• 关键词：贝叶斯方差分析  方差分解  二项分布  水质指标  时空变化

• 基金项目：国家水体污染控制与治理科技重大专项（No.2012ZX07503-002）

• 梁中耀
• 1. 北京大学环境科学与工程学院, 水沙科学教育部重点实验室, 北京 100871;2. 中国环境科学研究院, 国家环境保护饮用水水源地保护重点实验室, 北京 100012

• 余艳红
• 云南省高原湖泊流域污染过程与管理重点实验室, 昆明 650034

• 王丽婧
• 中国环境科学研究院, 国家环境保护饮用水水源地保护重点实验室, 北京 100012

• 李虹
• 中国环境科学研究院, 国家环境保护饮用水水源地保护重点实验室, 北京 100012

• 刘永
• 北京大学环境科学与工程学院, 水沙科学教育部重点实验室, 北京 100871

• 摘要：精细识别湖泊水质的时空变化特征是确定流域污染调控措施的基础.贝叶斯方差分析具有灵活的模型结构，可直接表征变量的时空动态特征.本文据此提出了基于该方法的湖泊水质时空变化特征识别的方法框架，研究了异龙湖稳态转换条件下富营养化指标的变化特征和滇池外海特征污染物达标率的时空变化2个案例，验证了该方法在总体服从正态分布和二项分布时的适用性.针对参数可交换性假设被忽视的问题，本文提出了一种基于模型选择准则的判定方法，并将其应用于滇池案例中.结果表明：1相对于清水稳态，异龙湖在浊水稳态时3种富营养化指标浓度更高，且年际方差所占总方差比例减小；2滇池外海总氮浓度超标率由2007—2013年间的40%左右降到2014—2016年间的10%左右，且波动性降低.随着监测数据的积累和监测时空精度的增加，贝叶斯方差分析在湖泊水质时空变化特征识别中具有广阔的应用前景.

• Abstract：The identification of the temporal and spatial variation of lake water quality variables is the basis for effective and scientific decision making. Bayesian Analysis of Variance (ANOVA) method has flexible model structure. It can test the significance of factors on the dependent variable, compare the relative importance of different factors and explore dynamics of the dependent variable easily and effectively. A Bayesian ANOVA-based methodological framework was proposed in this study for Lake Yilong and Lake Dianchi to verify its application for the normal distribution population and binomial distribution population respectively. Since most previous studies neglected the exchangeability assumption of the Bayesian ANOVA method, we proposed a model selection criteria method to identify the incompliance ratio of total nitrogen (TN) in Lake Dianchi. In the Lake Yilong case, results show that in the turbid state, compared with that in the clear state, three variables had significant higher concentrations and lower between-year variances/total variance ratios. In the Lake Dianchi case, the incompliance ration of TN decreased to about 10% with lower variations in the recent 3 years from 40% in the former 7 years with higher variations. With the accumulation of water quality monitoring data and the increase of resolution, Bayesian ANOVA method has broad application prospect in identification of the temporal and spatial dynamics of lake water quality variables.

• Key words：Bayesian ANOVA  variance components  binomial distribution  water quality variables  temporal and spatial dynamics

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