27 Nov 2023
 | 27 Nov 2023

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

Calvin Beck and Lindsey Nicholson

Abstract. In tectonically active mountain regions, the thinning of alpine glaciers due to climate change favors the development of debris covered glaciers. This debris layer significantly modifies a glacier’s melt depending on the debris thickness and therefore modifies its evolution. Debris thermal conductivity is a critical parameter for calculating ice melt beneath a debris layer. The most commonly used method to calculate apparent thermal conductivity of supraglacial debris layers is based on an estimate of volumetric heat capacity of the debris and simple heat diffusion principles presented by Conway and Rasmussen (2000). The analysis of heat diffusion requires a vertical array of temperature measurements through the supraglacial debris cover. This study explores the effect of the temporal and spatial sampling interval, and method on the thermal diffusivity values derived using this method. Results show that increasing temporal and spatial sampling intervals increase truncation errors and therefore systematically underestimate values of thermal diffusivity. Also, the thermistor precision, the shape of the diurnal temperature cycle, and vertical thermistor displacement result in systematic errors. Overall these systematic errors would result in an underestimation of glacier ice melt under a debris layer. We have developed a best practice guideline to help other researchers to investigate the effect of the sampling interval on their calculated sub-debris ice melt and better plan future measurement campaigns.

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Calvin Beck and Lindsey Nicholson

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on egusphere-2023-2766', Argha Banerjee, 01 Feb 2024
    • AC1: 'Reply on RC1', Calvin Beck, 21 Mar 2024
  • RC2: 'Comment on egusphere-2023-2766', Anonymous Referee #2, 12 Feb 2024
    • AC2: 'Reply on RC2', Calvin Beck, 21 Mar 2024
  • RC3: 'Comment on egusphere-2023-2766', Anonymous Referee #3, 15 Feb 2024
    • AC3: 'Reply on RC3', Calvin Beck, 21 Mar 2024
Calvin Beck and Lindsey Nicholson
Calvin Beck and Lindsey Nicholson


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Short summary
A glacier’s debris cover strongly modified its mass balance in contrast to a clean ice glacier. A key parameter for calculating sub-debris melt is the thermal diffusivity of the debris layer. Conway and Rasmussen (2000) present a method to estimate this value based on simple heat diffusion principles. Our analysis shows that the selected temporal and spatial sampling intervals effects the estimated value of thermal diffusivity, resulting in glacier melt being systematically underestimated.