### Application of Diurnal Phase Lag Analysis to Calculating Thermal Diffusivity Series and Early and Late Winter N-factors

Thursday, November 22, 2018 - 12:00 to 12:19 Theatre 3Improvements to temperature logging instrumentation have facilitated an increase in the collection of air and ground surface temperature series in permafrost areas. Analyzing these data improves our understanding of how permafrost is affected by increasing temperatures and other observed changes in climate conditions, especially in the Arctic. Essential to this understanding is transfer theory, particularly thermal diffusivity, which summarizes the heat transfer rate directly in the heat equation.

Since the thermal diffusivity is the ratio of the thermal conductivity to the specific heat capacity, a field measurement of the thermal diffusivity requires both of these values. They are often taken from nearby soil pits (as disturbing the ground near the logger changes the soil's thermal properties) and can only reflect the location's thermal diffusivity at that particular snapshot in time. Given that the harmonic solution to the heat equation relates the thermal diffusivity directly to each of the amplitude damping and the phase lag of the conduction wave as it travels between temperature sensors (e.g. an air and a ground surface sensor), a phase lag or amplitude series can provide a means to generate a thermal diffusivity series over time. However, existing analysis methods often use only temperature magnitudes for analysis (e.g. when calculating mean values or n-factors) or, if considering the phase lag and amplitude of the temperature sinusoid, will tend to look at the annual scale where there is little variation from year to year compared to the diurnal scale. In contrast to using the heat equation, n-factors are a commonly used technique for summarizing a seasonal air-surface temperature relationship. However, previous work has shown that seasonal winter n-factors are overestimates when considering only the early winter temperature values, and underestimates if only considering the later temperature values. Partitioning the winter n-factor may better capture seasonal variability.

This presentation will demonstrate a means to calculate diurnal amplitude and phase lag series of a coupled air-surface temperature series and some results thereof. It will begin with a brief discussion of the geographical context of heat transfer in permafrost areas based on the surface energy balance along with a description of the influences of snow, vegetation, and topography. A breakdown of how the diurnal phase lag and amplitude series are calculated will lead into a look at the underlying mathematical relationships of phase lag and amplitude to thermal diffusivity calculations (and, transitively, to one another) via the harmonic solution to the heat equation.

In the results section, diffusivity series will be calculated from the amplitude and phase lag series over the summer and winter seasons and compared to field values both in terms of spatial and temporal variation. Following this, an amplitude damping filter will be demonstrated that can separate early and late winter temperatures for partitioning freezing n-factors into early and late winter n-factors to see if this can better capture seasonal variability. The presentation will close with a summary and suggestions for future research.