Resolving the Paradox of the Jones Formula for Flood Discharge Estimation

The study demonstrates from theoretical considerations as well as using numerical examples that while a flood wave characterized by the form of kinematic wave used in the development of Jones formula is not necessarily a kinematic wave which is characterized by insignificant magnitude of the non-dimensional longitudinal water surface gradient (1/S₀)∂y/∂x, where S_o is the bed slope of the river; y is the flow depth and x is the variable denoting the spatial length, implying insignificant size of hysteresis of the rating curve under flood conditions. The paper demonstrates that the hysteresis size of the rating curve formed during flood flow is directly proportional to the absolute magnitude of (1/S₀)∂y/∂x characterizing a flood wave and the absence of subsidence of a flood wave may be attributed either to the insignificant magnitude of (1/S₀)∂y/∂x or due to forcing the diffusion coefficient of the equation governing flood wave to be zero. The study proves the point that the Jones formula developed using the form of kinematic wave equation is logically correct contrary to the viewpoint expressed in the literature.