Abstract
ABSTRACTMeltwater is important to understanding glacier health and dynamics. Since melt measurements are uncommon, ice ablation estimates are often based on models including the positive degree day (PDD) model. The PDD estimate is popular since it only requires air temperature as input, but suffers from the lack of physical motivation of an energy-balance model. We present a physics-based alternative to the PDD model that still only takes air/surface temperature as input. The model resembles the PDD model except accounting for time lags in ablation when cold ice needs to be warmed. The model is expressed as a differential equation with a single extra parameter related to the efficiency of heating a near-surface layer of ice. With zero thickness, the model reduces to the PDD model, providing a physical basis for the PDD model. Applying the model to data from Greenland, it improves modestly upon the PDD model, with the main improvement being better prediction of early season melting. This new model is a useful compromise, with some of the physics of more realistic models and the simplicity of a PDD model. The model should improve estimates of meltwater production and help constrain PDD parameters when empirical calibration is challenging.
Highlights
The ablation of ice and snow at glaciers and ice sheets is of much importance for the mass balance of glaciers, and contributes both to the direct loss of mass and indirectly through the lubricating effect that meltwater can have on glacier dynamics
We have presented a new simplified model in which observations of surface air temperature can be used to construct a physically meaningful estimate of ice ablation rates from the surface of an ice sheet or glacier
While it is certainly not expected to be as accurate as a full energy-balance model, the ability to use the model in essentially any circumstance in which the positive degree day (PDD) model can be used, while having a sound physical basis that the PDD model lacks, makes the new model attractive for use across a wide range of applications and in cases where empirical calibration is difficult
Summary
The ablation of ice and snow at glaciers and ice sheets is of much importance for the mass balance of glaciers, and contributes both to the direct loss of mass and indirectly through the lubricating effect that meltwater can have on glacier dynamics. Information about cloud cover and vertical profiles of wind speed, humidity, and air temperature are typically needed to calculate the relevant energy fluxes. These quantities are rarely measured in enough detail (if at all) to be able to use measured quantities. PDD models either assume that above 0°C temperatures can immediately cause ablation regardless of how cold the ice was immediately prior to that or how long those cold temperatures lasted, or that there is a nonphysical non-0°C melt threshold (e.g. van den Broeke and others, 2010) This clear inconsistency with physical expectation is one of the primary motivations of this work.
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