Modified Kostiakov Model Research Articles

Analysis of a simplified approach for the determination of modified Kostiakov model parameters.

Accurate estimation of infiltration losses is very important in many hydrologic projects. However, the lack of available data often forces hydrologists to resort to the application of empirical and semi-empirical models for estimating the infiltration rates. Estimation of infiltration rate from these empirical and semi-empirical models is highly dependent on the method adopted to determine the parameters of models. One of the most common infiltration models known as the Kostiakov model was modified to rectify zero infiltration at the start of the infiltration process. Recently, a simplified approach for determining the parameters of the modified Kostiakov model was proposed. The present article focuses on analyzing the reliability of the simplified approach for determining the parameters of the modified Kostiakov model. In this regard, six observed datasets were analyzed from different parts of the world to arrive at some generalized results on the reliability of the simplified approach. Cumulative infiltration obtained from simplified approaches was compared with that obtained through the application of an excel spreadsheet-based nonlinear optimization solver. It was found that on average Sum of Square of Error reduced by 72% on application of nonlinear optimization as compared to the simplified approach.

Analysing the Infiltration Rate of Different Types of Infiltration Model: A Review

The term "infiltration" refers to the process of water moving in all directions into the soil. The maximum rate at which water is absorbed into the soil at any given time is known as the infiltration rate. The rate of infiltration is measured in centimetres per hour (cm/hr) or millimetres per hour (mm/hr). Before the building can be built, the soil must be stabilized if it has a low infiltration capacity. The lifespan of a building is reduced if water remains stagnant at ground level. As a result, determining the rate of infiltration is critical. This paper makes an attempt to look into infiltrometers and models that are best for determining infiltration rate. The Kostiakov model, Horton model, Philips model, Green-Ampt model, Regression model, M5P model, Modified Kostiakov model, and Branched Modified Kostiakov model were all used by the significant proportion of the authors. The results show that the Kostiakov and Horton models were both effective in estimating the infiltration rate. Keyword : infiltration, infiltrometers, Kostiakov model, Horton model, Philips model, Green-Ampt model, Regression model, M5P model, Modified Kostiakov model, Branched Modified Kostiakov model.

Assessment of the Effect of Irrigation with Treated Wastewater on Soil Properties and on the Performance of Infiltration Models

An alternative strategy for saving limited water resources is using treated wastewater (TWW) originating from wastewater treatment plants. However, using TWW can influence soil properties owing to its characteristics compared to conventional water resources. Therefore, assessing the effect of TWW on soil properties and soil water infiltration is crucial to maintain sustainable use of TWW and to increase the water use efficiency of the precious irrigation water. Moreover, several studies were carried out to assess the performance of infiltration models. However, few studies evaluate infiltration models under the use of treated wastewater. Therefore, this study aims to assess the effect of TWW irrigation on soil properties after 2 and 5 years and to evaluate five classical infiltration models with field data collected from soil irrigated by treated wastewater for their capability in predicting soil water infiltration. This study revealed that using TWW for irrigation affects significantly on soil properties after 2 and 5 years. The soil irrigated with TWW had significantly higher electrical conductivity, organic matter, sodium adsorption ratio, cation exchange capacity, and lower soil bulk density compared to control. The basic infiltration rate and cumulative infiltration decreased significantly compared to control (60.84, 14.04, and 8.42 mm hr−1 and 140 mm, 72 mm, and 62 mm for control, 2, and 5 years’ treatments, respectively). The performance of the infiltration models proposed by Philip, Horton, Kostiakov, Modified Kostiakov, and the Natural Resources Conservation Service was evaluated with consideration of mean error, root mean square error, model efficiency, and Willmott’s index. Horton model had the lowest mean error (0.0008) and Philip model had the lowest root mean square error (0.1700) while Natural Resources Conservation Service had the highest values (0.0433 and 0.5898) for both mean error and root mean square error, respectively. Moreover, Philip model had the highest values of model efficiency and Willmott’s index, 0.9994 and 0.9998, respectively, whereas Horton model had the lowest values for the same indices, 0.9869 and 0.9967, respectively. Philip model followed by Modified Kostiakov model were the most efficient models in predicting cumulative infiltration, while Natural Resources Conservation Service model was the least predictable model.

Optimizing Height and Spacing of Check Dam Systems for Better Grassed Channel Infiltration Capacity

The check dams in grassed stormwater channels enhance infiltration capacity by temporarily blocking water flow. However, the design properties of check dams, such as their height and spacing, have a significant influence on the flow regime in grassed stormwater channels and thus channel infiltration capacity. In this study, a mass-balance method was applied to a grassed channel model to investigate the effects of height and spacing of check dams on channel infiltration capacity. Moreover, an empirical infiltration model was derived by improving the modified Kostiakov model for reliable estimation of infiltration capacity of a grassed stormwater channel due to check dams from four hydraulic parameters of channels, namely, the water level, channel base width, channel side slope, and flow velocity. The result revealed that channel infiltration was increased from 12% to 20% with the increase of check dam height from 10 to 20 cm. However, the infiltration was found to decrease from 20% to 19% when a 20 cm height check dam spacing was increased from 10 to 30 m. These results indicate the effectiveness of increasing height of check dams for maximizing the infiltration capacity of grassed stormwater channels and reduction of runoff volume.

Modified models for better prediction of infiltration rates in trapezoidal permeable stormwater channels

ABSTRACTIn stormwater management, it is important to accurately quantify the infiltration rates to solve urban runoff-related problems. This study proposes a method to improve estimates of the infiltration rate in permeable stormwater channels. As part of the analysis, five infiltration models were evaluated: the Kostiakov, Horton, modified Kostiakov, Philip and SCS (Soil Conservation Service) models. Infiltration tests with various initial water levels were performed on channel models with differing base width and side slopes. The results show that the addition of three parameters that describe the trapezoidal cross-sectional area, i.e. the depth, side slope and base width, in the infiltration models yielded better estimates of the infiltration rate. A comparison of the infiltration capacity values obtained from the models after the three parameters were added with those that were experimentally obtained, shows that the improved modified Kostiakov model is the most suitable model to predict infiltration rates in trapezoidal permeable stormwater channels.

Modeling the Infiltration Capacity of Permeable Stormwater Channels with a Check Dam System

The use of permeable stormwater channels has introduced concerns over the effects of infiltration on the hydraulic behavior of their flow and the effects of flow hydraulic conditions (e.g., the water level, channel section, flow velocity, and vegetation) on the channel infiltration capacity. A check dam system provides backwater ponding, which increases the flow water depth along a channel. In this study, a channel model was used to investigate the variation in the infiltration capacity of permeable stormwater channels under different flow hydraulic conditions. Increasing the downstream check dam height and using a grass cover increased the infiltration rate and cumulative infiltration because of the decreased velocity and increased flow depth. The presence of subsurface water did not affect the hydraulic characteristics of the channel flow but decreased the cumulative infiltration because of the fast saturation of the soil. An empirical equation was developed for predicting the infiltration capacity of grassed channels in which four hydraulic parameters (i.e., the water depth, base width, side slope, and velocity) are introduced to the modified Kostiakov model. The developed model was used to calculate the runoff reduction due to infiltration along a grassed channel with and without a check dam system. The percentage of infiltrated water increased from 8 to 14% with the check dam system. The developed model can be used to predict the infiltration capacity of permeable channels for improved stormwater management and provides a valuable decision support tool for permeable channel design.

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.

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 & Sons, Ltd.

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.

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.

Study on rain-runoff process in the peripheral mountainous area of the Sichuan Basin

Studies on rain-runoff process in the peripheral mountainous area of the Sichuan Basin, which is regarded as a key ecological shelter, will contribute to flood control and environmental protection for the Upper Yangtze River Basin. In two typical catchments—the Fujiang River Catchment and the Wujiang River Catchment, rainfall simulations have been conducted to study the rain-runoff processes of yellow soil and limestone soil in three types of land use—forestland, farmland and grassland. Results showed that (1) within the same rainfall process, overland flow occurs first on farmland, then on grassland, and finally on forestland; (2) soil surface coverage has a great impact on the occurrence and amount of overland flow. The runoff amount can increase 2–4 times after the coverage is removed; (3) the infiltration before the occurrence of overland flow will decrease because of higher gravel contents of soil, but it takes no effect on infiltration once overland flow becomes stable; (4) the runoff coefficient of the limestone soil forestland is greater than that of the yellow soil forest land, but less than that of the farmland; (5) three empirical infiltration models, including Horton’ model, Kostiakov’ model, and modified Kostiakov’ model, were compared by using the observed results under rainfall simulation. The results showed that the Kostiakov’ model performed better than both the Horton’ model and modified Kostiakov model. According to the results of this research, the Kostiakov’s model can be used to simulate rainfall infiltration when water erosion is modeled in the peripheral mountainous area of the Sichuan Basin.

Performance Evaluation of Infiltration Models in a Hydromorphic Soil

Four infiltration models were investigated for their capacity to describe water infiltration into hydromorphic (gleysol) soil. The Models were Kostiakov\'s (1932), Philip\'s (1957) Kostiakov- Lewis\'(1982) and Modified Kostiakov (1978). Field measurement of infiltration was made using double ring infiltrometers on an hydromorphic soil of the flood plain in Zango village, Samaru, Zaria, Nigeria. Infiltration tests were carried out in a land area of 80 m by 240 m divided into four strips of 20 m by 240 m, with the top strip located 90 m away from the main watercourse of the area. A total of 16 infiltration tests were carried out over the area. A set of the field-measured cumulative infiltration depths were used for estimation of parameters of the models studied, and the other set was used to evaluate the performance of the infiltration models in simulating cumulative infiltration depths. All four models studied provided good overall agreement with field-measured data. However, Kostiakov and Modified kostiakov models provided the best fit with experimental data for the hydromorphic soil. Keywords: Infiltration, Hydromorphic soil, Ring Infiltrometer, Infiltration models. Nigerian Journal of Soil and Environmental Research Vol. 7 2007: pp. 53-59

A Modification to Kostiakov and Modified Kostiakov Infiltration Models

Incorporating the time variant function of the otherwise used as steady infiltration rate, this paper presents revised versions of the popular and frequently used Kostiakov and modified Kostiakov infiltration models. The proposed, along with the existing, versions are tested on 40 datasets of infiltration observed on five different soils in India and USA The former indicated an improved performance over their respective existing versions. Further generalization of the improved modified Kostiakov model incorporating time to ponding showed an enhanced performance on all the soils.

Modified Kostiakov Infiltration Function: Accounting for Initial and Boundary Conditions

The effect of specific initial and boundary conditions is generally not considered when applying the Kostiakov infiltration functions. A methodology is developed to account for changes in water levels and initial soil moisture. First, Richards’ equation is solved numerically to generate a database of one-dimensional infiltration values, with varying initial (water content or pressure head) and boundary (ponding depth) conditions for three contrasting soils. These are then used to calibrate corresponding coefficients for modified Kostiakov models and, by considering linear regressions, to obtain simple correction factors. Results show that the correction factors are not universally valid, and only the correction to the Kostiakov k parameter shows statistically consistent applicability. However, examples demonstrate potentially significant improvement in the accuracy of irrigation models by correcting the Kostiakov equation to account for initial and boundary conditions.

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.

Testing the goodness of fit of infiltration models for highly permeable soils under different tropical soil management systems

The Kostiakov, modified Kostiakov (A), modified Kostiakov (B), Philip, modified Philip (A) and modified Philip (B) infiltration models were tested for their ability to describe water infiltration into highly permeable sandy soils from the Nsukka plains of SE Nigeria. Infiltration data were obtained on field plots with the following management systems: tilled-mulched, tilled-unmulched, untilled-mulched, untilled-unmulched and continous pasture. On all treatments, the cumulative infiltration values predicted by the classical Kostiakov, Philip and modified Philip (A) models deviated most from the experimental data. The other models produced values that agreed very well with the measured data. Considering the ease of determining the fitting parameters it is proposed that on soils with high infiltration rates, either the modified Kostiakov model ( I = Kt a + I c t) or modified Philip model ( I = St 1 2 + I ct ), (where I is cumulative infiltration, K is the time coefficient, t is the time elapsed, a is the time exponent, I c is the steady infiltration rate and S is the soil water sorptivity), be used for routine characterisation of the infiltration process.