Abstract
Melting calorimetry, a classic experiment often conducted in high-school chemistry laboratories, holds significant untapped potential for scientific applications beyond its educational context. Traditionally, this technique has been applied to measure the liquid water content in snow using two different formulations: melting calorimetry and freezing calorimetry. In contrast to freezing calorimetry, which is considered the reference method for measuring liquid water content, melting calorimetry has been perceived as prone to generating significant inaccuracies. This research revisits the formulations for both melting and freezing calorimeters to assess volumetric liquid water content in snow. By incorporating the calorimetric constant, we account for heat exchange with the calorimeter, a critical factor often neglected in melting-calorimetry experiments. This paper identifies the most effective and least uncertain method for determining this constant. A central contribution of this work is the introduction of a framework for estimating uncertainty in volumetric liquid water content measurements, adhering to established guidelines for uncertainty expression. This novel framework allows us to revisit past mathematical analyses and demonstrate that melting calorimetry delivers reliable measurements with an uncertainty 0.25 % greater than freezing calorimetry. Notably, despite this slightly higher uncertainty, melting calorimetry offers significant practical advantages for field applications. Moreover, we show how the proposed uncertainty framework can be expanded beyond instrumental uncertainty and also take into account the variability from environmental factors and operators, providing a more comprehensive characterization of the uncertainty. By exploiting the proposed uncertainty framework, we finally conduct an in-depth analysis for the optimal tuning of the experiment parameters. This analysis culminates in a robust field protocol for melting calorimetry that transcends commonsense procedural guidelines. Strict adherence to this protocol will maximize measurement accuracy. Applied in field tests in Italy and Switzerland, the melting calorimetry was demonstrated to accurately track the wet front penetration in the snowpacks, producing results comparable to independent dielectric measurements. These findings highlight the accuracy and the practical advantages of melting calorimetry as a reliable field tool for quantifying snowpack liquid water content. Melting calorimetry can potentially serve as a valuable tool for the independent calibration and validation of proximal and remote sensing techniques used for liquid water content retrieval.