Analysis of Bivariate Censored Low Flows

Abstract

In this paper, a bivariate model is established to characterize the seven-day, two-year (Q 7,2 ) and seven-day, 10-year (Q 7,10 ) low flows of streams in West-Central Florida under the restriction of Q 7,10 ≤ Q 7,2 . Analysis of prediction errors showed that our model describes these stream low flows well. The measurements under the detection limit were treated as censored data and a bivariate imputation method was developed to impute them into pseudo-complete samples. All-subsets regression was applied to these imputed data for selecting appropriate models, which link the low flows to their basin characteristics. The parameters are first estimated by the least-squares method in a bivariate normal regression and then adjusted to yield their maximum likelihood estimates. This process of imputation, model selection and parameter estimation is repeated iteratively until convergence of the selected model terms, parameter estimates, and imputed data. With the established model, predictions of low flows can be made at gauged and ungauged sites according to their basin variables for water-resources management.