Assessing uncertainties in a conceptual water balance model using Bayesian methodology / Estimation bayésienne des incertitudes au sein d’une modélisation conceptuelle de bilan hydrologique

Abstract

Abstract The aim of this study was to estimate the uncertainties in the streamflow simulated by a rainfall–runoff model. Two sources of uncertainties in hydrological modelling were considered: the uncertainties in model parameters and those in model structure. The uncertainties were calculated by Bayesian statistics, and the Metropolis-Hastings algorithm was used to simulate the posterior parameter distribution. The parameter uncertainty calculated by the Metropolis-Hastings algorithm was compared to maximum likelihood estimates which assume that both the parameters and model residuals are normally distributed. The study was performed using the model WASMOD on 25 basins in central Sweden. Confidence intervals in the simulated discharge due to the parameter uncertainty and the total uncertainty were calculated. The results indicate that (a) the Metropolis-Hastings algorithm and the maximum likelihood method give almost identical estimates concerning the parameter uncertainty, and (b) the uncertainties in the simulated streamflow due to the parameter uncertainty are less important than uncertainties originating from other sources for this simple model with fewer parameters.     

Daily rainfall projections from general circulation models with a downscaling nonhomogeneous hidden Markov model (NHMM) for south‐eastern Australia

An ensemble of stochastic daily rainfall projections has been generated for 30 stations across south‐eastern Australia using the downscaling nonhomogeneous hidden Markov model, which was driven by atmospheric predictors from four climate models for three IPCC emissions scenarios (A1B, A2, and B1) and for two periods (2046–2065 and 2081–2100). The results indicate that the annual rainfall is projected to decrease for both periods for all scenarios and climate models, with the exception of a few scenarios of no statistically significant changes. However, there is a seasonal difference: two downscaled GCMs consistently project a decline of summer rainfall, and two an increase. In contrast, all four downscaled GCMs show a decrease of winter rainfall. Because winter rainfall accounts for two‐thirds of the annual rainfall and produces the majority of streamflow for this region, this decrease in winter rainfall would cause additional water availability concerns in the southern Murray–Darling basin, given that water shortage is already a critical problem in the region. In addition, the annual maximum daily rainfall is projected to intensify in the future, particularly by the end of the 21st century; the maximum length of consecutive dry days is projected to increase, and correspondingly, the maximum length of consecutive wet days is projected to decrease. These changes in daily sequencing, combined with fewer events of reduced amount, could lead to drier catchment soil profiles and further reduce runoff potential and, hence, also have streamflow and water availability implications. Copyright © 2012 John Wiley & Sons, Ltd.     

山西地震带历史地震序列的统计分析

在工程地震工作中需要知道某地震带或某地区未来100年内的地震活动水平,以便适当选择历史地震的统计时段,从而得到和地震活动水平相适应的不同潜在震源区的各级地震的年平均发生率。 本文利用极值理论、最大熵原理、马尔可夫模型的方法、莫尔纳方法和伯努里模型方法计算了山西地震带未来100年内中强震的年平均发生率、平均重现期大于等于某级地震的个数和发震概率,计算结果表明,山西地震带未来百年内将发生≥6.0级地震3次,发震概率为0.94左右;将发生≥6.5级地震1—2次,发震概率为0.84左右;有可能发生≥7.0级地震,发震概率为0.53左右;发生≥7.5级地震的可能性不大,发震概率为0.32左右;发生≥8.0级地震的可能性很小,发震概率为0.15左右。     

Transport and sedimentation of particles in a fluid flow

A simple two-dimensional random walk model is developed for the motion of a particle in a fluid flow. Some earlier results for the persistent injection of particles into the flow are extended, and the distribution of the maximum number of particles in suspension over the period (0,t) is derived.     

Optimal operation model of a single reservoir with drought duration explicitly concerned

In this paper, a new model for a single reservoir operation optimization is proposed. The proposed model can design the optimal operation policy of a reservoir with explicit consideration of drought duration. The authors model this problem by formulating a single-stage loss function as a function of both the reservoir release and drought duration. Thereby the expected loss per period which is calculated based on the above extended single-stage loss function is minimized in infinite time horizon on the basis of Markov decision process (MDP) theory. The reliability indices are estimated as expected loss per period for specified extended loss functions. Finally, the features of the proposed model are illustrated through numerical analysis.     

利用马氏过程模拟和预测土壤侵蚀的动态演变─—以安徽省岳西县为例

本文根据安徽省岳西县１９５８－１９８２－１９９２年三个时期的遥感资料所编制的土壤侵蚀图，用点数转化法定量地分析岳西县上述两个阶段侵蚀演变和浸蚀类型之间的相互转化状况，确定相应的初始状态下（１９５８和１９８２）的转移概率矩阵，应用马尔科夫过程摸拟和预测岳西县土壤侵蚀及其格局的动态演变过程和未来演变趋势。     

川滇强震的回归—马尔可夫链联合预测

本文应用回归—马尔可夫链联合预测地震的方法,结合川、滇强震的特点,对川、滇强震进行了计算,并作了预测验证。结果表明,该方法对川、滇强震的预测效果较好。     

Stratigraphic analysis and the asymptotic distribution of the coefficient of cross-association

The asymptotic distribution of the coefficient of cross-association between two sequences of nominal data is investigated under the assumption of independent random sampling from a multinomial distribution slightly modified to suit geological applications. This modification is due to merging consecutive strata of the same rock type into one lithological unit, and can be described by a simple Markov chain. A distinction is made between the case in which the theoretical frequencies are known, and the situation where these have to be estimated from the observed data.     

Multi-year drought frequency analysis at multiple sites by operational hydrology - A comparison of methods

This paper compares two generators of yearly water availabilities from sources located at multiple sites with regard to their ability to reproduce the characteristics of historical critical periods and to provide reliable results in terms of the return period of critical sequences of different length. The two models are a novel multi-site Markov mixture model explicitly accounting for drought occurrences and a multivariate ARMA. In the case of the multisite Markov mixture model parameter estimation is limited to a search in the parameter space guided by the value of parameter λ to show the sensitivity of the model to this parameter. Application to two of the longest time series of streamflows available in Sicily (Italy) shows that the models can provide quite different results in terms of estimated return periods of historic droughts, although they seem to perform more uniformly when it comes to simulate drought-related statistics such as drought length, severity and intensity. The role of parameter selection for the multisite Markov mixture model and of the marginal probability of generated flows in providing results consistent with the characteristics of the observed series is discussed. Both models are applied to the system of sources supplying the city of Palermo (Sicily) and its environs showing the applicability of the newly developed multisite Markov mixture model to medium-to-large scale water resources systems.     

可数背景状态下QBD过程的平稳分布尾渐近态

考虑在可数背景状态下，时间离散的拟生灭过程（QBD过程）平稳分布的尾概率的渐近态。通过对QBD过程某些条件的限定，应用马尔可夫更新定理，得出在一定合理的条件下，当水平趋于无穷时的尾概率的几何衰变。通过初等方法，将该结论应用于时间离散的加入最短队模型。