Estimating Limited-Data Urban Bacterial TMDLs using Empirical Bayes Regionalization

摘要

The State of Georgia has numerous urban waterbodies requiring development of TMDLs for fecal coliform bacteria. The primary water quality criterion for fecal coliform bacteria is a geometric mean calculated from at least four samples within a 30-day period. Many waterbodies have been listed as impaired based on infrequent point-in-time observations, and sufficient data are not available to calculate geometric means or to reliably calibrate a watershed loading model. Our approach to estimating fecal coliform bacteria TMDLs for the waterbodies lacking geometric mean data relies on a relationship to other similar or “equivalent” waterbodies that do have data. This provides a preliminary TMDL that can be refined in future as additional sitespecific data are collected. rnDevelopment of the TMDLs via an “equivalent” site approach needed to address three important issues: (1) Any site-specific monitoring data for a waterbody should also be incorporated, even if it is not sufficient for direct estimation of geometric means; (2) Differences in land use will result in different fecal coliform bacteria concentrations, an equivalent waterbody that provides a perfect match in landuse to a subject site is unlikely to be available; and (3) The selection of an equivalent waterbody is likely to have a strong impact on the resulting TMDL estimates for a subject waterbody rnConsideration of these three issues led to a corresponding set of objectives for the approach: (1) Site-specific and equivalent site data should be combined in a weighted approach that reflects the relative accuracy of information provided by each data source; (2) Differences in land use among watersheds should be addressed through use of a regionalization model that identifies the extent to which changes in geometric mean fecal coliform concentrations can be explained by changes in land use; and (3) The influence of equivalent waterbody selection should be minimized through the use of multiple equivalent waterbodies for each subject waterbody.rn These three objectives were met through use of an Empirical Bayes statistical regionalization analysis. This method combines two important concepts: Bayesian maximum likelihood techniques for combining sources of data (local and regional), and hierarchical regionalization techniques. The data combination step assumes that both the regional or equivalent site information and the available site-specific data provide information on the true local geometric mean. The two sources of data are combined or weighted in accordance with the degree of precision or accuracy in each source. The regionalization step assumes that the true mean at any site is a result of random variability and a regression model on land use. Empirical Bayes techniques provide statistically optimal methods for computing both the data combination and regionalization steps from observed data. Use of this method enabled the State to rapidly estimate preliminary TMDLs for numerous sparsely monitored waterbodies in order to meet litigation deadlines while incorporating all available data. The regionalization method is an alternative to a watershed modeling approach to TMDLs. Strengths and weaknesses of this approach are discussed.