A Scale-Dependent Model To Represent Changing Aerodynamic Roughness Of Ablating Glacier Ice Based On Repeat Topographic Surveys

Turbulent fluxes make a substantial and growing contribution to the energy balance of ice surfaces globally, but are poorly constrained owing to challenges in estimating the aerodynamic roughness length (z(0)). Here, we used structure from motion (SfM) photogrammetry and terrestrial laser scanning (TLS) surveys to make plot-scale 2-D and 3-D microtopographic estimations of z(0) and upscale these to map z(0) across an ablating mountain glacier. At plot scales, we found spatial variability in z(0) estimates of over two orders of magnitude with unpredictable z(0) trajectories, even when classified into ice surface types. TLS-derived surface roughness exhibited strong relationships with plot-scale SfM z(0) estimates. At the glacier scale, a consistent increase in z(0) of similar to 0.1 mm d(-1) was observed. Space-for-time substitution based on time since surface ice was exposed by snow melt confirmed this gradual increase in z(0) over 60 d. These measurements permit us to propose a scale-dependent temporal z(0) evolution model where unpredictable variability at the plot scale gives way to more predictable changes of z(0) at the glacier scale. This model provides a critical step towards deriving spatially and temporally distributed representations of z(0) that are currently lacking in the parameterisation of distributed glacier surface energy balance models.