Estimation of the Interaction Between Groundwater and Surface Water Based on Flow Routing Using an Improved Nonlinear Muskingum-Cunge Method

The interaction between groundwater (GW) and surface water (SW) not only sustains runoff in dry seasons but also plays an important role in river floods. Lateral inflow is the recharge of groundwater to surface water during a river flood; this recharge is part of the GW-SW exchange. Hydrological engineers proposed the idea of modelling flood routing using the Muskingum-Cunge method, in which the GW-SW exchange is not fully considered. This study proposes an improved nonlinear Muskingum-Cunge flood routing model that considers lateral inflow; the new method is denoted as NMCL1 and NMCL2 and can simulate flood routing and calculate the GW-SW exchange. In addition, both the linear and nonlinear lateral inflows (with the channel inflows) are discussed, and the stable lateral inflows that occur due to the GW-SW exchange are considered for the first time. A sensitivity analysis shows that different parameters have different effects on the simulation results. Three different flood cases documented in the literature are selected to compare the four classical and two updated Muskingum-Cunge methods. Two different floods of the River Wye are selected to verify the accuracy of the calibrated model. The simulation results of the improved Muskingum-Cunge method are compared with the temperature inversion results measured from the Zhongtian River, China, to indicate the feasibility and reliability of the improved method. A comparison shows that, for several cases, the proposed method is capable of obtaining optimal simulation results. The proposed method inherits the ability of the Maskingum-Cunge method to simulate flood routing. Moreover, it can quantify the GW-SW exchange, and the reliability of the estimations is owed to the nonlinearity and sign flexibility of the calculated exchange process.