Modification of Kostiakov infiltration equation based on influence of initial soil water content

Infiltration is one of the most important parts of hydrologic cycle by which surface run off, groundwater recharge and design of irrigation systems can be linked. Numerous equations, some entirely empirical and others physically based, have been proposed over the years to express infiltration as a function of time. Among these equations, due to the simplicity and capability of fitting on most measured infiltration test data, the Kostiakov infiltration equation is widely used for design of irrigation systems. Influence of initial soil water content is not considered in this important equation. This study aims to investigate the effect of initial soil water content on empirical parameters of Kostiakov infiltration equation and to modify the equation based on influence of initial soil water content. In this research, two uniform sandy soils were prepared by passing a sandy soil through sieves. Following that, the two soil samples were dried at oven at 105 oC for 24 hr. Each dry soil sample was placed in a transparent acrylic cylinder with inner diameter of 7 cm and smoothly compacted by kicking a rubber hammer on cylinder body. After that, an initial water depth was placed on soil surface and falling head cumulative infiltration depth through the soil column was measured with the time. After diminishing of water level on soil surface, the humid soil column was drained by using a vacuum pomp. Then, the soil column water content was measured and the falling head infiltration test was repeated on the soil column. For two studied soil columns, falling head infiltration tests were conducted in three different values of initial soil water contents. To extend the experimental results to the field scale, a falling head infiltration test was also conducted on a clay textured field by using the double ring infiltrometers, with inner ring diameter of 25 cm, and outer ring diameter of 40 cm. Both the inner and outer rings were filled with the same initial water depth. Falling water level in inner ring was measured before water level would reach the soil surface. Simultaneously with last reading of water level, the two rings were pooled out and vertical distance from the soil surface to the wetting front was measured using an auger. Additionally, a steel cylinder was used and a soil sample with volume of 293 cm3 was taken from the vicinity of field test location and field initial soil water content was measured. For laboratory and field tests, wetness increment behind the wetting front was estimated by dividing the total infiltrated water through the soil by the depth of wetting front. The water content behind the wetting front of laboratory and field tests was also estimated by adding the wetness increment with initial water content. For laboratory and field tests, the Kostiakov infiltration equation is fitted on measured cumulative infiltration test data and empirical parameters of the equation are estimated for each test. Comparison between measured cumulative infiltration tests data of each laboratory soil column in different values of initial water contents indicated that water infiltration through the soil is strongly influenced by initial soil water content. With increasing initial soil water content, cumulative infiltration depth through the soil is significantly reduced. Additionally, laboratory results indicated that water content behind the wetting front of infiltration is a constant value and is not influenced by initial soil water content. Laboratory results indicated that the power of Kostiakov equation (b) is a constant value and is not influenced by initial soil water content, while the coefficient of equation (a) is strongly influenced by initial water content. With increasing initial soil water content, the a coefficient of Kostiakov equation is reduced. After analysis of experimental results, a coefficient of Kostiakov infiltration equation is related to the initial soil water content and the water content behind the wetting front of infiltration. Laboratory results were extended to the field scale. Based on laboratory results, the b coefficient of Kostiakov equation for the studied field was taken as a constant value. The obtained empirical equation for the a coefficient of Kostiakov equation was used and the a coefficient for the studied field was related to the initial soil water content and the water content behind the wetting front.