During the last few decades, bed-elevation profiles from radar sounders have been used to quantify bed roughness. Various methods have been employed, such as the ‘two-parameter’ technique that considers vertical and slope irregularities in topography, but they struggle to incorporate roughness at multiple spatial scales leading to a breakdown in their depiction of bed roughness where the relief is most complex. In this article, we describe a new algorithm, analogous to wavelet transformations, to quantify the bed roughness at multiple scales. The ‘Self-Adaptive Two-Parameter’ system calculates the roughness of a bed profile using a frequency-domain method, allowing the extraction of three characteristic factors: (1) slope, (2) skewness and (3) coefficient of variation. The multi-scale roughness is derived by weighted-summing of these frequency-related factors. We use idealized bed elevations to initially validate the algorithm, and then actual bed-elevation data are used to compare the new roughness index with other methods. We show the new technique is an effective tool for quantifying bed roughness from radar data, paving the way for improved continental-wide depictions of bed roughness and incorporation of this information into ice flow models.

中文翻译：

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一种自适应多尺度冰下地形粗糙度表征的两参数方法

在过去的几十年里，雷达测深仪的海床高度剖面已被用于量化海床粗糙度。已经采用了各种方法，例如考虑地形中垂直和坡度不规则性的“双参数”技术，但它们难以在多个空间尺度上结合粗糙度，导致它们对地势最复杂的地层粗糙度的描述出现故障. 在本文中，我们描述了一种类似于小波变换的新算法，用于在多个尺度上量化地层粗糙度。“自适应双参数”系统使用频域方法计算床层轮廓的粗糙度，允许提取三个特征因素：(1) 斜率、(2) 偏度和 (3) 变异系数。多尺度粗糙度是通过这些频率相关因素的加权求和得出的。我们使用理想化的床面高度来初步验证算法，然后使用实际床面高度数据将新的粗糙度指数与其他方法进行比较。我们展示了这项新技术是一种从雷达数据中量化地层粗糙度的有效工具，为改进大陆范围内的地层粗糙度描述以及将这些信息纳入冰流模型铺平了道路。