A Comparative Analysis of Areal Interpolation Methods

Over the years many approaches to areal interpolation have been developed and utilized. They range from the simple 2-D areal weighing method which uses only the spatial Z variable being processed, to more sophisticated approaches which use auxiliary variable(s) to provide more specificity to the results. In the research reported here, four promising approaches are implemented and comparatively tested. These approaches have widely varying conceptual foundations, and different auxiliary variables, if used. The areal weighing reflects many earlier methods which assumes uniform distributions of the spatial Z variable, and does not use any auxiliary variable. Tobler's pycnophylactic method uses a volumetric preservation approach, which assumes spatial Z variable is heterogeneously distributed, but does not use any auxiliary variable. The traditional dasymetric method of Wright is used with remote sensing spectral data of land use. Xie's road network hierarchically weighted interpolation uses the road network as the auxiliary variable, and assumes that population density is related to the class of the road, and to the density of the road network. The research design implemented here uses Census population distributions at different levels in the hierarchy as the source and target variables analyzed. The source zone population is taken at the Census Tract level, and the target zones are specified at the Census Block Group level in the hierarchy. The first two tests use only the Census population Z data, and no auxiliary variables, whereas the next uses remotely sensed land use data as the auxiliary data variable, and the fourth test utilizes the road network hierarchy as the auxiliary variable. The paper reports on the findings from these tests, and then interprets them in a spatial setting in terms of accuracy and effectiveness. This research points to the network method as the most accurate of the areal interpolation methods tested in this research.     

Data-enriched interpolation for temporally consistent population compositions

This research evaluates the performance of areal interpolation coupled with dasymetric refinement to estimate different demographic attributes, namely population sub-groups based on race, age structure and urban residence, within consistent census tract boundaries from 1990 to 2010 in Massachusetts. The creation of such consistent estimates facilitates the study of the nuanced micro-scale evolution of different aspects of population, which is impossible using temporally incompatible small-area census geographies from different points in time. Various unexplored ancillary variables, including the Global Human Settlement Layer (GHSL), the National Land-Cover Database (NLCD), parcels, building footprints and the proprietary ZTRAX® dataset are utilized for dasymetric refinement prior to areal interpolation to examine their effectiveness in improving the accuracy of multi-temporal population estimates. Different areal interpolation methods including Areal Weighting (AW), Target Density Weighting (TDW), Expectation Maximization (EM) and its data-extended approach are coupled with different dasymetric refinement scenarios based on these ancillary variables. The resulting consistent small area estimates of white and black subpopulations, people of age 18–65 and urban population show that dasymetrically refined areal interpolation is particularly effective when the analysis spans a longer time period (1990–2010 instead of 2000–2010) and the enumerated population is sufficiently large (e.g., counts of white vs. black). The results also demonstrate that current census-defined urban areas overestimate the spatial distribution of urban population and dasymetrically refined areal interpolation improves estimates of urban population. Refined TDW using building footprints or the ZTRAX® dataset outperforms all other methods. The implementation of areal interpolation enriched by dasymetric refinement represents a promising strategy to create more reliable multi-temporal and consistent estimates of different population subgroups and thus demographic compositions. This methodological foundation has the potential to advance micro-scale modeling of various subpopulations, particularly urban population to inform studies of urbanization and population change over time as well as future population projections.     

A New GIS-based Solar Radiation Model and Its Application to Photovoltaic Assessments

The solar radiation model r.sun is a flexible and efficient tool for the estimation of solar radiation for clear‐sky and overcast atmospheric conditions. In contrast to other models, r.sun considers all relevant input parameters as spatially distributed entities to enable computations for large areas with complex terrain. Conceptually the model is based on equations published in the European Solar Radiation Atlas (ESRA). The r.sun model was applied to estimate the solar potential for photovoltaic systems in Central and Eastern Europe. The overcast radiation was computed from clear‐sky values and a clear‐sky index. The raster map of the clear‐sky index was computed using a multivariate interpolation method to account for terrain effects, with interpolation parameters optimized using a cross‐validation technique. The incorporation of terrain data improved the radiation estimates in terms of the model's predictive error and the spatial pattern of the model outputs. Comparing the results of r.sun with the ESRA database demonstrates that integration of the solar radiation model and the spatial interpolation tools in a GIS can be especially helpful for data at higher resolutions and in regions with a lack of ground measurements.     

Integrating the Huff Model and Floating Catchment Area Methods to Analyze Spatial Access to Healthcare Services

Analysis of spatial access to healthcare services is critical for effective health resource planning. Gravity‐based spatial access models have been widely used to estimate spatial access to healthcare services. Among them, the floating catchment area (FCA) methods have been proved to be informative and helpful to the designation of Health Professional Shortage Areas (HPSAs). This article integrates the Huff Model with the FCA method to articulate population selection on services. Through the proposed approach, population demand on healthcare services is adjusted by a Huff Model‐based selection probability that reflects the impacts of both distance impedance and service site capacity. The new approach moderates the over‐ or under‐estimating of population demand that occurred with previous methods. Furthermore, the method uses a continuous distance impedance weight function instead of the arbitrarily defined subzones of previous studies. A case study of spatial access to primary care in Springfield, MO, showed that the proposed method can effectively moderate the population demand on service sites and therefore can generate more reliable spatial access measures.     

A GIS‐based Approach in Support of an Assessment of Food Safety Risks

A Geographical Information System (GIS)‐based approach was developed for the identification of vulnerabilities and the measurement of risks associated with contamination of food systems with biological agents. In this research work, a tight integration of ArcGIS with the Arena simulation tool has been implemented. Arena was used to simulate and track contamination in a food distribution network and transmit the time dependent information to GIS. ArcGIS was employed to provide the primary user interface, process network data, and visualize the results. In addition, the GIS, through its powerful capabilities to process spatial data, could allow decision‐ makers to quickly determine the potential impact of a contamination event, at any stage, as a function of both time and geography. Two contamination scenarios along the farm‐to‐fork chain were examined to show the geographic zone and the proportion of the population affected by the contamination. A constraint Voronoi data structure was developed to define influence zones (these were color coded according to a dynamic risk index), to identify those areas that are at greatest immediate risk as time progresses, and to estimate the population affected by these contamination events. This approach thus appears to have general application to many GIS‐based risk assessment problems.     

Street‐level Spatial Interpolation Using Network‐based IDW and Ordinary Kriging

This study proposes network‐based spatial interpolation methods to help predict unknown spatial values along networks more accurately. It expands on two of the commonly used spatial interpolation methods, IDW (inverse distance weighting) and OK (ordinary kriging), and applies them to analyze spatial data observed on a network. The study first provides the methodological framework, and it then examines the validity of the proposed methods by cross‐validating elevations from two contrasting patterns of street network and comparing the MSEs (Mean Squared Errors) of the predicted values measured with the two proposed network‐based methods and their conventional counterparts. The study suggests that both network‐based IDW and network‐based OK are generally more accurate than their existing counterparts, with network‐based OK constantly outperforming the other methods. The network‐based methods also turn out to be more sensitive to the edge effect, and their performance improves after edge correction. Furthermore, the MSEs of standard OK and network‐based OK improve as more sample locations are used, whereas those of standard IDW and network‐based IDW remain stable regardless of the number of sample locations. The two network‐based methods use a similar set of sample locations, and their performance is inherently affected by the difference in their weight distribution among sample locations.     

草地地上生物量高精度曲面建模

草地生物量的大区域精确估算对全球变化研究和草地资源的合理利用具有重要作用。为提高草地生物量的空间模拟精度,发展了草地地上生物量的高精度曲面建模方法HASM-GB(High Accuracy Surface Modeling for Grassland Biomass),基于内蒙古草地地上生物量野外调查资料和同时期的遥感影像数据,采用HASM-GB方法对内蒙古自治区草原地上生物量空间分布进行了模拟。通过野外实测数据采用修正的Jackknifing方法对HASM-GB方法模拟结果进行了验证,结果表明模拟结果与实测数据之间具有较低的均方根误差(28.03 g/m²)和较好的相关性,相关系数为0.62。将HASM-GB方法与遥感生物量回归模型、普通克里金和回归克里金3种方法进行了精度对比,结果表明与其他3种方法相比,HASM-GB方法的模拟结果具有相对较低的平均误差、平均绝对误差、均方根误差和与测定值较高的相关系数。通过对地上生物量空间分布格局模拟结果的分析可知,由于植被指数-生物量回归模型属于非空间方法,其模拟精度很大程度上取决于主、辅变量间的相关性水平,易受植被指数数据误差的影响。普通克里金不能考虑辅助变量的作用。HASM-GB方法能够充分考虑生物量采样点和辅助变量的空间变异信息和邻域样本的空间结构特征从而提高模拟精度,其对草地地上生物量的曲面模拟能力高于回归克里金。结果表明HASM-GB可以作为模拟草地地上生物量空间分布相对有效的方法。     

A New 3‐D Solar Radiation Model for 3‐D City Models

Estimates of solar radiation distribution in urban areas are often limited by the complexity of urban environments. These limitations arise from spatial structures such as buildings and trees that affect spatial and temporal distributions of solar fluxes over urban surfaces. The traditional solar radiation models implemented in GIS can address this problem only partially. They can be adequately used only for 2‐D surfaces such as terrain and rooftops. However, vertical surfaces, such as facades, require a 3‐D approach. This study presents a new 3‐D solar radiation model for urban areas represented by 3‐D city models. The v.sun module implemented in GRASS GIS is based on the existing solar radiation methodology used in the topographic r.sun model with a new capability to process 3‐D vector data representing complex urban environments. The calculation procedure is based on the combined vector‐voxel approach segmenting the 3‐D vector objects to smaller polygon elements according to a voxel data structure of the volume region. The shadowing effects of surrounding objects are considered using a unique shadowing algorithm. The proposed model has been applied to the sample urban area with results showing strong spatial and temporal variations of solar radiation flows over complex urban surfaces.     

Dasymetric Mapping Using High Resolution Address Point Datasets

Mismatching sets of boundaries present a persistent problem in spatial analysis for many different applications. Dasymetric mapping techniques can be employed to estimate population characteristics of small areas that do not correspond to census enumeration boundaries. Several types of ancillary data have been used in dasymetric mapping but performance is often limited by their relatively coarse resolution and moderate correspondence to actual population counts. The current research examines the performance of using high resolution ancillary data in the form of individual address point datasets which represent the locations of all addressable units within a jurisdiction. The performance of address points was compared with several other techniques, including areal weighting, land cover, imperviousness, road density and nighttime lights. Datasets from 16 counties in Ohio were used in the analysis, reflecting a range of different population densities. For each technique the ancillary data sources were employed to estimate census block group population counts using census tracts as source zones, and the results were compared with the known block group population counts. Results indicate that address points perform significantly better compared with other types of ancillary data. The overall error for all block groups (n = 683) using address points is 4.9% compared with 10.8% for imperviousness, 11.6% for land cover, 13.3% for road density, 18.6% for nighttime lights and 21.2% for areal weighting. Using only residential address points rather than all types of locations further reduces this error to 4.2%. Analysis of the spatial patterns in the relative performance of the various techniques revealed that address points perform particularly well in low density rural areas, which typically present challenges for traditional dasymetric mapping techniques using land cover datasets. These results provide very strong support for the use of address points for small area population estimates. Current developments in the growing availability of address point datasets and the implications for spatial demographic analyses are discussed.     

Using remotely sensed data for census surveys and population estimation in developing countries: examples from Nigeria

"Using examples from Nigeria, this paper demonstrates how remotely sensed data can be used to acquire some of the basic data requirements for census surveys and to estimate population. The result obtained shows that visual identification of settlements on Landsat MSS and TM is more accurate and economical than equivalent digital classification techniques. Black and white aerial photographs were used to estimate the population of a model town and to establish EAs [enumeration areas]. The population estimation method employed can be used to obtain intercensal population estimates for the rapidly growing central places, while the established EAs for the study area have created a permanent base for future census surveys and census cross-validation, population estimation and other social surveys."     

Temporal Uncertainty in a Small Area Open Geodemographic Classification

The 2001 Output Area Classification (2001 OAC) is an open source geodemographic classification of the UK built exclusively from 2001 UK Census data. There has been considerable user interest in its applicability to subsequent time periods, particularly given the potential propensity of characteristics and attributes in some areas to change during inter‐censual periods. Users often purchase commercial geodemographic classification products in the belief that purely census‐based classifications such as the 2001 OAC are uniformly unreliable because there is no temporal updating of input data. Yet there is evidence to suggest that whilst some UK neighborhoods are prone to sudden changes, many others change very little over protracted time periods. Using measures that are available at the small area level, temporal uncertainty indicators can be constructed to identify those areas that are less stable. Using mid‐year population estimates and dwelling stock data, this article develops three temporal uncertainty indicators. These provide a reliable means of gauging the stability or otherwise of neighborhood conditions. The conclusion from this is that while a large number of small areas in the UK do experience change over time, this change is not uniform in either degree or distribution, or by geodemographic type.     

Inferring Spatial Scale Change in an Isopleth Map

This study reunites areal interpolation with the isopleth mapping process to construct an inferred larger scale isopleth map. Intelligent areal interpolation is used to construct two types of population density surfaces that are used as inputs for pycnophylactic interpolation of an isopleth surface. One is a target zone population density surface (TZPDS) and the other is a control zone population density surface (CZPDS). Results suggest that an inferred isopleth map with remote sensing control data is a better surface depiction than an isopleth map without any control data, and the quality of such an isopleth map is further improved by enhancing the remote sensing data with residential parcel information. A CZPDS-derived intelligent isopleth map also has more peaks and variations in population distribution patterns than does a TZPDS-derived one due to the larger scale of the control data.     

Modeling Ambiguity in Census Microdata Allocations to Improve Demographic Small Area Estimates

This article describes a methodology for allocating demographic microdata to small enumeration areas such as census tracts, in the presence of underlying ambiguities. Maximum Entropy methods impute population weights that are constrained to match a set of census tract‐level summary statistics. Once allocated, the household characteristics are summarized to revise estimates of tract‐level demographic summary statistics, and to derive measures of ambiguity. The revised summary statistics are compared with original tract summaries within a context of expected variation. Allocation ambiguity is quantified for each household as a function of the distribution of imputed sample weights over all census tracts, and by computed metrics of confusion and variety of allocation to any census tract. The process reported here allows differentiation of households with regard to inherent ambiguity in the allocation decision. Ambiguity assessment represents an important component that has been neglected in spatial allocation work to date but can be seen as important additional knowledge for demographers and users of small area estimates. For the majority of tested variables, the revised tract level summaries correlate highly with original tract summary statistics. In addition to assessments for individual households, it is also possible to compute average allocation ambiguity for individual tracts, and to associate this with demographic characteristics not utilized in the allocation process.     

Assessing the spatial distribution of crop areas using a cross-entropy method

While crop production statistics are reported on a geopolitical – often national – basis, we often need to know, for example, the status of production or productivity within specific sub-regions, watersheds, or agro-ecological zones. Such re-aggregations are typically made using expert judgments or simple area-weighting rules. We describe a new, entropy-based approach to the plausible estimates of the spatial distribution of crop areas. Using this approach tabular crop production statistics are blended judiciously with an array of other secondary data to assess the areas of specific crops within individual ‘pixels’—typically 25–100 km² in size. The information utilized includes crop production statistics, farming system characterization, satellite-based interpretation of land cover, biophysical crop suitability assessments, and population density. An application is presented in which Brazilian state level production statistics are used to generate pixel level crop area data for eight crops. To validate the spatial allocation we aggregated the pixel estimates to obtain synthetic estimates of municipality level areas in Brazil, and compared those estimates with actual municipality statistics. The approach produced extremely promising results. We then examined the robustness of these results compared to simplified approaches to spatializing crop production statistics and showed that, while computationally intensive, the cross-entropy method does provide more reliable spatial allocations.     

Exploring nationally and regionally defined models for large area population mapping

Interactions between humans, diseases, and the environment take place across a range of temporal and spatial scales, making accurate, contemporary data on human population distributions critical for a variety of disciplines. Methods for disaggregating census data to finer-scale, gridded population density estimates continue to be refined as computational power increases and more detailed census, input, and validation datasets become available. However, the availability of spatially detailed census data still varies widely by country. In this study, we develop quantitative guidelines for choosing regionally-parameterized census count disaggregation models over country-specific models. We examine underlying methodological considerations for improving gridded population datasets for countries with coarser scale census data by investigating regional versus country-specific models used to estimate density surfaces for redistributing census counts. Consideration is given to the spatial resolution of input census data using examples from East Africa and Southeast Asia. Results suggest that for many countries more accurate population maps can be produced by using regionally-parameterized models where more spatially refined data exists than that which is available for the focal country. This study highlights the advancement of statistical toolsets and considerations for underlying data used in generating widely used gridded population data.     

Instructions for Contributors to Cartography and Geographic Information Science

A number of areal interpolation methods have been developed to estimate population for overlapping, discontinuous, or fragmented areas. Previous studies examined the relative accuracy of various methods; this research advances those endeavors by comparing the effectiveness of seven different methods using a national random sample of census block groups and blocks. As the results show, the areal interpolation methods produce good population estimates for nested census blocks except in areas of heterogeneous land use or unusual contexts. In addition, estimation conducted in areas with small populations or low population density was vulnerable to high percentage error. Amongst the different methods, road network allocation and statistical regression (with area and roads as predictors) produced the best population estimates for the sample blocks.     

Non-stationary Approaches for Mapping Terrain and Assessing Prediction Uncertainty

It is well known that terrain may vary markedly over small areas and that statistics used to characterise spatial variation in terrain may be valid only over small areas. In geostatistical terminology, a non-stationary approach may be considered more appropriate than a stationary approach. In many applications, local variation is not accounted for sufficiently. This paper assesses potential benefits in using non-stationary geostatistical approaches for interpolation and for the assessment of uncertainty in predictions with implications for sampling design. Two main non-stationary approaches are employed in this paper dealing with (1) change in the mean and (2) change in the variogram across the region of interest. The relevant approaches are (1) kriging with a trend model (KT) using the variogram of residuals from local drift and (2) locally-adaptive variogram KT, both applied to a sampled photogrammetrically derived digital terrain model (DTM). The fractal dimension estimated locally from the double-log variogram is also mapped to illustrate how spatial variation changes across the data set. It is demonstrated that estimation of the variogram of residuals from local drift is worthwhile in this case for the characterisation of spatial variation. In addition, KT is shown to be useful for the assessment of uncertainty in predictions. This is shown to be true even when the sample grid is dense as is usually the case for remotely-sensed data. In addition, both ordinary kriging (OK) and KT are shown to provide more accurate predictions than inverse distance weighted (IDW) interpolation, used for comparative purposes.     

Population at risk: using areal interpolation and Twitter messages to create population models for burglaries and robberies

Population at risk of crime varies due to the characteristics of a population as well as the crime generator and attractor places where crime is located. This establishes different crime opportunities for different crimes. However, there are very few efforts of modeling structures that derive spatiotemporal population models to allow accurate assessment of population exposure to crime. This study develops population models to depict the spatial distribution of people who have a heightened crime risk for burglaries and robberies. The data used in the study include: Census data as source data for the existing population, Twitter geo-located data, and locations of schools as ancillary data to redistribute the source data more accurately in the space, and finally gridded population and crime data to evaluate the derived population models. To create the models, a density-weighted areal interpolation technique was used that disaggregates the source data in smaller spatial units considering the spatial distribution of the ancillary data. The models were evaluated with validation data that assess the interpolation error and spatial statistics that examine their relationship with the crime types. Our approach derived population models of a finer resolution that can assist in more precise spatial crime analyses and also provide accurate information about crime rates to the public.     

顾及时空异质性的缺失数据时空插值方法

时空插值方法被广泛应用于缺失时空数据集的插值与估计。时空插值是时空建模与分析的一个重要内容,当前该研究关注的热点之一是异质条件下的时空插值与估计问题。因此,本文从时空数据的异质性出发,提出了一种顾及时空异质性的缺失数据时空插值方法。该方法首先对数据集进行时空分区,然后分别在时间和空间按照异质协方差模型计算缺失数据的估计值,进而利用相关系数确定时空权重、融合时间和空间估计值得到缺失数据的最终估计结果。最后通过两组气象数据集进行交叉验证对比分析试验。试验结果表明本文方法对比其他插值方法具有更高的精度和适用性。     

Positional Accuracy of TIGER 2000 and 2009 Road Networks

The Topologically Integrated Geographic Encoding and Referencing (TIGER) data are an essential part of the US Census and represent a critical element in the nation's spatial data infrastructure. TIGER data for the year 2000, however, are of limited positional accuracy and were deemed of insufficient quality to support the 2010 Census. In response the US Census Bureau embarked on the MAF/TIGER Accuracy Improvement Project (MTAIP) in an effort to improve the positional accuracy of the database, modernize the data processing environment and improve cooperation with partner agencies. Improved TIGER data were released for the entire US just before the 2010 Census. The current study characterizes the positional accuracy of the TIGER 2009 data compared with the TIGER 2000 data based on selected road intersections. Three US counties were identified as study areas and in each county 100 urban and 100 rural sample locations were selected. Features in the TIGER 2000 and 2009 data were compared with reference locations derived from high resolution natural color orthoimagery. Results indicate that TIGER 2009 data are much improved in terms of positional accuracy compared with the TIGER 2000 data, by at least one order of magnitude across urban and rural areas in all three counties for most accuracy metrics. TIGER 2009 is consistently more accurate in urban areas compared with rural areas, by a factor of at least two for most accuracy metrics. Despite the substantial improvement in positional accuracy, large positional errors of greater than 10 m are relatively common in the TIGER 2009 data, in most cases representing remnant segments of minor roads from older versions of the TIGER data. As a result, based on the US Census Bureau's suggested accuracy metric, the TIGER 2009 data meet the accuracy expectation of 7.6 m for two of the three urban areas but for none of the three rural areas. The suggested metric is based on the National Standard for Spatial Data Accuracy (NSSDA) protocol and was found to be very sensitive to the presence of a small number of very large errors. This presents challenges during attempts to characterize the accuracy of TIGER data or other spatial data using this protocol.