One of the earliest functions to express infiltration as a function of time was introduced by Green and Ampt. In this study their formula was modified to account for air compression and counterflow. Physically,infiltration, air compression, and counterflow occur simultaneously, while in this model they are decoupled within a time step. Counterflow is calculated as a mass flux and pressure is found using the perfect gas law. First, a comparison of three infiltration methods, the original Green and Ampt formulation, a modified version incorporating air compression only, and the third version including air compression and counterflow, was conducted. Then sensitivity of the model accounting for both air compression and counterflow was explored. Results showed that accounting for both air compression and counterflow improves the predicted infiltration rate. Air effect on infiltration can be significant even for environments with an impervious layer as deep as 10m; while for very deep water table environments (100m) the three models give similar results. In shallow water table environments (0.5m), air effect on infiltration rate, cumulative infiltration, ponding time, and saturation time is substantial. The model accounting for air compression and counterflow was then tested for different parameters. It provided reasonable results compared to the Green and Ampt model and the modified version accounting for air compression only. The advantages of this model are that no additional data is required other than what's needed for the original Green and Ampt formulation, and it can be applied for any environment. The assumption of uniform soil moisture content is a limitation for the model, especially for shallow water table environments where the variations in the soil moisture profile within the wetting front depth is substantial.

Water infiltration into the unsaturated zone especially in a shallow water table environment is affected by air compression ahead of the wetting front and air counterflow. Neglecting air compression in infiltration modeling can overestimate infiltration and infiltration rates, whereas not accounting for air counterflow can underestimate infiltration and infiltration rates due to unrealistic buildup of air pressure resistance ahead of the wetting front. A method, derived on the basis of the Green and Ampt (1911) infiltration model, is introduced to simulate air compression and air counterflow during infiltration into a shallow water table. The method retains the simplicity of the Green and Ampt (1911) model but adds the air pressure resistance term ahead of the wetting front. Infiltration equations are derived on the basis of the Green and Ampt (1911) and Sabeh’s (2004) infiltration model which accounts for air compression and air counterflow. The difference between this method and Sabeh’s (2004) model is that air counterflow, air compression, and infiltration are decoupled and updated with each wetting front increment whereas Sabeh’s (2004) method uses time step as a decoupling mechanism. Air compression ahead of the wetting front is predicted using the perfect gas law. Laboratory experiments showed that the introduced method is reasonably accurate when modeling cumulative infiltration values. Results of laboratory experiments were compared to results of the modeled infiltration methods: original Green and Ampt (1911) model and Green and Ampt with air compression and counterflow. The advantage of this new method is its simplicity. The new method uses parameters that are generally needed for modeling infiltration with the Green and Ampt (1911) approach. Disadvantages of the model are assumptions of the uniform water content and the uniform pressure. Another shortcoming of the model is that it does not account for air compression and air counterflow prior to ponding. Laboratory experiments described in this work and a proposed model can be further used for modeling and studying infiltration with air effects. In addition, this work can be of use to someone studying irrigation techniques of rice or other crops.