Assessing the Accessibility and Equity of Public Green Spaces in Buffalo

A Spatial Analysis of Urban Green Space Distribution

Author

Zhongyu Zhou

Published

December 4, 2024

Introduction

In urban settings, public green areas are essential because they improve inhabitants’ physical and emotional well-being. The accessibility of these areas has a direct impact on quality of life in light of growing urbanization and environmental issues. However, there are frequently differences in the distribution of green space in cities, which could lead to unequal access for various people.

This study examines the accessibility and spatial distribution of public green spaces in Buffalo, New York. The following are the main research questions: 1. How accessible are public green areas to Buffalo residents who live within a 400-meter (5-minute) walking distance? 2. How does the accessibility of green spaces change in various census tracts? 3. How does the accessibility of green spaces at the census tract level relate to median household income?

Materials and methods

This analysis integrates data from two primary sources:

  1. OpenStreetMap (OSM): Provides spatial data on public green spaces, specifically parks and gardens
  2. American Community Survey (ACS) 2020: Supplies census tract level demographic information including population counts and median household income

The methodology follows these key steps:

  1. Data Collection and Processing:
    • Extract green space polygons from OSM using the ‘osmdata’ package, filtering for leisure areas tagged as parks and gardens
    • Obtain demographic data (population and median income) using the ‘tidycensus’ package at the census tract level
    • Transform and intersect all spatial data with Buffalo city boundary using a consistent coordinate reference system (4326)
  2. Accessibility Analysis:
    • Calculate 400-meter buffers around green spaces (representing 5-minute walking distance)
    • Compute accessibility scores for each census tract using a weighted approach that considers:
      • Basic coverage ratio of green spaces
      • Green space size weights (logarithmically scaled)
      • Distance weights (linear decay with distance)
      • Population density adjustment factor
    • Normalize accessibility scores to a 0-1 scale, where higher scores indicate better accessibility
    • Analyze the relationship between accessibility scores and median household income using income quintiles
Code 
library(osmdata)
library(sf)
library(ggplot2)
library(tidyverse)
library(tidycensus)
library(tigris)
library(units)
library(kableExtra)

# Set Census API key
census_api_key("71ee368dd6a9d472f0ba814e6f90b8566a1a7192")

Data Collection and Processing

Code 
# Get Buffalo city boundary
buffalo_boundary <- places(state = "NY") %>%
  filter(NAME == "Buffalo") %>%
  st_transform(4326)

# Get green spaces data
buffalo_bbox <- st_bbox(buffalo_boundary)
buffalo_green <- opq(buffalo_bbox) %>%
  add_osm_feature(key = "leisure", value = c("park", "garden")) %>%
  osmdata_sf()

# Process green spaces
green_spaces <- buffalo_green$osm_polygons %>%
  select(osm_id, name) %>%
  st_transform(4326) %>%
  st_intersection(buffalo_boundary)

# Get demographic data
buffalo_pop <- get_acs(
  geography = "tract",
  variables = c(
    population = "B01003_001",
    median_income = "B19013_001"
  ),
  state = "NY",
  county = "Erie",
  year = 2020,
  geometry = TRUE
) %>%
  select(-moe) %>%
  pivot_wider(
    id_cols = c(GEOID, geometry),
    names_from = "variable",
    values_from = "estimate"
  ) %>%
  st_as_sf() %>%
  st_transform(4326) %>%
  st_intersection(buffalo_boundary)

Accessibility Analysis

Code 
calculate_accessibility <- function(tract, green_spaces, buffer_distance = 400) {
  tryCatch({
    # Convert to projected coordinate system
    tract_proj <- st_transform(st_geometry(tract), 32617)
    green_spaces_proj <- st_transform(green_spaces, 32617)
    
    # Get population data
    tract_population <- tract$population
    tract_area_km2 <- as.numeric(st_area(tract_proj)) / 1000000  # 转换到平方公里
    population_density <- tract_population / tract_area_km2
    
    # Create a buffer
    tract_buffer <- st_buffer(tract_proj, buffer_distance)
    
    # Find accessible green space
    intersecting <- st_intersects(tract_buffer, green_spaces_proj)
    
    if(length(unlist(intersecting)) == 0) {
      return(0)
    }
    
    # Get the intersecting green space
    accessible_gs <- green_spaces_proj[unlist(intersecting),]
    
    # Calculate intersection
    intersection <- st_intersection(tract_buffer, accessible_gs)
    
    # Basic calculations
    intersection_area <- sum(st_area(intersection))
    tract_area <- st_area(tract_proj)
    
    # 1. Basic coverage
    coverage_ratio <- as.numeric(intersection_area) / as.numeric(tract_area)
    
    # 2. Green space size weight
    gs_sizes <- st_area(accessible_gs)
    size_weight <- 1 + log1p(as.numeric(gs_sizes) / min(as.numeric(gs_sizes)))
    
    # 3. Distance weight
    distances <- st_distance(tract_proj, accessible_gs)
    distance_weights <- 1 - (as.numeric(distances) / buffer_distance)
    distance_weights[distance_weights < 0] <- 0
    
    # 4. Population density weight
    # Use an inverse relationship: the higher the population density, the greater the demand for green space
    density_factor <- 1 + log1p(population_density / mean(buffalo_pop$population / 
                                                        (as.numeric(st_area(buffalo_pop)) / 1000000)))
    
    # Comprehensive calculation
    # When the population density is high, the same green space coverage will get a lower score
    weighted_score <- coverage_ratio * mean(size_weight * distance_weights) / density_factor
    
    # Normalize to between 0 and 1
    return(min(1, weighted_score))
    
  }, error = function(e) {
    warning(paste("calculation mistake:", e$message))
    return(0)
  })
}

buffalo_pop$accessibility <- sapply(
  1:nrow(buffalo_pop),
  function(i) {
    if(i %% 10 == 0) cat(sprintf("Processing tract %d of %d\n", i, nrow(buffalo_pop)))
    calculate_accessibility(buffalo_pop[i,], green_spaces)
  }
)

Results

Our analysis reveals several key findings about green space accessibility in Buffalo:

Code 
# Create income distribution map
ggplot() +
  geom_sf(data = buffalo_pop, aes(fill = median_income)) +
  scale_fill_viridis_c(
    name = "Median Income",
    labels = scales::dollar_format(),
    na.value = "grey50",
    option = "magma"  # different color scheme from accessibility map
  ) +
  theme_minimal() +
  labs(
    title = "Median Household Income Distribution in Buffalo",
    subtitle = "Based on Census Tract Level Data"
  )

Code 
# Create accessibility map
ggplot() +
  geom_sf(data = buffalo_pop, aes(fill = accessibility)) +
  scale_fill_viridis_c(
    name = "Accessibility Score",
    limits = c(0, 1),
    labels = scales::percent,
    na.value = "grey50"
  ) +
  geom_sf(data = green_spaces, fill = "darkgreen", alpha = 0.3) +
  theme_minimal() +
  labs(
    title = "Green Space Accessibility in Buffalo",
    subtitle = "Percentage of area within 5-minute walking distance of green spaces"
  )

Code 
# Data cleaning and outlier handling
buffalo_pop_clean <- buffalo_pop %>%
  # Remove outliers in income
  filter(!is.na(median_income)) %>%
  filter(median_income > quantile(median_income, 0.01, na.rm = TRUE) &
         median_income < quantile(median_income, 0.99, na.rm = TRUE)) %>%
  # Remove extreme values of accessibility
  filter(accessibility > quantile(accessibility, 0.01, na.rm = TRUE) &
         accessibility < quantile(accessibility, 0.99, na.rm = TRUE))

# Create income quantiles
buffalo_pop_clean <- buffalo_pop_clean %>%
  mutate(
    income_quintile = cut(median_income,
                         breaks = quantile(median_income, probs = seq(0, 1, 0.2), na.rm = TRUE),
                         labels = c("Lowest 20%", "20-40%", "40-60%", "60-80%", "Highest 20%"),
                         include.lowest = TRUE)
  )

# Calculate the average accessibility for each income quantile
quintile_summary <- buffalo_pop_clean %>%
  group_by(income_quintile) %>%
  summarise(
    mean_accessibility = mean(accessibility, na.rm = TRUE),
    median_accessibility = median(accessibility, na.rm = TRUE),
    n_tracts = n()
  )

# Create a scatter plot
improved_income_plot <- ggplot(buffalo_pop_clean, 
                             aes(x = median_income, y = accessibility)) +
  # Add scatter points
  geom_point(aes(color = income_quintile), 
             shape = 18,  
             size = 3) +
  # Add a trend line
  geom_smooth(method = "loess", color = "black", linetype = "dashed") +
  scale_x_continuous(labels = scales::dollar_format(),
                    breaks = scales::pretty_breaks(n = 8)) +
  scale_y_continuous(labels = scales::percent_format(accuracy = 1),
                    limits = c(0, 1)) +
  scale_color_manual(values = c("#4B0082", "#4682B4", "#2E8B57", "#FFA500", "#DC143C")) +
  theme_minimal() +
  labs(
    title = "Relationship between Income and Green Space Accessibility",
    subtitle = "With smoothed trend line",
    x = "Median Household Income",
    y = "Green Space Accessibility Score",
    color = "Income Quintile" 
  )

print(improved_income_plot)

Code 
# Display quantile statistics
knitr::kable(quintile_summary, 
             caption = "Accessibility Statistics by Income Quintile") %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"))
Accessibility Statistics by Income Quintile
income_quintile mean_accessibility median_accessibility n_tracts geometry
Lowest 20% 0.3094663 0.2593383 15 MULTIPOLYGON (((-78.86848 4...
20-40% 0.3363453 0.3295316 15 MULTIPOLYGON (((-78.82441 4...
40-60% 0.3320864 0.1718203 14 MULTIPOLYGON (((-78.90868 4...
60-80% 0.2856320 0.2191314 15 MULTIPOLYGON (((-78.86808 4...
Highest 20% 0.2639786 0.1719957 15 MULTIPOLYGON (((-78.88936 4...

Conclusions

The results show a complex pattern of green space accessibility in Buffalo:

  1. There is an unequal spatial distribution, with the Central and Southeast having lesser accessibility and the Northeast and Midwest having better accessibility.

  2. The link between accessibility and income is U-shaped, with middle-income communities having the least accessibility.

  3. Accessibility is worse in heavily crowded areas and better around large parks.

Our analysis, which takes into account population density and spatial coverage, shows intricate trends in the accessibility of green spaces at various income levels. Future studies should look at other socioeconomic characteristics, road networks, and the quality of green spaces. Urban planning plans may be influenced by these findings to distribute green space more fairly among all communities.

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