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 (z0). 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 z0 and upscale these to map z0 across an ablating mountain glacier. At plot scales, we found spatial variability in z0 estimates of over two orders of magnitude with unpredictable z0 trajectories, even when classified into ice surface types. TLS-derived surface roughness exhibited strong relationships with plot-scale SfM z0 estimates. At the glacier scale, a consistent increase in z0 of ~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 z0 over 60 d. These measurements permit us to propose a scale-dependent temporal z0 evolution model where unpredictable variability at the plot scale gives way to more predictable changes of z0 at the glacier scale. This model provides a critical step towards deriving spatially and temporally distributed representations of z0 that are currently lacking in the parameterisation of distributed glacier surface energy balance models.

中文翻译：

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基于重复地形调查的尺度相关模型，用于表示消融冰川冰的空气动力学粗糙度变化

湍流通量对全球冰面的能量平衡做出了巨大且不断增长的贡献，但由于在估计空气动力学粗糙度长度方面存在挑战，因此受到的限制很差。z0）。在这里，我们使用来自运动 (SfM) 摄影测量和地面激光扫描 (TLS) 调查的结构来进行绘图尺度的 2-D 和 3-D 微地形估计z0并将这些放大到地图z0穿过消融的山地冰川。在地块尺度上，我们发现空间变异性z0估计超过两个数量级且不可预测z0轨迹，即使分类为冰面类型。TLS 衍生的表面粗糙度与绘图尺度 SfM 有很强的关系z0估计。在冰川尺度上，持续增加z0约 0.1 毫米 d-1被观测到。基于自地表冰被融雪暴露以来的时间的时空替代证实了这种逐渐增加的z0超过 60 d。这些测量允许我们提出一个与尺度相关的时间z0进化模型，其中地块尺度上不可预测的变化让位于更可预测的变化z0在冰川尺度上。该模型为推导空间和时间分布的表示提供了关键步骤z0目前缺乏分布式冰川表面能量平衡模型的参数化。