Introduction
Urban growth is an inevitable phenomenon in all human communities. Populations need accessible healthcare provision and the general hospital is the epitome of such a service. Oregon’s Lane County is home to the second most populous municipality in Oregon: Eugene and possesses four general hospitals within its geographic boundaries. But as growth continues, such healthcare facilities will undoubtedly experience stress on their serviceable populations due to their inherent capacity. The question is: As growth progresses through time, will any one hospital be overwhelmed? If so, where is suitable location for the additional facility? Geographic Information Systems have the adequate ability to solve the problem, a location problem. R.L. Church defines this problem as “identifying a specific position or place for a specific function or activity” (p. 293). A GIS software (ArcMap, QGIS) has the capacity to analyze facilities (hospitals) in relation to potential demand (households) based upon the minimum distance of the most efficient path between the demand location and the facility location. Location-allocation then weights the distance in relation to the total population of demand locations. The result is an agglomeration of places with potential demand for that facility’s service that has successfully minimized the distance between all demand locations and the facility in question. This fundamental location model is titled the “p-median” model (Church). To identify the increasing Demand upon each of the four Lane County hospitals, a p-median model can be employed, allowing one to observe proportional demand among the total population at interval time periods (eg. five years). Via a GIS, stress points can be both quantified and visualized as a result of location-allocation analysis. The p-median location model will be applied to the case of hospital capacities in hopes of finding the suitable location of an additional hospital if it is needed. Growth will be projected in five-year intervals for a complete temporal extent of fifteen years, observing urban growth in Lane County from 2015 to 2030.
Methodology
First, a map of current land use was created to represent t0 or the initial time step of Lane County urban growth. Visual data was acquired from the Oregon Geospatial Enterprises Office (GEO) in the form of a Lane County land use raster (2014) and the line borders of county from the counties feature file. Cell resolution was set to ‘2087’ x ‘2087’ in order to standardize all land use types in terms of 100-acre plots. 100 acres was founded on the assumption that all future residential development will occur in spatial units of this size. Land use was then sub-divided by land use type. Several land use identities were aggregated in order to produce two new land use raster layers: (1) Urban plots and (2) Forest/Agricultural plots. Land use type was redefined via a reclassification procedure through which several urban land uses (inc. ’Medium-density Residential’, ‘Commercial’) were given the name ‘Urban’. All agricultural and forested land was aggregated as ‘Farm/Ag’.
A growth algorithm was created in reference to public administrative data. The US Census Bureau’s website was consulted for Lane County and the City of Eugene population values from both 2000 and 2010 data sets. In conjunction with these data a 2014 estimate for Lane County, also published by the US Census, was referenced to help create an average five-year growth rate of approximately 4.6%. Lane County’s growth from April of 2014 to June of 2015, at 0.9%, was cited by Lane County’s Register-Guard newspaper and was also utilized for the growth rate estimate above. Growth was assumed to occur at ‘medium-density’ proportion which was defined via the Eugene City Code (9.9610) as “10 to 12 dwelling units per acre”. Selecting the median value of 11 dwelling units per acre with an assumed household population of 4 persons, the model’s cell resolution of 100 acres was equated to 4,400 persons for all cells representing growth over any of the five-year intervals. Eugene’s estimated 2015 population when multiplied by the Register-Guard’s reported county growth rate is 163,906. This value was then divided by the amount of ‘Urban’ cells at t0, yielding a per cell value of approximately 126 people. However, 4.6% growth would yield a population gain, over five years, of 7,540 new people. Given that the model’s ‘growth cell’ value is 4,400 individuals, each subsequent time step in the model should only yield approximately 1.71 cells as this amounts to 7,540 new urban residents.
Growth was then visualized through a sequence of procedures including euclidean distance and a reclassification of Distance values generated from this distance layer. Following the generation of a distance-from surface, all values within one cell’s distance (2,087 feet) away from the outermost ‘Urban’ cells were redefined as ‘0’(0=Urban). This sequence was performed three times with each new growth layer being overlaid atop the previous time intervals.
t0 through t3 ‘Urban’ cells were converted into point features to conduct a ‘p-median’ location-allocation. A network analysis was conducted with the intent to model demand of existing hospitals within the county with Demand points being all ‘Urban’ points and Facilities being hospital locations. A national road network was acquired from University of Oregon GIS Library and ESRI to be used as input for calculating a distance each point lies from all hospitals. Demand was defined as proportion of total population at t0, t1, t2 , and t3.
Finally, tipping points in capacity for each hospital were identified through a mathematical rule:
[ (D)ti ≥ 1/4(D)t0 ]
If at any one growth interval, the added population’s Demand on the facility equals or exceeds one quarter of that facility’s initial Demand, a new facility is needed to service that populous region.
Below is an illustration of the growth model workflow for t0 to t1:
Results
At present, there are four servicing hospitals in Lane County. In order of highest to lowest Demand by Facility, they are (1) Sacred Heart Medical Center in Eugene (58.8%), (2) McKenzie-Willamette Medical Center in Springfield (25.1%), (3) Cottage Grove Community Hospital (10.6%) and (4) PeaceHealth Peace Harbor Medical Center in Florence (5.5%).
Illustrated below are the hospital demand values (as a percentage of the total population in the county) at the growth time intervals of 2020, 2025, and 2030 respectively. Below are aggregated Demand Allocations for all hospitals at each time step from 2015 to 2030. Also, a graphic for each hospital’s Demand at all time steps is included. Within each graphic is the ‘tipping point’ value of 1/4(D)t0 for that specific facility.
Referring to this rule as an indicator of post-peak capacity it can be observed that at no time interval throughout the temporal extent of the model do any of the four listed hospitals reach ‘peak’ capacity. Not even close!
The first two maps below illustrate urban and forested/ag. land uses as they are currently, the second map including hospital locations.
The following three maps illustrate growth at each time step. The reclassified euclidean distance output however, is visually deceiving. Growth could not segregated to any one ‘Urban’ area over the other and so growth appears to occur at the perimeter of all ‘Urban’ land uses at all time steps. Urban growth will likely not occur in this fashion in reality and so the value of each cell was transformed in order to preserve the integrity of the growth algorithm and the population values underlying the growth model at each time step. At t0 each cell represents 126 people based on the estimated population of Lane County. However, at t1 through t3 each cell value was fixed to approximately 3 people in order to conform growing Demand by facility to the growth rate of 4.6% county-wide.
Uncertainty
Multiple systemic errors were propagated as the Lane County growth model was created. First, the growth algorithm was founded on a mixture of precise population measurements and county-wide growth average. Mean values were derived from this data to create a 5-year growth rate which disregards generational and gender populations of each urban area within the county. For this, a dynamic quality of real population growth was simplified, subtracting from the model’s accuracy. Second, the standardization of cell resolution created a generalization within the model omitting two land use categories entirely (‘5-acre farm’, ’10-acre farm’) overlooking urban growth patterns at this spatial resolution entirely. Third, all growth was assumed to fit a medium-density fashion. Different residential developments along the urban periphery will likely vary on the scale of low- to high- density dwellings and so projected growth at each time interval is likely conservative to a model that accounts for high-density development. Reclassification methods for defining 2015 ‘Urban’ land types was grossly overstated because non-residential land uses were defined as ‘Urban’ when all future ‘Urban’ growth was assumed to be exclusively residential. For this, the geographic locations of residential growth plots are inaccurate and farther-reaching than in reality. The lack of spatial constraints to growth exacerbates this model error (eg. urban growth spills over into Fernridge Reservoir West of Eugene). Finally, the formula for hospital capacity is founded on personal logic alone. Individual hospital capacities were not used nor found in the process of model design.
Conclusion
Through the use of GIS and the application of a location-allocation analysis on Lane County growth and hospital demand, albeit systemic error and uncertainty inherent in the model’s assumptions and standards, no alarming stress on hospital capacities was identified over the fifteen-year growth projection. However, because of unequal size in urban areas, the Eugene/Springfield area will likely encounter an overextension of services in its hospitals sooner than either Cottage Grove or Florence facilities. For a more fruitful (accurate) growth model, less generalization would need to occur in the design of a growth algorithm for Lane County urban areas. Even with growth projections favoring statistical averages, a more realistic fashion of spatial growth could be visualized if greater effort was put into creating spatial constraints (eg. water sources, public lands) on growth. Physical growth would also be reduced (and more accurate) if the error of vagueness had not persisted when reclassifying original land use data into a ‘Urban’/’Ag’ dichotomy. Urban encompasses all forms of human structure but the only human structures which are relevant to the location problem are residential structures. And so with increased diligence to realistically frame the phenomenon of growth in Lane County, the location analysis of existing hospitals would possess a level of veracity more respectable than what was generated through the model in discussion.
References
Church, R. L. (1999). Location modelling and GIS. Geographical information systems, 1, 293-303.
Eugene City Code. Department of Zoning. 9.9610.
Hubbard, Saul. “Oregon’s Population Hits 4 Million.” Register-Guard 18 Nov. 2015, Local sec. Print.
United States of America. Census Bureau. 2000, 2010 Population by County.