Numerical study of the error sources in the experimental estimation of thermal diffusivity: an application to debris-covered glaciers

Abstract

A surface debris layer significantly modifies underlying ice melt dependent on the thermal resistance of the debris cover, with thermal resistance being a function of debris thickness and effective thermal conductivity. Thus, these terms are required in models of sub-debris ice melt. The most commonly used method to calculate effective thermal conductivity of supraglacial debris layers applies heat diffusion principles to a vertical array of temperature measurements through the supraglacial debris cover combined with an estimate of volumetric heat capacity of the debris as presented by Conway and Rasmussen (2000). Application of this approach is only appropriate if the temperature data indicate that the system is predominantly conductive and, even in the case of a pure conductive system, the method necessarily introduces numerical errors that can impact the derived values. The sampling strategies used in published applications of this method vary in sensor precision and spatiotemporal temperature sampling strategies, hampering inter-site comparisons of the derived values and their usage at unmeasured sites. To address this, we use synthetic datasets to isolate the numerical errors of the temporal and spatial sampling interval and the precision of sensor temperature and position in recovering known thermal diffusivity values using this method. On the basis of this, we can establish sampling an analytical strategy to minimize the methodological errors. Our results show that increasing temporal and spatial sampling intervals increases (or leads to) truncation errors and systematically underestimates calculated values of thermal diffusivity. The thermistor precision, the shape of the diurnal temperature cycle, the debris thermal diffusivity, and misrepresenting the vertical thermistor position also result in systematic errors that show strong cross-dependencies dependent on signal-to-noise ratio with which spatiotemporal temperature gradients are captured. We provide an interactive analysis tool and best-practice guidelines to help researchers investigate the effect of the sampling interval on calculated sub-debris ice melt and plan future measurement campaigns. These findings can be used to plan optimal field-sampling strategies for future campaigns and as a guide for common reanalysis of existing datasets to allow intercomparison across sites.