Recent researches have highlighted the significance of nonlocal processes in understanding the morphodynamics and sediment transport across landscapes. Nonlocal processes in sediment transport refer to the influence of landscape properties beyond the immediate vicinity of a given point on the sediment flux. Existing nonlocal models, employing fractional operators, aim to capture global correlated nonlocality using a global convolution operator. Nevertheless, such models tend to disregard nonlocal phenomena occurring at regional scales, potentially resulting in substantial inaccuracies due to an inadequate representation of sediment transport processes at these scales. This study presents a novel and more comprehensive mathematical formulation of the nonlocal Exner law, leveraging the peridynamic differential operator (PDDO). The proposed regional nonlocal model incorporates nonlocal sediment transport processes by utilizing a pre-defined weight function and interaction domain within the framework of the PDDO. The novel regional nonlocal model effectively bridges the gap between local and global models by integrating both short-range and long-range interactions in sediment transport. Application reveals that the regional nonlocal model provides a significantly enhanced accuracy in depicting profiles at the bedform scale compared to the local and the global models.

中文翻译：

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在床型尺度上沉积物非局部运输的 Exner 定律的推广


最近的研究强调了非局部过程在理解地貌动力学和沉积物跨景观传输方面的重要性。沉积物输送中的非局部过程是指给定点附近以外的景观特性对沉积物通量的影响。现有的非局部模型，使用分数运算符，旨在使用全局卷积运算符捕获全局相关非局部性。然而，这些模型往往忽视了在区域尺度上发生的非局部现象，由于在这些尺度上对沉积物输送过程的表示不足，可能导致严重的不准确。本研究利用近动力微分算子 （PDDO） 提出了一种新颖且更全面的非局部 Exner 定律数学公式。拟议的区域非本地模型通过在 PDDO 框架内利用预定义的权重函数和交互域来整合非本地沉积物运输过程。新颖的区域非局部模型通过在沉积物传输中整合短程和长程相互作用，有效地弥合了局部和全球模型之间的差距。应用程序表明，与局部和全局模型相比，区域非局部模型在床形尺度上描绘剖面的准确性显著提高。