Enhancing areal interpolation frameworks through dasymetric refinement to create consistent population estimates across censuses

To assess micro-scale population dynamics effectively, demographic variables should be available over temporally consistent small area units. However, fine-resolution census boundaries often change between survey years. This research advances areal interpolation methods with dasymetric refinement to create accurate consistent population estimates in 1990 and 2000 (source zones) within tract boundaries of the 2010 census (target zones) for five demographically distinct counties in the US. Three levels of dasymetric refinement of source and target zones are evaluated. First, residential parcels are used as a binary ancillary variable prior to regular areal interpolation methods. Second, Expectation Maximization (EM) and its data-extended version leverage housing types of residential parcels as a related ancillary variable. Finally, a third refinement strategy to mitigate the overestimation effect of large residential parcels in rural areas uses road buffers and developed land cover classes. Results suggest the effectiveness of all three levels of dasymetric refinement in reducing estimation errors. They provide a first insight into the potential accuracy improvement achievable in varying geographic and demographic settings but also through the combination of different refinement strategies in parts of a study area. Such improved consistent population estimates are the basis for advanced spatio-temporal demographic research.     

基于RS和GIS的人口估计方法研究综述

随着RS和GIS技术的迅速发展, RS和GIS成为进行人口估计的主要手段。根据人口估计的目标和使用的数据源不同,可以把基于RS和GIS的人口估计方法分成两大类：面插值方法和统计模型方法。面插值方法根据插值过程中是否使用辅助数据可以进一步分成无辅助数据的面插值和有辅助数据的面插值两种。统计模型方法根据模型中自变量的不同可以分成建成区面积估计法、土地利用密度法、居住单元估计法、图像像元特征估计法和自然和社会经济特征综合估计法五种。本文按照上述分类标准综述了基于RS和GIS的各种人口估计方法,分析了各种方法的应用条件、优缺点和研究实例。最后提出了在基于RS和GIS进行人口估计方面需要进一步研究的问题。     

A Point-Based Intelligent Approach to Areal Interpolation

Areal interpolation is the data transfer from one zonal system to another. A survey of previous literature on this subject points out that the most effective methods for areal interpolation are the intelligent approaches, which often take two-dimensional (2-D) land use or one-dimensional (1-D) road network information as ancillary data to give insight on the underlying distribution of a variable. However, the 2-D or 1-D ancillary information is not always applicable for the variable of interest in a specific study area. This article introduces a point-based intelligent approach to the areal interpolation problem by using zero-dimensional (0-D) points as ancillary data that are locationally associated with the variable of interest. The connection between zonal variables and point locations can be modeled with a linear or a nonlinear exponential function, which incorporates the distribution of the variables in the transferring of the information from the source zone to the target zone. An experimental study interpolating the population data at a suburbanized area suggests that the proposed method is an attractive alternative to other areal interpolation solutions based on the evaluation of its resulting accuracy and efficiency.     

面插值的研究进展

空间插值从广义上讲包括点插值和面插值 ,本文从有无辅助数据的角度介绍了还不为多数人熟知的面插值 ,在无辅助数据的方法中介绍了基于点的面插值法、面域比重插值法、使用控制区的面域比重法、Pycnophylactic面插值法等的算法和特点 ,在有辅助数据的方法中介绍了 EM算法和遥感作为辅助数据的面插值法 ,并介绍了面插值中的特例 -统计数据的空间化方法。     

Areal interpolation of spatially extensive variables: A comparison of alternative techniques

Abstract

This paper presents a methodology which provides a practicable solution to a specific class of areal interpolation problems. The method allows for the transformation of the areal basis of land use data from a set of reporting units to a set of land capability classes within each of which land use mix is assumed to be homogeneous. Three alternative procedures, based on least squares criteria, are suggested for estimation of the land use mix in each land class. Although these are shown to produce similar and broadly plausible results in an empirical application, choice of procedure may be guided by consideration of the particular application and computational ease.     

人口统计数据的空间转换

在经济和社会研究中,所要研究的区域之上经常没有数据,而这些数据需要由已知区域的数据求得,即统计数据需要空间转换,这就通常涉及到面积内插。本文从GIS的角度研究如何解决人口内插问题,认为面积内插和GIS中的叠加分析是一致的。在传统的面积内插方法的基础上是提出了基于人口真实分布的面积内插方法,并推导出了公式。同时提出了人口密度的递归算法,即把居住区分为人口稀疏地区和人口稠密地区,估计出人口稀疏地区的人口密度,就可以求出人口密集地区的人口密度;再把人口密集区分为新的人口稀疏区和密集区,此过程反复直至求出接近于人口真实分布的人口模型。     

Beyond the epsilon band: polygonal modeling of gradation/uncertainty in area-class maps

A spatial modeling technique is proposed to represent boundary uncertainty or gradation on area-class maps using a simple polygon tessellation with designated zones of indeterminacy or transition zones. The transition zone can be conceptualized as a dual of the epsilon band, but is more flexible and allows for a wide range of polygonal configurations, including polygons with sinuous boundaries, spurs, three-way transition zones, and null polygons. The model is specified using the medial axis to capture the general shape characteristics of a transition zone. Graph theoretic representation of an extended version of the medial axis captures key junctions in both shape and classification and is used to identify well-formed transition zones that can be logically and unambiguously handled by the model. A multivariate classification surface is specified by first defining degrees or probabilities of membership at every point on the medial axis and transition zone boundary. Degrees or probabilities of membership at all other points are defined by linear interpolation. The technique is illustrated with an example of a complex transition zone, and a simple isoline representation that can be derived from the model is presented. The proposed modeling technique promises to facilitate expert characterization of soil formations, ecological systems, and other types of areal units where gradation and/or boundary uncertainty are prevalent.     

Quantification of Uncertainty in Ore-Reserve Estimation: Applications to Chapada Copper Deposit,State of Goiás,Brazil

Ordinary kriging (OK) has been used widely for ore-reserve estimation because of its superior characteristics in relation to other methods. One of these characteristics is related to the quantification of uncertainty by the kriging variance. However, the kriging variance does not recognize local data variability, which is an important issue in the process of ore-reserve estimation, when heterogeneous mineral deposits with richer and poorer parts are being evaluated. This paper proposes the use of interpolation variance as a reliable measure of local data variability and, therefore, adequate for ore-reserve classification. With a reliable measurement of data variability, local confidence can be calculated using the classical confidence interval around an estimate. Errors derived from local confidence then are used to assign classes according to a degree of certainty within some confidence level. Comparative tests using both OK variance and interpolation variance are carried out using exploration data from Chapada Copper Deposit, State of Goiás, Brazil. Results show that the interpolation variance provides a better way to measure uncertainty and consequently to classify reserves.     

Uncertainty Estimate in Resources Assessment: A Geostatistical Contribution

For many decades the mining industry regarded resources/reserves estimation and classification as a mere calculation requiring basic mathematical and geological knowledge. Most methods were based on geometrical procedures and spatial data distribution. Therefore, uncertainty associated with tonnages and grades either were ignored or mishandled, although various mining codes require a measure of confidence in the values reported. Traditional methods fail in reporting the level of confidence in the quantities and grades. Conversely, kriging is known to provide the best estimate and its associated variance. Among kriging methods, Ordinary Kriging (OK) probably is the most widely used one for mineral resource/reserve estimation, mainly because of its robustness and its facility in uncertainty assessment by using the kriging variance. It also is known that OK variance is unable to recognize local data variability, an important issue when heterogeneous mineral deposits with higher and poorer grade zones are being evaluated. Altenatively, stochastic simulation are used to build local or global uncertainty about a geological attribute respecting its statistical moments. This study investigates methods capable of incorporating uncertainty to the estimates of resources and reserves via OK and sequential gaussian and sequential indicator simulation The results showed that for the type of mineralization studied all methods classified the tonnages similarly. The methods are illustrated using an exploration drill hole data sets from a large Brazilian coal deposit.     

Dasymetric Spatiotemporal Interpolation

This research applies the principles of dasymetric mapping to spatiotemporal interpolation by extending the spatial concepts of zone and area to their temporal analogs of interval and duration, respectively. An example application of dasymetric spatiotemporal interpolation using crime event data is presented. Results indicate that dasymetric spatiotemporal interpolation significantly improves the accuracy of estimates over areal or duration weighting. In addition, even when dasymetric interpolation in either the spatial or temporal dimension is relatively weak, combining dasymetric estimation in both space and time dimensions simultaneously has the potential to amplify the accuracy of the overall dasymetric estimation.     

Examining the influence of settlement morphology and separation zones policies on the availability of shallow coal resources in the United Kingdom

In 2013, demand for coal in the UK was 60 million tonnes. Of this, 12.7 million tonnes (21%) came from indigenous sources; the majority of which was from surface mining (8.6 million tonnes). Many planning applications for surface mining of coal and the coal extraction that follows, are often a source of conflict with the communities who live within shallow coalfield areas. Policies which enforce a gap, or ‘separation zone’, between communities and surface coal mining operations exist in Wales and Scotland, but do not exist in England. This paper examines the effect of applying separation zones on the availability of shallow coal resources within two study areas; one within the South Wales Coalfield, the other within the Midlands Coalfield (comprising the Yorkshire, Nottinghamshire and North Derbyshire Coalfield areas). Density profiles and a shape-index algorithm are used to compare and contrast settlement morphology (i.e. shape or footprint) and distribution to determine whether they have a bearing on the areal extent of any potential separation zone applied. The implications on the availability of shallow coal resources of applying different separation zone distances around settlements within these two areas are explored. Results reveal that although the settlement morphology is important in determining the area of the separation zone, and has greatest influence in the South Wales Coalfield, the area of coal resource sterilised by the application of separation zones is greatest in the Midlands Coalfield due to it having a higher proportion of urban development situated on the surface extent of the shallow coal resource.     

基于贝叶斯最大熵的甘肃省多年平均降水空间化研究

 贝叶斯最大熵方法可以对具有一定不确定性的“软数据”和认为没有误差的“硬数据”进行插值。对甘肃省1961—1990年52个气象站点的多年平均降水数据进行空间化研究。通过比较普通克里格、共协克里格、三元回归建模后残差插值以及基于贝叶斯最大熵的3种不同软硬数据参与情况下的插值结果,发现考虑降水30 a时间序列不完整性以及辅助变量经验模型不确定性的插值结果的MAE和RMSE,比直接使用多年平均降水数据直接插值的MAE和RMSE小,表明贝叶斯最大熵方法通过对不确定性的考虑可以有效降低预测结果的绝对误差。从降水的空间分布来看,考虑辅助变量DEM的插值结果能相对较好的体现高程对降水的地形影响,尤其分区将辅助变量转换为软数据可以有效体现不同区域高程对降水的不同影响问题。综合误差评价以及降水插值结果的空间分布,认为BME插值过程中可以考虑数据本身以及辅助数据利用的不确定性,使降水空间化的结果更加真实客观,同时为合理利用辅助信息提供了一个新思路。     

Spatial autocorrelation and data uncertainty in the American Community Survey: a critique

ABSTRACT

We argue that the use of American Community Survey (ACS) data in spatial autocorrelation statistics without considering error margins is critically problematic. Public health and geographical research has been slow to recognize high data uncertainty of ACS estimates, even though ACS data are widely accepted data sources in neighborhood health studies and health policies. Detecting spatial autocorrelation patterns of health indicators on ACS data can be distorted to the point that scholars may have difficulty in perceiving the true pattern. We examine the statistical properties of spatial autocorrelation statistics of areal incidence rates based on ACS data. In a case study of teen birth rates in Mecklenburg County, North Carolina, in 2010, Global and Local Moran’s I statistics estimated on 5-year ACS estimates (2006–2010) are compared to ground truth rate estimates on actual counts of births certificate records and decennial-census data (2010). Detected spatial autocorrelation patterns are found to be significantly different between the two data sources so that actual spatial structures are misrepresented. We warn of the possibility of misjudgment of the reality and of policy failure and argue for new spatially explicit methods that mitigate the biasedness of statistical estimations imposed by the uncertainty of ACS data.     

Modeling Sensitivity to Accuracy in Classified Imagery: A Study of Areal Interpolation by Dasymetric Mapping*

Areal interpolation is the process by which data collected from one set of zonal units can be estimated for another zonal division of the same space that shares few or no boundaries with the first. In previous research, we outlined the use of dasymetric mapping for areal interpolation and showed it to be the most accurate method tested. There we used control information derived from classified satellite imagery to parameterize the dasymetric method, but because such data are rife with errors, here we extend the work to examine the sensitivity of the population estimates to error in the classified imagery. Results show the population estimates by dasymetric mapping to be largely insensitive to the errors of classification in the Landsat image when compared with the other methods tested. The dasymetric method deteriorates to the accuracy of the next worst estimate only when 40% error occurs in the classified image, a level of error that may easily be bettered within most remote sensing projects.     

降雨信息空间插值的不确定性分析

文章以潮白河流域为样区,根据58个雨量站1990年的降雨观测数据,采用反距离权重法、克立格法、样条函数法、趋势面法等插值方法,分析了站点数量变化、时间尺度变化、栅格像元的尺度变化、插值方法的差异对降雨数据空间插值结果的影响,剖析降雨插值中的不确定性。结果表明：（1）插值站点数量越大,区域降雨插值的不确定性越小;（2）像元尺度在50m~1000m间变化对降雨插值的不确定性只有微弱的影响;（3）对应于时间尺度由年到月到日的变化,降雨插值的不确定性随时间尺度的减小而显著增大;（4）不同插值方法影响到降雨空间插值的不确定性水平。为了减少降雨信息空间插值的不确定性,根本途径是要引入第三方相关变量,并将其整合到现有的插值算法中。高相关性变量的选取及其与插值模型的整合方式将成为降雨插值研究的主导方向。     

Combining spatial transition probabilities for stochastic simulation of categorical fields

Categorical spatial data, such as land use classes and socioeconomic statistics data, are important data sources in geographical information science (GIS). The investigation of spatial patterns implied in these data can benefit many aspects of GIS research, such as classification of spatial data, spatial data mining, and spatial uncertainty modeling. However, the discrete nature of categorical data limits the application of traditional kriging methods widely used in Gaussian random fields. In this article, we present a new probabilistic method for modeling the posterior probability of class occurrence at any target location in space-given known class labels at source data locations within a neighborhood around that prediction location. In the proposed method, transition probabilities rather than indicator covariances or variograms are used as measures of spatial structure and the conditional or posterior (multi-point) probability is approximated by a weighted combination of preposterior (two-point) transition probabilities, while accounting for spatial interdependencies often ignored by existing approaches. In addition, the connections of the proposed method with probabilistic graphical models (Bayesian networks) and weights of evidence method are also discussed. The advantages of this new proposed approach are analyzed and highlighted through a case study involving the generation of spatial patterns via sequential indicator simulation.     

降雨量地面观测数据空间探索与插值方法探讨

空间插值方法广泛应用于气象数据产品的制作,其精度与气象要素的空间变异特征、气象观测站分布和插值方法选择有关。选择美国得州599个地面观测站30年平均降雨量记录,设计了27个观测站样本方案,选择全年、1月和8月数据,利用空间统计、空间自相关、半变异函数等方法探索降雨量的空间变异特征,并采用5种常规方法进行空间插值,比较和解释插值结果,在此基础上讨论基于知识的气象要素空间插值方法。案例研究发现:①降雨量地面观测数据通常具有明显的空间趋势、较强的空间自相关特征和较稳定的空间变异规律,但针对不同时段或采样方案,其空间自相关强度和半变异函数模型会有一定的差异。②增加气象观测站数,空间插值误差有减小的趋势;但观测站数目达到一定数值后,增加观测站数,插值精度提高并不明显。③在观测站较少时,不同插值方法间的精度差异较大,而在观测站充足的情况下,其差异有减小的趋势。④探讨气象要素与地理环境要素之间的关系,获得定量化的先验知识,开发基于知识的空间插值模型,是高精度气象要素插值的关键;线性加权回归和地理加权回归方法的初步试验验证了这一思路的有效性。     

基于Landsat-TM和MODIS的非洲水体分布格局研究

卫星遥感是进行洲际或者全球尺度内陆水体信息提取的最有效、最为切实可行的技术手段。作为全球水资源较为匮乏的大洲,以遥感技术进行非洲内陆水体信息提取研究具有重要的应用价值。文章以2010年Landsat TM/ETM+卫星遥感影像数据为基础,辅以MODIS遥感影像,基于面向对象的分类方法,选用归一化差值水体指数（Normalized Difference Water Index,NDWI）及波段组合（Band 4/Band 2）进行水体信息提取。并根据不同气候区,选取4个典型区,监测年内水体的变化情况。结果表明：1）非洲内陆水体面积为311 479.2 km2,其中湖泊总面积为209 018.5 km2,占水体总面积的67.1%;河渠总面积64 550.1 km2,占20.7%;水库坑塘总面积37 910.7 km2,占12.2%。非洲拥有水库211个,总面积13 438.7 km2。2）撒哈拉以南的非洲是水体主要的分布区,统计分析表明约97%的水体分布在该地区。3）热带沙漠气候区湖泊面积呈减少趋势,热带草原气候区湖泊受干湿季节影响上下波动较大,热带雨林气候区和地中海气候区湖泊面积变化较小,总体上4个典型区水体面积变差系数＜10%。     

Evaluating geo-located Twitter data as a control layer for areal interpolation of population

Control data are critical for improving areal interpolation results. Remotely sensed imagery, road network, and parcels are the three most commonly used ancillary data for areal interpolation of population. Meanwhile, the open access geographic data generated by social networks is emerging as an alternative control data that can be related to the distribution of population. This study evaluates the effectiveness of geo-located night-time tweets data as ancillary information and its combination with the three commonly used ancillary datasets in intelligent areal interpolation. Due to the skewed Twitter user age, the other purpose of this study is to test the effect of age bias control data on estimation of different age group populations. Results suggest that geo-located tweets as single control data does not perform as well as the three other control layers for total population and all age-specific population groups. However, the noticeable enhancement effect of Twitter data on other control data, especially for age groups with a high percentage of Twitter users, suggests that it helps to better reflect population distribution by increasing variation in densities within a residential area delineated by other control data.     

Error‐sensitive historical GIS: Identifying areal interpolation errors in time‐series data

Historical GIS has the potential to re‐invigorate our use of statistics from historical censuses and related sources. In particular, areal interpolation can be used to create long‐run time‐series of spatially detailed data that will enable us to enhance significantly our understanding of geographical change over periods of a century or more. The difficulty with areal interpolation, however, is that the data that it generates are estimates which will inevitably contain some error. This paper describes a technique that allows the automated identification of possible errors at the level of the individual data values.