Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
General Unit Hydrograph from Chow’s Linear Theory of Hydrologic Systems and Its Applications
https://orcid.org/0000-0002-3868-3623
This research solves Chow’s linear hydrologic systems equations thoroughly to result in a theoretical instantaneous unit hydrograph (UH), which is a superposition of many (M) negative exponential functions. This implies that the instantaneous UH can be imagined as a superposition of many linear reservoirs in parallel. Mathematically, at M→∞, the theoretical UH (in terms of Taylor series) converges to the writer’s general UH that is a simple analytic expression derived inductively from empiricism. Therefore, this research turns the recent conceptual general UH to a theoretical law that approximates real-world watershed processes as a time-invariant linear hydrologic system. Specifically, we first review Chow’s linear hydrologic systems model and apply it to a conceptual watershed with an instantaneous storm, which results in a theoretical instantaneous UH and an S-hydrograph in the superposition of many negative exponential functions. The resulting S-hydrograph then is shown mathematically to be identical to the writer’s general UH at M→∞. Finally, the general theoretical UH is applied to 10 real-world watersheds for 19 rainfall-runoff simulations. It is noteworthy that the proposed method has two advantages: (1) it is general for storms with different rainfall durations, and (2) it does not require to define excess rainfall and direct runoff in advance because rainfall losses and baseflow can be a part of the solution process. It is expected that this research provides a deeper understanding of the general UH and thus helps promote its applications in practice.
General Unit Hydrograph from Chow’s Linear Theory of Hydrologic Systems and Its Applications
https://orcid.org/0000-0002-3868-3623
This research solves Chow’s linear hydrologic systems equations thoroughly to result in a theoretical instantaneous unit hydrograph (UH), which is a superposition of many (M) negative exponential functions. This implies that the instantaneous UH can be imagined as a superposition of many linear reservoirs in parallel. Mathematically, at M→∞, the theoretical UH (in terms of Taylor series) converges to the writer’s general UH that is a simple analytic expression derived inductively from empiricism. Therefore, this research turns the recent conceptual general UH to a theoretical law that approximates real-world watershed processes as a time-invariant linear hydrologic system. Specifically, we first review Chow’s linear hydrologic systems model and apply it to a conceptual watershed with an instantaneous storm, which results in a theoretical instantaneous UH and an S-hydrograph in the superposition of many negative exponential functions. The resulting S-hydrograph then is shown mathematically to be identical to the writer’s general UH at M→∞. Finally, the general theoretical UH is applied to 10 real-world watersheds for 19 rainfall-runoff simulations. It is noteworthy that the proposed method has two advantages: (1) it is general for storms with different rainfall durations, and (2) it does not require to define excess rainfall and direct runoff in advance because rainfall losses and baseflow can be a part of the solution process. It is expected that this research provides a deeper understanding of the general UH and thus helps promote its applications in practice.
General Unit Hydrograph from Chow’s Linear Theory of Hydrologic Systems and Its Applications
https://orcid.org/0000-0002-3868-3623
This research solves Chow’s linear hydrologic systems equations thoroughly to result in a theoretical instantaneous unit hydrograph (UH), which is a superposition of many (M) negative exponential functions. This implies that the instantaneous UH can be imagined as a superposition of many linear reservoirs in parallel. Mathematically, at M→∞, the theoretical UH (in terms of Taylor series) converges to the writer’s general UH that is a simple analytic expression derived inductively from empiricism. Therefore, this research turns the recent conceptual general UH to a theoretical law that approximates real-world watershed processes as a time-invariant linear hydrologic system. Specifically, we first review Chow’s linear hydrologic systems model and apply it to a conceptual watershed with an instantaneous storm, which results in a theoretical instantaneous UH and an S-hydrograph in the superposition of many negative exponential functions. The resulting S-hydrograph then is shown mathematically to be identical to the writer’s general UH at M→∞. Finally, the general theoretical UH is applied to 10 real-world watersheds for 19 rainfall-runoff simulations. It is noteworthy that the proposed method has two advantages: (1) it is general for storms with different rainfall durations, and (2) it does not require to define excess rainfall and direct runoff in advance because rainfall losses and baseflow can be a part of the solution process. It is expected that this research provides a deeper understanding of the general UH and thus helps promote its applications in practice.
General Unit Hydrograph from Chow’s Linear Theory of Hydrologic Systems and Its Applications
J. Hydrol. Eng.
Guo, Junke (Autor:in)
01.10.2022
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
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