Distance Decay Function Research Articles

Configuring the neighbourhood effect in irregular cellular automata based models

ABSTRACTCellular automata (CA) models have been widely employed to simulate urban growth and land use change. In order to represent urban space more realistically, new approaches to CA models have explored the use of vector data instead of traditional regular grids. However, the use of irregular CA-based models brings new challenges as well as opportunities. The most strongly affected factor when using an irregular space is neighbourhood. Although neighbourhood definition in an irregular environment has been reported in the literature, the question of how to model the neighbourhood effect remains largely unexplored. In order to shed light on this question, this paper proposed the use of spatial metrics to characterise and measure the neighbourhood effect in irregular CA-based models. These metrics, originally developed for raster environments, namely the enrichment factor and the neighbourhood index, were adapted and applied in the irregular space employed by the model. Using the results of these metrics, distance-decay functions were calculated to reproduce the push-and-pull effect between the simulated land uses. The outcomes of a total of 55 simulations (5 sets of different distance functions and 11 different neighbourhood definition distances) were compared with observed changes in the study area during the calibration period. Our results demonstrate that the proposed methodology improves the outcomes of the urban growth simulation model tested and could be applied to other irregular CA-based models.

Measuring Spatial Accessibility of Health Care Providers - Introduction of a Variable Distance Decay Function within the Floating Catchment Area (FCA) Method.

We integrated recent improvements within the floating catchment area (FCA) method family into an integrated ‘iFCA`method. Within this method we focused on the distance decay function and its parameter. So far only distance decay functions with constant parameters have been applied. Therefore, we developed a variable distance decay function to be used within the FCA method. We were able to replace the impedance coefficient β by readily available distribution parameter (i.e. median and standard deviation (SD)) within a logistic based distance decay function. Hence, the function is shaped individually for every single population location by the median and SD of all population-to-provider distances within a global catchment size. Theoretical application of the variable distance decay function showed conceptually sound results. Furthermore, the existence of effective variable catchment sizes defined by the asymptotic approach to zero of the distance decay function was revealed, satisfying the need for variable catchment sizes. The application of the iFCA method within an urban case study in Berlin (Germany) confirmed the theoretical fit of the suggested method. In summary, we introduced for the first time, a variable distance decay function within an integrated FCA method. This function accounts for individual travel behaviors determined by the distribution of providers. Additionally, the function inherits effective variable catchment sizes and therefore obviates the need for determining variable catchment sizes separately.

Spatial co-location pattern mining of facility points-of-interest improved by network neighborhood and distance decay effects

ABSTRACTThe aim of mining spatial co-location patterns is to find the corresponding subsets of spatial features that have strong spatial correlation in the real world. This is an important technology for the extraction and comprehension of implicit knowledge in large spatial databases. However, existing methods of co-location mining consider events as taking place in a homogeneous and isotropic context in Euclidean space, whereas the physical movement in an urban space is usually constrained by a road network. Furthermore, previous works do not take the ‘distance decay effect’ of spatial interactions into account, which may reduce the effectiveness of the result. Here we propose an improved spatial co-location pattern mining method, including the network-constrained neighborhood and addition of a distance-decay function, to find the spatial dependence between network phenomena (e.g. urban facilities). The underlying idea is to utilize a model function in the interest measure calculation to weight the contribution of a co-location to the overall interest measure instance inversely proportional to the separation distance. Our approach was evaluated through extensive experiments using facility points-of-interest data sets. The results show that the network-constrained approach is a more effective method than the traditional one in network-structured space. The proposed approach can also be applied to other human activities (e.g. traffic accidents) constrained by a street network.

An Empirical Study on the Relationship between Pedestrian Network Distance and Building Density in the Area of Urban Rail Station

This is an empirical study on the relationship between the pedestrian network distance and the building density in the area of urban rail station. The area around a station is, usually, highly developed for various urban activities. Since the floating population from or to the station are moving along the pedestrian road, the distance from a station to destination buildings should be calculated using pedestrian network. On the basis of the network the distance from each building to the closest station was calculated. It was found from this empirical analysis that the average building density is decreasing, while the distance between the two places is increasing. Although this result coincides with those of the relevant researches, the relationship was not firmly identical for the entire stations in the study area; only eight stations from fourteen showed a statistical significancy in the analysis and the parameter of the distance decay function was different for each station area. From this result it could be emphasized that the relationship of each station should be investigated individually as an indicator to present the real influence sphere of the station to the surrounding area.

The Shape of Mobility: Measuring the Distance Decay Function of Household Mobility

A well-known challenge to studies examining the distance of residential mobility patterns is that the estimates are often constrained to patterns only within a particular metro area or between metro areas. Thus, studies are unable to estimate the entire distance decay functional form. Using a unique data set on the distance of the most recent move for a large sample of households in twenty-three metropolitan areas in the United States over three waves, we flexibly estimate the distance decay function for the entire sample, as well as for a series of subpopulations based on key demographic information.

A Few GIS Clarifications on Tornado Density Mapping

AbstractA geographical information system (GIS) perspective is taken to examine conceptual and methodological complications present in tornado density and probability mapping. Tornado density is defined as the inverse-distance-weighted count of tornado touchdown points or tornado-affected cells within a neighborhood area. The paper first adds a few geographic elements into the tornado definition and then characterizes tornado density as a density field in GIS that depends on predefined, modifiable areas to exist. Tornado density is therefore conceptually distinguished from both individual tornadoes and tornado probability. Three factors are identified to be vital in tornado density mapping: the neighborhood size, the distance decay function, and the choice of tornado properties. Correspondingly, 12 neighborhood sizes ranging from 20 to 360 km are tested, four distance decay functions are compared, and two tornado properties—tornado touchdown locations and pathlengths—are separately incorporated in mapping. GIS interpretations, clarifications, and demonstrations are provided for these factors to reach a thorough understanding of how the factors function and affect the resultant tornado density maps. Historical tornado data of the eastern half of the United States from 1973 to 2013 are used in these demonstrations. Uncertainty and propagation analyses are recommended for future tornado density and probability mapping, and a Monte Carlo simulation using tornado pathlength data is conducted as an example of uncertainty modeling. In all, tornado density mapping is diagnosed as a largely subjective activity, and the mapper needs to make multiple choices according to the mapping purpose, scale, and the involved tornado record data.

Modeling and Prediction of Long-Distance Traffic Flows Through the Example of Road Transport in the Czech Republic

ABSTRACTThe construction of large-scale long-distance roads brings an irreversible impact on the landscape and therefore its careful and precise planning is very important. For this planning we use data on the intensity of traffic flows on existing roads and statistical tools for the modeling of planned traffic flows. The main objective of this paper is the modeling of the existing intensity of traffic flows on highways and expressways in the Czech Republic by determination of the optimal distance-decay function. On the basis of the resulting model and the resulting distance-decay function, it is possible to predict the intensity of traffic in the event of the completion and commissioning of new sections of highways and expressways. The subsequent analysis will allow us to make a qualified prediction of traffic intensity in the event of the completion of the R35 expressway, or after the completion of the R35 and R43 expressways. Besides the intensity on the above-mentioned roads themselves, the paper also predicts the expected reduction in traffic intensity on the busiest highway in the Czech Republic, that is, on the D1 highway between Prague and Brno.

영덕오십천 환경개선용수 공급의 경제적 편익측정: CVM 적용에 있어 저항응답의 처리와 거리소멸함수

영덕오십천 환경개선용수 공급의 경제적 편익측정: CVM 적용에 있어 저항응답의 처리와 거리소멸함수

The distance-decay function of geographical gravity model: Power law or exponential law?

The distance-decay function of the geographical gravity model is originally an inverse power law, which suggests a scaling process in spatial interaction. However, the distance exponent of the model cannot be reasonably explained with the ideas from Euclidean geometry. This results in a dimension dilemma in geographical analysis. Consequently, a negative exponential function was used to replace the inverse power function to serve for a distance-decay function. But a new puzzle arose that the exponential-based gravity model goes against the first law of geography. This paper is devoted for solving these kinds of problems by mathematical reasoning and empirical analysis. New findings are as follows. First, the distance exponent of the gravity model is demonstrated to be a fractal dimension using the geometric measure relation. Second, the similarities and differences between the gravity models and spatial interaction models are revealed using allometric relations. Third, a four-parameter gravity model possesses a symmetrical expression, and we need dual gravity models to describe spatial flows. The observational data of China's cities and regions (29 elements indicative of 841 data points) in 2010 are employed to verify the theoretical inferences. A conclusion can be reached that the geographical gravity model based on power-law decay is more suitable for analyzing large, complex, and scale-free regional and urban systems. This study lends further support to the suggestion that the underlying rationale of fractal structure is entropy maximization. Moreover, it suggests that many dimensional dilemmas of spatial modeling can be solved using the concepts from fractal geometry.

A53 Cycling health and climate: what are the circumstances under which cycling can contribute to substantive greenhouse gas emission reductions and whose travel should be targeted to achieve the biggest health and climate benefits?

Abstract Background Co-benefits are defined as the health and other benefits that can accompany greenhouse gas emission reductions. Modelling studies have identified the potential for large health co-benefits in the transport sector from a mode shift to physically active transport. Findings on emission reductions from active travel have been less clear. Cycling is usually an option for shorter trips, typically exhibiting a strong distance decay function, whilst in most settings the majority of emissions come from longer trips. Despite this there has been little systematic investigation of the circumstances under which active travel can achieve emission reductions and how such scenarios would relate to the size of the health benefits. Health and carbon benefits vary according to who is changing their behaviour and the kind of trips they make and policy goals may not always be aligned. Methods In this study we will fill this gap using a microsimulation model based on individual level travel survey data from England combined with the ITHIM health model. The ITHIM model estimates health impacts from transport scenarios using a comparative risk assessment approach and incorporates variation in disease risk and baseline physical activity levels both between and within age and gender groups. Changes to distributions of physical activity are applied to multiple diseases, using WHO Global Burden of Disease data. The microsimulation model has been implemented in R and parameterised with the English National Travel Survey. In the model four parameters are allowed to vary: 1) the cycling mode split, 2) the distribution of travel distances, 3) the distance decay function for cycling (based on electric bikes), 4) the proportion of multimodal trips amongst longer trips. The potential for trip distance reduction from changing destinations will be allowed to vary by trip purpose, with more individual level latitude for changing non-commuting trips. Results We will search the output of the model to identify those combinations of strategies that would achieve substantive emissions reductions and investigate how these correlate with health benefits. Using person level data we will investigate the top population groups to target for mode shift from a health, a carbon, and a co-benefits perspective. Conclusions The results of this study will guide policy on the extent on urban planning and inform development of cycling policies that can achieve multiple societal benefits.

Spatial influence of regional centres of Slovakia: analysis based on the distance-decay function

The uneven distribution of centres in settlement systems and the non-homogeneity of social-economic space are the stimuli for the existence of spatial interactions. The interactions, that manifest the changes in their intensity with an increasing distance from a centre, can be described by distance-decay functions. This paper presents the construction, analysis and typology of distance-decay functions for regional centres of Slovakia using the daily travel-to-work flow data. Apart from an estimation of individual distance decay functions for each centre, a universal distance-decay function is also constructed through more sophisticated statistical analyses, where not only distance is the input parameter, but also the population of a centre. The resulting distance-decay functions have a wide range of uses in spatial interaction modelling (commuting, transportation, etc.). They also define the range of spatial influence of regional centres and therefore they can be used, for example, in proposals and revisions for the administrative division of a territory.

The Economic Benefits of Reducing the Environmental Effects of Landfills: Heterogeneous Distance Decay Effects

This paper estimates the economic benefits of different alternative policies considered for reducing the external effects caused by the utilization of landfills in solid waste management. The preferences of the local population in the surrounding areas of a landfill are evaluated utilizing a discrete choice experiment in which subjects are presented with alternative policy decisions that involve reducing the material processed through the landfill. Various models were employed in order to capture heterogeneous preferences, resulting in a mixture of normals modelling approach (MN-MNL) outperforming other alternative models of heterogeneity. The results show that the policy of moving the landfill away from the population does not provide the most benefits when compared to a policy of increasing recycling in the household. The economic benefits of the waste management policies are heterogeneous across the population surrounding the landfill and so the distance decay functions. Thus, the economic benefits for most waste management policies can increase or decrease the further away the subject lives from the landfill, depending on the preferences of his/her segment and the type of policy employed.

Road network circuity in metropolitan areas

Circuity, the ratio of network to Euclidean distances, describes the directness of trips and the efficiency of transportation networks. This paper measures the circuity of the fifty-one most populated Metropolitan Statistical Areas (MSAs) in the United States and identifies trends in those circuities between 1990 and 2010. Overall circuity has increased between 1990 and 2010: random points have not only become farther apart in distance, their shortest network path has become more circuitous, suggesting that the more recently constructed parts of street networks are laid out more circuitously than older parts of the network. Over this period thirty-five MSAs experienced a statistically significant increase in circuity (six experienced a significant decrease). As expected, short trips are more circuitous than long trips. A new circuity distance-decay function describes how circuity varies with distance within metropolitan areas. The parameters of this function have changed from 1990 to 2010.

Which distance-decay function for migration and which one for commuting? A case study of Slovenia

The volume of social interactions like migration and commuting between two locations depends significantly on the distance between them. In the paper, we analysed the shape and parameters of several distance-decay functions for commuting and for migration flows, respectively. The analysis was performed for inter-municipal interactions in Slovenia in 2010–2011. The functions considered were power, exponential, normal, square root exponential, hyperbolic, power-exponential, and normalized power-exponential distance-decay functions. Distance was considered in three ways: as the Euclidean distance, as the shortest road distance, and as the fastest road distance between municipal centres under consideration. The analysis was performed for the whole set of interactions in the state, as well as for interactions to specific urban centres. We demonstrate that the power-exponential distance-decay function fits best for all analysed cases. The determination coefficients for this type of function are low when analysing all data together, but they increase significantly when distance-decay functions are modelled for urban centres at different levels of consideration.

Underground pedestrian trips—trip generation, spatial distribution and activities in the Montréal underground

Underground space for pedestrians has received little research attention, even though the pace of development is accelerating and in many cities worldwide. Privately financed underground planning requires clear and objective measures for the expected performance of planned space. Understanding how an existing pedestrian and commercial system works can help in defining the parameters for future development. This project involved understanding individual pedestrian itineraries in the Montréal underground as multiple-stop, network-based decisions, involving the surface walk environment. The effect of location, weather, and the availability of services on trip length and the portion of the trip that is executed underground are examined with a database of 760 observed itineraries. Distance distributions follow distance–decay function modified by the availability of services. Location had a major effect, the availability of services had a mixed effect and weather had no effect on trip length or the length of the underground trip portion. The results can be used to help construct a predictive model for new generator spaces such as office buildings on projected or existing underground development.

Spatial patterns of subsistence extraction of forest products – An indirect approach for estimation of forest degradation in dry forest

Successful implementation of a forest based climate change mitigation mechanism such as REDD + depends on robust and available methods for measurement and estimation of forest degradation. Currently available methods are for application in single-hit degradation incidents in high density humid forests. However, it has been suggested that gradual degradation, especially in dry forests, is more widespread and that methods are needed for measuring and estimating associated emissions. We assess the applicability of an indirect remote sensing approach for monitoring forest degradation: infrastructure and other indicators of human activities are mapped and used for spatial prediction of degradation activities. For proxy variables we tested distance to forest edge, distance to roads, and population pressure calculated as the sum of inhabitants per pixel in the Landscan 2010 population raster dataset multiplied by an inverse power distance decay function. Wood extraction incidents were counted in 160 plots in two dry forests in Tanzania with infrastructural entry from one side only. We analyzed the spatial pattern of forest degradation as a function of the chosen proxy variables using zero inflated count models which allows for an excess of zero counts. A jack-knife bootstrap using 10,000 runs was applied to optimize the population distance decay function. We found that the impact of forest degradation is highest near high population concentration, above 1000 individuals. Furthermore, distance to nearest forest edge or road was a significant proxy for estimation of the number of wood extraction incidents (p < 0.001), where degradation incidents decreased with increasing distance to forest edge or road. At 3000 m from the forest edge towards the forest core the probability of wood extraction is 20% and dropping. The population distance decay function was found to have a steep decline indicating a relative small impact on forest degradation. Further, and perhaps larger, studies are needed to be able to recommend a distance decay function for general application in Tanzania. However, the results are useful for understanding spatial patterns of wood harvesting as a function of distance to nearest forest edge or road in dry Miombo woodland areas with average population pressure at 1685 ± 101 persons within a radius of 4000 m from the wood extraction sites.

Spatial optimization of residential care facility locations in Beijing, China: maximum equity in accessibility.

BackgroundThe residential care system is rapidly developing and plays an increasingly important role in care for the elderly in Beijing. A noticeable disparity in the accessibility to existing residential care facilities, however, is demonstrated in existing studies. The spatial optimization of residential care facility (RCF) locations is urgently needed to promote equal access to residential care resources among the elderly population.MethodsA two-step floating catchment area method with an additional distance-decay function is adopted to measure accessibility to residential care facilities. The spatial optimization model is developed to maximize equity in accessibility by minimizing the total square difference between the accessibility score of each demand location and the weighted average accessibility score. The Particle Swarm Optimization (PSO) method is implemented for the solution.ResultsThe optimized RCF layouts improve equal spatial access to residential care resources with very low accessibility standard variation (0.0066). A relatively large number of beds (51% of the total beds) to be located in the suburban districts between the central and periphery districts of Beijing are optimized. A smaller number of beds to be located in the central and periphery districts (33% and 16% respectively) are optimized. The gaps between the existing and optimized layouts suggest that more RCF beds (5961 beds) are needed in suburban districts, while the RCF beds in some subdistricts located in the central and periphery districts are oversupplied (5253 and 1584 surplus beds respectively).ConclusionsThe optimized results correspond to the municipal special plan proposed by the Beijing government. The optimization objective of this study is different from traditional facility location optimization models, and the method is efficient in maximizing equal access to residential care facilities. This method can support knowledge-based policy-making and planning of residential care facilities.

Mapping beneficiaries of ecosystem services flows from Natura 2000 sites

There is a growing need to integrate ecosystem services into management strategies of protected areas, and only a comprehensive ecosystem services assessment allows effective strategies for biodiversity conservation to be defined. Beneficiaries are largely disregarded or only mentioned in ecosystem services assessments related to protected areas. Thus, we propose indicators for identifying potential beneficiaries on the local and regional level, focusing on 16 relevant ecosystem services of Natura 2000 sites. For a case study in northern Italy, we used spatially-explicit modelling approaches to map and quantify the potential beneficiaries of multiple ecosystem services, including distance decay functions and basin catchment modelling. The resulting maps indicate that for provisioning and cultural services, the majority of the beneficiaries are located outside the protected area, whereas the beneficiaries of regulating services are mostly situated within or very close to it. The indicators and the beneficiary maps offer an important basis for an exhaustive assessment of ecosystem services flows from Natura 2000 sites and support the implementation of conservation policies by involving the local population and the community of users of protected areas.

Market Reach for Retail Services

Retail is concentrated in areas where demand is high. A measure of market potential can be used to calculate place-specific demand for retail services. The effect of distance on market potential depends on the willingness of consumers to travel for the products they purchase. The spatial reach of demand is frequently operationalized using a distance-decay function. The purpose of this paper is to estimate such distance-decay functions for different branches of the retail sector. The paper uses spatial data from the Stockholm region in Sweden. The results indicate that, in line with theory, there are indeed differences in the distance decay of demand among retail subsectors.

Employment Accessibility Among Housing Subsidy Recipients

This article estimates the extent to which different types of subsidized households live near employment, measuring the extent of spatial mismatch between these households and employment. Using census tract–level data from the U.S. Department of Housing and Urban Development on housing subsidy locations and employment data from the U.S. Census Bureau, this article uses a distance-decay function to estimate job-accessibility indices for census tracts in metropolitan statistical areas with 100,000 people or more. I use these data to create weighted job-accessibility indices for housing subsidy recipients (public housing, Low-Income Housing Tax Credit, Section 8 New Construction, and housing voucher households) and the total population and renter households earning below 50% of area median income as points of comparison. I find that of all these groups, by a large margin, public housing households live in census tracts with the greatest proximity to low-skilled jobs. However, they also live among the greatest concentration of individuals who compete for those jobs, namely, the low-skilled unemployed. These findings suggest that we pay close attention to the trade-offs that public housing residents are making as these units are demolished and replaced with vouchers.