GLUE框架下似然函数对水文模型不确定性的影响

似然函数的选取对模型参数不确定性结果存在较大影响。本文以淮河上游大坡岭水文站控制流域为例,采用GLUE不确定性分析方法、SCE-UA优化算法与流域水循环系统模型(HEQM)耦合,探索Nash-Sutcliffe系数与水量平衡系数这两个似然函数对模型参数敏感性、取值分布特征以及不确定性的影响。结果表明:从敏感性分析结果来看,Nash-Sutcliffe系数作为似然函数时,所选择的9个参数均为敏感性参数,而水量平衡系数作似然函数时,仅有1个敏感性参数,Nash-Sutcliffe系数更适合作似然函数;从不确定性区间评价结果来看,水量平衡系数作为似然函数时,模拟结果的覆盖率和对称性均优于Nash-Sutcliffe系数。以上研究可为GLUE方法似然函数的选取提供参考,也为多目标GLUE方法中权重的分配提供理论依据。     

变化环境下雅砻江流域水文极值演变及不确定性分析

为了探讨环境变化前后雅砻江流域的水文极值演变特征及不确定性,以雅砻江流域雅江水文站和洼里水文站为代表站,基于年极大值和超门限阈值样本,结合序列变异理论、多种极值统计模型(GEV、GPD、P-III)和轮廓似然函数参数估计及不确定性分析方法,分析了变化环境下雅砻江水文极值序列演变特征。结果表明:受气候变化和人类活动的影响,雅江水文站和洼里水文站环境变化前后的最优分布线型由P-III型分布转变为GEV分布。环境变化后的水文极值序列相应设计流量增大,重现期变小。设计值估算中,重现期越长,相应设计流量的不确定性也越大,其中参数的不确定性对于设计值的影响最为显著,但极值选样及分布函数的不确定性也不容忽视。轮廓似然函数法的使用可有效降低设计值不确定性,基于极值理论与轮廓似然函数估计法进行变化环境下水文极值演变分析可提高设计值的可靠性。研究成果可为雅砻江流域水库设计管理及防洪规划等提供参考。     

基于FCM-SCEMUA的水文模型参数不确定性估计方法

引入模糊C-均值聚类(FCM)方法对水文过程进行分类,结合SCEMUA方法,建立了基于FCM-SCEMUA的水文模型参数不确定性分析方法。选择南水北调水源区所在的汉江上游的江口流域,以新安江模型为例进行了实例研究。结果表明,FCM-SCEMUA方法通过对不同分类的似然函数分别设置阈值,在阈值同样为70%的情况下,所得到的有效参数组比通过SCEMUA方法得到的减少了64.8%的不合理参数组。所推求的参数后验分布更能够朝着高概率密度区进化,推导出更加合理的水文模型参数的后验分布,从而得到更加合理的预测区间,有效地减少了水文模拟与预测的不确定性。     

大渡河流域超阈值降雨样本模拟及不确定性分析

大渡河流域地形十分复杂,流域内气候随高程变化差异较大。通过超阈值模型模拟大渡河流域范围内9个雨量站的逐日降水资料序列,利用极大似然估计法计算模型参数,采用概率图、分位数图、重现水平图、密度函数图4种较直观的诊断图形对模型的合理性进行了全面评估,并借助轮廓似然方法估计模型关键参数及设计强降雨的置信区间。研究结果表明,各站点超阈值降雨样本均服从Pareto分布,可以选择GPD模型作为大渡河流域强降雨统计推断的分布函数类型,轮廓似然法能反映重现期长短对设计降雨置信区间的影响。可为大渡河流域降雨不确定性的定量评估及梯级水库群洪水预报提供依据。     

水文模型模拟水文极值的不确定性分析

以黄河源区为研究区,运用GLUE法分析了HBV模型和新安江模型模拟水文极值的不确定性。目标似然函数阈值分别选用0.7、0.6、0.5,将得到的洪水和枯水水文极值以及选出的模拟结果按丰水年、平水年和枯水年过程分别进行分析。结果表明:两个模型均擅长于模拟洪水,而且对洪水模拟的不确定性较对枯水模拟的不确定性低;从两个水文模型模拟日过程估计区间的差别看,HBV模型估计区间与实测相比,洪水年总体偏低,枯水年总体偏高,平水年不存在明显趋势,新安江模型则不存在这个特点;在相同的参数采样方法和策略下,HBV模型的不确定性比新安江模型更显著;两个水文模型对枯水指标Q_(90)和Q_(75)模拟的不确定性都较大;新安江模型对洪水指标Q_(25)和Q_(10)的估计区间小于HBV模型的,不确定性水平较低。     

基于不同目标函数GLUE方法参数不确定性研究

水文模型在防洪预报中发挥着重要作用,然而由于模型参数具有不确定性,即使有实测的降雨资料,也可能会产生较大的预报误差。针对参数的不确定性问题,以半湿润的陈河流域为研究区域,基于单目标GLUE方法和多目标GLUE方法,分析不同目标函数GLUE方法对实测径流的模拟能力以及参数的敏感性。研究结果表明,参数可分为敏感性参数(SM,CS)和非敏感性参数(K,KG,KI,CG,CI),不同的似然目标函数对径流具有不同的模拟能力,相对于单目标函数,多目标函数预报的不确定性范围较大,区间覆盖率较大,洪水预报的精度更高。     

贝叶斯多模型分析方法的对比研究北大核心

多模型分析能够考虑模型本身存在的不确定性,在决策分析和风险评估中具有越来越重要的作用。对具有严谨统计分析理论基础的贝叶斯模型平均法和极大似然贝叶斯多模型平均法做了详细介绍,并改进了传统极大似然贝叶斯多模型平均法不能考虑参数不确定性的不足,使极大似然贝叶斯多模型平均法对贝叶斯模型平均法近似得更为准确。地质统计多模型对地层渗透系数的预测分析结果表明,2种多模型分析方法在参数空间确定、模型后验权重和渗透系数预测方面都具有很好的一致性。极大似然贝叶斯多模型平均法能和水文学现有的参数估计方法很好结合,且计算量小。     

融合马尔科夫链-蒙特卡洛算法的改进通用似然不确定性估计方法在流域水文模型中的应用

本文在Blasone研究工作的基础上,进一步提出了基于马尔科夫链-蒙特卡洛算法的改进通用似然不确定性估计方法(Markov Chain_Monte Carlo based Modified Generalized Likelihood Uncertainty Estimation,MMGLUE)。该方法结合近年来被广泛用于推求参数后验分布的MCMC方法,对基于Monte Carlo随机取样方法的传统GLUE方法进行改进,并以预测区间性质最优为标准,对可行参数组阈值进行判断与选择,提出了衡量预测区间对称性的标准,并就预测区间性质与可行参数组个数的相关关系进行了探索。在汉江玉带河流域的实例研究证明,MMGLUE方法较传统的GLUE方法能够推求出性质更为优良的预测区间,从而更真实合理地反映水文模型的不确定性。     

贝叶斯多模型分析方法的对比研究

多模型分析能够考虑模型本身存在的不确定性,在决策分析和风险评估中具有越来越重要的作用。对具有严谨统计分析理论基础的贝叶斯模型平均法和极大似然贝叶斯多模型平均法做了详细介绍,并改进了传统极大似然贝叶斯多模型平均法不能考虑参数不确定性的不足,使极大似然贝叶斯多模型平均法对贝叶斯模型平均法近似得更为准确。地质统计多模型对地层渗透系数的预测分析结果表明,2种多模型分析方法在参数空间确定、模型后验权重和渗透系数预测方面都具有很好的一致性。极大似然贝叶斯多模型平均法能和水文学现有的参数估计方法很好结合,且计算量小。     

变参数PDS/GP模型及其在洪水频率分析中的应用

传统的洪水频率分析模型一般假定研究区域是完全均质的,未能考虑分布函数参数会随协变量而变化,忽略了水文序列时空上的异质性。本文将广义Pareto(GP)分布函数的参数作为随机变量,利用自动阈值法确定独立样本的超定量系列(PDS),并将线性矩法和核回归法相结合估计含协变量的模型参数,从而构建了可考虑水文序列时空分布异质性的变参数PDS/GP模型。丹江口水库实例研究表明:定参数模型的尺度参数估计值和设计洪水预测值均在变参数PDS/GP模型的估计区间内,这说明本文提出的变参数PDS/GP模型能够更好地反映参数变化对模型不确定性的影响。而且,变参数PDS/GP模型的估计区间随重现期的增大而变宽,表明频率分析外延存在较大的不确定性,有必要考虑丹江口水库水文序列时空分布的异质性。     

基于GLUE的新安江模型参数不确定性分析及应用

结合新安江模型在东洋河流域的应用,提出了基于GLUE方法的新安江模型参数不确定性分析。采用GLUE算法抽样结果对东洋河流域进行不确定性预报,选用水文模拟中常用的确定性系数作为似然判据,通过设定0.7为阀值,得到的90%置信区间的流量过程,实例研究表明,以该结果进行不确定预报是可行的。     

Uncertainty Intercomparison of Different Hydrological Models in Simulating Extreme Flows

A growing number of investigations on uncertainty quantification for hydrological models have been widely reported in past years. However, limited studies are found on uncertainty assessment in simulating streamflow extremes so far. This article presents an intercomparison of uncertainty assessment of three different well-known hydrological models in simulating extreme streamflows using the approach of generalized likelihood uncertainty estimation (GLUE). Results indicate that: (1) The three modified hydrological models can reproduce daily streamflow series with acceptable accuracy. When the threshold value used to select behavioral parameter sets is 0.7, XAJ model generates the best GLUE estimates in simulating daily flows. However, the percentage of observations contained in the calculated 95 % confidence intervals (P-95CI) is low (<50 %) when simulating the high-flow index (Q10). (2) Decreasing average relative length (ARIL), P-95CI and increasing average asymmetry degree (AAD) are found, when the threshold value increases for both daily-flows and high-flows. However, there is a significant inconsistence between sensitivity of daily-flows and high-flows to various threshold values of the likelihood function. Uncertainty sources from parameter sets, model structure and inputs collectively accounts for above sensitivity. (3) The best hydrological model in simulating daily-flows is not identical under different threshold values. High P-95CIs of GLUE estimate for high-flows (Q10 and Q25) indicate that TOPMODEL generally performs best under different threshold values, while XAJ model produces the smallest ARIL under different threshold values. The results are expected to contribute toward knowledge improvement on uncertainty behaviors in simulating streamflow extremes by a variety of hydrological models.     

Semi-parametric and Parametric Inference of Extreme Value Models for Rainfall Data

Extreme rainfall events and the clustering of extreme values provide fundamental information which can be used for the risk assessment of extreme floods. Event probability can be estimated using the extreme value index (γ) which describes the behavior of the upper tail and measures the degree of extreme value clustering. In this paper, various semi-parametric and parametric extreme value index estimators are implemented in order to characterize the tail behavior of long-term daily rainfall time series. The results obtained from different estimators are then used to extrapolate the distribution function of extreme values. Extrapolation can be employed to estimate the occurrence probability of rainfall events above a given threshold. The results indicated that different estimators may result in considerable differences in extreme value index estimates. The uncertainty of the extreme value estimators is also investigated using the bootstrap technique. The analyses showed that the parametric methods are superior to the semi-parametric approaches. In particular, the likelihood and Two-Step estimators are preferred as they are found to be more robust and consistent for practical application.     

参数率定过程中目标函数选择的不确定性对径流模拟的影响

在水文模型率定过程中,不同目标函数侧重于径流模拟的不同层面。为了探究目标函数选择的不确定性对模型参数和径流模拟的影响,将HyMod模型应用于黄河源区,选择纳什效率函数f_NS、总水量平衡误差函数f_t、低水量误差函数f_d和高水量误差函数f_g作为目标函数,采用遗传算法(GA)分别率定出不同目标函数下对应的最优参数值,并依次代入水文模型模拟水文过程;通过对比分析年尺度及年内各月实测与模拟径流过程、纳什效率系数NSE、决定系数R²和均方根误差RMSE评价指标来探究参数率定的目标函数不确定性对年尺度水资源演变过程的影响。结果表明:当HyMod模型应用于黄河源区水文模拟的率定期和验证期时,目标函数选择的不确定性对各评价指标的影响差异明显,如f_NS目标函数下NSE值最大,在f_g下次之,在f_d下最小,此外率定期模拟精度优于验证期;同样,目标函数不确定性对不同特征时期径流的影响差异显著,其中,f_NS和f_t目标函数下,非汛期分别高估和低估模拟流量。研究成果可为水文模型参数率定目标函数的选择提供理论参考。     

Predicting Variability in a Lake Ontario Phosphorus Model

The prediction of a model always has a degree of uncertainty. Because the level of uncertainty is inversely related to the value of information contained in the prediction, there is a need to quantify the uncertainty. One approach to estimate prediction uncertainty is first-order error analysis. In this method, the error in a characteristic (variable or parameter) is defined by its first nonzero moment (the variance). Errors are propagated through the model using first-order terms in the Taylor series, and the variances are then combined to yield the total prediction uncertainty. An alternative approach to model prediction error analysis is Monte Carlo simulation. In this technique, probability density functions are assigned to each characteristic (variable or parameter), reflecting the uncertainty in that characteristic. Then, values are randomly selected from the distribution for each term and inserted into the model, to calculate a prediction. Repeating this process a number of times produces a distribution of predicted values, which reflects the combined uncertainties. These two approaches (first-order error analysis and Monte Carlo simulation) are applied to Lake Ontario data using a steady state mass balance phosphorus model. Comparisons are made which suggest guidelines for the use of each.     

Transferability of Conceptual Hydrological Models Across Temporal Resolutions: Approach and Application

The temporal resolution of observed data is a critical element in determining the parameters, prediction performance, and applicability of hydrological models. In this study, runoff simulations were performed at different temporal resolutions using the Xinanjiang model to evaluate the influence of temporal resolution on the model parameters and performance. Based on the sensitivity analysis of the model parameters, the posterior distribution of the sensitive parameters was derived using the Bayesian method and Differential Evolution Adaptive Metropolis (DREAM) algorithm at different temporal resolutions. The transformation functions of the model parameters were put forward to transform the parameters according to the regulatory between the parameters and time-steps on the basis of the parameters posterior distribution. The model performance and uncertainty for runoff simulation were compared and discussed at each temporal resolution. The results show that (1) the parameters related with the process of the water balance and runoff routing are identified as sensitive to the temporal resolutions, and there exist linear or power function relationships between parameter values at different temporal resolutions; and (2) the quantitative relationship equations have been verified to have good capacity for model simulation when the model parameters are transformed from other temporal resolution.     

基于分位点回归模型的洪水概率预报方法

采用分位点回归模型分析洪水预报的不确定性, 提供洪水预报倾向值( 预报概率分布的中位数) 和 90% 置信度的预报区间成果, 实现了洪水概率预报。基于/ 精度2可靠性0 联合评价指标对分位点回归模型计算的预报倾向值 和预报区间成果进行了评估。在信江流域梅港站的应用结果表明: 基于分位点回归模型提供的倾向值定值预报结 果可进一步提升洪水预报的精度; 同时该模型提供的 90% 预报区间结果具有较高的覆盖率( 约 90% ) 且离散度较小 ( 小于 01 20) , 表明预报区间以较窄的宽度包含了绝大多数的实测值, 预报可靠性较强。