The rapidly increasing prevalence of obesity and overweight in last two decades has become a dominant public health problem in the United States (US). According to the National Health and Nutrition Examination Survey (NHANES), the estimated age-adjusted obesity prevalence has increased from 14.5% in 1976-1980 to 33.8% in 2007-2008 among adults age 20 years and older in the United States[1
]. The current obesity epidemic has become a significant contributing factor of several leading causes of mortality and morbidity, including heart disease, stroke, diabetes and some cancers. The estimated healthcare costs of obesity in the US are as high as $147 billion[4
]. If the prevalence of obesity remains unchanged, per capita spending on health care for adults would rise by 65 percent by 2020[5
]. Both population disease burden and healthcare costs highlight the urgent need to increase population physical activity and healthy eating. An emerging field of study, the impact of the built environment on high energy intake and sedentary behaviors, has gained increased attention[6
]. Promoting physical activity is a critical public health strategy to contain the current obesity epidemic and to prevent the occurrence of major chronic diseases. Shaping or improving the local built environment to better support healthy behaviors, such as physical activity, has a potential long-term effect on population health and could be a key avenue for successful obesity prevention[7
Neighborhood parks are critical components of the neighborhood built environment context, especially in urbanized areas. Neighborhood parks provide ideal open spaces for leisure-time physical activity and important venues to promote population-level physical activity[8
]. Lack of, or limited, park access can constrain the physical activity opportunities of local residents, which may increase the prevalence of obesity. Having good access to green space, especially parks, in urban areas is associated with increased physical activity [9
]. The Task Force on Community Preventive Services recommended creating or enhancing access to places for physical activity as one of eight identified strategies to increase physical activity [11
]; and parks are the most common places for local populations for outdoor physical activities[12
]. Parks are one of eight societal sectors to promote physical activity recommended by the U.S. National Physical Activity Plan http://www.physicalactivityplan.org/theplan.htm
However, a review of the research of the relationship between neighborhood park access and residents' physical activity outcomes showed mixed results[13
]. The reasons for these inconsistencies could be complex and various across studies. Park access and physical activity could be very different by gender and age groups[14
] as well as socioeconomic status[15
]. But different methods that quantify/measure the neighborhood park access in previous studies at least contribute to these inconsistencies, since measuring park access is critical to evaluating the effects of park use on physical activity. Park access, by nature, is a multiple dimension concept, at least including: park proximity to neighborhoods (location), park size, park safety, and park attractiveness (amenities, and facility types, quality and quantity). This complicates the methods and the contents to measure park access.
From a geographical perspective, the spatial configuration of neighborhood parks, the number of parks and their spatial distribution across neighborhood areas or local regions, represents the basic park access potential for local residential populations. Thus, it is not surprising that the spatial accessibility of neighborhood parks, mainly based on park proximity and location and size, is commonly used to evaluate the contribution of parks to physical activity in most studies. From a public health intervention perspective, spatial accessibility of neighborhood parks lays the foundation to inform and evaluate further needs for park environment improvement in terms of safety, amenities and/or facilities, and even the need for new parks in some neighborhood areas.
There are an increasing number of studies that examine the linkage between park access and physical activity behaviors. A recent multiple-site study of public park and objectively-measured physical activity for adolescent girls in the US shows that park access (the presence and density of parks in local neighborhoods and proximity to neighborhood parks) was associated with higher levels of nonschool moderate-to-vigorous physical activity[16
]. Thus, the spatial accessibility of parks is relevant to physical activity. Developing park access measures is important because they are critical to establishing key correlates and determinants that drive physical activity and inform intervention strategies. However, there is no national existing study that evaluates the potential spatial accessibility of parks in the US. Thus, we aim to create a national database for a neighborhood park spatial accessibility index that could objectively quantify the spatial distribution of neighborhood parks based on residential proximity to parks as well as park sizes; could provide a basic platform for further park access equity inquiry as well as studies of health and health behavior outcomes; and could be used for specific local as well as nationwide studies.
Methods for spatial accessibility measurement
Current methods for measuring spatial accessibility of neighborhood parks in the literature can be categorized into three general approaches: 1) spatial proximity to parks, which measures travel costs in overcoming spatial separation between the locations of population and parks; 2) the container approach, which measures the existence or density of parks in a defined geographic area; and 3) the spatial interaction modeling approach, commonly known as gravity model-based approach, which measures the potential spatial accessibility of parks. In this paper, we proposed a new approach to measure potential spatial access to parks: population weighted distance. In this paper, we did not consider park accessibility incorporating both space and time dimensions as those space-time accessibility measures in some planning and transportation studies [17
The travel cost approach
The travel cost approach includes some simple intuitive measures, such as the distance from residential neighborhood to the nearest park or the minimum travel time to the nearest park. These direct (Euclidean or network) distance measures of park accessibility are intuitive and also convenient to generate in a geographic information systems (GIS) environment. The major problem of this approach is that it assumes residents would always use the nearest park with the least travel cost as a space for physical activity. The exclusive use of one nearest park by local neighborhood residents is not realistic. A modified distance measure goes to another unrealistic extreme, which takes the average distance from an origin (home or residential neighborhood) to all its potential park destinations to measure spatial proximity to parks[19
The container approach
A more common approach for measuring park accessibility used in previous studies is the container-based method. In this method one summarizes the number of parks, or the total area of parks within a geographic unit. This geographic unit is often defined by the basic neighborhood unit under study, such as census tract, ZIP code, or local neighborhood unit; this geographic unit could also be defined by the area within the specified walking distances from residential locations. Specific measures of spatial accessibility of parks include a simple indicator of the existence of parks within the defined geographic unit, the number of parks, the total park area size within a neighborhood or within walking distance buffers. The percentage of land area used for parks per neighborhood, as well as the total area of park space averaged by population size are commonly used measures in park access equity analysis.
However, there are several problems associated with these container-based accessibility measures. First, the container-based measures are subject to a well known spatial analysis problem: the Modifiable Areal Unit Problem (MAUP). In geographic studies, MAUP means geographic measures or relationships of interest could change because of the definition of spatial scales of the geographic unit of analysis. The spatial accessibility of parks may change depending on the spatial size (extent) of geographic containers. So a neighborhood or residential place could have very different park accessibility measures, depending on the size of the geographic container. For example, a quarter mile (400 meters), half mile and one mile are often used for walking distance to create a buffer area (geographic container) for highly-urbanized areas to define spatial accessibility of parks; and these differences in walking distances to define the geographic container could lead to inconsistencies in park accessibility measures for the same neighborhood or residential places. For most suburban and rural populations, cars may be used to access local parks. The concept of neighborhood parks thus could be very different from those inside the central cities. Neighborhood parks were defined as outdoor public areas within 10 miles or a 20-minute drive from residents' locations [21
]. This will make the definition of geographic container very difficult. Also, larger sizes of geographic containers could result in a serious ecological fallacy problem that population within a neighborhood share the same spatial accessibility of parks. Another obvious problem with a container approach is edge effects. A defined neighborhood or a neighborhood with buffer areas may have no parks inside but may have some or more outside ones near its boundary, but this neighborhood assumes no access to these parks. Thus, the traditional container-based measures could be very biased indicators and could create some unrealistic areas that have no access to parks at all[22
Kernel density estimation, an improved container method, was recently applied to better characterize the spatial accessibility to neighborhood parks [23
]. The kernel density estimation method assumes that the park accessibility will decrease from the park location to its neighborhood areas within a threshold distance (called kernel bandwidth). The kernel density function determines how the value of park accessibility decreases from the peak value at park location to zero at the threshold distance. Kernel density estimation has two basic components: kernel functions and kernel bandwidth. The choice of kernel bandwidth usually has much stronger effects on park accessibility density surface than the choice of kernel functions. The larger the distance for kernel bandwidth, the smoother the resulting park accessibility surface. Each park has a spatial accessibility density surface. A neighborhood's park accessibility is the sum of all park accessibility density surfaces that are covering this neighborhood. If a neighborhood is not located within any park kernel zones, its park accessibility would become zero. How to select an appropriate kernel bandwidth is always challenging and adaptive kernel density may be a better choice[24
]. Obviously kernel bandwidth strongly depends on the spatial behaviors or processes under study. In park accessibility studies, one-mile or quarter-mile walking distances are often used as the kernel bandwidth; but this will leave many neighborhood areas without any access to parks. So by nature, this is a modified container approach. Compared to traditional container-based measures, the kernel density park accessibility measure overcomes the assumption of equal accessibility within the container and could quantify the heterogeneity of park accessibility within it.
Spatial interaction modeling approach
Another important method for measuring geographic accessibility is the spatial interaction model, which is an extension of a gravity model (here we assume these two terms are exchangeable). This approach assumes that the spatial interaction declines with a larger spatial separation (travel distance or time) between origins and destinations; spatial interaction increases with a greater demand at origins or with higher supply capacity and/or attractiveness at destinations. In the context of park access, the spatial interaction (Aij
) from a residential place (i
) to a destination park (j
) is defined as
is the destination park size j
is the distance from a residential neighborhood i
to destination park j
are the parameters associated with park size and distance respectively and measures their effects on park accessibility. The potential spatial accessibility index Ai
for a residential neighborhood i
, is defined as the sum of spatial interaction (Aij
) with all its destinations parks:
is used to measure the potential park accessibility from a residential place to its neighboring parks. Thus, residential neighborhoods with shorter distances to parks will have higher potential park accessibility; similarly, parks with a larger size will attach more residents. Besides the large physical space, larger parks usually have more facilities and public service programs that could attract more local residents[25
There are two theoretical advantages for the spatial interaction model-based accessibility measures. First, the spatial interaction model approach avoids a significant problem of the container-based approach, which requires that a neighborhood or a local geographic area has to be defined to generate park accessibility measures. The spatial extent of parks for a local neighborhood could vary according to different geographic settings (inner city, suburban and rural areas) and it completely depends on the spatial distribution of parks for a specific neighborhood. Without the concerns of defining neighborhood size, this approach would minimize the influence of MAUP on accessibility measures. Second, this approach could easily generate more-accurate localized population exposures to parks, which will reduce the ecological bias of park accessibility measures and the influence of an ecological fallacy for population park access measurement. When linked to individual health outcomes, park accessibility measures could be based on accurate individual home locations or residential census blocks, the smallest census geographic unit in the US.
Spatial interaction measures have been developed and used for numerous studies on urban facilities or services, however only a few studies [26
] employed them for measuring park accessibility. Besides park size and distance to parks, these studies also incorporate the park quality or attractiveness in their park accessibility measures in the form
is the attractiveness measure of park j
with an influence parameter λ
. It highlights another methodological advantage: the spatial interaction modeling framework could flexibly incorporate other park features that may affect park access and use, such as park safety, quality, and facilities, when these information or measures are available.
Distance decay in spatial interaction modeling
Any approach to measuring park accessibility will have its own limitations. There are two common methodological drawbacks associated with spatial interaction accessibility measures: distance decay parameter and spatial destination choice set. The first is the choice of the magnitude of parameter associated with distance, often called distance decay or friction parameter (β
). Theoretically the distance decay effects on spatial interaction processes or behaviors, reflected by this friction parameter, could be very context-specific, such as the influence of geographic settings (urban, suburban and rural areas) and could vary significantly among different human activities, such as shopping versus
recreational activities. A larger distance decay parameter indicates that human behavior is more sensitive to distance. The distance decay parameter could even be very different among different types of destinations for the same type of activities. For example, in recreational physical activity behaviors, the distance decay parameter is 1.91 for the public's use of public open space and 1.16 for sporting and recreation centers and golf courses(1.06)[27
]. Empirical study is the best way to estimate this parameter for a particular type of human behavior. However the information or data needed to calibrate this parameter usually are not available. Many studies just arbitrarily set a value for this distance decay parameter for the spatial interaction accessibility measures according to their experience or by following some common practice[20
]. Biles-Corti and Donovan used the data collected from a social ecological project on environmental determinants of physical activity and explore the distance decay parameters for nine different types of facilities for recreational physical activity in metropolitan Perth, Western Australia. Publically accessible facilities or services usually have larger distance decay parameters than membership or fee-based facilities or services. The distance decay parameter for public open space, such as parks, was estimated at 1.91[27
], and this is close to the value of 2.0 which is a commonly used distance decay parameter. In the US, there are no empirical studies that evaluate the parameters for distance as well as park sizes in spatial interaction models. So we adopt this 1.91 as the decay parameter in our spatial interactions of park accessibility analysis.
Destination set formation in spatial choice modeling
The second problem associated with spatial interaction accessibility measures is the uncertainty associated with the availability and formation of destination choice sets. Most gravity model-based measures of geographic accessibility say little about the availability and formation of destination choice sets[30
]. Destination set formation is not a problem for either container-based measures or nearest distance measures. The destination set is defined as all parks within the predefined geographic areas containing the residential neighborhoods or the nearest park to the residential places. As discussed above, for the container-based measures, all the parks within a container are included in the final access measure computation. When a neighborhood does not have any parks in the defined container, its container-based measures will be zero. For the nearest distance measure, it only counts the nearest park to a neighborhood, and populations only access this nearest park. However, the destination set formation problem arises for spatial interaction model-based measures, since we have to find a set of destinations (e.g. parks) that could interact with the population of a neighborhood. Current spatial interaction measures assume a neighborhood could interact with all the parks in the study area and hence would include all the parks to compute accessibility for this neighborhood. Theoretically, this is not a problem. In the context of park access, a person does have access to all destinations (parks), regardless of where he or she resides in the US. Thus, potential park accessibility should always be greater than zero for all US residential populations. But most parks are mainly used by nearby residents. In reality, a resident population actually uses a much smaller subset of all the parks in a region and even local areas. If all the parks in the study area are included to calculate the potential park spatial accessibility measures of a neighborhood, significant bias could be introduced. So the park destination set should be more than one but less than the full set of parks in a region. Especially in our study, we could not assume that a neighborhood population will interact with all US parks. This is a problem not recognized by most studies which have utilized spatial interaction model-based measures, especially in the context of park access. This is also related to a still unsolved destination set formation problem in spatial choice modeling[31
The formation of a destination set of parks for a neighborhood population is very complex and could be associated with many demographic and geographic factors. From a psychological perspective, one significant factor is our brain's capacity for information processing. Marketing research shows that individuals have a limited capacity for processing large amounts of information when the choice set of destinations is large[32
]. This means the information to make a choice among a set of alternative destinations easily could be beyond the individual's capacity for information processing. This reflects an upper limit on our brain's capacity to process information on simultaneously interacting elements with reliable accuracy and validity[33
]. This upper limit is seven plus or minus two: Saaty and Ozdemir mathematically showed that, in order to make consistent preference judgments on pairs of elements in a group, the number of elements in the group should be no more than seven[34
]. Our spatial cognition capacity should share this upper limit of seven plus or minus two, as determined from information processing. Our individual limited knowledge (cognition) of spatial alternatives is related to location proximity[35
]. Pellegrini et al. empirically examined parameter sensitivity to choice set specification in the context of shopping destination choice and found that model parameters show encouraging stability with relatively small choice sets of seven to ten stores[36
]. A choice set of the seven nearest parks may be the possible set that a resident most likely takes into consideration to make a preference decision for park visits with reliable certainty. The choice set of seven nearest parks may be a sample set that evaluates the potential significant correlations between park access and physical activity behaviors as shown in a theoretical analysis of sampling distributions for detection of correlations[37
New park accessibility measure: population-weighted distance (PWD)
The spatial interaction accessibility index (
and its various forms) is directly used to quantify the potential spatial access to parks but lacks the intuitiveness of the direct distance measures. Thus, we further introduced the probability access surface from the market penetration approach that assumes the probability of residential population in a neighborhood to visit a park is proportional to its accessibility to this park[38
]. We used the spatial interaction accessibility measure as weights for the sampling probabilities of park choice for residential populations and applied the Huff trade area model to compute the probability (Pij
) that a resident at a neighborhood (i
) will choose to visit a park (j
), as the following formula[38
This formula shows residents are more likely to visit nearby parks and larger parks could attract more distant residents. The expected distance (Di
) for a neighborhood population (Popi
) to its nearby parks was calculated as the following:
Where n is the number of parks that the population in the neighborhood (i) are most likely to visit. So Di is the population-weighted distance (PWD) from the neighborhood (i) to its nearby parks. This measure has the intuitiveness of direct distance measures, and more importantly, it incorporates the concept of population probability access to parks based on the spatial interaction accessibility index. It allows us to evaluate the population accessibility to parks as well as the potential park service population burden.
In the remainder of this paper, we develop a method that makes use of the advantages of spatial interaction accessibility measures and the choice set of destination parks and probability access surface in order to calculate the PWDs to parks in the US at different geographic levels.