Highly variable aerodynamic roughness length (z₀) for a hummocky debris‐covered glacier

Abstract

The aerodynamic roughness length (z0) is an essential parameter in surface energy balance studies, but few literature values exist for debris‐covered glaciers. We use microtopographic and aerodynamic methods to assess the spatial variability of z0 for Lirung Glacier, Nepal. We apply structure from motion to produce digital elevation models for three nested domains: five 1 m2 plots, a 21,300 m2 surface depression, and the lower 550,000 m2 of the debris‐mantled tongue. Wind and temperature sensor towers were installed in the vicinity of the plots within the surface depression in October 2014. We calculate z0 according to a variety of transect‐based microtopographic parameterizations for each plot, then develop a grid version of the algorithms by aggregating data from all transects. This grid approach is applied to the surface depression digital elevation model to characterize z0 spatial variability. The algorithms reproduce the same variability among transects and plots, but z0 estimates vary by an order of magnitude between algorithms. Across the study depression, results from different algorithms are strongly correlated. Using Monin‐Obukov similarity theory, we derive z0 values from the meteorological data. Using different stability criteria, we derive median values of z0 between 0.03 m and 0.05 m, but with considerable uncertainty due to the glacier's complex topography. Considering estimates from these algorithms, results suggest that z0 varies across Lirung Glacier between ∼0.005 m (gravels) to ∼0.5 m (boulders). Future efforts should assess the importance of such variable z0 values in a distributed energy balance model.

Glacial Aerodynamic Roughness Estimates: Uncertainty, Sensitivity, and Precision in Field Measurements

“…The relationship between z 0 and scale is as expected for SK (cf. Miles et al, ; Quincey et al, ). Raster z 0 follows a clear trend with plot size, whereas transect z 0 shows some variation but increases overall—both demonstrate significant relationships ( r 2 > 0.9, p < 0.05).…”

“…As with other similar studies, we found that using wind/temperature profiles to find z 0 is a very low‐yield approach (cf.Brock et al, ; Denby & Smeets, ; Miles et al, ; Quincey et al, ; Sicart et al, ; Smeets et al, ). Moreover, sensors had to be monitored and repaired due to harsh weather conditions meaning that instruments cannot be set up and left unattended for long periods (the wind tower at Storglaciären collapsed overnight from 12 to 13 July, hence the shortened dataset).…”

“…These methods allow rapid data acquisition over much larger areas and shorter timescales than is feasible with more traditional manual surveys. Recent studies have used digital elevation models (DEMs) constructed from SfM (Irvine‐Fynn et al, ; Miles et al, ; Rounce et al, ) or TLS (Nield et al, ) data, from which transects can be extracted as the grid rows and columns. Smith, Quincey, et al () obtained terms for (3) from both DEMs and filtered point clouds, allowing the previous assumptions to be relaxed by accounting for the total exposed frontal area and giving a value for each cardinal wind direction.…”

“…With 3D data, the same effect is achieved by subtracting the fitted plane (Smith, Quincey, et al, ). This is a robust approach with smaller transects/plots; however, linear (and planar) detrending is susceptible to scale dependence (Miles et al, ). For larger plots/transects or more complex topography, other detrending methods may be more appropriate to remove overall trends, such as coarse‐DEM removal, median filtering, or splines (Miles et al, ; Quincey et al, ).…”

“…Recently, fine‐resolution survey techniques such as Structure from Motion (SfM) photogrammetry and terrestrial laser scanning (TLS) have been explored for their ability to enhance glacier surface microtopographic data collection. These methods have been used to collect transects rapidly and at fine resolution (Miles et al, ) and to devise 3D geometric approaches to finding z 0 that relax the previously mentioned assumptions (see section ), including initial steps toward glacier‐wide z 0 maps (Smith, Carrivick, et al, ) and calculating z 0 from remotely sensed data products (Fitzpatrick et al, ). Potential for cryosphere‐wide z 0 measurements increases in line with the expansion of available fine‐resolution data sources (e.g., ArcticDEM, global DEM, and NASA High Mountain Asia DEM).…”