Derived Flow–Duration Relationships for Surface Runoff Dominated Small Urban Streams

Abstract

For many locations, exponential probability distributions fit well the frequency distributions of rainfall event volume, duration, and interevent time. Based on these exponential distributions and a simplified scheme for rainfall-streamflow transformation, closed-form analytical expressions were derived for the determination of the flow–duration relationships of surface runoff dominated small urban streams. The main advantage of the derived analytical relationships is that they relate the flow–duration characteristics of a stream directly to its upstream catchment’s and local rainfall characteristics. Using the derived relationships, flow–duration curves that are needed for stream restoration design can be directly constructed for small urban streams without observed streamflow data. Verification studies demonstrated that simplifying assumptions invoked in the derivation process are generally acceptable for small urban streams where baseflow variations are insignificant or streamflows are generated predominantly by surface runoff.