Current flood forecasting tools for river basins subject to extreme seasonal monsoon rainfall are of limited value because they do not consider nonlinearity between basin hydrological properties. The goal of this study is to develop models that account for nonlinearity relationships in flood forecasting, which can aid future flood warning and evacuation system models. Water storage estimates from the Gravity Recovery and Climate Experiment, along with observed discharge and rainfall data were used to develop two multivariate autoregressive monthly discharge models. Model-I was based on rainfall only, while Model-II was based on rainfall and water storage estimates for the Koshi subbasin within the Ganges River basin. Results indicate that the saturation of water storage units in the basin play a vital role in the prediction of peak floods with lead times of 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. Model-II was then tested with a 3-month lead to predict the 2008 Koshi floods – with NSE of 0.75. This is the first study to use ‘fixed effects’ multivariate regression in flood prediction, accounting for the nonlinear hysteresis effect of basin storage on floods.