Basin hydrological processes are nonlinear in nature, however, most flood forecasting models do not take into account nonlinearity and instead assume linear relationships. Such models have limited flood forecasting capability, especially, flood forecasting tools for river basins subject to extreme seasonal monsoon rainfall. In the current study, flood prediction models were developed that account for nonlinearity relationships, which can aid future flood warning and evacuation system models. Terrestrial water storage estimates from the Gravity Recovery and Climate Experiment, along with observed discharge and rainfall data were used to develop two multivariate autoregressive discharge models, at monthly time scales. The Model-I was based primarily on rainfall, while the Model-II was based on rainfall and terrestrial water storage estimates for the Koshi subbasin, which is within the Ganges basin and has the world’s largest alluvial fan. The models clearly indicate the precedence of complex non-linear hysteresis behaviour. Modelling results show that the inclusion of the basin’s water storage and non-linearity improves the prediction of peak floods with lead times ranging from 1 to 12 months. Model-II predicted monthly discharge with Nash–Sutcliffe efficiency (NSE) ranging from 0.66 to 0.87, while NSE was 0.4 to 0.85 for Model-I, lower due to non-inclusion of water storage units. It is noted that, this study is the first of its kind to use ‘fixed effects’ multivariate regression in flood prediction, accounting for the nonlinear hysteresis effect of basin storage on floods.