Thermodynamics of the hydraulic head, pressure head, and gravitational head in subsurface hydrology, and principles for their spatial averaging

Introduction Conclusions References Tables Figures ◭ ◮ ◭ ◮ Back Close Full Screen / Esc Papers published in Hydrology and Earth System Sciences Discussions are under open-access review for the journal Hydrology and Earth System Sciences Abstract Introduction Conclusions References Tables Figures ◭ ◮ ◭ ◮ Back Close Full Screen / Esc Abstract In order to establish a thermodynamic justification of the theoretical relationship between the hydraulic, pressure/matric, and gravitational head in subsurface hydrology, the thermodynamic literature pertaining to subsurface flow processes is reviewed. The incompressibility of liquids negates a thermodynamic definition of pressure, which 5 gives rise to several inconsistencies in pore scale theories. At larger scales, the grav-itational potential and fluid pressure are treated as additive potentials. This superpo-sition principle is replicated in the well-established relationship between the various heads according to subsurface hydrological theory. The necessary requirement that the superposition be maintained across scales is combined with conservation of en-10 ergy during volume integration to establish consistent upscaling equations for the various heads. The power of these upscaling equations is demonstrated by the derivation of an upscaled water content-matric head relationship and the resolution of an apparent paradox reported in the literature that is shown to have arisen from a violation of the superposition principle.