Multilevel Model for Gage and Paleoflood Data

A model is developed to estimate the parameters of a lognormal flow‐frequency distribution, and it can include multiple historical or paleoflood periods in which the largest flow within the period is defined and a current gage record. Asymptotic approximations of the variances and covariances of the distribution parameters are presented and used to compute first‐order approximations of the standard deviations of 100‐year and 500‐year floods. The model is applied to gage paleoflood data for Black Bear Creek at Pawnee, Oklahoma. Distribution parameters, their approximate variances and covariance $Q_{100}$ and $Q_{500}$, and their standard deviations were computed. A simulation experiment using 300 samples was performed. The $Q_{100}$ and $Q_{500}$ estimated using the multiple‐period model had lower standard errors than those estimated using either a single‐threshold or gage‐record‐only model. First‐order approximations of the standard deviations of $Q_{100}$ and $Q_{500}$ were compared to the simulation results and the largest error was 13%.