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\begin{document}

\title{Modeling gas flow velocities in soils induced by variations in surface
pressure, heat and moisture dynamics}



\author[1]{W J Massman}%
\author[1]{J M Frank}%
\affil[1]{USDA Forest Service}%


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  \date{May 17, 2024}


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\begin{abstract}
Changes in atmospheric pressure continuously ventilate soils and
snowpacks. This physical process, known as pressure pumping, is a major
factor in the exchange fluxes of H2O, CO2 and other trace gases between
the soil and atmosphere. Thus models of pressure pumping are relevant to
many areas of critical importance. This study compares the three
principal models used to describe pressure pumping. Beginning with the
fundamental physical principles and whether the flow field is
compressible or incompressible, these models are categorized as linear
parabolic (one model -- compressible) or nonlinear hyperbolic (two
models -- incompressible). Using observed soil surface pressure data,
measured vertical profiles of soil permeability and standard linear
analysis and numerical methods, this study shows that nonlinear models
produce advective velocities that are one to two orders of magnitude
greater than those associated with the linear model. Incorporating soil
temperature and moisture dynamics made very little difference to the
linear model, but a significant difference in the nonlinear models
suggesting that advective velocities induced by pressure changes
associated with soil heating and moisture dynamics may not always be
small enough to ignore. All numerical results are sensitive to the
frequency of the pressure forcing, which was band-pass filtered into
low, mid and high frequencies with the greatest model differences at low
frequencies. Partitioning the pressure forcing and model responses
helped to establish that mid-frequency weather-related phenomena
(empirically identified as inertia gravity waves and solitons) are
important drivers of gas exchange between the soil and the atmosphere.%
\end{abstract}%



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