AMPT Model Research Articles

Closure to “Improved Decomposition Solution to Green and Ampt Equation” by Sergio E. Serrano

Michel presents an interesting comment to the writer’s contribution Serrano 2003a . His Eqs. 1 – 4 represent a novel approximate solution to the Green and Ampt equation. The problem I see is that his solution falls into the category of successive numerical approximation schemes of the implicit Green and Ampt model, of which there are many available in the literature and as such suffers from the typical limitations of numerical approximations, for example, results are obtained after a series of numerical approximations, solutions are not general in analytic form, or solutions are implicit. The result presented by Serrano 2003a constitutes an explicit general analytical solution with remarkable accuracy for the set of applications required by Eq. 11 by Serrano 2003a . Nonetheless, the method proposed in the discussion by Michel is worth pursuing an analysis on the accuracy, convergence, and numerical stability that may prove useful in hydrologic applications. The discussion by Barry et al. raises many of the same questions as in their former discussion Barry et al. 2003 to the writer’s paper on the Green and Ampt equation Serrano 2001a . This writer replied in detail to those questions Serrano 2003b and the writer will not repeat those comments here. In summary, the writer demonstrated conclusively that the result by Serrano 2001a and its corollary by Serrano 2003a constitute the first explicit solutions of the Green-Ampt infiltration equation; they are neither a difficult to calculate and mostly unavailable Lambert W series approximation, or empirical approximations to the Lambert W series approximation. It was demonstrated that the empirical expressions proposed by Barry et al. 2003 are incorrect as shown by Serrano 2003b, Figs. 1, 2, and 3 . The results by Serrano 2001a and Serrano 2003a were obtained using a decomposition series Adomian 1994 , which is a systematic procedure to obtain analytical solutions to nonlinear equations without linearization, perturbation, or discretization see Serrano 1997, 2001b . In this case, decomposition yields a remarkably accurate result when the convergence criterion is satisfied. However, there are several characteristics that are obvious to anyone familiar with asymptotic series. Eq. 6 by Serrano 2003a follows directly from Eq. 5 , after a logarithmic series pattern is identified. This produces a general series, Eqs. 6–8 by Serrano 2003a , that obviously contain more terms in partial closure than Eq. 5 . The essence of the argument presented in the discussion by Barry et al. is that the improved solution, Eq. 9 by Serrano 2003a is not better than the original decomposition solution Eq. 15 by Serrano 2001a . They present two tables of numerical comparisons between the above equations and another approximation, the Lambert W series approximation, Eq. 7 by Serrano 2001a . The discussers call the Lambert W series approximation “the exact GA formula” and define the “maximum relative error” as the difference between the various approximations. This analysis is inappropriate because it does not compare with respect to the exact Green and Amp solution. This is possibly the reason why the discussers’ Tables 1 and 2 completely contra-

PSEM_2D: A physically based model of erosion processes at the plot scale

This paper presents the development and first applications of the Plot Soil Erosion Model 2D (PSEM_2D). Infiltration is computed using a Green and Ampt model, overland flow is computed using the depth‐averaged two‐dimensional unsteady flow equations (Saint Venant equations), and soil erosion is computed by combining the equation of mass conservation of sediment and a detachment‐transport coupling model for erosion by runoff. A shear stress approach is used to determine the transport capacity. The formation of a covering cohesionless layer as a result of depositing sediment and action of rainfall impact before runoff is considered. The erosion processes involved are rainfall and runoff detachment of original soil, rainfall redetachment, and overland flow entrainment of sediment from the deposited layer, and deposition. The model uses a single representative particle size. Complex rainfall events on natural slopes can be simulated. The accuracy of the predictions for erosion of planar surfaces is tested by comparison with observed data obtained from experiments and with an analytical solution. Good agreement between the calculated results and measured data was found. A sensitivity analysis was also performed. Limitations related to the description of overland flow on plane soil surface are pointed out. Finally, an application to a nonplanar natural surface of 75 m2 illustrated the distribution of erosion and sedimentation over the plot.

Scaling of Infiltration and Redistribution of Water across Soil Textural Classes

Results with an empirically based one‐parameter model showed that the pore‐size distribution index (λ) described in the Brooks and Corey formulation of soil hydraulic properties can scale the soil–water retention curves below the air‐entry pressure head (ψb) values across dissimilar soils. It is shown here that ψb and saturated hydraulic conductivity (Ks) are also strongly related to λ, and thus all hydraulic parameters may be estimated from λ. The major objective here was to examine how these relationships to λ lead to relationships for infiltration and soil water contents during redistribution across soil textural classes. The Root Zone Water Quality Model simulated infiltration for four rainfall intensities and two initial pressure head conditions and redistribution for four initial wetting depths and two initial pressure head conditions in 11 textural class mean soils. All infiltration results across textural classes were scaled quite well by using the λ‐derived normalization variables based on the dimensional analysis of the Green–Ampt model. Thus, if infiltration for one soil (λ) is known, infiltration for other soils (λs) can be estimated. Additionally, we present infiltration, as well as redistribution, as explicit functions of λ. These functions can be used to approximately estimate infiltration and soil water contents across soil types for other soils and conditions by interpolation. This study enhances our understanding of the soil–water relationships among soil textural classes, and hopefully, provides a basis of further studies under field conditions for (i) estimating spatial variability of soil water for site‐specific management and (ii) for scaling up results in modeling from plots to fields to watersheds.

Étude de la migration du soluté d’un lixiviat dans un sol non saturé par la méthode TDR

The protection of the environment requires building waste containment systems made up of liners of compacted soil. In this paper, infiltration tests are carried out on soil columns equipped with TDR probes to investigate how water and pollutants migrate in the liners. The TDR method is a technique to measure simultaneously the volumetric water content and the electrical conductivity lor the impedance) of the soil in a continuous manner. Using six soils and three different leachates, new relationships between the volumetric water content (θ) of the soil and its dielectric constant (e) is established. These relationships appear to be more accurate than the one of Topp et al. (1980). They are used to determine water content profiles in a soil column. The relationship between the leachate solute concentration and the electrical conductivity allows to compute the solute concentration profiles in the soil column and the solute breakthrough curve. These curves are used to determine solute convection rate and solute apparent dispersion coefficient. Infiltration test results show that the soil permeability and the diffusivity increase when the leachate is infiltrated. The infiltration rate and the solute convection rate are higher than the leachate outflow rate and the three rates yield to a same value which depends on the soil permeability. The Green and Ampt (1911) model applied to the infiltration shows that the movement of the wet front is faster than the movement of the pollution front. The apparent dispersion coefficient and the solute convection rate are computed by applying the statistic distribution law to the moisture and the solute concentration profiles. It is observed that the apparent dispersion coefficient increases during the saturation of the sample. The electrical conductivity and the solute concentration of the percolated leachate are scaled with the initial values. The evolution curves of these scaled values with elapsed time are used to compute the apparent dispersion coefficient. There is little difference between the apparent dispersion values obtained with the scaled electrical conductivity evolution curve and the scaled solute concentration evolution curve. The use of the TDR measurements allows comparison between solute and water migration parameters and the obtained results can be applied to in situ permeability measurements.

RECHARGE ESTIMATION USING INFILTRATION MODELS

ABSTRACT Different infiltrations models were tested at 50 locations in a basin based on the soil type and land use variations at Neyveli. Infiltration models namely Green Ampt model, Modified Kostiakov model and Horton model were found to be fit to the observed field data to estimate infiltration rates at any given time and their parameters were determined using least square method. The basin is divided into four zones based on location of rain gauge stations. Ground water recharge was estimated using three infiltration models for each zone. Their results were compared with that of the standard SWAT (Soil and Water Assessment Tool) model developed by the USDA agricultural research service (ARS). Horton model was found to be high correlated with SWAT model when compared to the other two infiltration models. It can be concluded that Horton model is the most appropriate infiltration model for estimating recharge in Neyveli region.

Influence of rainfall-induced wetting on the stability of slopes in weathered soils

Shallow failures of slopes in weathered soil are caused by infiltration due to prolonged rainfall. These failures are mainly triggered by the deepening of the wetting band accompanied by a decrease in matric suction induced by the water infiltration. This paper reports trends of rainfall-induced wetting band depth in two types of weathered soils that are commonly found in Korea. Both theoretical and numerical analyses for wetting band depth are presented based on the soil–water characteristic curve obtained using filter paper as well as tensiometer tests. It is found that the magnitude of wetting front suction plays a key role in the stability of slopes in weathered soils. Theoretical analysis based on modified Green and Ampt model tends to underestimate the wetting band depth for typical Korean weathered soils. It was also deduced that for Korean weathered soils, the factor of safety drops rapidly once the wetting band depth of 1.2 m reached.

Kaon interferometry at RHIC from the AMPT model**Slides of this conference talk can be downloaded from http://nt3.phys.columbia.edu/people/zlin/PUBLICATIONS/

The two-kaon interferometry at RHIC is studied in a multi-phase transport model. Similar to the pion case, we find strong spacetime correlation at freeze-out for the kaon emission source, which results in a large positive Rout–t term and tends to reduce the Rout/Rside ratio. Unlike in the pion case, the source radii for kaons determined from the emission function are close to the radius parameters extracted from a Gaussian fit to the correlation function.

Role of run-on for describing field-scale infiltration and overland flow over spatially variable soils

This study examines the role of run-on process on field-scale infiltration and one-dimensional overland flow over spatially heterogeneous hillslopes. Because of the high degree of heterogeneity exhibited by the soil parameters that govern the mechanisms of infiltration and overland flow on slopes, the analysis of hillslope hydrological processes requires a stochastic approach. The saturated hydraulic conductivity K s is considered to be the only random quantity and is represented by a lognormal random field in the horizontal directions, and the soil is assumed to be homogeneous in the vertical direction. The analysis is performed by comparing the behavior of field-scale ensemble mean and variance of infiltration and overland flow rates for cases with and without run-on. The Green–Ampt model is used to describe infiltration at the local scale as it has parameters that can be easily estimated for a wide range of soils. An extensive set of Monte-Carlo simulations for all cases is supplemented with supporting theoretical analysis for the case when run-on is negligible. Field-scale mean and variance of infiltration as functions of time are computed for different parameters of the random K s field. Results reveal that in the presence of run-on, mean field-scale infiltration increases, which in turn has a significant influence on hillslope hydrograph. Non-dimensional formulation of the ensemble averaged mean and variance of infiltration and overland flow is presented with the aid of scaled variables. Two dimensionless numbers γ and β expressing the characteristic time scales that govern infiltration and overland flow are developed.

Analytical solutions in a hydraulic model of seepage with sharp interfaces

Flows in horizontal homogeneous porous layers are studied in terms of a hydraulic model with an abrupt interface between two incompressible Darcian fluids of contrasting density driven by an imposed gradient along the layer. The flow of one fluid moving above a resting finger-type pool of another is studied. A straight interface between two moving fluids is shown to slump, rotate and propagate deeper under periodic drive conditions than in a constant-rate regime. Superpropagation of the interface is related to Philip's superelevation in tidal dynamics and acceleration of the front in vertical infiltration in terms of the Green–Ampt model with an oscillating ponding water level. All solutions studied are based on reduction of the governing PDE to nonlinear ODEs and further analytical and numerical integration by computer algebra routines.

Development of WEP model and its application to an urban watershed

AbstractA distributed hydrological model, water and energy transfer processes (WEP) model, is developed to simulate spatially variable water and energy processes in watersheds with complex land covers. In the model, state variables include depression storage on land surfaces and canopies, soil moisture content, land surface temperature, groundwater tables and water stages in rivers, etc. The subgrid heterogeneity of land use is also taken into consideration by using the mosaic method. For hydrological processes, evapotranspiration is 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 doing balance analysis in unsaturated soil layers. A two‐dimensional simulation of multilayered aquifers is performed for groundwater flow. Flow routing is conducted by using the kinematic wave method in a one‐dimensional scheme. For energy processes, short‐wave radiation is based on observation or deduced from sunshine duration, long‐wave radiation is calculated according to temperatures, latent and sensible fluxes are computed by the aerodynamic method and surface temperature is solved by the force–restore method. In addition, anthropogenic components, e.g. water supply, groundwater lift, sewerage drainage and energy consumption, etc. are also taken into account. The model is applied to the Ebi River watershed (27 km2) with a grid size of 50 m and a time step of 1 h. The model is verified through comparisons of simulated river discharges, groundwater levels and land surface temperatures with the observed values. A comparison between water balance at present (1993) and that in the future (2035) is also conducted. It is found that the hydrological cycle in the future can be improved through the implementation of infiltration trenches for the storm water from urban canopies. Copyright © 2001 John Wiley & Sons, Ltd.

Modelling of water and sediment transport over grassed areas

Grassed areas, such as grass filter strips (GFS) and grassed swales, have been used extensively for the protection of surface water against erosion and polluted runoffs. A mathematical model of sediment transport in runoff over grass has been developed, allowing an assessment of the sediment removal efficiency of GFS and swales for non-submerged flow conditions. The model is one-dimensional and simulates two main processes: (1) generation of runoff and (2) sediment transport. The modified Green–Ampt model is used for assessment of infiltration, while a kinematic wave model is used for simulation of overland flow. A transport equation is used for modelling of sediment movement through grass, where sediment deposition is assessed by the method developed at the University of Aberdeen. The model does not simulate particle trapping in a pond (which may develop upstream from a GFS), re-suspension of particles already deposited, or infiltration of particles into soil. For a known particle size distribution of inflow sediment, the model is capable of predicting the particle size distribution of the outflow sediment. The model was developed for modelling single rain events. However, it could be also applied for a sequence of rain events assuming that the initial soil wetness is constant. An example of model application in an urban area is presented in the paper, along with sensitivity analysis of the main model results.

Analysis of Infiltration and Runoff in an Olive Orchard under No‐Till

Four infiltration techniques (falling head, ring, rainfall, and tension infiltrometer) were used to determine the saturated hydraulic conductivity, Ks, and the wetting potential front, hf, of the Green–Ampt model. Water release curves from soil cores were also used for estimating hf The objective was to compare the performance of the different techniques for the assessment of infiltration in a no‐tillage olive (Olea europaea L. subsp. europaea) orchard. Measurements were performed in two areas of the orchard, below canopy (C) and interrow among trees (IR). With the exception of the tension infiltrometer, all techniques showed significant differences in Ks and hf between C and IR areas, attributed to different compaction. Differences in Ks among techniques were within the range observed previously. The hf estimated from the falling‐head technique was significantly higher than that measured with the other techniques. The discrepancies in the results obtained with the tension infiltrometer were attributed to insufficient time of measurement, leading to recommendations for a different field procedure and analysis of this technique. To assess the use of the techniques described above for the characterization of plot infiltration, rainfall and runoff were measured in a 128‐m2 plot. A numerical model was then used to predict runoff using the infiltration measurements. The results showed that runoff prediction is improved when different values of Ks and hf are considered for the C and IR areas instead of a single average value. The numerical analysis of the effects of tree arrangement on runoff prediction from infiltration measurements indicated that if the trees were placed along the contour lines, runoff would decrease relative to the standard tree arrangement.

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.

PREDICTION OF CRUST-INDUCED SURFACE RUNOFF WITH DISC INFILTROMETER DATA

The process of rainfall infiltration into crusted soil has been the focus of many analytical and numerical studies. However, most of these studies have been supported by laboratory data because no field data were available. Following recent field experiments on crusted soils, which provided crust conductivity values using the disc infiltrometer technique, a simple two-layer Green and Ampt model is proposed. This model is of interest because it uses only measured variables-saturated hydraulic conductivity (K), pressure head, initial and saturated volumetric water content, and microscopic capillary length-as input data. Runoff in the model is calculated as the difference between cumulative rainfall and infiltration. Because actual runoff data is available and no parameter calibration is required, the comparison with model output serves as a validation test for the input data. Close agreement between measured and calculated runoff is found when the surface crust is considered, which demonstrates the importance of surface crusting and increases the confidence in the measured K values. It also shows that K measured at the 1-m2 scale remains a relevant parameter, even for the study of a process that involves a scale two orders of magnitude larger.

The absorption of water into a porous solid consisting of two dissimilar layers

SummaryAnalytical modelling of the movement of water through porous solids consisting of more than one homogeneous layer is a problem in soil science and in construction engineering. In this paper equations based on the Green and Ampt model describe the absorption of water into a two‐layer composite bar for the cases of absorption through a material of large sorptivity into one of smaller sorptivity and vice versa. These predictions are compared with experimental results. There is broad agreement between theory and experiment at all times. We conclude that the absorption of water into a two‐layer composite is ultimately controlled by the second material in the absorbing sequence irrespective of whether this material has the larger or the smaller sorptivity.

A sharp wet front analysis of capillary absorption into n-layer composite

New analytical results are found for the capillary absorption of a liquid into a porous (sorptive) composite solid composed of n parallel layers of arbitrary thickness and material properties. The analysis is based on the `sharp wet front' model (also known as the the Green - Ampt model) and the results are exact for that model. A contact impedance acting at the interface between layers is included. The physical approximations of the model are discussed. The cumulative capillary absorption as a function of time is expressed in terms of the sorptivity, permeability and porosity of the materials of the individual layers. Experimental data obtained on composite bars of gypsum plaster and plaster/sand materials agree well with model predictions, although they test the model over only a limited range of parameter values. For these composite specimens, there is no evidence of a hydraulic contact impedance at the interface between layers. An asymptotic expression is given for the effective sorptivity of an alternating composite ABAB....