Kostiakov Model Research Articles

Spatial analysis of infiltration in agricultural lands in arid areas of Iran

Infiltration plays an important role in the hydrologic cycle, runoff generation, soil erosion, as well as irrigation. In the current study, we evaluated a variety of infiltration models, in order to determine the model that is best suited to predict infiltration on agricultural lands in arid areas of the Semnan province in Iran. Additionally, we analyzed spatial variability of the infiltration process using scaling parameters. A number of 60 points were determined for the measurement of water infiltration using the conditioned Latin hypercube sampling (cLHS) method. Each infiltration measurement was carried out with a tension infiltrometer apparatus. Several infiltration models, including Philip, Horton, Kostiakov (KO), Modified Kostiakov (MKO) and Revised Modified Kostiakov (RMKO) models, were fitted to the measured infiltration data. Among the mean coefficient of determination (R2) values, the highest R2 values were associated with the RMKO, MKO and Horton models, respectively. While base on the Akaike criterion (ACI), the MKO model was slightly better than the RMKO model for prediction of cumulative infiltration. Cumulative infiltration was scaled using Sorptivity (αS) and transmissivity (αA) scaling factors. By minimizing the differences of the sum of squares between the scaled and the average infiltration, the optimum scaling factors (αopt) were estimated. Arithmetic, geometric and harmonic means (i.e. αm, αG, αH; respectively) of αS and αA scaling factors were calculated and the infiltration data were scaled utilizing the mentioned scaling factors. Our findings indicated that the best result was yielded by αH. Strong correlations were found for αG (r = 0.86) and αH (r = 0.86) with αopt. For defining the relationship between αopt and αA, αS, αm, αG and αH data, a regression analysis was performed. According to our results, curves reflecting the relationship between αopt and αA, αS, αm, αG and αH were sigmoid. Based on the results of this study, infiltration in agricultural lands in the arid area displays a great spatial variability.

Support vector regression-based modeling of cumulative infiltration of sandy soil

This paper examines the capability of the support vector machine-based regression approach to predict the cumulative infiltration from sandy soil. A data-set consisting of 413 cumulative infiltration measurements was used in the present analysis. Results drawn from radial basis function (RBF) and polynomial (poly) kernel-based support vector regression (SVR) were compared with multiple linear regression (MLR), M5P tree, generalized regression neural network (GRNN), and two conventional models, Kostiakov model and US-Soil Conservation Service (SCS) model. Out of 413, a total of 289 data were randomly selected for training different algorithms, whereas residual 124 data were used to test the models. The correlation coefficient (C.C) of 0.9837 with root mean square error (RMSE) value of 0.3073 was achieved by RBF kernel-based support vector regression in comparison to C.C value is 0.9255 with RMSE value of 0.6423 through M5P tree model. Comparisons of results propose that RBF based SVR works well. Single-factor ANNOVA results conclude that there is an insignificant difference between observed and predicted values using different models. Sensitivity analyses further suggest that the time is the most important parameter when SVR-based modeling approach is used for prediction of cumulative infiltration.

Effects on Infiltration and Evaporation When Adding Rapeseed-Oil Residue or Wheat Straw to a Loam Soil

The application of additives (e.g., wheat straw (WS) or rapeseed-oil residue (RR)) to soils is a common agronomic practice, used for improving soil water retention. Through a laboratory investigation, this study examined the effects of RR and WS on infiltration, evaporation, water distribution, and water retention. The results indicated that the migration rate of the wetting front, as well as the accumulative infiltration and evaporation, decreased with the amount of applied additives. RR was more effective than WS for infiltration and evaporation suppression. Furthermore, in the Kostiakov model, the value of a decreased with an increasing amount of additive, becoming smaller than the corresponding control treatment (CK) value; by contrast, the value of n decreased with increasing amount of applied additive, remaining larger than the CK value. In the Rose model, the values of A for the soils mixed with additives were smaller than those of the CK, and decreased with increasing amount of additive. Moreover, compared with the CK, the maximum water content for the RR-applied soils increased by 17.84% after infiltration and by 47.66% after evaporation. In addition, the water retention coefficients (calculated as the soil moisture after evaporation divided by that after infiltration) for soils mixed with RR were the highest, indicating that RR is more effective than WS for improving the water retention of the soil layer.

Modelling of infiltration of sandy soil using gaussian process regression

The aim of this paper to assesses the potential of machine learning approaches, i.e. multi-linear regression (MLR), support vector regression (SVR), Gaussian process (GP) regression of cumulative infiltration and compares their performances with three traditional models [Kostiakov model, US-Soil Conservation Service (SCS) model and Philip’s model]. Data set as many as 413 were obtained by conducting experiments in laboratory of NIT Kurukshetra. It is observed from the experiments that moisture content influences the cumulative infiltration of soil. Out of 413 data set 289 arbitrary selected were used for training the models, whereas remaining 124 were used for testing. Input data set consist of time, sand, rice husk ash, fly ash, suction head, bulk density and moisture content where as cumulative infiltration was considered as output. Two kernel function i.e. Pearson VII and radial based kernel function were used with both SVR and GP regression. The results after comparison suggests that the GP regression based approach works better than SVR, MLR, Kostiakov model, SCS model and Philip’s model approaches and it could be successfully used in prediction of cumulative infiltration data.

Applicability of five models to simulate water infiltration into soil with added biochar

As a soil amendment, biochar can reduce soil bulk density, increase soil porosity, and alter soil aggregates and thus affect the infiltration. Researchers have proposed and revised several theoretical models to describe the process of soil infiltration. Although these models have been successfully used to evaluate the soil infiltration in different scenarios in agricultural fields, little effort has been devoted to assess their performances in arid and semi-arid soils after the addition of biochar. A laboratory experiment was performed to study the infiltration characteristics of two typical Loess Plateau soils at three particle sizes (2–1, 1–0.25, and <0.25 mm) and five biochar application amounts (0, 10, 50, 100, and 150 g/kg). The performance of five models (i.e., the Philip model, Kostiakov model, Mezencev model, USDA-NRCS model, and Horton model) in simulating the infiltration process was then evaluated based on the adjusted coefficient of determination and a reduced Chi-Square test. Results indicated that the Horton model best simulated the water-infiltration process in an aeolian sandy soil with added biochar. However, the Mezencev model best simulated the infiltration process in a loamy clay soil (Eum-Orthic Anthrosol). The three-parameter model, i.e., Mezencev and Horton models can better describe the relationship between cumulative infiltration and infiltration time. In conclusion, biochar reduced the soil infiltration capacity of the aeolian sandy soil and increased that of the Eum-Orthic Anthrosol.

Influencing Factors and Simplified Model of Film Hole Irrigation

Film hole irrigation is an advanced low-cost and high-efficiency irrigation method, which can improve water conservation and water use efficiency. Given its various advantages and potential applications, we conducted a laboratory study to investigate the effects of soil texture, bulk density, initial soil moisture, irrigation depth, opening ratio (ρ), film hole diameter (D), and spacing on cumulative infiltration using SWMS-2D. We then proposed a simplified model based on the Kostiakov model for infiltration estimation. Error analyses indicated SWMS-2D to be suitable for infiltration simulation of film hole irrigation. Additional SWMS-2D-based investigations indicated that, for a certain soil, initial soil moisture and irrigation depth had the weakest effects on cumulative infiltration, whereas ρ and D had the strongest effects on cumulative infiltration. A simplified model with ρ and D was further established, and its use was then expanded to different soils. Verification based on seven soil types indicated that the established simplified double-factor model effectively estimates cumulative infiltration for film hole irrigation, with a small mean average error of 0.141–2.299 mm, a root mean square error of 0.177–2.722 mm, a percent bias of −2.131–1.479%, and a large Nash–Sutcliffe coefficient that is close to 1.0.

Assessment of Dimensionless Form of Kostiakov Model

Infiltration is the process by which water enters the earth's surface. Although contribution of soil water to total water present on earth surface is negligible, but it is of prime importance for plant life. Very recently, dimensionless form of Kostiakov equation was proposed for precise estimation of Kostiakov model parameters. The present paper is an assessment of accuracy of proposed dimensionless form of Kostiakov model. However, it has been found that the cumulative infiltration estimated by nonlinear optimization technique are more accurate than those estimated by dimensionless form of Kostiakov equation and the graphical method. Therefore, the present paper proposes application of Generalized Reduced Gradient (GRG), a nonlinear optimization technique to estimate Kostiakov model parameters precisely rather than using dimensionless form of Kostiakov equation. Infiltration data of various types of soil have been considered in the present study for the generalization of the results.

Assessment of Dimensionless Form of Kostiakov Model

Infiltration is the process by which water enters the earth's surface. Although contribution of soil water to total water present on earth surface is negligible, but it is of prime importance for plant life. Very recently, dimensionless form of Kostiakov equation was proposed for precise estimation of Kostiakov model parameters. The present paper is an assessment of accuracy of proposed dimensionless form of Kostiakov model. However, it has been found that the cumulative infiltration estimated by nonlinear optimization technique are more accurate than those estimated by dimensionless form of Kostiakov equation and the graphical method. Therefore, the present paper proposes application of Generalized Reduced Gradient (GRG), a nonlinear optimization technique to estimate Kostiakov model parameters precisely rather than using dimensionless form of Kostiakov equation. Infiltration data of various types of soil have been considered in the present study for the generalization of the results.

Method to measure soil matrix infiltration in forest soil

Infiltration of water into forest soil commonly involves infiltration through the matrix body and preferential passages. Determining the matrix infiltration process is important in partitioning water infiltrating into the soil through the soil body and macropores to evaluate the effects of soil and water conservation practices on hillslope hydrology and watershed sedimentation. A new method that employs a double-ring infiltrometer was applied in this study to determine the matrix infiltration process in forest soil. Field experiments were conducted in a forest field on the Loess Plateau at Tianshui Soil and Water Conservation Experimental Station. Nylon cloth was placed on the soil surface in the inner ring and between the inner and outer rings of infiltrometers. A thin layer of fine sands were placed onto the nylon cloth to shelter the macropores and ensure that water infiltrates the soil through the matrix only. Brilliant Blue tracers were applied to examine the exclusion of preferential flow occurrences in the measured soil body. The infiltration process was measured, computed, and recorded through procedures similar to those of conventional methods. Horizontal and vertical soil profiles were excavated to check the success of the experiment and ensure that preferential flow did not occur in the measured soil column and that infiltration was only through the soil matrix. The infiltration processes of the replicates of five plots were roughly the same, thereby indicating the feasibility of the methodology to measure soil matrix infiltration. The measured infiltration curves effectively explained the transient process of soil matrix infiltration. Philip and Kostiakov models fitted the measured data well, and all the coefficients of determination were greater than 0.9. The wetted soil bodies through excavations did not present evidence of preferential flow. Therefore, the proposed method can determine the infiltration process through the forest soil matrix. This method can also be applied to explore matrix infiltration in other land-use types.

Effects of mulching management of Phyllostachys heterocycla forests on the characteristics of soil infiltration and biometrics in southwest Zhejiang Province, China

Soil infiltration, soil physical and chemical properties, root length density and soil fauna diversity were studied in Phyllostachys heterocycla forests with different mulching times in southwest Zhejiang Province, China. Significant differences of soil infiltration capability were found among the forests with different mulching times and among soil layers. Soil infiltration capability generally declined in the deeper soil layers. With mulching management, soil infiltration capability increased under the first mulching, and then declined with the increase of mulching times. The Kostiakov model was suitable for simulating soil infiltration process. With the extending of mulching times (4 to 6 years), soil pH and total/non-capillary porosity decreased, while soil bulk density, soil orga-nic matter and total nitrogen contents increased significantly. Soil initial, steady, and average infiltration rates as well as the cumulative infiltration amount correlated closely with the length density of roots with diameter from 0.5 mm to 5.0 mm, showing a decreasing tendency with the decrease in root length density. Soil fauna density was highest in the forest under the first mulching, and was lowest after third mulching. The decreased numbers of large and meso-arthropods, including Symphyla, Chilopoda, Diplopoda, Hymenoptera and pseudoscorpions, and the micro-arthropods, including Oribatida, Mesostigmata, Onychiuridae, Neanuridae, Cyphoderidae, and Entomobryidae, showed negative effects on soil infiltration. In conclusion, long-term mulching changed soil physical and chemical properties, decreased soil infiltration capability, and suppressed the development of soil fauna, which might cause the decline ofP. heterocycla forests.

Field Steady State Infiltration Rates of Soils in Kumba - Cameroon: Validation of Some Empirical Predictive Infiltration Models and GIS Applications

Kumba capital of Meme Division, one of the largest cocoa cash crop producing areas in Cameroon, is a typically agrarian town that needs a good understanding of the soil properties of the area. The evaluation of steady state infiltration rates of soils is important in agriculture, groundwater resources preservation and civil engineering to; increase the availability of data, determine regions of aquifer recharge and discharge, infer soil types, evaluate soil suitability for agriculture and provide another tool for generating water resources management parameters in the area. The double ring infiltrometer method was used to measure field infiltration rates from which steady state infiltration rates were determined. The steady state infiltration rates were compared to those determined using empirical predictive models to rate these models’ performance in Kumba. There is significant spatial variation in the steady state infiltration rates (vertical saturated hydraulic conductivities) in the vadose zone of the phreatic aquiferous formations in Kumba. The steady state infiltration rate values range from 0.01-0.96 m/d. Inferred soil types are 7.7% sandy soils, 26.9% sandy silty soils, 19.2% loam and 42.3% clays and 3.8% sodic clayey soils. Infiltration rate classes determined are; very slow to slow (46.1%), slow to moderately slow (19.2%), moderately-slow-to-moderatelyrapid (19.2%), moderately rapid to rapid (7.7%) and very rapid (7.7%). Soil’s suitability for surface irrigation is 38.5% optimum, 7.7% suitable, 34.6% marginally suitable and 7.7% unsuitable. 7.7% of soils are suitable and 34.6 % marginally suitable for rice cultivation. Recharge zones are located towards the south and southwestern parts of Kumba. Comparing measured and predictive model-estimated infiltration rates, the Kostiakov model gives the best prediction for the final infiltration rate in Kumba.

Study of the water transportation characteristics of marsh saline soil in the Yellow River Delta

One-dimensional soil column water infiltration and capillary adsorption water tests were conducted in the laboratory to study the water transportation characteristics of marsh saline soil in the Yellow River Delta, providing a theoretical basis for the improvement, utilization and conservation of marsh saline soil. The results indicated the following: (1) For soils with different vegetation covers, the cumulative infiltration capacity increased with the depth of the soil layers. The initial infiltration rate of soils covered by Suaeda and Tamarix chinensis increased with depth of the soil layers, but that of bare soil decreased with soil depth. (2) The initial rate of capillary rise of soils with different vegetation covers showed an increasing trend from the surface toward the deeper layers, but this pattern with respect to soil depth was relatively weak. (3) The initial rates of capillary rise were lower than the initial infiltration rates, but infiltration rate decreased more rapidly than capillary water adsorption rate. (4) The two-parameter Kostiakov model can very well-simulate the changes in the infiltration and capillary rise rates of wetland saline soil. The model simulated the capillary rise rate better than it simulated the infiltration rate. (5) There were strong linear relationships between accumulative infiltration capacity, wetting front, accumulative capillary adsorbed water volume and capillary height.

An Improvement to the Waterfront Advance–Time Relation for Irrigation Borders

AbstractUsing the Kostiakov, modified Kostiakov and improved modified Kostiakov infiltration models, three alternate solutions of the Philip and Farrel equation are suggested for the determination of waterfront advance–time relations for irrigation borders. To test the solutions with field data of waterfront advance–time relations, each accumulated infiltration–time relation was used in the Philip and Farrel equation and the waterfront advance–time relation was determined using six observed data sets on irrigation borders. The results show that the improved modified Kostiakov model performed best in prediction of accumulated infiltration time as well as the waterfront advance–time relation as compared with the modified Kostiakov and Kostiakov infiltration model. Also, the modified Kostiakov infiltration model performed better in prediction of the infiltration and advance–time relation as compared to Kostiakov. Hence this paper suggests the use of the improved modified Kostiakov infiltration model in the Philip and Farrel equation with the help of computer programs to determine the waterfront advance–time relation in irrigation borders most accurately, as compared to the modified Kostiakov and Kostiakov infiltration models. Copyright © 2016 John Wiley &amp; Sons, Ltd.

Irrigation potential of Inuakpa in Odukpani local government of Cross river using Kostiakov model

Infiltration measurements were carried out using cylindrical infiltrometer with height and diameter of 15cm and 5cm respectively. Sixteen infiltration runs were carried out in a composite grid (30m x 30m) in Inuakpa, Odukpani Local Government Area of Cross River State to test the efficiency of Kostiakov’s model, measure infiltration rate and relate same to some soil physical properties. Mean infiltration rate of 9.01 cmhr-1 was obtained at the end of the runs. The soil textural class was loamy sand with particle size distribution indicating mean values of 82.4, 7.2 and 10.4 % for sand, silt and clay respectively. The bulk density, particle density and total porosity had mean values of 1.35 Mgm-3, 2.48 Mgm-3 and 44.86 % while their coefficients of correlation with infiltration rate where 0.58, 0.48 and 0.69 respectively. There were also linear and positive relationships between infiltration rate and sand and silt contents with coefficients of correlation of 0.92** and 0.55* (p ≤ 0.05) respectively while clay content was not specifically linear or positive. Kostiakov infiltration model fitted well in evaluating infiltration parameters for sustained agricultural production. The soil infiltration rate, physical and chemical properties studied placed the soil in class 2 - irrigable. Mulching with plant residues, cover cropping, the use of restorative crops and zero tillage should be practiced in the area as soil management strategies.

Application of spreadsheet to estimate infiltration parameters

Summary Infiltration is the process of flow of water into the ground through the soil surface. Soil water although contributes a negligible fraction of total water present on earth surface, but is of utmost importance for plant life. Estimation of infiltration rates is of paramount importance for estimation of effective rainfall, groundwater recharge, and designing of irrigation systems. Numerous infiltration models are in use for estimation of infiltration rates. The conventional graphical approach for estimation of infiltration parameters often fails to estimate the infiltration parameters precisely. The generalised reduced gradient (GRG) solver is reported to be a powerful tool for estimating parameters of nonlinear equations and it has, therefore, been implemented to estimate the infiltration parameters in the present paper. Field data of infiltration rate available in literature for sandy loam soils of Umuahia, Nigeria were used to evaluate the performance of GRG solver. A comparative study of graphical method and GRG solver shows that the performance of GRG solver is better than that of conventional graphical method for estimation of infiltration rates. Further, the performance of Kostiakov model has been found to be better than the Horton and Philip's model in most of the cases based on both the approaches of parameter estimation.

An investigational approach for the modelling of infiltration process in a clay soil

Prediction of soil infiltration rate is of prime importance in irrigation and drainage studies. Infiltration seems to be very simple, but field determination of soil infiltration is very tedious and time consuming task. This investigation was employed to predict the soil infiltration rate and estimate the soil infiltration model parameters. Two infiltration models namely, Kostiakov and Modified Kostiakov were studied to assess the predictability of water infiltration into a clay soil in Kopargaon of Maharashtra region. The double ring Infiltrometer was used to measure soil infiltration rate in the field. The soil infiltration measurements were made at 10 points over the study area. The infiltration model parameters were determined graphically and analytically using Davis method. Results of the investigation shows that the cumulative infiltrations predicted by Kostiakov and Modified Kostiakov models were very close to the field measured cumulative infiltration. The soil physical properties like moisture content, textural analysis and electrical conductivity exhibit the effect on soil infiltration rate and the amounts of infiltration model parameters for both the models. The statistical parameters, coefficient of determination (R2) reported very high values for both the models, while values of Root Mean Square Error (RMSE) were low, which reflected accuracy in estimation of infiltration. Absolute Mean Difference (AMD) between field measured and predicted by models were also very low.

Infiltration Characteristics of Topsoil in Reclamation Farmland Filled with Yellow River Sediment

Infiltration is an important indicator of water and nutrient holding capacity of soil. Lap infiltration apparatus was used to measure vertical water infiltration process in the third year of Yellow River sediment filling reclamation. Five infiltration models were selected to fit the infiltration characteristic curves, analyzed the infiltration experimental results during 3 years of reclamation. The results showed that, the mean initial infiltration rate and mean stable infiltration rate of filling farmland in the third year were 17.06mm/min and 2.38mm/min, and were 8.81mm/min and 0.99 mm/min higher than that of the first year, 3.58mm/min and 0.39mm/min higher than that of the second year. It indicated that, infiltration rate of filling farmland increased significantly after cultivation due to the farming practices and roots development, and the role of soil microorganisms and small animals. Filling farmland has some self-recovery capabilities. In addition, Kostiakov model has better fitting effect than Mezencev model for both filling farmland and control farmland.

Research on the infiltration processes of lawn soils of the Babao River in the Qilian Mountain.

Using a Guelph Permeameter, the soil water infiltration processes were analyzed in the Babao River of the Qilian Mountain in China. The results showed that the average soil initial infiltration and the steady infiltration rates in the upstream reaches of the Babao River are 1.93 and 0.99 cm/min, whereas those of the middle area are 0.48 cm/min and 0.21 cm/min, respectively. The infiltration processes can be divided into three stages: the rapidly changing stage (0-10 min), the slowly changing stage (10-30 min) and the stabilization stage (after 30 min). We used field data collected from lawn soils and evaluated the performances of the infiltration models of Philip, Kostiakov and Horton with the sum of squared error, the root mean square error, the coefficient of determination, the mean error, the model efficiency and Willmott's index of agreement. The results indicated that the Kostiakov model was most suitable for studying the infiltration process in the alpine lawn soils.

Modelling infiltration and geostatistical analysis of spatial variability of sorptivity and transmissivity in a flood spreading area

Knowledge of infiltration characteristics is useful in hydrological studies of agricultural soils. Soil hydraulic parameters such as steady infiltration rate, sorptivity, and transmissivity can exhibit appreciable spatial variability. The main objectives of this study were to examine several mathematical models of infiltration and to analyze the spatial variability of observed final infiltration rate, estimated sorptivity and estimated transmissivity in flood spreading and control areas in Ilam province, Iran. The suitability of geostatistics to describe such spatial variability was assessed using data from 30 infiltration measurements sampled along three lines. The Horton model provided the most accurate simulation of infiltration considering all measurements and the Philip’s two-term model provided less accurate simulation. A comparison of the measured values and the estimated final infiltration rates showed that the Kostiakov-Lewis, Kostiakov, and SCS models could not estimate the final infiltration rate as well as Horton model. Estimated sorptivity and transmissivity parameters of the Philip’s two-term model and final infiltration rate had spatial structure, and were considered to be structural variables over the transect pattern. The Gaussian model provided the best-fit theoretical variogram for these three parameters. Variogram values ranged from 99 and 88 m for sorptivity and final infiltration rate to 686 (spherical) and 384 m (Gaussian) for transmissivity. Sorptivity, transmissivity and final infiltration attributes showed a high degree of spatial dependence, being 0.99, 0.81 and 1, respectively. Results showed that kriging could be used to predict the studied parameters in the study area.

Evaluation of infiltration models with different numbers of fitting parameters in different soil texture classes

In this study, the ability of eight different infiltration models (i.e. Green and Ampt, Philip, SCS (US-Soil Conservation Service), Kostiakov, Horton, Swartzendruber, Modified Kostiakov (MK) and Revised Modified Kostiakov (RMK) models) were evaluated by least-squares fitting to measured infiltration data. Six comparison criteria including coefficient of determination (R2), mean root mean square error (MRMSE), root mean square error (RMSE), the F-statistic (F), Cp statistic of Mallows (Cp) and Akaike information criterion (AIC) were used to determine the best performing model with the least number of fitting parameters. Results indicated that R2 and MRMSE were not suitable for model selection. A more valid comparison was achieved by F, Cp, AIC and RMSE statistics. The RMK model including four parameters had the best performance with the majority of soils studied. RMK was better than the MK model in approximately 51.6, 57, 68.5 and 70.6% of soils, when using F, Cp, AIC and RMSE statistics, respectively, and for the other models, a higher per cent of soils was obtained. The RMK model was the best for loam, clay loam and silty clay loam soils, but the MK model was the best for silty loam soils.