Uncertainty as the overlap of alternate conditional distributions

An important task in modern geostatistics is the assessment and quantification of resource and reserve uncertainty. This uncertainty is valuable support information for many management decisions. Uncertainty at specific locations and uncertainty in the global resource is of interest. There are many different methods to build models of uncertainty, including Kriging, Cokriging, and Inverse Distance. Each method leads to different results. A method is proposed to combine local uncertainties predicted by different models to obtain a combined measure of uncertainty that combines good features of each alternative. The new estimator is the overlap of alternate conditional distributions.     

Estimating the minimum in-stream flow requirements via wetted perimeter method based on curvature and slope techniques

Under the assumptions of triangular cross section channel and uniform stable flow, an analytical solution of the minimum ecological in-stream flow requirement (MEIFR) is deduced. Based on the analytical solution, the uncertainty of the wetted perimeter method is analyzed by comparing the two techniques for the determination of the critical point on the relationship curve between wetted perimeter, P and discharge, Q. It is clearly shown that the results of MEIFR based on curvature technique (corresponding to the maximum curvature) and slope technique (slope being 1) are significantly different. On the P-Q curve, the slope of the critical point with the maximum curvature is 0.39 and the MEIFR varied prominently with the change of the slope threshold. This indicates that if a certain value of the slope threshold is not available for slope technique, curvature technique may be a better choice. By applying the analytical solution of MEIFR in the losing rivers of the Western Route South-to-North Water Transfer Project in China, the MEIFR value via curvature technique is 2.5%-23.7% of the multi-year average annual discharge, while that for slope technique is 11%-105.7%. General conclusions would rely on the more detailed research for all kinds of cross-sections.     

Representing and communicating deep uncertainty in climate-change assessments

IPCC reports provide a synthesis of the state of the science in order to inform the international policy process. This task is made difficult by the presence of deep uncertainty in the climate problem that results from long time scales and complexity. This paper focuses on how deep uncertainty can be effectively communicated. We argue that existing schemes do an inadequate job of communicating deep uncertainty and propose a simple approach that distinguishes between various levels of subjective understanding in a systematic manner. We illustrate our approach with two examples. To cite this article: M. Kandlikar et al., C. R. Geoscience 337 (2005).     

铜镍硫化物铼-锇标准物质定值的溯源性讨论及总不确定度评估

对按国家一级标准物质技术规范研制的铜镍硫化物Re-Os标准物质定值的溯源性及其总不确定度进行讨论与评估。铜镍硫化物标准物质样品采用Carius管溶解,高精度的TRITON同位素质谱仪、MAT-262热电离质谱仪、四极杆等离子体质谱仪、多接收器等离子体质谱仪和高分辨四极杆等离子体质谱仪测量Re、Os含量和Os同位素比值,其中Re-Os含量可以溯源至基准物质,而187Os/188Os同位素比值可以溯源至国际纯粹与应用化学联合会(IUPAC)。在定值数据误差计算时,采用国际通用的ISOPLOT软件利用加权的方法对数据进行处理;在合成总不确定度时,考虑了物质的均匀性和稳定性,同时考虑了稀释剂标定和同位素丰度以及称量误差等影响测定因素的不确定度。标准值的不确定度由三部分组成:第一部分是通过所有参与定值数据,采用ISOPLOT软件,利用加权的方法对数据进行计算处理得到的不确定度;第二部分是物质的均匀性和稳定性的不确定度;第三部分是影响测定其他因素的不确定度。     

基于CMIP5多模式集合资料的中国气温和降水预估及概率分析

选用国际耦合模式比较计划第五阶段（CMIP5）提供的30个全球大气-海洋耦合模式（AOGCMs）在典型浓度路径（RCPs）情景下气温和降水量的预估结果,采用扰动法,用站点观测资料作为气候背景场替代AOGCM模拟的气候平均,尝试校正气候预估结果的系统性偏差。通过集合方法,用概率的形式给出中国平均气温升高1 ℃,2 ℃和3 ℃以及降水量增加10%,20%和30%概率的空间分布,讨论了中国未来平均气温和降水量可能的变化。结果表明：经过扰动法处理后的气温和降水量预估集合保留了当前气候的局地信息。预估平均气温在中国均有上升,北方地区尤其是青藏高原地区变暖的程度大于南方地区,北方大部分地区平均气温升高的趋势为0.28 ℃/10a。在21世纪初,中国北方地区年平均气温升高1 ℃的可能性超过50%。到了21世纪末期,中国大部分地区平均气温升高2 ℃的可能性超过60%,新疆北部以及青藏高原南部地区气温升高3 ℃的可能性超过50%。预估中国降水量普遍增多,中国北方地区降水量增多的程度要明显大于江淮流域及其以南地区,尤其是西北地区降水量增多非常显著,降水量增多30%的可能性超过70%以上。     

Method of Data Reduction and Uncertainty Estimation for Platinum-Group Element Data Using Inductively Coupled Plasma-Mass Spectrometry

A data reduction method is described for determining platinum-group element (PGE) abundances by inductively coupled plasma-mass spectrometry (ICP-MS) using external calibration or the method of standard addition. Gravimetric measurement of volumes, the analysis of reference materials and the use of procedural blanks were all used to minimise systematic errors. Internal standards were used to correct for instrument drift. A linear least squares regression model was used to calculate concentrations from drift-corrected counts per second (cps). Furthermore, mathematical manipulations also contribute to the uncertainty estimates of a procedure. Typical uncertainty estimate calculations for ICP-MS data manipulations involve: (1) Carrying standard deviations from the raw cps through the data reduction or (2) calculating a standard deviation from multiple final concentration calculations. It is demonstrated that method 2 may underestimate the uncertainty estimate of the calculated data. Methods 1 and 2 do not typically include an uncertainty estimate component from a regression model. As such models contribute to the uncertainty estimates affecting the calculated data, an uncertainty estimate component from the regression must be included in any final error calculations. Confidence intervals are used to account for uncertainty estimates from the regression model. These confidence intervals are simpler to calculate than uncertainty estimates from method 1, for example. The data reduction and uncertainty estimation method described here addresses problems of reporting PGE data from an article in the literature and addresses both precision and accuracy. The method can be applied to any analytical technique where drift corrections or regression models are used.     

Exploring the sensitivity of coastal inundation modelling to DEM vertical error

As sea level is projected to rise throughout the twenty-first century due to climate change, there is a need to ensure that sea level rise (SLR) models accurately and defensibly represent future flood inundation levels to allow for effective coastal zone management. Digital elevation models (DEMs) are integral to SLR modelling, but are subject to error, including in their vertical resolution. Error in DEMs leads to uncertainty in the output of SLR inundation models, which if not considered, may result in poor coastal management decisions. However, DEM error is not usually described in detail by DEM suppliers; commonly only the RMSE is reported. This research explores the impact of stated vertical error in delineating zones of inundation in two locations along the Devon, United Kingdom, coastline (Exe and Otter Estuaries). We explore the consequences of needing to make assumptions about the distribution of error in the absence of detailed error data using a 1 m, publically available composite DEM with a maximum RMSE of 0.15 m, typical of recent LiDAR-derived DEMs. We compare uncertainty using two methods (i) the NOAA inundation uncertainty mapping method which assumes a normal distribution of error and (ii) a hydrologically correct bathtub method where the DEM is uniformly perturbed between the upper and lower bounds of a 95% linear error in 500 Monte Carlo Simulations (HBM+MCS). The NOAA method produced a broader zone of uncertainty (an increase of 134.9% on the HBM+MCS method), which is particularly evident in the flatter topography of the upper estuaries. The HBM+MCS method generates a narrower band of uncertainty for these flatter areas, but very similar extents where shorelines are steeper. The differences in inundation extents produced by the methods relate to a number of underpinning assumptions, and particularly, how the stated RMSE is interpreted and used to represent error in a practical sense. Unlike the NOAA method, the HBM+MCS model is computationally intensive, depending on the areas under consideration and the number of iterations. We therefore used the HBM+ MCS method to derive a regression relationship between elevation and inundation probability for the Exe Estuary. We then apply this to the adjacent Otter Estuary and show that it can defensibly reproduce zones of inundation uncertainty, avoiding the computationally intensive step of the HBM+MCS. The equation-derived zone of uncertainty was 112.1% larger than the HBM+MCS method, compared to the NOAA method which produced an uncertain area 423.9% larger. Each approach has advantages and disadvantages and requires value judgements to be made. Their use underscores the need for transparency in assumptions and communications of outputs. We urge DEM publishers to move beyond provision of a generalised RMSE and provide more detailed estimates of spatial error and complete metadata, including locations of ground control points and associated land cover.     

Uncertainty analysis of CO_2 flux components in subtropical evergreen coniferous plantation

We present an uncertainty analysis of ecological process parameters and CO2 flux components (Reco, NEE and gross ecosystem exchange (GEE)) derived from 3 years’ continuous eddy covariance meas-urements of CO2 fluxes at subtropical evergreen coniferous plantation, Qianyanzhou of ChinaFlux. Daily-differencing approach was used to analyze the random error of CO2 fluxes measurements and bootstrapping method was used to quantify the uncertainties of three CO2 flux components. In addition, we evaluated different ...     

Robustness of Precipitation Projections in China:Comparison between CMIP5 and CMIP3 Models

Three sources of uncertainty in model projections of precipitation change in China for the 21st century were separated and quantified: internal variability,inter-model variability,and scenario uncertainty.Simulations from models involved in the third phase and the fifth phase of the Coupled Model Intercomparison Project(CMIP3 and CMIP5) were compared to identify improvements in the robustness of projections from the latest generation of models.No significant differences were found between CMIP3 and CMIP5 in terms of future precipitation projections over China,with the two datasets both showing future increases.The uncertainty can be attributed firstly to internal variability,and then to both inter-model and internal variability.Quantification analysis revealed that the uncertainty in CMIP5 models has increased by about 10%–60% with respect to CMIP3,despite significant improvements in the latest generation of models.The increase is mainly due to the increase of internal variability in the initial decades,and then mainly due to the increase of inter-model variability thereafter,especially by the end of this century.The change in scenario uncertainty shows no major role,but makes a negative contribution to begin with,and then an increase later.