We define the equivalent precipitation to include local precipitation, inflow water and soil water storage change as the water supply in the Budyko framework. With the newly defined water supply, the Budyko curve can successfully describe the relationship between the evapotranspiration ratio and the aridity index at both annual and monthly timescales in unclosed basins. We develop a new Fu-type Budyko equation with two non-dimensional parameters (ω and λ) based on the deviation of Fu's equation.