How Much Storage Does a River Need? Sequent-Peak Storage–Yield Analysis of the Potomac at Point of Rocks, 1896–2025, and a Test of the Hurst Effect

The sequent-peak algorithm is the standard way to size a reservoir from a flow record, but it is usually stated without proof. I prove that it returns exactly the smallest capacity that meets a constant draft without failure over the record, by showing that the storage deficit of a reservoir that starts full follows the Lindley recursion. I apply it to 130 complete water years (1896 to 2025) of daily flow for the Potomac River at Point of Rocks, Maryland (USGS gauge 01638500), whose mean annual flow is 8.525 cubic kilometres. Meeting a draft of 50% of mean flow needs 2.333 cubic kilometres of storage, or 0.274 years of mean flow, set by the 1930 to 1931 drought. A draft of 90% needs 1.717 years of storage, set by a 199-month critical period from 1953 to 1969. Simulating each reservoir confirms zero failures at the computed capacity and at least one at 99% of it. The record shows a Hurst coefficient K of 0.667, which looks like long memory, but 2000 independent lognormal series of the same length give a mean log-log slope of 0.569 against an observed 0.590, and 16.6% of them have a rescaled range at least as large as observed. Annual flows are close to independent (lag-1 autocorrelation 0.071). The 1930 to 1931 sequence still matters: at a 50% draft, only 1.6% of year-shuffled bootstrap records need as much storage as the observed one.