College of William and Mary, Virginia Institute of Marine Science, Gloucester Point, Virginia 23062, USA.
J Environ Sci Health A Tox Hazard Subst Environ Eng. 2009 Dec;44(14):1574-84. doi: 10.1080/10934520903263553.
Large uncertainty in the estimation of bacterial nonpoint sources often results in the poor simulation of bacteria concentration in estuaries using a deterministic model. To better quantify the uncertainty in bacterial modeling, a Bayesian approach was incorporated into a tidally averaged estuarine model for estimating bacterial loading using in-stream observations. This was accomplished by using Bayes' theorem to develop a joint probability distribution for nonpoint source loadings based on the bacteria observations in the estuary. To overcome the geometry variation along the estuary for a non-linear transport problem with no analytical solution, the approach was implemented on a finite difference model. The approach was applied to Holdens Creek, a tidal river of the Pocomoke Sound of the Chesapeake Bay, to explore the feasibility of estimating bacteria sources and to develop an allowable load for the Creek to attain water quality standards. Further experiments were conducted to investigate the convergence for loading estimation, and the errors and uncertainties associated with load estimation using different data sets with varied sample sizes. With the use of limited observations, the nonpoint source loads can be estimated within an acceptable error range by selecting appropriate prior loading distributions. Because of the high spatial correlations among observations in the estuary, the errors in loading estimation at adjacent watersheds compensated each other, resulting in a good estimation of loads for the entire watershed. The approach not only provides an efficient methodology to assess the nonpoint source contribution for watershed management, but also has the additional advantage of addressing the problems of the uncertainty and error associated with bacterial simulation in the estuary.
由于使用确定性模型估算细菌非点源时存在较大不确定性，因此常常导致河口细菌浓度的模拟效果不佳。为了更好地量化细菌建模的不确定性，采用贝叶斯方法将潮汐平均河口模型与河道内观测数据相结合，以估算细菌负荷。这是通过贝叶斯定理来实现的，该定理可根据河口的细菌观测值，为非点源负荷建立联合概率分布。为了克服无解析解的非线性输运问题在河口沿线的几何变化，该方法在有限差分模型上得以实现。该方法应用于切萨皮克湾波科莫克声音的潮汐河霍尔顿斯克里克，以探索估算细菌源和为克里克制定允许负荷以达到水质标准的可行性。进一步的实验用于研究负荷估算的收敛性，以及使用不同数据集和不同样本大小进行负荷估算时的误差和不确定性。通过使用有限的观测值，通过选择适当的先验负荷分布，可以在可接受的误差范围内估算非点源负荷。由于河口观测值之间存在高度的空间相关性，相邻流域的负荷估算误差可以相互补偿，从而可以很好地估算整个流域的负荷。该方法不仅为流域管理评估非点源贡献提供了一种有效的方法，而且还具有解决河口细菌模拟相关的不确定性和误差问题的额外优势。
