一种高频雷达回波谱反演海浪的新算法

在高频地波雷达海浪谱反演问题中,广泛采用的Barrick后向散射公式属于第一类非线性Fredholm积分方程。此类积分方程的解在本质上是不适定的,加之高频雷达二阶回波信号信噪比较低,使得反演海浪谱存在解不稳定的问题。本文提出一种稳定且低复杂度的反演算法,此算法首先根据高频雷达一阶回波谱测量海浪方向,并将其引入积分方程求解过程,减少求解变量的个数,降低反演算法的复杂度。为解决反演结果不稳定的问题,使用Tikhonov正则化方法并利用广义交叉验证法(GCV)确定其正则化系数。通过在不同测试条件下对反演算法的仿真测试分析,表明此方法具有运算量小、稳定性好的特点。     

基于贝叶斯融合方法的高分辨率地面-卫星-雷达三源降水融合试验

为了探讨一种适用于区域性的地面、雷达、卫星等多源降水资料融合的方法,一种曾用于高分辨雷达、卫星土壤湿度产品反演的贝叶斯融合(Bayesian Merging)方法被尝试应用于江淮地区1 h-0.05°×0.05°经纬度高分辨率的雷达估测降水、卫星反演降水与地面站点观测降水3种资料的融合。在应用该方法时,通过2009年8月样本统计分别估计卫星和雷达反演降水的误差关系,通过曲线拟合建立误差方程,并以卫星资料作为背景场,但在融合时将雷达估测降水作为新的观测信息与地面观测降水同时引入。融合试验检验结果表明:贝叶斯融合方法能够有效实现雷达、地面、卫星3种不同来源资料的融合,该方法生成的多源融合产品的精度均优于任何单一来源的降水产品。     

基于贝叶斯模型的器测、古气候重建与气候模拟数据的融合试验

气象部门馆藏的西部最早的器测气象资料始于20世纪30年代,不能满足建立20世纪以来中国气候变化序列的需求,而古气候重建或气候模拟资料则可以延伸到器测时代以前。为了探讨长序列多源气候资料序列融合方法,采用贝叶斯方法对中国北疆地区8条树轮气温重建资料、器测资料与国际耦合模式比较计划第5阶段（CMIP5）模式模拟资料进行了融合试验。首先利用器测资料对气温代用资料进行校验与网格重建,并以此作为贝叶斯模型的先验分布,然后,用泰勒图选出了该区域气候模拟效果最佳的几个模式;最后将网格重建和气候模拟序列用贝叶斯模型进行了融合试验。结果表明,贝叶斯融合模型能有效提取各种数据来源的有用信息进行融合,融合结果的长期变化（线性）趋势更接近器测气候序列,并在一定程度上提高了序列的精度,减小了结果的不确定性;并且,融合结果能够纠正先验分布及气候模拟数据的明显偏差,为长年代气候序列重建提供了一个可行的思路。      

基于贝叶斯网络的地下水环境系统决策管理研究

应用贝叶斯网络解决地下水环境管理中具有不确定性的多目标决策问题,通过对决策变量氮肥施用量以及灌溉模式的调控,减少水中的硝酸盐含量,达到既能有效改善水环境又不至使农民经济利益受到损害的目标。通过分析具体的地下水环境管理系统中变量间的相互关系,构建描述变量间不确定性关系的贝叶斯网络模型,其中包括表示其依赖关系的有向无环图和表示其具体概率依赖程度的条件概率表。并在多个水环境管理目标均达到最优的前提下进行概率推理,得到决策变量氮肥施用量以及灌溉模式取不同值时目标变量的概率分布情况。最终确定出能使所有目标均达到最优的合理的水环境管理决策:(1)使用喷灌,将氮肥施用量控制在0.01~0.03 kg/m2;(2)使用漫灌,将氮肥施用量控制在0.01~0.02 kg/m2。     

Using a Bayesian estimator to combine information from a cluster analysis and remote sensing data to estimate high-resolution data for agricultural production in Germany

In Germany, a county-resolution data set that consists of 35 land-use and animal-stock categories has been used extensively to assess the impact of agriculture on the environment. However, because such environmental effects as emission or nutrient surplus depend on the location, even a county resolution might produce misleading results. The aim of this article is to propose a Bayesian approach which combines two sorts of information, with one being treated as defining the prior and the other the data to form a posterior, used to estimate a data set at a municipality resolution. We define the joint prior density function based on (i) remote sensing data, thus accounting for differences in county data and missing data at the municipality level, and (ii) the results of a cluster analysis that was previously applied to the micro-census, whereas the data are defined by official statistics at the county level. This approach results in a fairly accurate data set at the municipality level. The results, using the proposed method, are validated by the national research data centre by comparing the estimates to actual observations. The test statistics presented here demonstrate that the proposed approach adequately estimates the production activities.     

Evaluation of oceanic transport parameters using transient tracers from observations and model output

A method is presented to find the age distribution of ocean waters, the transit-time distribution (TTD), by combining an eddying global ocean model’s estimate of the TTD with hydrographic observations of CFC-11, temperature, and salinity. The method uses a mixture model of an assumed form of the TTD, an inverse Gaussian (IG), and an established Bayesian statistical method. All known significant sources of uncertainty are propagated to arrive at estimates of two oceanic transport parameters associated with the IG TTD, the mean age (Γ) and either the half-variance (${\mathrm{\Delta }}^2$) or the Peclet number ($\mathit{Pe}={\mathrm{\Gamma }}^2/{\mathrm{\Delta }}^2$). It is found that the uncertainties on Γ do not overlap zero in most locations using only CFC-11, temperature, and salinity. However, the uncertainty on the other IG parameter does not overlap zero in only a few locations. With the inclusion of another transient tracer (³He/³H), the uncertainty on this other IG parameter does not overlap zero in just a few additional locations in the deep North Atlantic Ocean. Neither a single- nor mixture-IG representation is adequate for representing the full TTD in the ocean, particularly in the Southern Ocean.Differences between the IG parameters estimated using the model’s tracers as data (BayesPOP) and those estimated using tracer observations as data (BayesObs) provide information about the sources of model biases, and give a more nuanced picture than can be found by comparing the simulated CFCs with observed CFCs. Using the differences between each of the oceanic transport parameters from BayesObs and those from BayesPOP with and without a constant Pe assumption along each of the hydrographic cross-sections considered here, it is found that the model’s eddy mixing biases often lead to larger model errors than the model’s mean advection time biases. It is also found that mean advection time biases in the model can be statistically significant at the 95% level where mode water is found in the Southern Ocean.     

基于最小支持的2.5维直流电阻率正则化反演研究

地球物理反问题存在多解性和不稳定性,正则化是得到稳定解的重要手段之一,正则化方法中稳定因子的设计与正则化因子的选择是两项重要研究内容。稳定因子的主要功能是对模型的解空间进行限制,以减少多解性,求得稳定解;为更好的定位地下目标体,研究工作采用了最小支持稳定因子,并给出了统一表达形式。正则化因子在模型误差与数据误差之间起到平衡作用,研究工作在＂L曲线法＂自动选取正则化因子的基础上,提出一种修正的计算正则化因子算法。以2.5维直流电阻率为例,运用非线性共轭梯度法,进行了试算研究,结果表明了修正的＂L曲线法＂算法快速、稳定,最小支持稳定因子具有较好的聚焦特性,有利于实现陡变边界反演。     

基于贝叶斯层次时空模型的甘肃省土地利用程度演变分析

以甘肃省为例,在基于Google Earth Engine (GEE)平台实现1995年、2000年、2005年、2010年、2015年和2020年土地变化监测的基础上,利用贝叶斯层次时空模型(BHM)分析土地利用程度的时空变化特征。结果表明：① 研究期间内甘肃省土地利用程度呈增长趋势,其中1995―2000年和2010―2015年增长速度较明显;② 土地利用程度空间格局“东高西低”,热点区域主要分布在陇中、陇东和陇南地区;③ 土地利用程度局部变化呈现明显区域差异,整体表现为“东弱西强”,局部变化热点区域主要分布在河西地区;④ 影响土地利用程度变化的主要因素是经济规模和产业结构,其中经济因素影响程度最高。     

基于贝叶斯网络的生态系统服务空间格局优化——以泾河流域为例

城市高速发展引起了区域土地利用格局的改变,不仅影响生态环境质量,而且还对生态系统服务的空间格局产生影响,在此基础上优化生态系统服务显得至关重要。在泾河流域2000—2020年净初级生产力（Net primary productivity, NPP）、农业生产力、土壤保持和产水服务空间评估的基础上,将贝叶斯网络和生态系统服务相结合,在关键变量子集和可视化的最优状态子集的基础上,评估了4种生态系统服务需要优化的区域,为区域经济和生态和谐发展提供参考。结果表明：（1） 水文评价模型（Soil and water assessment tool, SWAT）模型能较准确地模拟区域的径流量。通过模拟值和观测值对比分析,该模型具有较高的决定性系数（R²>0.6）和纳什效率系数（NSE>0.5）,可为进一步评估产水服务提供保障。（2） 2000—2020年泾河流域4种生态系统服务的时空差异性较为显著。在时间尺度上,4种生态系统服务均呈现波动中上升的趋势,在空间尺度上呈现较为稳定的变化趋势。（3） 通过对4种生态系统服务优化区域进行叠加分析,发现综合优化区域集中在彭阳县的中部和西南部以及环县的零星区域。研究结果对指导优化区域进行生态系统的可持续管理以及改善生态系统的退化状况具有重要意义。     

Bayesian area-to-point kriging using expert knowledge as informative priors

Area-to-point (ATP) kriging is a common geostatistical framework to address the problem of spatial disaggregation or downscaling from block support observations (BSO) to point support (PoS) predictions for continuous variables. This approach requires that the PoS variogram is known. Without PoS observations, the parameters of the PoS variogram cannot be deterministically estimated from BSO, and as a result, the PoS variogram parameters are uncertain. In this research, we used Bayesian ATP conditional simulation to estimate the PoS variogram parameters from expert knowledge and BSO, and quantify uncertainty of the PoS variogram parameters and disaggregation outcomes. We first clarified that the nugget parameter of the PoS variogram cannot be estimated from only BSO. Next, we used statistical expert elicitation techniques to elicit the PoS variogram parameters from expert knowledge. These were used as informative priors in a Bayesian inference of the PoS variogram from BSO and implemented using a Markov chain Monte Carlo algorithm. ATP conditional simulation was done to obtain stochastic simulations at point support. MODIS (Moderate Resolution Imaging Spectroradiometer) atmospheric temperature profile data were used in an illustrative example. The outcomes from the Bayesian ATP inference for the Matérn variogram model parameters confirmed that the posterior distribution of the nugget parameter was effectively the same as its prior distribution; for the other parameters, the uncertainty was substantially decreased when BSO were introduced to the Bayesian ATP estimator. This confirmed that expert knowledge brought new information to infer the nugget effect at PoS while BSO only brought new information to infer the other parameters. Bayesian ATP conditional simulations provided a satisfactory way to quantify parameters and model uncertainty propagation through spatial disaggregation.