Laboratory examination of linearity in rainfall–runoff relationships

Abstract

ABSTRACT Certain rainfall–runoff models, e.g. the unit hydrograph, assume linear relationships between the variables. These are proportionality of runoff discharges to (net) rainfall depth and linear summations of discharges resulting from (net) rainfalls during different time intervals or over different sectors of a watershed. This study examines the validity of these assumptions by use of an extensive two-dimensional laboratory experimentation. The results indicate that proportionality would be found under high rainfall intensity through a long duration. Spatial summations would more likely yield correct discharges in cases where rainfall duration is equal to, or is longer than, the time of concentration. Temporal summations may yield correct discharges when rainfall duration is longer than one half of the time of concentration. Here, the time of concentration is determined at the beginning of gradual approach of the discharge towards the equilibrium state.