The central hypothesis of a nonlinear geophysical flood theory postulates that, given space‐time rainfall intensity for a rainfall‐runoff event, solutions of coupled mass and momentum conservation differential equations governing runoff generation and transport in a self‐similar river network produce spatial scaling, or a power law, relation between peak discharge and drainage area in the limit of large area. The excellent fit of a power law for the destructive flood event of June 2008 in the 32,400‐km2 Iowa River basin over four orders of magnitude variation in drainage areas supports the central hypothesis. The challenge of predicting observed scaling exponent and intercept from physical processes is explained. We show scaling in mean annual peak discharges, and briefly discuss that it is physically connected with scaling in multiple rainfall‐runoff events. Scaling in peak discharges would hold in a non‐stationary climate due to global warming but its slope and intercept would change.