Monthly hydrological models are useful tools for runoff simulation and prediction. This study proposes a three-parameter monthly hydrological model based on the proportionality hypothesis (TMPH) and applies to the Upper Hanjiang River Basin (UHRB) in China. Two major modules are involved in the TMPH: the actual evapotranspiration and runoff, in which the coupled water–energy balance equation and the proportionality hypothesis are used for calculation, respectively. It is worth mentioning that the proportionality hypothesis was extended to the partitioning of the available water into water loss and runoff at the monthly scale, which demonstrates that the ratio of runoff to its potential value is equal to the ratio of continuing water loss to its potential value. Results demonstrate that the TMPH model performs well when the NSE values are 0.79 and 0.83, and the KGE values are 0.86 and 0.78 for calibration period and validation period, respectively. The widely used two-parameter monthly water balance (TWBM) model and ABCD model are compared with the proposed model. Results show that TMPH performs better than TWBM model with NSE increased by 0.07 and 0.11, and KGE increased by 0.02 and 0.16, respectively, whereas the TMPH performs similarly as the ABCD model in the calibration period, and performs slightly better in the validation period, with NSE increased by 0.02, and KGE increased by 0.03. Sensitivity analysis show that the simulation result is most sensitive to parameter n, followed by SC and $\lambda$. In summary, the proposed model has strong applicability to the study area.

Accurate projection of floods is of great significance to safeguard economic and social development as well as people’s life and property. The development of hydrological models can improve the level of flood projection, however, the numerous uncertainties in the models limit the projection accuracy. By adding observations to correct the operation of prediction models, the accuracy can be improved to some extent. In this paper, taking the Xun River, of the Hanjiang River Basin in China, as the research object, combined with the soil moisture satellite data obtained by the soil moisture active and passive satellite (SMAP), the ensemble Kalman filter (EnKF) algorithm was used to assimilate the upper soil water content (WU) of the Xinanjiang model. In addition, based on the simultaneous assimilation of state variables and parameters, two improved assimilation schemes were proposed here, namely, the augmented ensemble Kalman filter (AEnKF) scheme and the dual ensemble Kalman filter (DEnKF) scheme. The results showed that compared with the WU assimilation scheme, the simultaneous assimilation of parameters and WU improved the prediction ability of the Xinanjiang model to a greater extent. The two improved schemes had similar effects on flood prediction accuracy, and improved the overall Nash–Sutcliffe efficiency coefficient (NSE) from 0.725 for non-assimilated, and 0.758 for assimilated WU, to 0.781. Among them, AEnKF and DEnKF schemes, respectively, improved the NSE by 10.1% and 11% at maximum. This study demonstrated that the application of data assimilation for the Xun River effectively improved the flood forecast accuracy of the Xinanjiang model, which will provide a reference basis and technical support for future flood prevention and mitigation and flood projection in this basin.

Initial condition can impact the forecast precision especially in a real-time forecasting stage. The discrete linear cascade model (DLCM) and the generalized Nash model (GNM), expressed in different ways, are both the generalization of the Nash cascade model considering the initial condition. This paper investigates the relationship and difference between DLCM and GNM both mathematically and experimentally. Mathematically, the main difference lies in the way to estimate the initial storage state. In the case of n = 1, it was shown theoretically that the difference between the two models is whether the current outflow is estimated (DLCM) or observed (GNM). The GNM is the unique solution of the Nash cascade model with a non-zero initial condition, while the DLCM is an approximate solution and it can be transformed to the GNM when the initial storage state is calculated by the approach suggested in the GNM. At last, a test example obtained by the solution of the Saint-Venant equations is used to illustrate this difference. The results show that the GNM provides a unique solution while the DLCM has multiple solutions depending on the estimate accuracy of the current state.

HIGHLIGHTS. The main difference lies in the way to estimate the initial storage state.The GNM is the unique solution of the Nash cascade model.The DLCM is an ap