How to Assess Unfrozen Water Content Using Capacitance Sensors in Frozen Soils: A New Physics Based Conversion Curve

Abstract

Over the past 50 years, the effects of anthropogenic climate change has lead to steady global warming. Despite the alarming rate at which our planet is experiencing those environmental disturbances, the scientific community has only just begun to understand and catalog their impact. Among the most impacted systems are polar and sub-polar regions which are warming at up to four times the average global rate, resulting in permafrost thaw. The amount of unfrozen water in soils governs their thermal, physical and chemical properties, and the rapid decay of permafrost around the globe has led to a resurgence in interest for accurate and reliable measurements of unfrozen water content in soils. This measurement is hard to acquire because most (if not all) existing measurement techniques are indirect. That is, another property/value is measured and is used as an indication of the amount of unfrozen water in the soil. Accordingly, there is a need for what is called a conversion curve: a relationship that can transform the measured raw data into the desired unfrozen water content values. Regardless of the precision and accuracy of the measurement apparatus, if the conversion curve is lacking, so are the data reported. Among current measurement techniques, capacitance based sensors are frequently used for both field and laboratory application because of their low cost and ease of installation and maintenance. The current conversion curve used in those sensors is the \textit{Topp, 1980} equation, an empirical third-degree polynomial fit obtained from pooled wetting-drying experimental data. The \emph{Topp} relation is empirically fitted to entirely unfrozen data, resulting in a \textit{Topp, 1980} equation that is not intended for use on frozen soil data. The goal of this paper is to present an alternative conversion curve for capacitance-based sensors using a multiphase dielectric mixing model that is physically grounded. This improves the mathematical conversion of field and laboratory dielectric permittivity measurements into an estimate of volumetric water content.