BKW is a highly efficient Storage Function-type rainfall-runoff model that utilizes the steady-state storage (S) and outflow (Q) of a catchment at different rainfall intensities as the S-Q relation of the catchment. For the inundation nowcasting of urban areas under high-intensity, short-duration rainfall, a Storage Function-type model is a judicious choice. However, S-Q hysteresis exists in the catchment S-Q relation, and BKW is unable to exhibit hysteresis due to assuming that the S-Q relation of a catchment is a nonlinear relation. The S-Q hysteresis can influence the outflow estimation of BKW, reducing the model's accuracy. Through the evaluation of analytical solutions, we found that the change in rainfall intensity dominates the S-Q relation of a catchment. The S-Q relation during a rainfall event is a dynamic process rather than a monotonic nonlinear relation. By applying the dynamic S-Q relation in BKW, we improved BKW to become a highly efficient and accurate rainfall-runoff model for small urban catchments.