generalized to model infiltration into a multi-layered soil during an unsteady rain. One dimensional numerical simulation scheme of the Richards equation is also developed which is suitable to deal with transfers between two kinds of boundary conditions…water flux control and water head control. Modeling results of the generalized Green-Ampt model are compared with a numerical simulation for cases of 2 and 3 layered soil as examples. It is shown that the proposed model matches the Richards equation quite well with computation time less than tenth of the latter, thus promising to play a role in watershed modeling.

Use of Green-Ampt model for analyzing one-dimensional convective transport in unsaturated soils

A general analytical solution to the equation describing purely convective vertical transport of a conservative solute under transient water flow conditions is presented. Richards equation does not yield analytical solutions for the flow field, except under restrictive choices of hydraulic properties relating water content, hydraulic conductivity and the soil matric potential. The utility of the Green-Ampt model for homogeneous unsaturated soils is investigated as an alternative to Richards equation. This model, though approximate, provides analytical solutions to the flow field. It is found that the flow quantities required for the analytical solution of convective transport (specifically the soil water storage) are predicted accurately by the Green-Ampt model. Comparisons of numerical and analytical solutions of solute concentration profiles suggest that the Green-Ampt water flow model is adequate for convective solute transport predictions, and that the flow field need not be computed by the more numerically expensive Richards equation for this problem.

Effective Porosity and Flow Rate with Infiltration at Low Tensions into a Well-structured Subsoil

A combination of tension infiltrometers and dye tracers was used to investigate the extent and nature of water movement at low tensions through the well-structured subsoil of Ships clay (very-fine, mixed, thermic, Chromic Hapluderts). Dyed-water was placed in the reservoirs of tension infiltrometers and allowed to infiltrate into the soil under seven tension sequences to separate different size pores effective in transmitting water. Flow patterns were then revealed by exposing dye-stained soil after each infiltration sequence. The results showed that, when water was supplied at tensions <24 cm, the effective porosity (fraction of pores that were stained) in this subsoil was primarily macro- and mesoporosity, which constituted about 5% of the total soil porosity. Under flow at 0-cm tension, macropores =0.5 mm and mesopores from 0.06 to 0.5 mm (radius for cylindrical pores or width for planar pores) contributed about 89% and 10% of the total water flux, respectively. Micropores <0.06 mm contributed the remaining 1% of the total water flux, but constituted about 95% of the total soil porosity. Dye stain patterns showed that water flow at tensions <24 cm in this structured subsoil was primarily controlled by slickenside fissures, root channels, and vertical fissures. The nonuniform flow pattern caused water to penetrate to depths as much as 11 times deeper than expected from a Green-Ampt model that considered the total soil porosity to be active in transmitting water. By replacing the air-filled porosity in the Green-Ampt model with the active macro- plus mesoporosity, calculated wetting front depths were close to the observed maximum dye depths.

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.

Experimental Study on the Decreasing and Recovery of Infiltration and the Application of the Green-Ampt Model

In order to apply an infiltration model to determine excess rain-fall in long term runoff analysis or water balance analysis, it is necessary to examine whether the model is suitable to describe not only the decreasing of infiltration capacity due to rainfall but also the recovery due to evapotranspiration. In this study, we used a soil column with impermeable bottom to investigate the change of infiltration capacity for various antecedent evaporation under ponding condition. The observed data showed that the infiltration capacity decreased abruptly when the wetting front reached the bottom. Green-Ampt and Horton's infiltr-ation model were used to fit these experimental data. The results indicated that, in every instance, Green-Ampt equation gives better results than Horton's equation.

Falling-head ponded infiltration with evaporation

The problem of falling-head ponded infiltration with evaporation is solved using the Green-Ampt (or delta-function) model. A significant parameter is ε K ̄ , the ratio of evaporation rate to mean hydraulic conductivity in the wetted region. An illustrative example with ε K ̄ = 1.633 gives a time for disappearance of water from the soil surface only 45.6% of that for the case ε K ̄ = 0 . When ε K ̄ = 1.633 , only 57.8% of the water infiltrates, with 42.2% lost by evaporation.

Infiltration experiments on loess soils and their implications for modelling surface runoff and soil erosion

Infiltration parameters such as infiltration rate, the infiltration control zone depth and the initial soil moisture content, used in the Holtan/Overton equation, have a strong impact on the output of the erosion model ‘ANSWERS’. Therefore, infiltration was measured accurately and spatial and temporal variability were taken into account. 72 infiltration experiments on three types of loess soils under simulated rain show that the Holtan/Overton equation describes infiltration correctly. Both Philip's equation and the Green-Ampt model yield similar results. Because the infiltration parameters show a “within-unit” variance which is larger than the “between-unit” variance, no differences in infiltration characteristics between the three loess soil types could be detected statistically. To evaluate the consequences of the large spatial variability of infiltration, stochastic methods must be used in combination with a distributed hydrologic model. Consecutive simulated rainstorms applied to the same samples show the influence of temporal variability in infiltration behaviour. This type of variability is attributed to the formation of surface crusts. The influence of crust formation on Holtan infiltration can be expressed in terms of a change in infiltration control zone depth. Assuming a relation between crusting and cumulative kinetic energy of rain, the temporal variability of infiltration behaviour was successfully modelled, yielding an empirical relation between control zone depth and cumulative kinetic energy of rain. However, a more physically based hydrologic sub-model of the influence of crusting on infiltration during the growing season is needed.

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.

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.

Integrable flow equations that incorporate spatial heterogeneity

Exactly solvable models are constructed in the Darcy-Buckingham approach to unsaturated flow in porous media with continuous spatial variability. The steady soil water potential distribution, for evaporation from a scale-heterogeneous soil with water table, is given explicitly. The cumulative infiltration predicted by a scale-heterogeneous Green-Ampt model is shown to be inconsistent with that expected from a temporal power series solution of the general flow equation. New integrable forms of the unsaturated heterogeneous flow equation are built up from those exactly solvable forms of the homogeneous flow equation which possess special Lie-Backlund symmetry groups.

Asymptotic infiltration into a soil which contains cracks or holes but whose surface is otherwise impermeable

An asymptotic, one-dimensional Green-Ampt model is derived for infiltration into a soil whose surface is impermeable except for regularly spaced vertical cracks, and infiltration into a cylindrical soil column whose top surface is also impermeable except for a central hole. The model is valid at times when the wetting front has become horizontal and corresponds to one-dimensional infiltration initiated from a plane lying above or below the soil surface, depending on the crack spacing/depth ratio (or column radius/hole depth ratio). When applicable, asymptotic Green-Ampt solutions are shown to agree well, in selected cases, with corresponding finite difference solutions of the saturated-unsaturated flow equations.