FLOW-DuRATION CURVES. I: NEW INTERPRETATION AND CONFIDENCE INTERVALS By Richard M. Vogel,J Member, ASCE, and Neil M. Fennessey,2 Associate Member, ASCE ABSTRACT: A flow-duration curve (FDC) is simply the complement of the cu- mulative distribution function of daily, weekly, monthly ( or some other time interval of) streamflow. Applications of FDCs include, but are not limmited to, hydropower planning, water-quality management, river and reservoir sedimentation studies, habitat suitability, and low-flow augmentation. Although FDCs have a long and rich history in the field of hydrology, they are sometimes criticized because, tra- ditionally, their interpretation depends on the particular period of record on which they are based. If one considers n individual FDCs, each corresponding to one of the individual n years of record, then one may treat those n annual FDCs in much the same way one treats a sequence of annual maximum or annual minimum streamflows. This new annual-based interpretation enables confidence intervals and recurrence intervals to be associated with FDCs in a nonparametric framework. INTRODUCTION "It is a capital mistake to theorize before one has data," Sir Arthur Conan Doyle. A flow-duration curve (FDC) represents the relationship between the magnitude and frequency of daily, weekly, monthly (or some other time interval of) streamflow for a particular river basin, providing an estimate of the percentage of time a given streamflow was equaled or exceeded over a historical period. An FDC provides a simple, yet comprehensive, graphical view of the overall historical variability associated with streamflow in a river basin. An FDC is the complement of the cumulative distribution function ( cdf) of daily streamflow. Each value of discharge Q has a corresponding ex- ceedance probability p, and an FDC is simply a plot of Qp, the pth quantile or percentile of daily streamflow versus exceedance probability p, where p is defined by p = 1 -P{Q :s; q} (la) p = 1- FQ(q) (lb) The quantile Qp is a function of the observed streamflows, and since this function depends upon empirical observations, it is often termed the em- pirical quantile function. Statisticians term the complement of the cdf the "survival" distribution function. The 'term survival results from the fact that most applications involve survival data that arise in various fields I Assoc. Prof. , Dept. of Civ. and Envir. Engrg. , Tufts Univ. , Me 2Res. Assoc., Dept. of Civ. and Envir. Engrg., Tufts Univ., Medford, MA. Note. Discussion open until January 1, 1995, To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on January 28, 1993. This paper is part of the Journal of Water Resources Planning and Management, Vol. 120, No.4, July/August, 1994. @ASCE, ISSN 0733-9496/94/0004- 0485/$2.00 + $.25 per page. Paper No.5474. 485