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Exploring parsimonious daily rainfall-runoff model structure using the hyperbolic tangent function and Tank model
The Rural Water Resources Systems Engineering laboratory, which is run by Professor Moon-Seong Kang in the Department of Landscape Architecture and Rural Systems Engineering at the College of Agriculture and Life Sciences, found that the response of a watershed to rainfall could be expressed as a hyperbolic tangent function of rainfall depth and the available storage of a linear tank model. Such finding enabled developing a simple modeling strategy capable of accurately predicting daily runoff from rainfall only with four parameters. The parsimonious structure advanced the state-of-art of hydrological modeling. The new model also carries direct and vital implications for practical applications such as hydrologic designs and planning for flood control and drainage infrastructure.
Predicting the response (runoff) of watersheds to rainfall is one of the most critical interests in hydrology and water resources engineering, and it is a necessary process to solve water resource problems such as floods or droughts. Hydrologists and water resources engineers use mathematical models to conceptually represent hydrological processes happening in a real-world system such as a watershed. Various methods and tools have been proposed to describe hydrological cycle and processes, and they employ parameters to relate inputs (e.g., rainfall) to outputs (e.g., runoff) with given model structure and assumptions. The large number of parameters helps to improve accuracy statistics in model calibration but deteriorate the predictive power of a model. Thus, the parsimonious model structure is desired for reliable hydrological prediction by reducing uncertainty and equifinality. Professor Kang and a Ph.D. student, Jung-Hun Song explored how to achieve the required prediction accuracy with the minimum number of parameters.
The research team designed a numerical experiment with different model structures by combining a Two-Parameter Hyperbolic Model (TPHM) with of a general 3-tank model (Figure 1). The numerical experiment systematically evaluated the accuracy and complexity of the combinations of parts of the two models in 41 watersheds distributed across South Korea (Figure 2). The results showed that one of the model structure combinations, called M2 and denoted as Five-Parameter Hyperbolic Model (FPHM) later, provided accuracy statistics equal to or better than those of other models that employ more parameters. In the FPHM structure, the TPHM developed to predict quick surface runoff mounted on the bottom layer of the 3-tank model known suitable to describe slow response of a watershed.
Figure 1. The previous model (a, b) predicting the rainfall-runoff process, and the model (c, d) developed through this study.
Figure 2. Spatial variations in the hydrologic characteristics of 41 study watersheds
This study demonstrated daily runoff can be accurately predicted only with four parameters by integrating the strengths of existing models. Such finding has significant implications on hydrological model application to solving water resources management issues as well as the theoretical and experimental hydrology. Especially, this study will give theoretical basis and practical assistance for the management of agricultural water resources by providing accurate but simple hydrological prediction model. Based on the results of this study, follow-up studies have tried to establish strategies and frameworks for hydrological prediction in ungauged watershed and to develop a water-environment integrated modeling platform for a comprehensive analysis and management of water resources.
《Professor Moon-Seong Kang》