Combining Model Results and Monitoring Data for Water Quality Assessment SONG S. QIAN* AND KENNETH H. RECKHOW Nicholas School of the Environment and Earth Sciences, Duke University, Durham, North Carolina 27708-0328 A Bayesian approach is used to update and improve water quality model predictions with monitoring data. The objective of this work is to facilitate adaptive management by providing a framework for sequentially updating the assessment of water quality status, to evaluate compliance with water quality standards, and to indicate if modification of management strategies is needed. Currently, most water quality or watershed models are calibrated using historical data that typically reflect conditions different from those being forecast. In part because of this, predictions are often subject to large errors. Fortunately, in many instances, postmanagement implementation monitoring data are available, although often with limited spatiotemporal coverage. These monitoring data support an alternative to the one-time prediction: pool the information from both the initial model prediction and postimplementation monitoring data. To illustrate this approach, a watershed nutrient loading model and a nitrogen-chlorophyll a model for the Neuse River Estuary were applied to develop a nitrogen total maximum daily load program for compliance with the chlorophyll a standard. Once management practices were implemented, monitoring data were collected and combined with the model forecast on an annual basis using Bayes Theorem. Ultimately, the updated posterior distribution of chlorophyll a concentration indicated that the Neuse River Estuary achieved compliance with North Carolina’s standard. 1 Introduction If a total maximum daily load program (TMDL) or other water quality management plan is developed and implemented to meet a water quality criterion, monitoring is usually the basis for assessing compliance and determining if any management modifications are needed. Yet, we know that lags in imple- mentation of plans, lags in pollutant concentration change and/or in biotic response, measurement uncertainty, and natural variability all may lead to errors in inferences based on measurements. This has led some in the water quality modeling community to recommend the use of models to assess progress. An example of this conflict between model and data is the TMDL program implemented to reduce nitrogen loading to the Neuse River Estuary in North Carolina. The Neuse River Estuary was placed in State of North Carolina’s Water Quality Assessment and Impaired Waters List (305(b) and 303(d) Report) in 2000 for chlorophyll a standard violation (1). However, the available chlorophyll a data from the Estuary do not support the conclusion that the Neuse River Estuary is in danger of water quality standard violation (see the Supporting Information). Furthermore, an earlier study of the estuary and the river basin (2) indicated that nutrient inputs to the estuary have been either steady or decreasing from early 1970 to 2001. The decision to prepare a TMDL for the Neuse River basin apparently was made based on a combination of fish-kill incidents in mid-1990s and modeling studies. This conflict between the TMDL decision and the compliance of water quality reflects the different interpreta- tions of what is the “true” water quality status. All water quality models have prediction uncertainties, some of which can be quite large. So, which assessment is more reliable: the model forecast or the monitoring data? On the one hand, routine monitoring data are often regarded as “happenstance data” (3) not designed for inference about the water quality status of an entire basin. In other words, they may not have the proper spatiotemporal coverage to reflect the true concentration conditions. In addition, water quality response to management actions tends to have a time lag. As a result, using monitoring data alone will not give us confidence that the estimated water quality status is close to the truth. On the other hand, models are simplifications of the real world and a model’s predictions are limited by the model’s own structural limitations, as well as by the data used to calibrate the model. For the Neuse River Estuary, we observed large scale fish-kill incidents in the mid-1990s’ and the rapid increase in concentrated animal farming in the river basin. These observations along with model predictions indicated a need for reducing nutrient input to the estuary to keep water quality in compliance. Both approaches (using data or using a model) can be justified, and both approaches can be justifiably criticized. It is often impossible to determine which source of information is more reliable. Consequently, the question should be whether we can combine these two sources of information to better support the water quality management decision making process. We believe that both assessments can, and should, be used to evaluate compliance and the adequacy of management actions. That is, even though the model is just that: a model, and even though it will always yield uncertain predictions, it has value in forecasting impacts (otherwise we would not be using it to develop the management plan). Likewise, lags, natural variability, and measurement uncertainty do not prevent useful inferences to be derived from measurements, even though adjustments to account for these assessment short- comings may be required. The objective of this study is not to compare the two approaches, but rather to introduce a Bayesian approach for combining preimplementation model forecasts with postim- plementation measurements for assessing water quality standard compliance. In its simplest form, this Bayesian approach involves a variance-weighted combination of the model forecast and the postimplementation monitoring data. There is a well-established analytic basis for combining (or pooling) information (4); however, it requires measures of uncertainty (or variability) to weight each contributing piece of information by its precision. The logic of this approach is unassailable; the more precise (less uncertain) the infor- mation, the higher that information is weighted. So, measures of uncertainty are necessary to yield the most defensible basis for pooling information. We illustrate the process of combining modeling results and monitoring data to obtain a better understanding of the * Corresponding author phone: 919-613-8105; fax: 919-684-8741; e-mail: song@duke.edu. Environ. Sci. Technol. 2007, 41, 5008-5013 5008 9 ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 41, NO. 14, 2007 10.1021/es062420f CCC: $37.00  2007 American Chemical Society Published on Web 06/13/2007