Philip Equation Research Articles

Determining the Coefficients of Philip's Equation and the Optimal Roughness Coefficient Using the Simulation of the Advancing Phase in Border Irrigation with the Dynamic Wave Model

Determining the Coefficients of Philip's Equation and the Optimal Roughness Coefficient Using the Simulation of the Advancing Phase in Border Irrigation with the Dynamic Wave Model

Comparison of Methods Predicting Advance Time in Furrow Irrigation

In the design of furrow irrigation, and in general in surface irrigation, the reliable estimation of the advance time at the furrow end (tL) is a key issue for improving the efficiency and uniformity of irrigation. In this study, three methods are used for estimating the tL, and their results are compared with the experimental data of fifteen different furrows from the international literature. These methods are as follows: (a) the Valiantzas equation, (b) the method presented by Walker and Skogerboe, based on solving the volume balance equation by the Newton–Raphson iterative procedure and (c) the method of Philip and Farrell. The first two methods assume that the infiltration is described by the Lewis–Kostiakov equation and the extended Lewis–Kostiakov equation, respectively, while in the case of the Philip and Farrell method, the infiltration is described by the Philip equation and the Lewis-Kostiakov equation. The results showed that in most cases of the first two methods, the absolute relative error value of the predicted time tL was less than 10%. The Philip and Farrell method using the Lewis–Kostiakov infiltration equation underestimates the time tL and fails especially in the case where the volume of the surface water is not negligible compared to the total volume of water entering the system. The Valiantzas method is recommended because it was simpler and easier to use and showed greater prediction accuracy of tL, resulting in better planning of irrigation systems and contributing to water saving, which is currently a big issue.

Long-term effects of barley residue managements on soil hydrophysical properties in north-western Iran

The cold semi-arid cropping system is facing soil degradation, climate variability, and drought. For this reason, crop residue management is critical to soil and water conservation and the sustainability of farmers' livelihood. This study was conducted to test the hypothesis that in a cold semi-arid climate, the hydraulic properties of soil can be significantly affected by long-term crop residue management. To test this hypothesis, we investigated the changes in soil hydraulic properties (saturated hydraulic conductivity (Ks), soil water retention (SWR), cumulative infiltration (CI), parameters of van Genuchten SWR (θs, θr, α, and n), and Philip's equation indices (sorptivity and A) following long-term (five years) crop residue management. There were three treatments: (i) complete removal of crop residue from the soil surface (T1), (ii) incorporation of crop residue into the soil after harvest (T2), and (iii) burning of crop residue on the field (T3). The results showed that the Ks value was higher (p ≤ 0.05) in T2 (incorporation, 0.36 cm min−1) than in T1 (removal, 0.30 cm min−1) or T3 (burning, 0.26 cm min−1). Also, the α value was lower (p ≤ 0.05) in incorporation treatment (0.032 cm−1) than in removal treatment (0.042 cm−1) or burning treatment (0.048 cm−1). The value of S (1.72 cm min-0.5) in incorporation treatment differed significantly (p ≤ 0.05) from that of removal (1.09 cm min-0.5) and burning (1.31 cm min-0.5) treatments. Noticeable differences in soil water retention were greater at low soil water suction heads in the SWR. The differences between the SWR of treatments at low suction heads grew over time. A little difference was observed between the SWR of treatments in high suction heads. The cumulative infiltration curve for incorporation treatment differed from that obtained for removal and burning treatments, with no sizable differences observed between removal and burning over five years. The results of this study indicated that the increase in soil organic matter (SOM) for burning reduced the negative effects of burned barley residue on soil hydraulic properties to some extent. Thus, burning residues may have a little negative impact on a sustainable cropping system. The results revealed that the incorporated barley residue increased the infiltration of water into the soil more than other residue management practices in the cold semi-arid region.

Modelling soil water infiltration variability using scaling

One of the most substantial and crucial parameters for irrigation in agriculture is water infiltration into the soil. Given the variability of soil properties, the infiltration characteristics also vary. The present study aims to model soil water infiltration using scaling. In the present research, a new approach for scaling the infiltration equation was developed and evaluated for 22 infiltration tests. In the new method, the scaling factor ( F s ) for each equation equals the depth of infiltrated water after the specified time ( t s ) in the reference infiltration equation. This new method was applied to Philip's equation and was compared with previous Philip equation scaling methods such as sorptivity coefficient ( α s ), transmissivity coefficient ( α A ), the optimal factor obtained using the least squares error ( α o p t ), geometric, arithmetic and harmonic mean α s and α A . Results showed that scaling using F s has the best match with measured data (R2 = 0.99, MBE = 0.0006 and RMSE = 0.001) when compared to other Philip equation scaling methods. Among scaling techniques from the literature, F s had the highest correlation with α o p t (R2 = 0.96). The proposed method applied to the Kostiakov–Lewis infiltration equation was also evaluated. The results of the scaling of the Kostiakov–Lewis equation showed that to use reference curve is optional and each of the infiltration curves can be used as reference curve. As a whole, the results of the proposed method showed that the cumulative infiltration curve can be obtained using minimum infiltration-time measurement data.

Estimating the parameters of Philip infiltration equation using artificial neural network

Infiltration rate is one of the most important parameters used in irrigation water management. Direct measurement of infiltration process is laborious, time consuming and expensive. Therefore, in this study application of some indirect methods such as artificial neural networks (ANNs) for prediction of this phenomenon was investigated. Different ANNs structures including two training algorithms (TrainLM and TrainBR), two transfer functions (Tansig and Logsig), and different combinations of the input variables such as sand, silt, and clay fractions, bulk density (BD), soil organic matter (SOM), cumulative infiltration (CI) and elapsed time were used to predict sorption coefficient (S) and hydraulic conductivity (A) in Philip equation (I=S*t0.5+A*t), which corresponded to 30 soil samples from study areas located in the Agricultural College, Shiraz University, (Bajgah). A two-hidden layer ANNs with two and three neurons in the hidden layers, respectively and TrainLM algorithm performed the best in predicting S when Logsig and Tansig were used. Silt+ clay+ sand+ time+ CI combination was the most basic influential variables for the S prediction. Furthermore, a two-hidden layer ANNs with two and three neurons in the hidden layers, respectively and TrainBR algorithm performed the best in predicting A when Tansig and Tansig were used. Silt +clay +sand +BD + OM+ time+ CI combination was the most basic influential variables for A prediction. Results showed that increasing the hidden layers and input variables significantly improved the ANNs performance. The coefficient of determination (R2) confirmed that the ANNs predictions for A (84.6 %) fit data better than S (77.5 %).

Управління функціональними властивостями моделей техноземів за допомогою первинної стратиграфії насипок

<p><span lang="EN-US">The article examines the hypothesis that the structure of the </span><span lang="UK">soil-like </span><span lang="EN-US">body in zero-point of its existence directs the dynamics and trajectory of soil formation. To test the hypothesis at the Dnepropetrovsk State Agricultural and Environmental University science satiation the field experiment was laid out lizymetres, each contain a constructive combination of rock or chornozem-like mass. It is shown that the design of the </span><span lang="UK">soil-like </span><span lang="EN-US">body in zero-point of its existence controls the dynamics and trajectory of soil formation. Philip equation was modified to more suitable simulate the infiltration process in tehnozems which allows to accurately describe the water absorption process at the infiltration and filtration stages. The nature of the underlying rocks located at a certain depth impacts significantly on the process of soil formation within the whole soil profile. Underlying rock layer regulates the processes of the tehnozems contact with the environment, as well as determining the intensity profile migration of moisture and dissolved salts. The presence of water resistant biogenic origin aggregates smoothes the varying density clay soils resulting from swelling and shrinkage processes that can maintain stable structure of the pore space. As a result, the soil after reclamation phase gets such features as reduced infiltration rate, but increased level of filtration. Optimal values of sorptivity and filtering corresponds closely with relevant properties of soil that can be investigated using indicators of the soil mechanical impedance. Uniformity preparation and impermeable aggregate structure determines the optimal functional modes of the tehnozemes.</span></p>

Estimating Soil Saturated Hydraulic Conductivity using the Kostiakov and Philip Infiltration Equations

Core Ideas We analyzed the relationships between the parameters of the Kostiakov and Philip infiltration equations. A new method was proposed to estimate the Ks by parameters in Kostiakov equation. Effect of soil hydraulic parameters on a new method was discussed. Direct measurement of saturated hydraulic conductivity (Ks) is time and labor consuming, so Ks is often estimated by mathematical models describing soil–water infiltration. The Kostiakov infiltration equation is widely used to estimate soil–water infiltration rate (i) with only two empirical parameters m and n, which are highly dependent on Ks. The objective of this study was to develop a new method to estimate Ks using the parameters of the Kostiakov equation for short infiltration times. The new method is based on the relationship between the Kostiakov equation and Philip's two‐term equation. We used infiltration data of one‐dimensional vertical water absorption simulated by Hydrus‐1D to evaluate the applicability of the new method. The parameters of Philip's equation were applied to estimate the parameters of the Kostiakov equation with relative errors for m and n <1.15 and 4.20%, respectively. The estimated Ks agreed closely with the parameters of the Kostiakov equation, and the optimal depth of the wetting front (zf) was used as an indicator to confirm the infiltration time in the one‐dimensional vertical water‐absorption simulation. The inverse of the air‐entry value, the saturated hydraulic conductivity, the pore‐size distribution index, and the initial water content had significant effects on zf, which could be described as a power function of these parameters, with an R2 of 0.9717. The parameters of the Kostiakov equation can thus be used to calculate Ks for most soils when the depth of the wetting front is approximately 20 ± 5 cm.

Effect of Pisha sandstone on water infiltration of different soils on the Chinese Loess Plateau

The infiltration of water into soil is one of the most important soil physical properties that affect soil erosion and the eco-environment, especially in the Pisha sandstone area on the Chinese Loess Plateau. We studied the one-dimensional vertical infiltration of water in three experimental soils, created by mixing Pisha sandstone with sandy soil, irrigation-silted soil, and loessial soil, at mass ratios of 1:1, 1:2, 1:3, 1:4, and 1:5. Our objective was to compare water infiltration in the experimental soils and to evaluate the effect of Pisha sandstone on water infiltration. We assessed the effect by measuring soil bulk density (BD), porosity, cumulative infiltration, infiltration rate and saturated hydraulic conductivity (Ks). The results showed that Pisha sandstone decreased the infiltration rate and saturated hydraulic conductivity in the three experimental soils. Cumulative infiltration over time was well described by the Philip equation. Sandy soil mixed with the Pisha sandstone at a ratio of 1:3 had the best water-holding capacity. The results provided experimental evidence for the movement of soil water and a technical support for the reconstruction and reclamation of mining soils in the Pisha sandstone area.

Effect of soil texture on water infiltration in semiarid reclaimed land

The infiltration of water and its influencing factors in disturbed or reclaimed land are not well understood. A better understanding would provide essential information for assessing the hydrological processes in disturbed ecosystems. We measured the infiltration of water in soils from loamy and sandy reclaimed land. The relationships between infiltration and soil properties were analyzed based on three models: the Kostiakov, Philip, and Green–Ampt equations. Our objectives were to understand water infiltration in reclaimed land with a variety of soil textures and to establish the dependence of water infiltration on soil properties. Both the rate of infiltration and the cumulative infiltration were higher in sandy than in loamy soils. The rate of infiltration and the cumulative infiltration decreased with soil depth in undisturbed land. The sorptivity rate (S) from the Philip equation, empirical coefficient (K) from the Kostiakov equation, and the satiated hydraulic conductivity (Ksl) from the Green–Ampt equation were 22%, 16%, and 7.1% higher, respectively, in sandy than in loamy soils. The Ksl increased significantly with Ks (saturated hydraulic conductivity) in both sandy and loamy soils. These indicated that the Green–Ampt equation can be used to describe Ks and the characteristics of infiltration for soils on disturbed land.

Soil Wetting Patterns and Water Distribution as Affected by Irrigation for Uncropped Ridges and Furrows

The ridge-furrow tillage combined with furrow irrigation is being more widely applied and has been shown to be effective in the Loess Plateau of China. Accurate characterization of water infiltration behavior under ridge-furrow irrigation could provide guidelines and criteria for future irrigation system design and operation. Our objective was to investigate soil water behavior during ponding infiltration in a cross-sectional ridge-furrow configuration. Soil water movement within three different soil textures was tested by tracking the spatial and temporal soil water content (SWC) variations in a soil chamber. The two-dimensional transient flow initially transferred rapidly, but gradually decreased with elapsed infiltration time, approaching a stable flow after 90 min. A technical parameter equation incorporating the Philip equation was developed using the water balance method to accurately predict total applied water volume (TAWV). The wetting patterns moved outward in an elliptical shape. The wetted lateral and downward distances fitted using equations accounted for capillary and gravitational driving forces in variably wetted soil media. Increasing initial SWC resulted in an increase in wetted soil volume, which can also be caused by decreasing bulk density in a homogeneous soil. Higher water level produced greater wetted lateral distance and more irrigation uniformity. The wetted lateral distance was almost identical to the wetted depth in silty clay loam soil; hence ridge-furrow irrigation should be implemented in such finer-textured soils. The wetted soil volume differed markedly among different soil textures (hydraulic properties), demonstrating that these properties can largely determine soil water spreading patterns and distribution.

Estimation of infiltration parameters and the irrigation coefficients with the surface irrigation advance distance.

A theory based on Manning roughness equation, Philip equation and water balance equation was developed which only employed the advance distance in the calculation of the infiltration parameters and irrigation coefficients in both the border irrigation and the surge irrigation. The improved procedure was validated with both the border irrigation and surge irrigation experiments. The main results are shown as follows. Infiltration parameters of the Philip equation could be calculated accurately only using water advance distance in the irrigation process comparing to the experimental data. With the calculated parameters and the water balance equation, the irrigation coefficients were also estimated. The water advance velocity should be measured at about 0.5 m to 1.0 m far from the water advance in the experimental corn fields.

A method for estimating spatially variable seepage and hydraulic conductivity in channels with very mild slopes

AbstractInfiltration along ephemeral channels plays an important role in groundwater recharge in arid regions. A model is presented for estimating spatial variability of seepage due to streambed heterogeneity along channels based on measurements of streamflow‐front velocities in initially dry channels. The diffusion‐wave approximation to the Saint‐Venant equations, coupled with Philip's equation for infiltration, is connected to the groundwater model MODFLOW and is calibrated by adjusting the saturated hydraulic conductivity of the channel bed. The model is applied to portions of two large water delivery canals, which serve as proxies for natural ephemeral streams. Estimated seepage rates compare well with previously published values. Possible sources of error stem from uncertainty in Manning's roughness coefficients, soil hydraulic properties and channel geometry. Model performance would be most improved through more frequent longitudinal estimates of channel geometry and thalweg elevation, and with measurements of stream stage over time to constrain wave timing and shape. This model is a potentially valuable tool for estimating spatial variability in longitudinal seepage along intermittent and ephemeral channels over a wide range of bed slopes and the influence of seepage rates on groundwater levels. Copyright © 2012 John Wiley & Sons, Ltd.

Hydrodynamic drag-force measurement and slip length on microstructured surfaces

In this paper, a drainage experiment of water between a borosilicate sphere and a microstructured surface constituted by regularly spaced pillars is presented. The microstructured surface has two parts: on one part the liquid forms a Cassie interface and on the second it forms a Wenzel interface. The measured hydrodynamic drag force is larger on the Cassie part compared to the Wenzel part. Furthermore, for the Cassie part, from the hydrodynamic drag force measurements on a pillar and between pillars the corresponding local slip lengths have been extracted. The area average slip length on the surface is in agreement with the value expected by Philip's equation.

ESTIMATED INFILTRATION PARAMETERS AND MANNING ROUGHNESS IN BORDER IRRIGATION

ABSTRACTBased on the volume balance (VB) equation, the surface water profile was shown to be a power function and Philip equation equal to the Kostiakov–Lewis equation when the infiltration parameter a = 0.5. With this assumption, an equation was proposed for estimating infiltration parameters together with Manning roughness. The method requires only multi‐point water advance data of border irrigation. Solving the equation requires use of the nonlinear least‐squares fitting technique by Matlab software. The proposed method was validated with field experimental data and some reported border tests. The solution procedure was analysed, the results showing that the values of infiltration parameters S and A are not changed, but Manning roughness n varies when σh were given different values (0.70, 0.75, 0.80, respectively). Alternative measures of subsurface water storage and water advance trajectory were used to validate the method. Errors between measured and estimated were 2.0–13% for subsurface water storage, in which the infiltration parameters S and A were estimated with the proposed method. The maximum average absolute error was 6.07% for water advance in all border tests when different Manning roughness n was used (for an n value was estimated when different the shape factor of surface profile σh values were adopt by the proposed method in this paper). Copyright © 2011 John Wiley & Sons, Ltd.

Effects of Coal Gangue Content on Water Movement and Solute Transport in a China Loess Plateau Soil

AbstractThe mining industry has grown strongly in China in recent decades, resulting in large amounts of coal gangues, which cause water and soil pollution, soil erosion, and various other environmental problems. They are often used in reclamation projects in attempts to restore land damaged by mining, hence they are frequently present (in widely varying proportions) in the topsoil in areas around mines. Their presence can strongly affect key soil variables, including its bulk density, structure, water retention, water movement, and solute transport rates. In the study presented here, the effects of gangue contents on infiltration, saturated hydraulic conductivity, and solute transport parameters of a Chinese Loess plateau soil were examined. The results show that infiltration rates and saturated hydraulic conductivity decreased with increasing gangue content. The Peck–Watson equation modeled these relationships well, but Bouwer–Rice equations provided poorer matches with the acquired data. Cumulative infiltration over time was described well by both the Philip equation and Kostiakov equation. Both the simplified convection–dispersion equation and a two‐region model described the solute transport processes well. In addition, the dispersion increased, while both the Peclet number and mobile water fraction decreased, with increases in gangue contents.

Modeling water movement in horizontal columns using fractal theory

Fractal mathematics has been used to characterize water and solute transport in porous media and also to characterize and simulate porous media properties. The objective of this study was to evaluate the correlation between the soil infiltration parameters sorptivity (S) and time exponent (n) and the parameters dimension (D) and the Hurst exponent (H). For this purpose, ten horizontal columns with pure (either clay or loam) and heterogeneous porous media (clay and loam distributed in layers in the column) were simulated following the distribution of a deterministic Cantor Bar with fractal dimension H" 0.63. Horizontal water infiltration experiments were then simulated using Hydrus 2D software. The sorptivity (S) and time exponent (n) parameters of the Philip equation were estimated for each simulation, using the nonlinear regression procedure of the statistical software package SAS®. Sorptivity increased in the columns with the loam content, which was attributed to the relation of S with the capillary radius. The time exponent estimated by nonlinear regression was found to be less than the traditional value of 0.5. The fractal dimension estimated from the Hurst exponent was 17.5 % lower than the fractal dimension of the Cantor Bar used to generate the columns.

Toward Physically Based Estimation of Surface Irrigation Infiltration

Irrigation practitioners use empirical infiltration equations. Theoretical infiltration equations are currently not capable of capturing surface irrigation infiltration behavior, particularly during initial wetting. For a coarse textured soil, an example is shown where the Green-Ampt equation can be adjusted to match field “average” infiltration conditions by altering the soil’s physical properties. For finer textured soils, a time offset is proposed for adjusting the Green-Ampt equation to account for cracking and soil consolidation upon wetting. This results in a nonzero infiltration amount at time 0, a phenomenon commonly observed for infiltration of cracking soils. Applying this concept to the Philip equation (same as Modified Kostiakov equation with a=1/2) suggests the addition of an offset parameter. A modification to the two-point method is presented for this equation with the aim to better fit mathematical parameter functions to infiltration data.

Method for estimating spatially variable seepage loss and hydraulic conductivity in intermittent and ephemeral streams

A method is presented for estimating seepage loss and streambed hydraulic conductivity along intermittent and ephemeral streams using streamflow front velocities in initially dry channels. The method uses the kinematic wave equation for routing streamflow in channels coupled to Philip's equation for infiltration. The coupled model considers variations in seepage loss both across and along the channel. Water redistribution in the unsaturated zone is also represented in the model. Sensitivity of the streamflow front velocity to parameters used for calculating seepage loss and for routing streamflow shows that the streambed hydraulic conductivity has the greatest sensitivity for moderate to large seepage loss rates. Channel roughness, geometry, and slope are most important for low seepage loss rates; however, streambed hydraulic conductivity is still important for values greater than 0.008 m/d. Two example applications are presented to demonstrate the utility of the method.

Long-term farmyard manure application effects on properties of a silty clay loam soil under irrigated wheat–soybean rotation

Increasing importance has been placed on the use of agricultural soils for the mitigation of atmospheric CO 2 through sequestration of soil C. Although crop productivity is sustained mainly through the application of organic manure in the Indian Himalayas, little information is available on C sequestration, C content in different aggregate size fractions and soil water transmission properties (infiltration and saturated hydraulic conductivity) as affected by long-term manure addition. We analyzed results of an 8-year experiment, initiated in 1995–1996 on a silty clay loam soil, to determine the influence of fertilizer and fertilizer + farmyard manure (FYM) application on those important soil properties. The overall increase in soil organic C (SOC) content in the 0–45 cm soil depth in NPK + FYM treatment as compared to NPK and control treatments was 11.0 and 13.9 Mg C ha −1 at the end of 8 years, respectively. Application of FYM significantly reduced soil bulk density and increased mean weight diameter (MWD) and SOC contents in different aggregate size fractions. Soil organic C content in macroaggregates was greater than in microaggregates. The response of SOC content to FYM application was dependent upon inorganic fertilization and more upon balanced application of NPK than N only. Steady state infiltration rate under NPK + FYM (1.98 cm h −1) was higher than under unfertilized (0.72 cm h −1) and NPK (1.2 cm h −1). Soil water sorptivity (calculated from Philip's equation) under NPK + FYM (1.06 cm min −0.5) was higher than under NPK (0.61 cm min −0.5). We conclude that hill farmers in northern India should be encouraged to use FYM along with chemical fertilizers to increase SOC content and improve soil physical properties.

APPLICATION OF TIME COMPRESSION APPROXIMATION METHOD TO INCORPORATE MULTI-STORM INFILTRATION PROCESSES IN YAMANASHI HYDROLOGICAL MODEL FOR ARID AND SEMI-ARID REGIONS

An approach is presented to solve the Philip's equation with time compression approximation (TCA) for simulating infiltration under variable rainfall. This approach brings understanding into physical processes of infiltration and ponding during variable rainfall storms. In particular, we apply it into the Yamanashi Hydrological Model (YHyM) for analyzing the infiltration excess runoff in arid and semi-arid regions. The soil water redistribution is also included to simulate the soil moisture changing during the temporal gaps among storms. The modified YHyM was tested by a case study of Lushi River basin, China. Through comparisons of results from the modified YHyM with results from the unmodified YHyM, the presented TCA based infiltration model is proved to be able to improve the performance of YHyM in peak runoff calculation during variable rainfall multi-storms in arid and semi-arid regions.