受气候变化和人类活动的双重影响，流域水文情势异常复杂，流域水文过程的不确定性特征更加突出。水文模拟可为水库调度、生态环境保护、水资源开发利用、防灾减灾等提供科学依据。然而，由于水文系统蕴含大量的不确定性，水文系统模拟及其多重不确定性（如模型、数据和参数等不确定性）定量解析存在着诸多问题和挑战。不可靠的水文模拟将直接影响水资源系统的灾害预报和综合调控，甚至可能危害人民群众的生命财产安全。党的十八大以来，国家高度重视生态文明建设，对水文、水资源、水环境等领域提出了新的挑战。因此，亟需开发可靠的水文模拟模型及不确定性分析方法，以预测多重不确定性条件下径流的分布特征，进而为水资源系统风险分析与管理提供依据。

为应对以上挑战，本研究着眼于“长江经济带大开发”和“黄河流域生态保护”等国家重大战略需求，密切结合领域研究前沿，在充分考虑流域过程多重不确定性的前提下，以流域水文过程复杂性辨识为基础，耦合逐步聚类、概率配点、Copula理论、多水平析因分析和数据同化等技术，开发了一系列随机水文模拟及不确定性分析方法，并在国内外多个典型流域开展了实例研究。具体研究内容及结论包括：

（1）针对水文模型参数辨识过程中多参数间互动关系难以量化的问题，通过把Vine-Copula函数引入到Bayesian参数推断过程，开发Copula-Bayesian理论的模型参数辨识方法。通过对四个方法、五个案例，九个评价指标的对比分析，发现基于Vine-Copula函数建立参数间的多元联合分布，可有效量化参数间的互动关系，降低样本自相关性、并提高采样效率。

（2）在模型参数辨识的基础上，针对传统水文模型难以预测径流随机特征的问题，开发逐步聚类-多项式混沌展开（CPCE）随机水文预报模型。CPCE模型通过建立多项式混沌展开的系数与水文模型输入（如降水和潜在蒸散量）之间的多元离散非函数关系，可有效表征参数的不确定性在水文模拟过程中的演进过程，并实现径流随机特征的预测分析。最后，借助多水平析因分析，动态评估了模型参数对径流预测的敏感性。结果表明汭河流域内最大土壤水分容量Cmax对低径流预测的准确性起着关键作用（大于0.8），而土壤水分容量的空间变异程度Bexp对高流量预测的准确性有显著影响（高于0.5）。该研究克服了传统多项式混沌展开模型无法实现径流预报功能的难题，为随机水文模拟与不确定性分析提供了关键性技术支持。

（3）随机水文预报模型存在多源多重不确定性，针对单一的模型、参数和输入难以反映这些不确定性的难题，本研究通过耦合多水平析因分析、贝叶斯模型平均以及Copula函数，构建多水平析因集合水文预报模型（MFEDHM）。该模型通过水文集合预报，得到径流的概率分布，并量化具有随机特征的模型输入对集合水文预报系统响应的多重交互效应。研究将开发的集合水文预报模型应用于中国16个典型流域，定量分析了气候因素对水文过程的多重交互影响，并揭示这些影响的空间异质性。结果发现集合模型在模拟降雨-径流关系方面比任何单一模型更可靠，且气候因素对中国径流的影响存在显著的空间异质性。例如，同期气候条件对中国南方径流变化的影响为57 ~ 64%，而前期气候条件对中国北方径流变化的影响为20 ~ 67%。于此同时非气候因素对径流变化的影响范围是1.91 ~ 24.70％，随流域面积增加（10000 km²）而降低（0.12％）。

（4）针对当前研究主要集中在单站点水文预报，难以反映流域内多站点径流间互动关系的问题，本研究开发了逐步聚类多站点联合水文预报模型（SCMW）。SCMW模型通过多维逐步聚类分析建立多预测因子和多径流响应间的复杂非函数关系，实现多站点径流联合预报，并识别导致多站点径流联合变化的主导气候因子。将开发的SCMW应用于三个案例，结果表明SCMW模型能够较好捕捉多站点的降雨-径流关系，得到径流预测均值和预测区间。与单站点模拟模型相比，开发的SCMW模型可显著提高径流模拟准确度。同时，析因分析结果表明SCMW模型受多因素交互影响显著，其中三因子交互作用的贡献可达24.1%。最后，对聚类树的统计后分析结果表明，前30%的气候变量可以解释Iskut-Stikine流域多站点径流联合变化的83.9%。此外，BelowJohnson站的近地表最低温度的RDI最大，可以解释25.6%的多站点径流联合变化；TelegraphCreek和Wrangell站的降水分别可以解释17.5和4.6%。

（5）针对传统析因分析技术中ANOVA估算存在偏差的问题，提出集合析因不确定性解析技术（IFA）。该方法通过耦合再抽样技术、ANOVA估算和集合平均，对样本进行再抽样，以减少有偏方差估计对不确定性量化结果的影响。将开发的IFA应用于三参数回归模型、GR4J水文模型和水文数据同化模型三个案例，以探讨所提出方法的适用性。研究结果表明再抽样技术有效减少ANOVA的估算偏差。与传统方法（例如Sobol）相比，开发的IFA技术不仅可以用于非数值型因子的不确定性量化，而且可显著降低计算需求（如GR4J模型运行次数由21万降低到256）。水文数据同化模型结果表明，径流观测误差是径流确定性和概率性预测的主要不确定性来源（在EnKF中贡献为42 ~ 48%，在EnKFsks中贡献为54 ~ 76%）。与此同时，数据同化方案在水文预测中起着至关重要的作用，特别是对于概率预测（贡献了41%）。

整体而言，针对流域水文模拟过程中的多重不确定性特征，本研究在水文模拟多重不确定性辨识的基础上，开发了一套可靠的随机水文模拟与不确定性分析技术，可处理多参数互动、单站点/多站点随机水文预报以及不确定性来源定量解析问题。所开发的随机水文模拟与不确定性分析方法及其应用结果可为多重不确定性条件下的水文系统风险分析与水资源管理提供科学支持。

Under the combined effect of climate change and human activities, hydrological system is extremely complex, and the uncertain characteristics are more prominent. Hydrological simulation can provide scientific basis for reservoir regulation, ecological environment protection, water resources development and utilization, disaster prevention and mitigation, etc. However, due to uncertainties in the hydrological system, there are challenges in the quantitative analysis of hydrological system simulation and its multiple uncertainties (such as models, data, and parameter uncertainties). Unreliable hydrological simulation will directly affect the disaster forecasting and comprehensive regulation of the hydrological system. Since the 18th National Congress of the Communist Party of China, the construction of ecological civilization has received great attention, which has raised new challenges in hydrology, water resources, and water environment. Therefore, it is desired to develop reliable hydrological simulation models and uncertainty analysis methods to predict distribution characteristics of runoff under multiple uncertainties and provide suggestions for risk analysis/water resources management.

To meet the above challenges, stochastic hydrological simulation models and uncertainty analysis methods are developed to serve the major national strategic needs such as "development of the Yangtze River Economic Belt" and "ecological protection of the Yellow River Basin". Considering multiple uncertainties in hydrological process, multivariate stochastic techniques such as stepwise clustering, probability collocation, Copula theory, multilevel factorial analysis, and data assimilation are coupled in this study. Case studies have been carried out in many typical river basins. The main researches and conclusions are as follows.

(1) In the process of parameter identification, the interactions between multiple parameters are difficult to quantify. Through introducing Vine-Copula function into Bayesian parameter inference, a model parameter identification method based on Copula-Bayesian theory is developed. Through the comparative analysis between four methods under five cases, it is found that the joint distributions between multiple parameters can be well established through the Vine-Copula function, which can effectively quantify the interaction between model parameters, reduce sample autocorrelation, and improve sampling efficiency.

(2) Based on model parameter identification, a clustered polynomial chaos expansion (CPCE) stochastic hydrological model is developed. In the CPCE model, multivariate discrete non-functional relationships are established between the coefficients of the polynomial chaotic expansion and hydrological model inputs such as precipitation and potential evapotranspiration. The CPCE model can characterize the evolution of parameter uncertainty in hydrological simulation and realize the runoff stochastic forecasting. Finally, with the help of multilevel factorial analysis, the dynamic sensitivity analysis of parameters is evaluated. The results show that the maximum soil moisture capacity Cmax plays a key role in the accuracy of low runoff predictions (greater than 0.8) in the Ruihe River Basin, while the spatial variability of soil moisture capacity Bexp has a significant impact on the accuracy of high runoff predictions (greater than 0.5). The contribution of this research is to overcome the problem that polynomial chaotic expansion model cannot achieve the prediction function, and provide key technical support for stochastic hydrological simulation and uncertainty analysis.

(3) There are multiple uncertainties in hydrological modeling, and it is difficult to reflect these with single model, parameter and input. Therefore, a multi-level factorial ensemble hydrological forecasting model (MFEDHM) is developed through coupling multi-level factorial analysis, Bayesian model averaging and Copula function. The model obtains the probability distribution of runoff through hydrological ensemble forecasting, and quantifies multiple interaction effects of multiple model parameters. The developed ensemble hydrological forecasting model is applied to 16 river basins in China to quantitatively analyze the multiple interactive effects of climatic factors on hydrological processes and reveal the spatial heterogeneity. The results show that the ensemble model is more reliable than any single model in simulating rainfall-runoff relationship. The impacts of climatic factors on runoff show significant spatial heterogeneity in China. For example, the influence of climatic conditions on runoff changes in southern China during the same period is 57 ~ 64%, while the influence of previous climatic conditions on runoff in northern China is 20 ~ 67%. At the same time, the influence of non-climatic factors on runoff is 1.91 ~ 24.70%, and it decreases (0.12%) with the increase of watershed area (10000 km²).

(4) Most researches mainly focuse on single-site hydrological forecasting, which are difficult to reflect the cross-correlation between multi-site runoff. Therefore, a stepwise-clustered multi-catchment hydrological model (SCMW) is developed in this study to tackle the interactive relationships among multi-catchment runoffs and their concurrent variations within a watershed system. Through multivariate inference based on Wilks likelihood ratio criterions and F tests, the proposed model can deal with both continuous and discrete variables as well as nonlinear relations among multiple variables without assumptions of functional relationships. The developed SCMW is applied to three cases. The results show that the SCMW model can capture the multi-site rainfall-runoff relationship well, and obtain forecast mean and forecast interval. Compared to single-site simulations, the developed SCMW model can significantly improve the runoff simulation accuracy. At the same time, the results of factorial analysis showed that the SCMW model is significantly affected by multi-factor interaction, and the contribution of three-factor interaction could reach 24.1%. Finally, the post-statistical analysis of clustering tree shows that the top 30% climate variables can explain 83.9% of the combined multi-site runoff variation in the Iskut-Stikine watershed. In addition, the RDI of the near-surface minimum temperature at the BelowJohnson station is the largest, which can explain 25.6% of the combined multi-site runoff variation; the precipitation at the TelegraphCreek and Wrangell stations can explain 17.5 and 4.6%, respectively.

(5) To overcome the problem of bias in ANOVA estimation, an ensemble factorial uncertainty analysis technique is proposed. Through coupled resampling technique, ANOVA estimation and ensemble averaging, the samples are resampled to reduce the biased variance. Estimate the impact on contribution quantification. The proposed model was applied to three cases, inclouding a three-parameter regression model, GR4J hydrological model, and a hydrological data assimilation model, to explore the it’s applicability. The results show that the resampling technique can effectively reduce the bias caused by the variance decomposition of ANOVA. Compared with traditional methods (such as Sobol), the developed ensemble factorial uncertainty analysis technique can not only be used for sensitivity analysis of non-numerical factors, but also significantly reduce the computational requirements (eg, the number of GR4J model runs is reduced from 210,000 to 256). The results of the hydrological data assimilation model show that the runoff observation error is the main source of uncertainty in the deterministic and probabilistic predictions of runoff (42 ~ 48% in EnKF and 54 ~ 76% in EnKFsks). Meanwhile, data assimilation schemes play a crucial role (41%) in hydrological predictions, especially for probabilistic predictions.

Overall, a set of reliable stochastic hydrological simulation and uncertainty analysis techniques are developed in this study to identify multiple uncertainties in hydrological simulations under complex conditions. The developed methods can handle multi-parameter interaction, single-site/multi-site stochastic hydrological forecasting, and quantitative analysis of uncertainty sources. The developed method and its application results can provide scientific support for the risk analysis and management of hydrology and water resources system under multiple uncertainties.