The following visualization shows how ice temperature varies with depth over a year. $T = T_0 - \Delta T e^{-z*\sqrt{\omega /2\kappa }}cos(\omega t-z*\sqrt{\omega /2 \kappa})$ where T is the ice temperature at depth z, $T_0$ is the average ice surface temperature (yearly average), $\Delta T$ is the temperature oscillation at the surface, $\omega$ is the period of temperature oscillations set as a constant to equal seasonal temperature variations at the surface, and $\kappa$ is thermal diffusivity. Using the interactive window below you can see how temperature changes over time and you can adjust $T_0$ and $\Delta T$ to see how these variables impact ice temperature. this means that if $T_0$ is $-15^oC$ the average ice surface temperature is -5 degrees and if $\delta T$ is $10^oC$then the ice surface temperature varies from $-5^oC$ in the summer to $-15^oC$ in the winter. Source: Cuffey and Paterson, 2010, "The Physics of Glaciers" 4th Edition, Academic Press. - Ch 9.
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