STEP FUNCTION TECHNIQUE FOR ESTIMATING DATA UNCERTAINTY IN EXPERIMENTAL RESULTS

An additive model is used to express the observed value of a sample characteristic as the sum of the truesample characteristic and a value of the data collection error,commonly known as experimental error.The data uncertainty of the experimental results(or of a survey data set)is defined as the expectedsquared error.The expected squared error may change with the sample characteristic,e.g.the errormoment could be concentration-dependent.The relationship between the error variance and the analyteconcentration may not be very distinct.In such a case the data transformation to stabilize the errormoments may not be appropriate.A step function is proposed as an alternative way to represent thesecond moment of the error.The data uncertainty is defined as the weighted average of the step valuesof the second raw moment of the error,using the appropriate proportions of the routine samples asweights.The data uncertainties associated with the different data collection stages were evaluated by usingregional soil survey data.     

THREE-WAY METHODS FOR THE CALIBRATION OF CHROMATOGRAPHIC SYSTEMS:COMPARING PARAFAC AND THREE-WAY PLS

For the calibration of chromatographic systems,different methods can be used.One class of methodsutilizes three-way approaches.The calibration problem is stated in such a way that the decompositionof a three-way array can serve for the prediction of retention on new stationary phases.Two three-way approaches are presented:the Unfold-PCA and PARAFAC models.The theory ofboth methods is presented and the differences are highlighted,the main difference being that PARAFACis a trilinear decomposition whereas Unfold-PCA is not.Both three-way methods are evaluated on asmall data set consisting of retention measurements of eight solutes at six mobile phase compositions onsix stationary phases.The differences in performance of the two models are minor,For calibration purposes,two variants of the methods are discussed:three-way PLS and an extensionof PARAFAC.Again the theory and differences between the two methods are explained.The predictiveperformance of the two methods is compared using the same data set as earlier.The differences inpredictive performance,however,are minor.Both methods are capable of predicting 98% of thevariation in the test sets.Yet,there are other considerations when comparing methods than predictiveperformance,e.g.the quality of the predictions.     

The statistical distribution of magnetotelluric apparent resistivity and phase

The marginal distributions for the magnetotelluric (MT) magnitude squared response function (and hence apparent resistivity) and phase are derived from the bivariate complex normal distribution that describes the distribution of response function estimates when the Gauss–Markov theorem is satisfied and the regression random errors are normally distributed. The distribution of the magnitude squared response function is shown to be non-central chi-squared with 2 degrees of freedom, with the non-centrality parameter given by the squared magnitude of the true MT response. The standard estimate for the magnitude squared response function is biased, with the bias proportional to the variance and hence important when the uncertainty is large. The distribution reduces to the exponential when the expected value of the MT response function is zero. The distribution for the phase is also obtained in closed form. It reduces to the uniform distribution when the squared magnitude of the true MT response function is zero or its variance is very large. The phase distribution is symmetric and becomes increasingly concentrated as the variance decreases, although it is shorter-tailed than the Gaussian. The standard estimate for phase is unbiased. Confidence limits are derived from the distributions for magnitude squared response function and phase. Using a data set taken from the 2003 Kaapvaal transect, it is shown that the bias in the apparent resistivity is small and that confidence intervals obtained using the non-parametric delta method are very close to the true values obtained from the distributions. Thus, it appears that the computationally simple delta approximation provides accurate estimates for the confidence intervals, provided that the MT response function is obtained using an estimator that bounds the influence of extreme data.     

北太平洋海面温度的年变化型及区划

本文用主成分分析方法,根据1949—1987年北太平洋286个格点的月平均海面温度资料,求得北太平洋海面温度的12种年变化型。讨论了前三种年变化型(占总方差的95%)的特点。分别计算了前三种年变化型对各格点的贡献率,再根据贡献率的空间分布图,将北太平洋海面温度分成八个区域,每个区域海温都有各自的统计特征。     

Automatically enhancing CityGML LOD2 models with a corresponding indoor geometry

The international standard CityGML defines five levels of detail (LODs) for 3D city models, but only the highest of these (LOD4) supports modelling the indoor geometry of a building, which must be acquired in correspondingly high detail and therefore at a high cost. Whereas simple 3D city models of the exterior of buildings (e.g. CityGML LOD2) can be generated largely automatically, and are thus now widely available and have a great variety of applications, similarly simple models containing their indoor geometries are rare.

In this paper we present two contributions: (i) the definition of a level of detail LOD2+, which extends the CityGML LOD2 specification with indoor building geometries of comparable complexity to their exterior geometries in LOD2; and more importantly (ii) a method for automatically generating such indoor geometries based on existing CityGML LOD2 exterior geometries. We validate our method by generating LOD2+ models for a subset of the Rotterdam 3D data set and visually comparing these models to their real counterparts in building blueprints and imagery from Google Street View and Bing Maps. Furthermore, we use the LOD2+ models to compute the net internal area of each dwelling and validate our results by comparing these values to the ones registered in official government data sets.     

ENHANCING THE DECONVOLUTION OF NOISY CHROMATOGRAPHIC DATA BY JANSSON''S METHOD

In previous papers Jansson's method was found to be successful at deconvolving severely overlapped gaschromatographic peaks.In the most recent paper the method was evaluated with respect to quantitativeaceuracy,peak area and retention time repeatability.The problems associated with deconvolving noisydata and some alternatives which can improve the ability of Jansson's method to deconvolve noisy dataare discussed.These alternatives include presmoothing the data with a nine-point,third-order polynomialfilter and data reblurring.This paper will test these methods on peaks with various degrees of resolutionand signal-to-noise ratios.     

EVALUATION OF MODEL PERFORMANCE WHEN THE OBSERVED DATA ARE SUBJECT TO ERROR

In many cases of model evaluation in physical geography, the observed data to which model predictions are compared may not be error free. This paper addresses the effect of observational errors on the mean squared error, the mean bias error and the mean absolute deviation through the derivation of a statistical framework and Monte Carlo simulation. The effect of bias in the observed values may either decrease or increase the expected values of the mean squared error and mean bias error, depending on whether model and observational biases have the same or opposite signs, respectively. Random errors in observed data tend to inflate the mean squared error and the mean absolute deviation, and also increase the variability of all the error indices considered here. The statistical framework is applied to a real example, in which sampling variability of the observed data appears to account for most of the difference between observed and predicted values. Examination of scaled differences between modelled and observed values, where the differences are divided by the estimated standard errors of the observed values, is suggested as a diagnostic tool for determining whether random observational errors are significant.     

A TEST OF THREE FITTING CRITERIA FOR MULTIRESPONSE NON-LINEAR MODELING

This work evaluates objective functions for multiresponse non-linear modeling using computersimulations.Tests are performed under a variety of signal-to-noise ratios and noise variance-covariancestructures.The standard error of prediction for the model parameters,computed from 50 trials,is usedfor performance comparisons.The full rank and rank-deficient problems are considered.For the fullrank problem one model was investigated,a first-order two-step consecutive reaction model,and twoobjective functions were considered,the total sum of squares and the determinant criterion.Nodistinction could be made between the two objective functions for this model.For the rank-deficient case two models were investigated,a first-order two-step consecutive reactionas in the full rank case,and a pH titration model described by the Henderson-Hasselbalch equation.Three objective functions were investigated for the rank-deficient case,the total sum of squares,aweighted total sum of squares and the determinant criterion.The total sum of squares was found toperform poorly under all conditions tested compared to the weighted total sum of squares and thedeterminant criterion.The determinant criterion was found to perform much better than the other twocriteria when the data have a combination of a low signal-to-noise ratio and high variance-covariancenoise structure.     

THE GEOMETRY OF MULTIVARIATE OBJECT PREPROCESSING

The geometric properties of three common object-preprocessing transformations(constant sum,orclosure;constant length,or normalization;and maximum value,or ratioing)are investigated.Anargument is made for using absolute values in the constant sum and maximum value transformations.In general,each transformation distorts the shape and dimensionality of patterns in the data:transformed data lie on(C-l)-dimensional surfaces in the original C-dimensional space.A data set thathas been closed by one of these transformations can be reopened if a vector containing the constant sums,constant lengths or maximum values of the original objects was retained.Transformed data sets may befreely interconverted among these three transformations without the loss of information.     

A TEST OF SIGNIFICANCE FOR PARTIAL LEAST SQUARES REGRESSION

Partial least squares (PLS) regression is a commonly used statistical technique for performingmultivariate calibration, especially in situations where there are more variables than samples. Choosingthe number of factors to include in a model is a decision that all users of PLS must make, but iscomplicated by the large number of empirical tests available. In most instances predictive ability is themost desired property of a PLS model and so interest has centred on making this choice based on aninternal validation process. A popular approach is the calculation of a cross-validated r~2 to gauge howmuch variance in the dependent variable can be explained from leave-one-out predictions. Using MonteCarlo simulations for different sizes of data set, the influence of chance effects on the cross-validationprocess is investigated. The results are presented as tables of critical values which are compared againstthe values of cross-validated r~2 obtained from the user's own data set. This gives a formal test forpredictive ability of a PLS model with a given number of dimensions.     

无定河流域侵蚀产沙过程对水土保持措施的响应

以黄河中游多沙粗沙区代表性支流无定河为例,研究了降水量变化的背景下水土保持措施对无定河流域侵蚀产沙的影响。从总体上看,年输沙量和年径流量都表现出随时间而减小的趋势,梯田、造林、种草和淤地坝拦沙造地4项水土保持措施面积随时间增大的趋势极其显著。全流域面平均年降水量和汛期 (6~9月) 降水量则略有减少的趋势,但其减少趋势的显著性远低于水土保持措施随时间变化的显著性。产沙模数与梯田、坝地、造林和种草面积的关系,均表现出明显的负相关。对基准期 (1956~1969年) 和措施期 (1970~1996) 进行了比较,结果表明,实施水土保持措施以后,产沙模数、径流系数和汛期径流能够被降水所解释的百分比,分别由69%、80%和77%,下降为26%、31%和54%。说明在后一时期中,水土保持措施起了很大作用,因而降水变化对于产沙模数、径流系数、汛期径流量变化的贡献率大大减小了。以1956~1996年间41年的资料为基础,建立了全沙产沙模数与径流系数、汛期降雨量、最大一日雨量、最大30日累积雨量、梯田林草面积和坝地面积之间的多元回归方程,该方程表明,全沙产沙模数随汛期降雨量、最大一日雨量、最大30日累积雨量的增大而增大,随梯田林草面积和坝地面积的增大而减小, 随径流系数的增大而增大。为了区分人为因素与气候变化对侵蚀产沙变化的影响,采用对数据进行标准化处理之后再进行多元回归分析的方法,来确定相对贡献率。结果表明,降水变化和水土保持措施变化对无定河全沙产沙模数变化的贡献率大致相等,前者占50.3%,后者占49.7%。文中还建立了粗泥沙产沙模数与上述影响因子之间的多元回归方程。     

Spatially-explicit sensitivity and uncertainty analysis in a MCDA-based flood vulnerability model

This study presents a methodology for conducting sensitivity and uncertainty analysis of a GIS-based multi-criteria model used to assess flood vulnerability in a case study in Brazil. The paper explores the robustness of model outcomes against slight changes in criteria weights. One criterion was varied at-a-time, while others were fixed to their baseline values. An algorithm was developed using Python and a geospatial data abstraction library to automate the variation of weights, implement the ANP (analytic network process) tool, reclassify the raster results, compute the class switches, and generate an uncertainty surface. Results helped to identify highly vulnerable areas that are burdened by high uncertainty and to investigate which criteria contribute to this uncertainty. Overall, the criteria ‘houses with improper building material’ and ‘evacuation drills and training’ are the most sensitive ones, thus, requiring more accurate measurements. The sensitivity of these criteria is explained by their weights in the base run, their spatial distribution, and the spatial resolution. These findings can support decision makers to characterize, report, and mitigate uncertainty in vulnerability assessment. The case study results demonstrate that the developed approach is simple, flexible, transparent, and may be applied to other complex spatial problems.     

Urban sprawl: neighbourhood dissatisfaction and urban preferences. Some evidence from Flanders

Early studies suggest that people living in rural neighbourhoods are more satisfied with their residential location than people living in cities. Consequently, most individuals seem to prefer low-density environments to reside in. More recent studies, however, state that rural residents are no more likely to be satisfied with their residential neighbourhood than their urban counterparts. In addition, a considerable, growing part of the population seems to have a clear preference for urban neighbourhoods. The results of our research, conducted in Flanders, Belgium, suggest that urbanites are more satisfied with their neighbourhood than rural residents are. Neighbourhood preferences differ less between urbanites and rural residents. However, there are differences indicating that urbanites have a preference for rural neighbourhoods and rural residents a preference for urban neighbourhoods. In sum, it seems that people, once they have selected their residential location, are not satisfied with the neighbourhood characteristics and tend to develop a preference for a different neighbourhood type. This mismatch can be partly explained by the strongly developed urban sprawl in Flanders, reducing the residential qualities of urban and especially rural environments. Restricting further urban sprawl, with the help of a more active spatial planning policy, seems necessary to increase neighbourhood satisfaction.     

Two-dimensional finite-difference model of seafloor compliance

Seafloor compliance is the measure of seafloor deformation under a pressure signal. Our new 2-D finite-difference compliance modelling algorithm presents several advantages over the existing compliance models, including the ability to handle any gridded subsurface structure with no limitations on the gradients of the material properties, as well as significantly improved performance. Applying this method to some of the problems inaccessible to previously existing methods, demonstrates that lateral variations in subsurface structure must be accounted for to adequately interpret compliance data. In areas with significant lateral variations, the utilization of 1-D modelling and inversion is likely to result in high interpretation errors, even when additional subsurface structure information is available. We find that flattened pure melt bodies have a significantly higher compliance than cylindrical melt bodies with the same cross-sectional area. The compliance created by such bodies often has side peaks over their edges, which are as strong as or stronger than the central peak, requiring a series of measurements to best constrain their size and shear velocity. Finally, we find that the compliance data are far and away most sensitive to the broad, thick, lower-crustal partial melt zone. Our simple data fitting model for the compliance measurements on the East Pacific Rise at 9°48'N required shear velocities as low as 700 m s⁻¹ in the centre of this zone, far below the values previously estimated using 1-D model based inversions, suggesting higher melt percentages than those previously estimated, while small melt bodies in the upper part of the crust were found to have little or no effect on the measured compliance.     

THE USE OF A CROSS-CORRELATION TECHNIQUE TO ENHANCE JANSSON''S DECONVOLUTION PROCEDURE

The use of a cross-correlation prefiltering technique to enhance the ability of Jansson's iterativedeconvolution procedure to deconvolve extremely noisy chromatographic data is investigated.Test casesinclude peaks whose resolutions are as low as 0.35 and whose signal-to-noise ratios are as low as 1:1.Evaluation criteria include RMS error,relative peak error and peak area repeatability.For comparisonpurposes,relative peak area errors and peak area variances are also evaluated for noisy but well resolvedpeaks that have only been prefiltered with the cross-correlation filter.Jansson's method in conjunctionwith cross-correlation prefiltering is shown not only to resolve overlapped peaks but in some cases toimprove their signal-to-noise ratios.The study also establishes some limits to the capabilities of Jansson'smethod will regard to adverse data conditions.     

空间数据挖掘的地理案例推理方法及试验

从空间数据挖掘的角度谈地理案例推理方法,认为地理案例推理是面向问题的一种空间数据挖掘方法。针对这一思想进行了基于地理案例的空间数据挖掘具体算法介绍。首先在明确地理案例具体定义的基础上,给出了面向问题的空间数据挖掘地理案例界定和组织方法;其次,鉴于地理空间的自然地带性和区域分异性规律的影响,深入探讨了地理案例自身或其间所可能存在的相互依赖和相互制约关系,并给出了采用粗糙集方法进行地理案例内蕴空间关系的定量挖掘方法;第三,针对地理案例表达时考虑的空间特征和空间关系的不同,给出了三种状况下的空间相似性计算模型;最后,以土地利用这一典型的地学现象为例,给出具体实例,一方面进行土地利用问题的定量分析与推测;另一方面,通过实例展示地理案例推理方法在地学问题求解以及空间数据定量分析上的特点和优势。     

Soil erosion assessment tools from point to regional scales—the role of geomorphologists in land management research and implementation

Geomorphological research has played an important role in the development and implementation of soil erosion assessment tools. Because policy and management approaches include the use of soil erosion assessment tools, soil erosion research directly affects the public in terms of providing information on natural hazards and human impacts, and also as the basis for regulatory policy on land management. For example, soil loss calculations and geomorphological expertise are used to support soil conservation planning, both through agricultural legislation that defines maximum tolerable soil loss rates, and through federal and local legislation that requires soil erosion controls on many construction sites.To be useful for decision makers, soil erosion models must have simple data requirements, must consider spatial and temporal variability in hydrological and soil erosion processes, and must be applicable to a variety of regions with minimum calibration. The growing use of erosion models and Geographic Information Systems (GIS) in local to regional scale soil and water conservation raises concerns about how models are used. This has prompted interest in methods to assess how models function at management scales and with the types of data that are commonly available to users. A case study of a GIS-based soil erosion assessment tool using the process-based Water Erosion Prediction Project (WEPP) shows that using commonly available data rather than research grade data can have (predictably) a significant impact on model results. If model results are then used in management decisions, it is critical to assess whether the scale and direction of variation in results will affect management and policy decisions. Geomorphologists provide unique perspectives on soil erosion and can continue to affect policy through soil erosion research. This research should focus on fundamental processes, but equally important is continued development and evaluation of models that are matched to real world data availability, geomorphic settings, and information needs.     

长江上游干支流悬移质含沙量的变化及其原因

河流含沙量的变化是流域自然与人文因子变化的反映。以长江上游干支流1956~2000年的水沙和降水资料为基础,运用时间系列分析和统计分析方法进行研究。研究发现,干流宜昌站和4条主要支流含沙量的变化不是同步的,4条主要支流含沙量的变化呈现出复杂变化图形。流域面平均年降水量的变化,仅能解释含沙量变化的15.86%~37.21%,说明气候因素的变化不是长江干支流含沙量变化的主要原因。运用双累积曲线分析方法,研究了人类活动 (如水库修建,交通、矿山和城市建设,水土保持,植被破坏和恢复等 )对含沙量变化的影响。人类活动影响在不同的流域有较大差异。与4条主要支流相比,长江干流宜昌站含沙量的变化较小,反映了尺度效应的影响。多元回归分析表明,屏山 、高场、北碚、武隆4站的年均含沙量变化对宜昌站年均含沙量变化的贡献率分别为28.5%、12.6%、44.2%和14.7%。     

基于时空窗口改进的时空加权回归分析——以湖北省黄石市住房价格为例

针对地理加权回归(GWR)模型不能有效处理样本数据空间自相关性这一问题,构造局部时空窗口统计量,尝试改进时空加权回归(GTWR)模型。定义多时空窗口的概念,给出其选取、计算和验证方法;计算时空窗口包含的各样本点的被解释变量平均值,与样本拟合点的被解释变量值的比值,作为新的解释变量,构建改进的时空加权回归(IGTWR)模型。以土地稀缺、多中心、资源型城市——湖北省黄石市为例,收集2007~2012年商品住宅成交价格1.93万个数据和398个楼栋样本点,选取小区等级、绿化率、楼栋总层数、容积率、距区域中心距离和销售年份6个解释变量,分别利用常规线性回归(OLS)、GWR、GTWR和IGTWR方法进行回归分析。模型结果表明：计算Moran’s I指数和分析时间序列的自相关性,能确定时空窗口的大小和数量的选取;IGTWR模型和各变量的回归统计均通过0.05的显著性水平检验,有关解释变量的系数估计值在空间分布上能合理解释;GWR拟合结果优于OLS,GTWR优于GWR,而IGTWR拟合精度最好。与GTWR模型分析相比, IGTWR模型R²从0.877提升到0.919,而AICc、残差方(RSS)和均方差(MSE)分别从6 226、49 996 201和354.427下降到6 206、32 327 472和284.969。案例研究表明：IGTWR能够表达一定时空范围的时空自相关特征,减小了估计误差,提高了回归拟合精度。     

Paedomorphosis and shell-colour polymorphism of a desert landsnail

Environmentally-driven paedomorphosis, the retention of juvenile characteristics by adults, is an overlooked alternative to adaptive genetic hypotheses regarding shell colour in landsnails. We previously considered two adaptive explanations of shell-colour polymorphism in the desert landsnailTrochoidea simulata, namely temperature and predation. However, neither of these factors adequately explained this colour variation. We subsequently described the importance of available CaCO₃as the driving force underlying colour variation in this species. Here we consider the consequences of differential access to CaCO₃by individuals of different colour morphs. We describe variation in shell shape of different colour morphs, and conclude that shell-colour variation in this species is a consequence of paedomorphosis in brown individuals. Individuals may change colour ontogenetically from brown to white, while some remain brown-shelled throughout their lives. Brown snails, like juveniles, are thin- and flat-shelled, and have relatively larger apertures than white snails. This paedomorphosis is environmentally-based, being correlated with soil CaCO₃content.