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.

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.

Gupta, V.K., R. Mantilla, B.M. Troutman, D. Dawdy, and W.F. Krajewski. “Generalizing a Nonlinear Geophysical Flood Theory to Medium Size River Basins,” Geophysical Research Letters, 37, L11402, 2010.