保证生态需水对湖泊生态保护至关重要。目前湖泊生态需水的研究主要基于确定性假设，其研究结果应用于实践，会与实际需求有一定的偏差。不确定性是生态需水研究中不可避免的内在属性。为有效地将不确定性纳入湖泊生态需水研究中，本论文基于贝叶斯理论，从机理不确定性、核算不确定性和保障不确定性三个方面开展研究。机理不确定性方面：从单要素、双要素、三要素三个层面研究了水生植物和水位各自的不确定性、水生植物与水位响应关系的不确定性、水生植物与水位水质响应关系的不确定性。核算不确定性方面：重点研究了面向水生植物保护的湖泊生态需水核算不确定性。保障不确定性方面：首先分析了水库调度参数不确定性对湖泊生态需水保障的影响，然后构建了面向湖泊生态需水保障的水库下泄量误差纠正方法。本论文以白洋淀为研究案例，为提高湖泊生态需水研究的准确性提供了科学依据。方法构建过程及主要结论如下：

湖泊水文生态响应机理不确定性的研究，从单要素、双要素、三要素三个层面开展。（1）从单要素层面研究了水生植物和水位各自的不确定性。采用不确定性分布模型和K-S检验方法，分别确定了水位和四种水生植物多样性指标的分布模型。结果表明，水生植物多样性的Margalef指数、Simpson指数、Shannon-Wiener指数和水位呈现韦布尔分布，Pielou’s均匀度指数呈现伽玛分布。（2）从双要素层面研究了水生植物与水位响应关系的不确定性。首先将水位和水生植物多样性划分状态。然后根据状态转移模型，得到各个水位状态下，水生植物多样性的状态转移矩阵。结合水位过程数据，进而确定各个时刻水生植物多样性的状态和对应的概率分布。通过建立两类水位过程情景，比较了不同水位过程（改变水位状态高低顺序）对水生植物多样性的影响。结果表明，水位高低分布均匀，有利于改善水生植物多样性。该研究结果为后续湖泊生态需水保障策略的制定提供了指导。（3）从三要素层面研究了水生植物与水位水质响应关系的不确定性。首先基于贝叶斯线性回归模型，建立了水生植物与水位水质的线性关系。然后，利用Gibbs采样方法实现了参数的后验估计，从而定量了水生植物多样性对水位水质响应的不确定性。结果表明，在每个水位或水质取值下，水生植物多样性模拟值分布在一定范围内。随水质（总磷）的增加，Margalef指数呈现下降趋势，Margalef指数的范围呈现先增加后减小的趋势；在总磷为0.215mg/L时，Margalef指数范围最大。

基于贝叶斯网络，在充分保护水生植物多样性的基础上，对湖泊生态需水的核算进行不确定性研究。通过概率推断，在贝叶斯网络中，将生态水位、水生植物多样性、降雨量和水质等变量相关联。在构建完贝叶斯网络后，进行决策分析，以探究不同情景对生态水位概率分布的影响。通过分析不同情景下生态需水核算结果，发现水生植物多样性处于最好状态时的生态水位不只一种。通过对比贝叶斯网络中有无水生植物多样性节点，结果发现：两种情况得到的生态水位概率分布完全不同；无水生植物多样性节点时，生态水位处于最好状态的概率减少了31.6%。因此，为了更好地保护湖泊，在贝叶斯网络中加入水生植物多样性节点十分必要。最后，根据模糊集理论中的级别特征值方法，确定了不同水平年下的生态水位值，枯水年、平水年和丰水年的生态水位分别为8.05m、8.41m和8.54m。该结果是后续生态需水保障研究的保障目标。

湖泊生态需水保障的准确性与水库调度的不确定性密切相关。本文重点研究了水库调度参数不确定性对水库调度性能和湖泊生态需水保障的影响。本文提出一个在水库生态调度中可以进行参数不确定性分析的模型框架。该模型框架既考虑了生态需求，也考虑了发电量需求，以维持生态环境和社会经济的和谐发展。在分析了白洋淀历年补水和调水情况后，确定了基于下游湖泊保护的水库最小下泄生态流量要求。为了对比不同生态流量管理对调度不确定性的影响，建立了三种生态流量管理情景。马尔科夫链蒙特卡洛采样方法，被用来进行参数估计和不确定性定量。并以置信区间的形式，定量表达了水库下泄量和水文情势改变度的不确定性。通过对比不同生态流量管理情景，发现更详细的生态流量管理情景具有较低的水文情势改变度和较小的下泄量范围估计。并且该情景在一年时间尺度上，有助于降低湖泊生态需水保证率的不确定性。

Sustaining the environmental flows (e-flows) is important for lake protection. Previous researches on e-flows have ignored uncertainty. The uncertainty inherent in the e-flow analysis is a major factor influencing the accuracy of e-flows. To effectively incorporate uncertainty into the e-flow analysis in lakes, this thesis conducts researches from three aspects: uncertainty in mechanism, uncertainty in accounting, and uncertainty in guaranteed rate, based on Bayesian theory. From the aspects of the uncertainty in mechanism, the uncertainty of aquatic plants and water level, the uncertainty of the relationship between aquatic plants and water level, and the uncertainty of the relationship among aquatic plants, water level, and water quality, are studied from three levels of a single element, dual elements, and three elements. From the aspects of the uncertainty in accounting, the uncertainty of e-flow requirements aiming at protecting aquatic plants is studied. From the aspects of the uncertainty in guaranteed rate, the effect of parameter uncertainty in reservoir operation on sustaining e-flows in lakes is analyzed, and a method for post-processing reservoir releases to sustain e-flows in lakes is established. This thesis takes Baiyangdian Lake as a study case. The methods and main conclusions are following:

The study of the uncertainty in mechanism includes three aspects. (1) From the aspects of the uncertainty of aquatic plants and water level: The Kolmogorov‐Smirnov test is adopted to determine the distribution models of the water level and four aquatic plant diversity indicators, respectively. The results showed that the Margalef index (d_Ma), Simpson index (D), and Shannon-Wiener index (H) of aquatic plant diversity, and water level have a Weibull distribution, while Pielou’s evenness index (J) has a Gamma distribution. (2) From the aspects of the uncertainty of the relationship between aquatic plants and water level: Firstly, aquatic plant diversity and water level are divided into several states. Then, according to the state transition model, the state transition matrix of the aquatic plant diversity in each water level state is obtained. The state of the aquatic plant diversity and corresponding probability distribution at each period are determined with water level process data. The impact of different water level processes (changing the order of water level state) on the aquatic plant diversity is compared by two types of water level process scenarios. The results showed that the evenly distributed water level is conducive to improving aquatic plant diversity. This result provides guidance for the formulation of subsequent e-flow protection strategies. (3) From the aspects of the uncertainty of the relationship among aquatic plants, water level, and water quality: Firstly, a linear relationship among aquatic plants, water level, and water quality is established based on the Bayesian linear regression model. Then, the Gibbs sampling method is applied for parameter estimation, thereby quantifying the uncertainty of the relationship among aquatic plants, water level, and water quality. The results showed that the simulated values of aquatic plant diversity have a certain range at each water level and water quality value. The value of d_Ma decreases and the range of d_Ma initially increases and then decreases with increasing water quality (total phosphorus). When the total phosphorus is 0.215mg/L, the range of d_Ma is the largest.

Based on the Bayesian network, the uncertainty in accounting for e-flow requirements is analyzed based on fully protecting the aquatic plant diversity. The variables such as e-flows, aquatic plant diversity, rainfall, and water quality are correlated by probabilistic inference in the Bayesian network. Decision analysis is carried out to explore the effect of different scenarios on the probability distribution of e-flows. By analyzing the results of e-flows under different scenarios, it is found that the value of e-flow is a possible range rather than a single value, when the aquatic plant diversity is at its best state. The results showed that the probability distribution of e-flows is completely different when the aquatic plant diversity node is or isn’t concerned in the Bayesian network. When the aquatic plant diversity node isn’t concerned in the Bayesian network, the probability that the e-flow is in the best state, is reduced by 31.6%. It’s necessary to have aquatic plant diversity nodes in the Bayesian network. Finally, according to the fuzzy set theory, the e-flow requirements in dry, normal, and wet years are 8.05m, 8.41m, and 8.54m, respectively. This result is the target of guarantee research.

The effects of parameter uncertainty in reservoir operation on a reservoir’s operational performance and the guaranteed rate of e-flow requirements in lakes are evaluated. This study proposes a model framework for conducting the parameter uncertainty in eco-friendly reservoir operation. The e-flow requirements and hydropower generation are considered in reservoir operation to sustain the harmonious development between the ecological environment and human society. After analyzing the water replenishment and water transfer over the years of the Baiyangdian Lake, the minimum e-flow discharge requirement aiming at protecting downstream lakes was determined. To compare the effect of different e-flow managements on the uncertainty of reservoir operation, three e-flow management scenarios are set. The Metropolis-Hastings algorithm of the Markov Chain Monte Carlo sampling approach was applied for parameter estimation and uncertainty quantification. The uncertainties of reservoir releases and flow regimes are quantitatively expressed in the form of a confidence interval. The comparison of different e-flow management scenarios shows that a reservoir operation with a more detailed e-flow management has a lower degree of flow regime and a smaller range of reservoir releases. Besides, this reservoir operation helps to reduce the uncertainty of the guaranteed rate for e-flow in the Baiyangdian Lake on a one-year time scale.

Current research focuses on reducing the uncertainty of inflow to improve the operational performance, and then improve the accuracy of the reservoir releases. Little attention has been paid to directly improve the accuracy of the reservoir releases. Release data provides more accurate information than inflow data for the protection of downstream river ecosystems. This study focuses on post-processing reservoir releases to improve the accuracy of sustaining e-flows in lakes. Through a hypothetical reservoir system with five numerical experiments, we found the error variances of reservoir releases are always larger than those of inflow forecasts. This indicates that the post-processing of reservoir releases is required to improve the accuracy of release data. Then, the Bayesian joint probability (BJP) model, an effective method to correct errors, is employed to post-process release data to reduce errors and quantify uncertainty. Flow duration curve-based ecodeficit/ecosurplus is applied to evaluated hydrological alterations to further demonstrate the necessity of processing release data and investigate the effectiveness of the BJP model. Finally, this study is applied to the Xidayang Reservoir to sustain e-flows for the Baiyangdian Lake, and the practical application of this study on post-processing reservoir releases is demonstrated.