Joint Probability Distribution of Streamflows and Tides in Estuaries

A procedure for estimating the joint probability of occurrence of correlated extreme tides and corresponding freshwater flows in estuaries is presented. The method uses the Box-Cox transformation to transform the original data to near normality, and therefore the search for a parent distribution is avoided. It is also shown that the traditional assumption of statistical independence for the jointly distributed random variables may lead to the underestimation of flows and tidal heights. The methodology is applied to the Rappahannock River in Virginia which flows into the Chesapeake Bay.