How Distance to Common Household Destinations Varies as a Function of Household Density DRAFT – not for distribution Christian.Jacqz@state.ma.us

GIS Analysis in Support of the Massachusetts Climate Roadmap In January of 2008, the Massachusetts Executive Office for Energy and Environmental Affairs (EEA) started working on a “Climate Roadmap”– a detailed plan to reduce greenhouse gas (GHG) emissions in the 2020 and 2050 time frames. Working groups were organized by sector or category of greenhouse gas reduction to analyze the potential impact of various policy options. In the transportation sector, accounting for approximately 30% of all GHG emissions, options currently being discussed (March 2008) include “feebates,” sliding scale excise taxes and other incentives for fuel-efficient cars, raising the gas tax and reducing speed limits. Also under consideration are investments in public transportation and a variety of financial and regulatory incentives for municipalities to adopt local land use controls which would lead to more compact and efficient patterns of growth. All these are being evaluated on the basis of political feasibility and economic impact as well as effectiveness. In this context, staff at EEA’s Office for Geographic and Environmental Information (MassGIS) are working to analyze the relationship between land use patterns and GHG emissions from private automobiles. The first phase of this project involved constructing a model for local trips of residential origin, using newly constructed geographic datasets which combined population, land use and business locations. The unit of analysis was a statewide grid of individual cells 250m square in size, which were used to aggregate detailed mapping of land use, block level Census statistics and geocoded point locations for individual businesses and other destinations. In the second phase, the analysis will reference data on vehicle location, type and actual vehicle mileage per year from inspection records at the registry of motor vehicles to the same statewide grid. What follows describes the approach used to construct the initial model and presents the results of our analysis to date. The construction of the initial model involved a series of steps.

1. A detailed map of household locations and counts was created by combining land use and population (number of households).

2. A grid of 250 meter cells was created to serve as the framework for analysis. 3. Each grid cell was coded with an estimated count of households. 4. Common household destinations were identified based on a transportation survey

and mapped from address information or other sources. Point locations of each destination were assigned to grid cells.

5. For all cells, the distance to the nearest of each type of household destination was computed.

6. Finally, for all cells, the weighted sum of distances to common destinations was computed based on a national survey of household trips,

This weighted sum, multiplied by the number of trips daily, and adjusted for the fact that it represents distance “as the crow flies” rather than driving distance, can be taken as a preliminary estimate, for each grid cell, of daily vehicle miles traveled for non-work, non-social trips. These steps are explained in detail below.

1) Population/Land Use GIS mapping from the US Census, linked to population figures for 2000, is widely used in socio-economic, transportation, health and many other kinds of studies. Unfortunately, Census geography is all-inclusive, that is, it covers the whole landscape, so that it is impossible to tell within any particular block, block group or tract exactly where people live. Since the Census more or less equalizes the population count for the different levels of the geographic hierarcy, even the smallest units of Census geography may be still be rather large in rural areas. This is a problem for any detailed study of travel patterns based on household location. For the purposes of this study, we set about to improve the Census map of population, that shows how many households are in a given area, by combining it with a map showing more precisely where people live, that is residential land use. To do this, we used the GIS to overlay the Census mapping with land use mapping from 1999 which includes the delineation of residential areas classified into four different categories of density based on a visual interpretation of aerial photograpy. By computing the area of each kind of residential use within each Census block, we were able to to allocate the household numbers to the land use polygons, accounting for all households. The graphic below shows the first step in this process - Census household counts and Census block boundaries for a portion of Southeastern Massachusetts in purple and actual residential areas in various shades of yellow depending on their classification.

Block-level household counts (purple), residential areas (yellow/brown)

The allocation of household counts to the residential areas was done on the basis of both area and relative density of different land use classifications. The graphic below shows the final allocation.

Household counts allocated to land use polygons

2) Using a Grid Cell Approach In many GIS analyses, there is a fundamental choice to be made about the analytic environment – should it be raster or vector? A raster approach uses set of regular, square grid cells to which the input variables in question are assigned. This provides a consistent unit of analysis across all the datasets of interest and allows for combination of different datasets on this basis. Another advantage of this approach is to vastly speed up the processing of large, complex datasets. Finally, using a raster approach, one can take advantage of sophisticated algorithms which have been developed to model spatial correlations, means, proximity and other spatial relationships. The disadvantage is that some detail is lost since the minimum unit of area is one grid cell. Vector processing preserves the original, irregular geography of the inputs – but as more and more datasets are combined the geographic boundaries become increasingly complex and fragmented. In the present case, where there were a great many inputs, there was a strong impetus to use a raster approach. We chose a 250 meter grid cell as a reasonable compromise between precision and processing speed – the analysis is intended to model distances at the scale of common household trips by automobile so a resolution of one quarter of a kilometer or about 200 yards seemed adequate. This resolution allows for identification of distances which are considered walkable – at least for some kinds of destinations (public library as opposed to grocery store).

3) Assigning Household Counts to Grid Cells The raster methodology, as described above, requires that all inputs be assigned to grid cells – so the first step was to do this for the enhanced population mapping described above. The result is shown below.

Household numbers assigned to 250m grid cells Fractional household numbers are generated in order to keep the totals accurate. Since the grid cells are all the same size, the values in the cells represent household density and a thematic map can be generated on that basis. The graphic below shows the result for a somewhat larger area.

Household density shown in shades of brown

4) Map Common Destinations and Assign to Grid Cells The following list of common destinations was taken from the National Household Transportation Survey done by the US Department of Transportation in 2001. Unfortunately, the only comparable information for Massachusetts is much older. The relative frequency of trips to each destination is expressed as a percentage; the survey also determined that there were an average of 4.2 trips per household per day.

Trip type % of trips Commute 13.13%Friends/family 11.76%Restaurants 10.15%Groceries 7.26%Malls 7.26%School 6.52%Dentists 4.96%Church 3.79%Hardware Stores 3.63%Gyms 3.00%Parks 2.90%Gas Stations 2.90%Doctors 2.49%Convenience Stores 2.39%Pharmacy 2.39%Clothing 2.27%Dry Cleaners 1.82%Banks 1.82%Post Office 1.36%Bars 1.09%Cinema 1.09%Auto Repair 0.91%Limited service eateries 0.91%Day Care 0.87%Performing Arts 0.73%Beauty 0.69%Sports stadiums 0.54%Library 0.45%Museums 0.36%Town Hall 0.36%Vets 0.18%

We made only a pro-forma attempt to account for the journey to work or “social” trips in this phase of the project since our expertise is not transportation modeling and we have no way of estimating those distances at the same level of detail as the other components, as will become clear. We did map all the other kinds of destinations, however, as points on the map. For the business locations, we used Dun and Bradstreet listings which provided a NAICS business code and an address; we used the GIS to “geocode” or estimate the point location for the address. We used existing GIS sources for the locations of schools, libraries, town halls etc which were in many cases more accurate than geocoding.

Grocery stores (green dots) and all other businesses (brown dots) in relation to residential areas The point locations of common destinations were aggregated to the grid cells as well, so that for every cell we had a count for each kind of destination which fell within that cell. Usually, of course, it would be zero or one, although one might expect to occasionally find more than a single restaurant within a box two hundred yards on a side.

5) Compute distances As mentioned above, the grid cell approach allows a user of GIS software to take advantage of very sophisticated algorithms for combining different grid cell layers, computing distances and other statistics and modeling spatial relationships. These algorithms typically take one or more input grids (such as the count of households by cell) and produce an output grid (such as the mean number of households within one kilometer, for each cell.) For the current purpose, we were interested in computing the distance from each cell, in particular from cells where there was a non-zero count of households, to the closest of

each household destination. This would be an overwhelming task to perform manually, but fortunately the powerful functions available with grid based software make it easy.

The grid layer illustrated at left records the distance value for the single closest of each kind of destination – this is appropriate for a grocery store but probably not very realistic for a church or a restaurant where individual preference plays a much stronger role. An alternate approach was developed for those types of destinations which records the distance within which there is a reasonable choice.

Grid records distance to each type of destination In the illustration to the right, the search radius around the individual cell has been increased to include two restaurants. This number could be higher or lower for each type of destination.

Radius which provides desired level of choice, in this case 2 restaurants are within a 4 cell radius

At this point in the analysis, the ability to combine different grid cell layers arithmetically is key. First, for each type of destination, the grid layer representing distances to the nearest point of that type can be multiplied by a factor for the relative frequency of trips to that destination. That product represents the total distance traveled to that destination as a fraction of the total number of trips. Thus, distance to groceries x % of trips = total distance traveled to groceries / total number trips distance to church x % of trips = total distance traveled to church / total number of trips etc. for 30 different destinations Then if we add all the grid layers, what we have in each cell is the sum of the weighted distances and we can multiply that by the total number of trips to get the total distance. The reason that we hold off multiplying by the total number of trips until the end is to allow for flexibility in adjusting that number by region. In grid layer terms, we will be able to develop a grid representing total number of trips per household that varies regionally to be used in the calculation. There is one more step, which is that an estimate of the total distance traveled by car has to include an adjustment for the greater distance traveled by road than “as the crow flies”– this adjustment ranges from 30% to 40% in our initial testing. We did not expend a great deal of effort in refining this adjustment, since our work with the actual mileage figures from the RMV will allow us to estimate this adjustment and test its variability in relation to a number of factors such as road density. In other words, we would guess that distance by car is closer to straight line distance in more densely populated areas, and in areas with less topographic relief, but having real data will allow us to test this assumption. Once we have estimated the total distance traveled for each household in each cell, we then can multiply by the total number of households to get the total To express the same series of steps in formulas, which may help make the math involved a little clearer.

Wi = Ti / Ttotal ∑Wi = 1

Wi is the weight for destination i Ti / Ttotal is the number of trips to destination i divided by total trips

∑Wi is the sum of weights, which has to total 100%

and

Dtotal = ∑(Wi * Di)

Dtotal is the distance traveled per trip Di is the distance to each destination ∑(Wi * Di) is the sum of the weight times the distance for each destination

and finally, in order to estimate total vehicle miles traveled by households (again, in this case we excluded certain types of destinations):

VMThouseholds = H * Dtotal * Ttotal * N

VMThouseholds is the total distance traveled by all households in a cell H is the number of households Dtotal is the distance per trip Ttotal is the number of trips daily N is the adjustment factor for network distance

The correlation that we were interested in was actually between the Dtotal grid and the household density – again, in words: Does the distance traveled to common household destinations (excluding social and work destinations) vary in a predictable way according to residential density? As it turns out, there is a very strong relationship, depicted in the following graph:

The points represent sample means for class intervals of 0.1 units per acre, with a total of 10,000 random sample points, of which 4,000 fell within a residential land use and were used to develop the relationship shown.