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It is well known that product moment ratio estimators of the coefficient of variation Cν, skewness γ, and kurtosis κ exhibit substantial bias and variance for the small (n ≤ 100) samples normally encountered in hydrologic applications. Consequently, L moment ratio estimators, termed L coefficient of variation τ2, L skewness τ3, and L kurtosis τ4 are now advocated because they are nearly unbiased for all underlying distributions. The advantages of L moment ratio estimators over product moment ratio estimators are not limited to small samples. Monte Carlo experiments reveal that product moment estimators of Cν and γ are also remarkably biased for extremely large samples (n ≥ 1000) from highly skewed distributions. A case study using large samples (n ≥ 5000) of average daily streamflow in Massachusetts reveals that conventional moment diagrams based on estimates of product moments Cν, γ, and κ reveal almost no information about the distributional properties of daily streamflow, whereas L moment diagrams based on estimators of τ2, τ3, and τ4 enabled us to discriminate among alternate distributional hypotheses.

A streamfiow duration curve illustrates the relationship between the frequency and magnitude of streamflow. Flow duration curves have a long history in the field of water-resource engineering and have been used to solve problems in water-quality management, hydropower, instream flow methodologies, water-use planning, flood control, and river and reservoir sedimentation, and for scientific comparisons of streamflow characteristics across watersheds. This paper reviews traditional applications and provides extensions to some new applications, including water allocation, wasteload allocation, river and wetland inundation mapping, and the economic selection of a water-resource project.

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