Regional Flow‐Duration Curves for Ungauged Sites in Massachusetts

Abstract

A regional hydrologic model is developed for estimating flow‐duration curves at ungauged and unregulated basins in Massachusetts. Flow‐duration curves often exhibit complex shapes, requiring probability density functions with three or more parameters. This study approximates the lower half of daily flow‐duration curves using a two‐parameter lognormal probability density function. A conjugate gradient algorithm is employed to fit lognormal density functions to the lower half of observed flow‐duration curves at 23 basins. Regional regression equations are developed to describe the lognormal model parameters in terms of easily measured basin characteristics. The resulting regional flow‐duration model only requires estimates of the watershed area, and a basin relief parameter, both of which are easily obtained from U.S. Geological Survey 7.5‐min quadrangle maps. In addition, confidence intervals are derived for flow‐duration curves estimated at ungauged sites. A validation experiment reveals that the resulting regional hydro‐logic model can provide remarkably precise estimates of a flow‐duration curve at an ungauged site, considering the simplicity of the model and its ease of application.