Exploring the effects of hillslope-channel link dynamics and excess rainfall properties on the scaling structure of peak-discharge

• We examine how catchment physical and rainfall properties control the scaling of peak-discharges.
• The scaling exponent is mainly controlled by rainfall duration and hillslope velocity.
• The intercept is controlled by the interplay among rainfall intensity, duration, hillslope velocity, and channel velocity.
• Very quick hillslope velocity leads to a scale break and the scale at which the break happens is controlled by rainfall duration, hillslope velocity, and channel velocity.

Several studies revealed that peak discharges (Q) observed in a nested drainage network following a runoff-generating rainfall event exhibit power law scaling with respect to drainage area (A) as Q(A) = αAθ. However, multiple aspects of how rainfall-runoff process controls the value of the intercept (α) and the scaling exponent (θ) are not fully understood. We use the rainfall-runoff model CUENCAS and apply it to three different river basins in Iowa to investigate how the interplay among rainfall intensity, duration, hillslope overland flow velocity, channel flow velocity, and the drainage network structure affects these parameters. We show that, for a given catchment: (1) rainfall duration and hillslope overland flow velocity play a dominant role in controlling θ, followed by channel flow velocity and rainfall intensity; (2) α is systematically controlled by the interplay among rainfall intensity, duration, hillslope overland flow velocity, and channel flow velocity, which highlights that it is the combined effect of these factors that controls the exact values of α and θ; and (3) a scale break occurs when runoff generated on hillslopes runs off into the drainage network very rapidly and the scale at which the break happens is determined by the interplay among rainfall duration, hillslope overland flow velocity, and channel flow velocity.