water Article Infiltration under Ponded Conditions Ioannis Argyrokastritis * , Maria Psychogiou and Paraskevi A. Londra *   Citation: Argyrokastritis, I.; Psychogiou, M.; Londra, P.A. Infiltration under Ponded Conditions. Water 2021, 13, 3492. https:// doi.org/10.3390/w13243492 Academic Editors: Roberto Greco, George Kargas, Petros Kerkides and Paraskevi Londra Received: 6 October 2021 Accepted: 3 December 2021 Published: 7 December 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Laboratory of Agricultural Hydraulics, Department of Natural Resources Management and Agricultural Engineering, School of Environment & Agricultural Engineering, Agricultural University of Athens, 75 Iera Odos Street, 11855 Athens, Greece; lhyd4psm@aua.gr * Correspondence: jarg@aua.gr (I.A.); v.londra@aua.gr (P.A.L.) Abstract: Ponded infiltration processes occur in agricultural lands irrigated by flooding of their soil surface or under insufficient drainage conditions. The existing equations describing the phenomenon of vertical infiltration under ponded conditions have not considered the actual contribution of the pressure head gradient to the flow. In this study, simple equations are proposed to describe the horizontal and vertical infiltration under various ponding heads incorporating the actual contribution of the pressure head gradient to the flow. Six soils with known hydraulic properties, covering a wide range of soil textures, were used. Horizontal and vertical infiltration data are obtained by numerical simulation for all soils studied using the Hydrus-1D code. To validate the accuracy of the proposed equations, the solutions of horizontal and vertical infiltrations provided by the proposed equations were compared with numerically simulated ones provided by the Hydrus 1-D. The analysis of the results showed a very good agreement in all soils studied. The proposed vertical infiltration equation was also compared to a simple and accurate equation which does not incorporate the actual contribution of the pressure head gradient to the flow and differences between them were observed in all soils studied. Keywords: ponding head; vertical infiltration; pressure head gradient; horizontal infiltration 1. Introduction The infiltration process is of great importance in hydrology and agricultural sciences since it provides the water available for plants and groundwater recharge and defines water runoff at soil surface. A rainfall or irrigation intensity greater than soil infiltration capacity will lead to water runoff at the soil surface, causing ponded conditions. Additionally, in agricultural lands ponded conditions may be developed under insufficient drainage and in irrigation practices when irrigation water is applied by flooding the soil surface. Further ponded conditions are met in lakes, natural or artificial. Consequently, the study of the vertical infiltration under ponding heads is of great interest. For this, Philip [1,2] tackled the problem of the vertical infiltration under ponded condi- tions, and he presented analytical solutions relative to this flow problem. Other researchers, later, investigated the same infiltration case and proposed equations to estimate the cu- mulative ponded infiltration in a homogeneous soil [3–14]. The main difference among these equations is the number of physical or fitting parameters used. In several models, the common physical parameters used are the soil sorptivity, S, and the saturated hydraulic conductivity, K s , which are often met as the main parameters of the two-parameter models. Green and Ampt [3] proposed a two-parameter equation assuming a piston-type water content profile with a well-defined wetting front characterized by a constant pressure head and constant pressure head at the surface. Brutsaert [4] proposed a three-parameter equation based on the quasi-analytical time-series infiltration solution of Philip [5] which can be converted into a two-parameter form by fixing the value of the third parameter. Parlange et al. [6] proposed a three-parameter equation based on integration of the water content-based form of Richards’ equation which can be converted into a two-parameter Water 2021, 13, 3492. https://doi.org/10.3390/w13243492 https://www.mdpi.com/journal/water