贝叶斯框架的Copula季节水文干旱预报模型构建及应用

根据季节径流量相关特性,利用标准径流指数(SRI),通过优选Copula函数和径流量分布函数,构建贝叶斯框架的Copula季节水文干旱预报模型,并对阿克苏河西大桥水文站进行实证分析。结果表明：① Gamma、Lognormal、Normal、Gumbel、Exponential 5种分布函数中,Gamma、Gumbel能较好拟合夏、秋季径流量;② Gumbel-Hougaard、Clayton、Frank 3种Copula函数中,Clayton能较好联结夏、秋季径流量分布函数;③ 构建模型预报表明,2001~2009年秋季发生干旱概率较低(24%~38%),以轻微、中度干旱为主,而2010年发生干旱的概率极高(95%),发生异常干旱的概率偏高(81%),与实际发生的干旱情况基本一致;④ 贝叶斯框架下构建的Copula模型能准确预报季节水文干旱发生,减少预报的不确定性,为特定区域干旱预报提供了一条新的途径。     

运用贝叶斯方法的PM2.5浓度时空建模与预测

针对当前我国大部分地区正面临严重的空气污染问题,对重污染区域进行时空建模具有重要的意义。该文基于贝叶斯时空模型建立了京津冀区域的PM2.5浓度时空预测模型,该模型充分考虑了PM2.5浓度的时间变异特性与空间分布特性,并引入了气象数据作为协变量对没有监测站的位置进行预测。实验结果表明,该方法具有很好的预测精度,其在测试站点上的拟合优度达到了0.9以上,能够应用于区域级PM2.5浓度的时空分布建模与预测。     

集合资料同化方法的理论框架及其在海洋资料同化的研究展望

在海洋动力系统的数值模拟中,海洋资料同化是一种能够有效融合多源海洋观测资料和数值模式的方法。它不仅可以显著地提高数值模拟的效果,构造海洋再分析资料场,还能有效减少海洋和气候预报时模式初始条件的不确定性。因此,海洋资料同化对于海洋研究和业务化应用具有非常重要的意义。资料同化方法的研究一直是大气、海洋科学的热门课题之一。其中,集合卡尔曼滤波器(EnKF)是一种有效的资料同化方法,自提出以来经过了20多年的发展和改进,已经在海洋资料同化中得到了广泛的研究和应用。近年来,随着动力模式的不断发展和计算能力的提高,粒子滤波器由于不受模型线性和误差高斯分布假设的约束,也逐渐成为了当前资料同化方法研究的热点。本文分析和总结了目前关于集合卡尔曼滤波器和粒子滤波器的一些最新理论研究结果,在贝叶斯滤波理论的框架下讨论了这两类算法的关联和区别,以及各自在资料同化实践中的优势和不足。在此基础上,我们探讨了粒子滤波器应用于海洋模式资料同化的主要困难和目前可行的一些解决方法,展望了集合资料同化方法研究的新趋势,为集合资料同化方法的进一步发展和应用提供理论基础。     

EnKF和SIR-PF在贝叶斯滤波框架下的比较和结合

贝叶斯估计理论为非线性、非高斯系统的数据同化提供了一个统一的框架。在本文中,我们利用著名的洛伦茨吸引子(Lorenz'63)模式对两种基于贝叶斯滤波理论的数据同化方法——集合卡尔曼滤波器(EnKF)和重取样粒子滤波器(SIR-PF)——进行了较为全面的比较。比较的结果揭示了两种方法的优缺点:即当集合成员数目较多时,SIR-PF的同化效果优于EnKF;反之,则EnKF的表现较好。进一步地,我们使用统计方法分析了两者表现的差异和原因。最近提出的一种集合卡尔曼粒子滤波器(EnKPF)通过使用一个可控的参数整合EnKF和SIR-PF的分析格式,可以结合两者的优点。本文在充分比较两种方法的前提下,重新阐释并改进了原有的EnKPF算法,使之适用于非线性的观测算子。通过使用相同的洛伦茨模式实验,我们揭示了EnKPF实质上提供了关于EnKF和SIR-PF的连续插值,使得后两者可以视为其特殊情况。并且,在集合成员数目有限的前提下,EnKPF可以在一定程度上避免滤波退化的发生,取得优于EnKF和SIR-PF的同化效果。     

Response of Growing Season Gross Primary Production to El Ni?o in Different Phases of the Pacific Decadal Oscillation over Eastern China Based on Bayesian Model Averaging

Gross primary production (GPP) plays a crucial part in the carbon cycle of terrestrial ecosystems. A set of validated monthly GPP data from 1957 to 2010 in 0.5° × 0.5° grids of China was weighted from the Multi-scale Terrestrial Model Intercomparison Project using Bayesian model averaging (BMA). The spatial anomalies of detrended BMA GPP during the growing seasons of typical El Ni?o years indicated that GPP response to El Ni?o varies with Pacific Decadal Oscillation (PDO) phases: when the PDO was in the cool phase, it was likely that GPP was greater in northern China (32°–38°N, 111°–122°E) and less in the Yangtze River valley (28°–32°N, 111°–122°E); in contrast, when PDO was in the warm phase, the GPP anomalies were usually reversed in these two regions. The consistent spatiotemporal pattern and high partial correlation revealed that rainfall dominated this phenomenon. The previously published findings on how El Ni?o during different phases of PDO affecting rainfall in eastern China make the statistical relationship between GPP and El Ni?o in this study theoretically credible. This paper not only introduces an effective way to use BMA in grids that have mixed plant function types, but also makes it possible to evaluate the carbon cycle in eastern China based on the prediction of El Ni?o and PDO.     

Estimation of ultimate bond strength for soil nails in clayey soils using maximum likelihood method

This paper presents a maximum likelihood estimation of the ultimate bond strength for soil nails in clays. Both uncensored and censored ultimate bond strength data for soil nails are collected from the literature. Based on the concept of maximum likelihood, a log-likelihood function is constructed for estimating the mean and coefficient of variation (COV) of the ultimate bond strength jointly using the two types of data. The mean and COV are determined as the pair that maximises the log-likelihood function. Two distribution models (normal and lognormal) are used for the estimation. A comparison of the relative competence between the two candidate distribution models that are adopted for describing the collected uncensored and censored data is performed using the Bayesian Information Criterion. Example designs of soil nail walls against internal pullout limit state of nails and overall stability limit state are provided to demonstrate the benefit of taking censored data into account for estimation of the ultimate bond strength of soil nails.     

Determination of site-specific soil-water characteristic curve from a limited number of test data— A Bayesian perspective

Determining soilewater characteristic curve(SWCC) at a site is an essential step for implementing unsaturated soil mechanics in geotechnical engineering practice, which can be measured directly through various in-situ and/or laboratory tests. Such direct measurements are, however, costly and timeconsuming due to high standards for equipment and procedural control and limits in testing apparatus. As a result, only a limited number of data points(e.g., volumetric water content vs. matric suction)on SWCC at some values of matric suction are obtained in practice. How to use a limited number of data points to estimate the site-specific SWCC and to quantify the uncertainty(or degrees-of-belief) in the estimated SWCC remains a challenging task. This paper proposes a Bayesian approach to determine a site-specific SWCC based on a limited number of test data and prior knowledge(e.g., engineering experience and judgment). The proposed Bayesian approach quantifies the degrees-of-belief on the estimated SWCC according to site-specific test data and prior knowledge, and simultaneously selects a suitable SWCC model from a number of candidates based on the probability logic. To address computational issues involved in Bayesian analyses, Markov Chain Monte Carlo Simulation(MCMCS), specifically Metropolis-Hastings(M-H) algorithm, is used to solve the posterior distribution of SWCC model parameters, and Gaussian copula is applied to evaluating model evidence based on MCMCS samples for selecting the most probable SWCC model from a pool of candidates. This removes one key limitation of the M-H algorithm, making it feasible in Bayesian model selection problems. The proposed approach is illustrated using real data in Unsaturated Soil Database(UNSODA) developed by U.S. Department of Agriculture. It is shown that the proposed approach properly estimates the SWCC based on a limited number of site-specific test data and prior knowledge, and reflects the degrees-of-belief on the estimated SWCC in a rational and quantitative manner.     

Radiocarbon chronology of occupation of the site Chicha and Bayesian statistics for the assessment of a discontinuous transition from Late Bronze to Early Iron Age (West Siberia)

The Late Bronze to Iron Age transition in West Siberia involved significant cultural and political changes, which were reflected in the emergence of protourban settlements in the forest-steppe zone. The transition is roughly dated to the turn from the 2nd to the 1st mil. BC, mainly based on archaeological artefacts and on the general sociocultural development. A more precise radiocarbon dating for this transition was problematic mainly because of the general lack of data for West Siberia. This paper analyzes the chronology of the Late Bronze to Iron Age transition at Chicha, a reference site in the region for this period. The assessment of a possible hiatus between the Late Bronze Age and the following transitional period at Chicha is the key issue of our paper, as its presence may have far reaching cultural implications. To increase the precision of the radiocarbon chronology with focus on the possible hiatus, the samples from well-defined stratigraphic contexts were analyzed using Bayesian modeling incorporating stratigraphic information. The performed chronological modeling supports existing archaeological hypothesis of a hiatus at the very end of the 2nd mil. BC, just before the regular emergence of a new protourban settlement at the site of an abandoned Late Bronze settlement. A sensitivity analysis including the simulated hiatus confirms the reliability of the model. A complete population change seems to be plausible. The protourban settlement of Chicha, typical of the Transitional period, did not exist very long. With the emergence of the early nomadic cultures in the South Siberian steppes at the beginning of the 1st mil. BC, it most probably stopped functioning. The cultural development of that time, former believed to be continuous, was deeply interrupted several times.     

Model selection in Bayesian framework to identify the best WorldView-2 based vegetation index in predicting green biomass of salt marshes in the northern Gulf of Mexico

Coastal wetlands are among the most productive ecosystems globally but have experienced dramatic degradation and loss within the past several decades. Vegetation biomass of coastal wetlands is not only the key component of blue carbon storage but also plays an important role in vertical accretion, important for maintaining these habitats under relative sea-level rise. Remote sensing offers a cost-effective approach to study vegetation biomass at a broad spatial scale. We developed statistical models to predict peak aboveground green biomass of Spartina alterniflora and Juncus roemerianus, two dominant species of salt marshes using WorldView-2 satellite imagery at the Grand Bay National Estuarine Research Reserve (NERR) on the Mississippi coast in the northern Gulf of Mexico. The model accounted for nested data structures in the sampled biomass, assimilated uncertainties from data, parameters and model structures, and helped determine the best vegetation index among a variety of commonly-used indices to predict aboveground green biomass. We developed a series of mixed-effects models, which included different combinations of fixed effect(s), random intercept, and random slope(s). The fixed effects were species and one of the 60 vegetation indices derived from a WorldView-2 image obtained on 6 October 2012. The random effect used was site. We implemented the models in a Bayesian framework and selected the best model structure and vegetation index based on minimum posterior predictive loss and deviance information criterion. The results showed that the best vegetation index to predict peak green biomass was the green chlorophyll index derived from the reflectance values of band 8 (near-infrared) and band 3 (green), and its effect on biomass prediction varied among sites. The inclusion of species as a fixed effect improved the model prediction. The study demonstrated the need to account for spatial dependence of data in developing a robust model, and the importance of the second WorldView-2 near-infrared band (860–1040 nm) in predicting aboveground green biomass for the Grand Bay NERR. The analysis using mixed-effects modeling in Bayesian inference which coherently combined field and WorldView-2 data with uncertainties accounted for provides a robust and nondestructive tool for resource managers to monitor the status of coastal wetlands at a high spatial resolution in a timely manner. Through this study, we hope to emphasize the importance of appropriately accounting for nested data structures using mixed-effects models and promote wider application of Bayesian inference to facilitate assimilation of uncertainties in remote sensing applications.     

Evaluating Bayesian Radiocarbon-dated Event Count (REC) models for the study of long-term human and environmental processes

Chronological uncertainty complicates attempts to use radiocarbon dates as proxies for processes such as human population growth/decline, forest fires and marine ingression. Established approaches involve turning databases of radiocarbon-date densities into single summary proxies that cannot fully account for chronological uncertainty. Here, I use simulated data to explore an alternative Bayesian approach that instead models the data as what they are, namely radiocarbon-dated event counts. The approach involves assessing possible event-count sequences by sampling radiocarbon date densities and then applying a Markov Chain Monte Carlo method to estimate the parameters of an appropriate count-based regression model. The regressions based on individual sampled sequences were placed in a multilevel framework, which allowed for the estimation of hyperparameters that account for chronological uncertainty in individual event times. Two processes were used to produce simulated data. One represented a simple monotonic change in event-counts and the other was based on a real palaeoclimate proxy record. In both cases, the method produced estimates that had the correct sign and were consistently biased towards zero. These results indicate that the approach is widely applicable and could form the basis of a new class of quantitative models for use in exploring long-term human and environmental processes.