Environmental Earth Sciences manuscript No. (will be inserted by the editor) A coupled surface / subsurface flow model accounting for air entrapment and air pressure counterflow Jens-Olaf Delfs · Wenqing Wang · Thomas Kalbacher · Ashok Kumar Singh · Olaf Kolditz Received: date / Accepted: date Abstract This work introduces the soil air system into integrated hydrology by simu- lating the flow processes and interactions of surface runoff, soil moisture and air in the shallow subsurface. The numerical model is formulated as a coupled system of partial differential equations for hydrostatic (diffusive wave) shallow flow and two-phase flow in a porous medium. The simultaneous mass transfer between the soil, overland, and at- mosphere compartments is achieved by upgrading a fully established leakance concept for overland-soil liquid exchange to an air exchange flux between soil and atmosphere. In a new algorithm, leakances operate as a valve for gas pressure in a liquid-covered porous medium facilitating the simulation of air out-break events through the land surface. General criteria are stated to guarantee stability in a sequential iterative cou- pling algorithm and, in addition, for leakances in order to control the mass exchange between compartments. A benchmark test, which is based on a classic experimental data set on infiltration excess (Horton) overland flow, identified a feedback mechanism between surface runoff and soil air pressures. Our study suggests that air compression in soils amplifies surface runoff during high precipitation at specific sites, particularly in near-stream areas. Keywords: Coupled flow; Two-phase flow; Horton runoff; Leakance; Soil gas release; OpenGeoSys (OGS). 1 Introduction Surface runoff models employ the Richards’ approach, when they simulate the water fluxes in the variably saturated soil compartment with partial differential equations, J.-O. Delfs Water & Earth System Science (WESS) Cluster, T¨ ubingen, Germany Tel.: +7071-2976468 Fax: +7071-295046 E-mail: jens-olaf.delfs@uni-tuebingen.de W. Wang, T. Kalbacher, A. K. Singh, O. Kolditz Department of Environmental Informatics, Helmholtz Centre for Environmental Research - UFZ Leipzig, Leipzig, Germany