Calculation method and application of the geomorphic unit hydrograph based on spatial energy conversion

Abstract: Flood in small and medium-sized catchments can be characterized by the short concentration time, high flow velocity, fierce attack, and violent stage change. Mountain torrents also occur frequently in these small and medium-sized catchments. But, it is very difficult to carry out flood forecasting and early warning, due mainly to those located in the ungauged areas. Therefore, it is a high demand to improve the forecast accuracy in the operational hydrology, especially in the areas without enough measured data. In this study, an energy model was proposed to estimate the velocity of overland flow for the high accuracy in the simulation of flow concentration. Firstly, the spatial distribution of the energy was determined for the water particles in the basin. The gravitational potential energy was gradually transformed into kinetic energy using the iterative computation from the upstream to the downstream, according to the flow direction. Secondly, the spatial energy field was constructed considering the energy loss, and then the overland flow velocity was estimated to generate the spatial velocity field. Thirdly, the concentration time was calculated to count the number of grids, when the water particles on each grid reached the outlet of the watershed. Finally, the geomorphic unit hydrograph was generated to determine the relationship between the catchment area and concentration time. The study area was set as the Zhuxipo basin in Yiyang City, Hunan Province, China, located at the source of Yixi, a tributary of the Zishui River. The Zhuxipo basin was divided into 57 sub watersheds using Digital Elevation Model (DEM) data with a resolution of 30 m×30 m. A distributed model was then constructed to simulate 36 floods in the study area from 1984 to 2020. A Xinanjiang model, geomorphic unit hydrograph model, and Muskingum Routing were used to calculate the runoff generation, overland flow concentration, and river network flow concentration, respectively. The geomorphic unit hydrograph was also extracted by the Energy Conversion Method (EC-GUH) and Slope Rain Intensity Method (SR-GUH). At the same time, the EC-GUH and SR-GUH were also used to compute the overland flow concentration for the evaluation. The average flow velocity of the hydrological section was then calculated to estimate the range of energy residual coefficient (the only parameter of EC-GUH), according to the total water volume and kinetic energy of 36 floods. The results show that the EC-GUH method performed better than the SR-GUH method, where the proportion of floods with a peak time error no more than 1 h increased from 30.5% to 83.3%, the number of floods with Nash-Sutcliffe efficiency coefficient no less than 0.9 increased from 9 to 17, and the average Nash-Sutcliffe efficiency coefficient increased from 0.82 to 0.89, indicating a significantly improved simulation accuracy. It was estimated that the range of energy residual coefficient was 0.008, 0.014 under the flow velocity. In this case, the proportion of flood simulation with the Nash-Sutcliffe efficiency coefficient not less than 0.9 was 44%-50%, which was close to the calibration. It infers that the parameter can be estimated indirectly using the average velocity of the outlet section. Consequently, the concentration model presented a clear physical meaning, whose parameters were determined by the calibration or measurement for the cross and vertical section of the channel. As such, the obtained velocity can be used to simulate the flow concentration of overland and river networks. The finding can also provide a reliable idea for the concentration evaluation in the ungauged basins.