Evaluating morphological estimates of the aerodynamic roughness of debris covered glacier ice

Abstract

Aerodynamic roughness length (z 0 ), the height above the ground surface at which the extrapolated horizontal wind velocity profile drops to zero, is one of the most poorly parameterised elements of the glacier surface energy balance equation. The fully three-dimensional cloud-based approach is shown to be most stable across different scales and these z 0 values are most correct in relative order when compared to the wind tower data. Popular profile-based methods perform less well providing highly variable values across different scales and when using data of differing resolution. These findings hold relevance for all studies using microtopographic methods to estimate aerodynamic roughness lengths, including those in non-glacial settings.

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

“…Mechanistic microtopographic models [e.g., Lettau , ; Counihan , ; Munro , ] measure topographic roughness and attempt to link this property to the aerodynamic roughness length [ Smith , ], but still require validation across a wider range of surface types. While such models are thoroughly established for many glacier surfaces [ Brock et al , ; Smith et al , ] and may be accurate for smoother debris surfaces as well [ Quincey et al , ], validation data for hummocky topography is difficult to assemble. Thus, while a mechanistic model of z 0 based on surface drag is appealing, empirical parameterizations of z 0 [ Nield et al , ] may still be more reliable models to relate the two types of roughness.…”

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

“…The filters listed below were then applied, either retaining or rejecting those profiles where the extrapolated model deviated more than an acceptable amount away from a log‐linear profile, changes in temperature over time indicate conditions were not stationary, and wind speeds were too low to be reliably recorded by our instruments. Profiles of wind speed and temperature were filtered in three stages: relaxed filters: rejected poor log‐linear profile fits ( r 2 < 0.95) and low wind speeds (<1 m s −1 ) while assuming stability is valid for MO theory; standard filters (as used by Quincey et al, ) again assume valid MO stability, applying a stricter r 2 filter (rejecting r 2 < 0.99), a minimum wind speed filter (<1 m s −1 ) and a stationarity filter (which identifies when mean air temperature changed by >0.25 °C min −1 ); finally, a stability correction based on MO similarity theory was applied as a third step, in addition to the standard filters. We found L using an iterative approach, in which any profiles that required more than 10 iterations to converge with MO theory (and were thus unlikely to converge at all) were discarded. …”

“…Microtopographic z 0 was calculated using the commonly applied Munro () transect method (treating each row/column of a DEM as a separate transect), and the DEM method used by Smith, Quincey, et al () and Quincey et al (), with the difference that h* was calculated from twice the standard deviation of elevations above the detrended plane rather than the mean elevation. As noted by Smith, Quincey, et al (), the choice of statistic is somewhat arbitrary; twice the standard deviation above the detrended plane was chosen as it provided the closest approximation of average roughness height as used by Lettau ().…”

“…Smith, Quincey, et al () point out that in such cases, exposed frontal area (and thus impact on flow) would appear much larger than is realistic, resulting in erroneously high z 0 . Additionally, streamlined features exhibit a small drag coefficient (Macdonald et al, ; Wieringa, ), raising questions about whether Lettau's () average of 0.5 is an overestimate for bare ice (Smith, Quincey, et al, ) or an underestimate for debris‐covered ice (Quincey et al, ). Lettau adopted the 0.5 value after the drag coefficient ( C d ) of upturned >4 m 3 bushel baskets was given as 0.45 in experiments by Kutzbach (1961), who followed Schlichting's () expression, which is valid for regular arrays of geometrically similar roughness elements (Wooding et al, ).…”

“…Whether 2D or 3D methods are employed, the inclusion of an average height index imposes a spatial boundary (Smith, ), and as such, the resulting z 0 value is dependent on the length of transect or the area of the plot (Fitzpatrick et al, ; Quincey et al, ; Rees & Arnold, ; Smith, Quincey, et al, ). Further dependence is placed on the resolution of the data, with coarser resolution data effectively representing a filtered fine‐resolution dataset (Quincey et al, ); that is, for a given transect length, a surface that is sampled every 10 cm will appear smoother than one that is sampled every millimeter, artificially reducing z 0 .…”