The temporal dynamics of the land surface are commonly modeled by so-called landscape evolution models, consisting of coupled partial differential equations accounting for the balance of sediment and water. An average sediment budget equation for a landscape evolution model in detachment-limited condition is derived in terms of curvature-dependent and curvature-independent components. This highlights the role of plane curvature and spatial distribution of surface divergence/convergence on the average erosion rate. Performing a Reynolds-type averaging of the original equations leads to a decomposition of the erosion into an unchannelized erosion sink and a channelization sediment flux. The latter is the derivative of a potential (referred to as “channelization sediment potential”) that arises from the negative correlation of elevation and specific drainage area and closely resembles, in both form and behavior, the Reynolds stress in fluid turbulence. The negative elevation-area covariance emerges as a statistical signature of surface channelization. Building on analogies between landscape channelization and fluid turbulence, these theoretical results may provide a path to estimate model parameters from observations and offer useful benchmarks for numerical simulations in the channelized regime.

中文翻译：

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景观演化模型中的平均动态和海拔贡献面积协方差

陆地表面的时间动态通常由所谓的景观演化模型建模，该模型由解释沉积物和水平衡的耦合偏微分方程组成。根据曲率相关分量和曲率无关分量，推导出了在脱离限制条件下的景观演化模型的平均沉积物收支方程。这突出了平面曲率和表面发散/收敛的空间分布对平均侵蚀率的作用。对原始方程进行雷诺式平均会导致侵蚀分解为非渠道化侵蚀汇和渠道化沉积物通量。后者是由高程和特定流域面积的负相关引起的势（称为“渠道沉积势”）的导数，在形式和行为上与流体湍流中的雷诺应力非常相似。负高程-面积协方差作为表面通道化的统计特征出现。基于景观通道化和流体湍流之间的类比，这些理论结果可以提供一条从观测中估计模型参数的途径，并为通道化区域的数值模拟提供有用的基准。