Exploring the application of flood scaling property in hydrological model calibration

Model calibration has always been one major challenge in hydrological community. Flood scaling property (FS) is often used to estimate the flood quantiles for data-scarce catchments based on the statistical relationship between flood peak and contributing areas. This paper investigates the potential of applying FS and multivariate flood scaling property (MLR) as constraints in model calibration. Based on the assumption that the scaling property of flood exists in four study catchments in Northern China, eight calibration scenarios are designed with adopting different combination of traditional indicators and FS or MLR as objective functions. The performance of the proposed method is verified by employing a distributed hydrological model, namely Soil and Water Assessment Tool (SWAT) model. The results indicate that reasonable performance could be obtained in FS with less requirements of observed streamflow data, exhibiting better simulation on flood peak than Nash-Sutcliffe efficiency coefficient calibration scenario. The observed streamflow data or regional flood information are required in MLR calibration scenario to identify the dominant catchment descriptors, and MLR achieve better performance on catchment interior points, especially for the events with uneven distribution of rainfall. On account of the improved performance on hydrographs and flood frequency curve at watershed outlet, adopting the statistical indicators and flood scaling property simultaneously as model constraints is suggested. The proposed methodology enhances the physical connection of flood peak among sub-basins and considers watershed actual conditions and climatic characteristics for each flood event, facilitating a new calibration approach for both gauged catchments and data-scarce catchments.

Dimensional Regularization Approach to the Renormalization Group Theory of the Generalized Sine-Gordon Model

We present the dimensional regularization approach to the renormalization group theory of the generalized sine-Gordon model. The generalized sine-Gordon model means the sine-Gordon model with high frequency cosine modes. We derive renormalization group equations for the generalized sine-Gordon model by regularizing the divergence based on the dimensional method. We discuss the scaling property of renormalization group equations. The generalized model would present a new class of scaling property.