Bounding linear rainfall-runoff models with fractional derivatives applied to a barren catchment of the Jordan Rift Valley
Bounding linear rainfall-runoff models with fractional derivatives applied to a barren catchment of the Jordan Rift Valley
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DOI：
10.1016/j.jhydrol.2020.125879
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发表时间：
2020-12
影响因子：
6.4
通讯作者：
K. Unami;R. Fadhil;O. Mohawesh
中科院分区：
文献类型：
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作者：
K. Unami;R. Fadhil;O. Mohawesh
一个新的概念是发展数学理解的动态，在贫瘠的集水区的约旦裂谷的径流事件。在集水区的一个观测点获得了降雨和径流的时间序列数据。由于极端干旱的环境，水流作为径流来自流域是短暂的，并且径流事件彼此之间有明显的区别。首先，利用线性规划的单纯形法，辨识出一对具有外生输入的线性自回归模型（ARX模型），使每个径流时间序列紧密结合。外生输入部分与传统的单位线方法兼容，而自回归部分被视为分数阶离散微分算子。然后，确定一个线性分数阶微分方程来近似每个线性ARX模型，该线性分数阶微分方程限制了降雨强度与径流量之间的实际因果关系的扰动。在系统理论框架下，研究了具有分数阶导数的上、下界径流模型。最后，名义上的模型，从实际的非线性和随机现象的扰动被安排在频域中的所有上界的径流模型，导致制定一个具有挑战性的分数最优控制问题，涉及随机过程。
A new concept is developed to mathematically understand the dynamics of the rainfall-runoff events in a barren catchment of the Jordan Rift Valley. Time series data of rainfall and runoff have been acquired at an observation point in the catchment. Due to the extreme arid environment, water current as the runoff from the catchment is ephemeral, and the rainfall-runoff events are clearly distinguishable from each other. Firstly, a pair of linear autoregressive models with exogenous input (ARX models) is identified to tightly bound each runoff time series using the simplex method of linear programming. The exogenous input part is compatible with the conventional unit hydrograph method, while the autoregressive part is regarded as a discretized differential operator of fractional orders. Then, a linear fractional differential equation is determined to approximate each linear ARX model, which restricts the perturbation of the actual causal relationship between rainfall intensity and runoff discharge. The resulting lower and upper bounding rainfall-runoff models with fractional derivatives are examined in the system-theoretic framework. Finally, a nominal model from which actual nonlinear and stochastic phenomena perturb is arranged to envelope the all upper bounding rainfall-runoff models in the frequency domain, leading to the formulation of a challenging fractional optimal control problem involving stochastic processes.