Comparing the transport-limited and ξ−q models for sediment transport
Comparing the transport-limited and ξ−q models for sediment transport
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比较沉积物输运的输运限制模型和 Σ−q 模型
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发表时间：
2021
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通讯作者：
J. Braun
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作者：
J. Braun
抽象的。我们比较了两种最广泛使用的描述泥沙输运和沉积过程的低复杂性模型，即输运受限(或TL)模型和最近由Davy和Lague(2009年)发展起来的容量不足(或ξ−Q)模型。使用这两个模型，我们研究了由来自附近活动造山带的固定沉积通量提供的沉积大陆系统的行为，沉积物通过该造山带转移到代表大河、湖泊或海洋的固定基准面。我们的比较表明，这两个模型共享相同的稳态解，为此，我们得到了一个简单的一维解析解，它再现了这种沉积系统的主要特征：连接到较浅冲积平原的陡峭扇体。得到的风扇几何形状遵守关于风扇大小和相对于上游流域A0的坡度的基本观测约束。该解强烈依赖于系统的大小，L，与由A0的大小决定的距离L0相比，L0产生了两种根本不同的沉积系统：约束系统，其中LL0。我们推导出了系统响应时间与系统特性的关系的简单表达式，如系统的长度、上游集水区的大小、输入沉积通量的幅度以及两个模型各自的速率参数(扩散率或可蚀性)。我们表明，ξ−Q模型预测了更长的响应时间，这与其在整个长度上传播信号的更高效率有关。我们证明，尽管信号在沉积体系中传播的方式在两种模型之间有很大的不同，但它们都预测持续时间长于体系响应时间的扰动可以记录在沉积体系的地层学中，特别是扇的地层学中。有趣的是，ξ−Q模型预测进入的沉积通量中的所有扰动都将通过该系统传输，而TL模型预测快速扰动不能。最后，我们讨论了为什么和在什么条件下这些差异是重要的，并提出了观测方法来确定这两个模型中的哪一个最适合代表自然系统。
Abstract. We present a comparison between two of the most widely used reduced-complexity models for the representation of sediment transport and deposition processes, namely the transport limited (or TL) model and the under-capacity (or ξ−q) model more recently developed by Davy and Lague (2009). Using both models, we investigate the behavior of a sedimentary continental system fed by a fixed sedimentary flux from a nearby active orogen though which sediments transit to a fixed base level representing a large river, a lake or an ocean. Our comparison shows that the two models share the same steady-state solution, for which we derive a simple 1D analytical solution that reproduces the major features of such sedimentary systems: a steep fan that connects to a shallower alluvial plain. The resulting fan geometry obeys basic observational constraints on fan size and slope with respect to the upstream drainage area, A0. The solution is strongly dependent on the size of the system, L, in comparison to a distance L0 that is determined by the size of A0 and gives rise to two fundamentally different types of sedimentary systems: constrained system where LL0. We derive simple expressions that show the dependence of the system response time on the system characteristics, such as its length, the size of the upstream catchment area, the amplitude of the incoming sedimentary flux and the respective rate parameters (diffusivity or erodibility) for each of the two models. We show that the ξ−q model predicts longer response times, which we relate to its greater efficiency at propagating signals through its entire length. We demonstrate that, although the manner in which signals propagates through the sedimentary system differs greatly between the two models, they both predict that perturbations that last longer than the response time of the system can be recorded in the stratigraphy of the sedimentary system and in particular of the fan. Interestingly, the ξ−q model predicts that all perturbations in incoming sedimentary flux will be transmitted through the system whereas the TL model predicts that rapid perturbations cannot. We finally discuss why and under which conditions these differences are important and propose observational ways to determine which of the two models is most appropriate to represent natural systems.