We consider a linearized dynamical system modeling the flow rate of water along the rivers and hillslopes of an arbitrary watershed. The system is perturbed by a random rainfall in the form of a compound Poisson process. The model describes the evolution, at daily time scales, of an interconnected network of linear reservoirs and takes into account the differences in flow celerity between hillslopes and streams as well as their spatial variation. The resulting stochastic process is a piece-wise deterministic Markov process of the Orstein–Uhlembeck type. We provide an explicit formula for the Laplace transform of the invariant density of streamflow in terms of the geophysical parameters of the river network and the statistical properties of the precipitation field. As an application, we include novel formulas for the invariant moments of the streamflow at the watershed’s outlet, as well as the asymptotic behavior of extreme discharge events, and conditions for the statistical scaling of streamflow with respect to Horton order.

中文翻译：

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随机降雨下河网排水动力学

我们考虑一个线性动力系统，该系统模拟任意流域的河流和山坡上的水流量。该系统受到复合泊松过程形式的随机降雨的扰动。该模型描述了线性水库互连网络在每日时间尺度上的演变，并考虑了山坡和溪流之间流动速度的差异以及它们的空间变化。由此产生的随机过程是 Orstein-Uhlembeck 类型的分段确定性马尔可夫过程。我们根据河网的地球物理参数和降水场的统计特性，为河流流量不变密度的拉普拉斯变换提供了一个明确的公式。作为应用程序，