Method Dependence in Thermal Conductivity and Aerodynamic Roughness Length Estimates on a Debris-Covered Glacier

Abstract

Rock debris partially covers glaciers worldwide, with varying extents and distributions, and controls sub-debris melt rates by modifying energy transfer from the atmosphere to the ice. Two key physical properties controlling this energy exchange are thermal conductivity $\left(k\right)$ and aerodynamic roughness length $\left(z_0\right)$. Accurate representation of these properties in energy-balance models is critical for understanding climate-glacier interactions and predicting the behavior of debris-covered glaciers. However, $k$ and $z_0$ have been derived at very few sites from limited local measurements, using different approaches, and most model applications rely on values reported from these few sites and studies. We derive $k$ and $z_0$ using established and modified approaches from data at three locations on Pirámide Glacier in the central Chilean Andes. By comparing methods and evaluating melt simulated with an energy-balance model, we reveal substantial differences between approaches. These lead to discrepancies between ice melt from energy-balance simulations and observed data, and highlight the impact of method choice on calculated ice melt. Optimizing $k$ against measured melt appears a viable approach to constrain melt simulations. Determining $z_0$ seems less critical, as it has a smaller impact on total melt. Profile aerodynamic method measurements for estimating $z_0$, despite higher costs, are independent of ice melt calculations. The large, unexpected differences between methods indicate a substantial knowledge gap. The fact that field-derived $k$ and $z_0$ fail to work well in energy-balance models, suggests that model values represent bulk properties distinct from theoretical field measurements. Addressing this gap is essential for improving glacier melt predictions.