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Roadless Space of the Conterminous United States

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Science  04 May 2007:
Vol. 316, Issue 5825, pp. 736-738
DOI: 10.1126/science.1138141

Abstract

Roads encroaching into undeveloped areas generally degrade ecological and watershed conditions and simultaneously provide access to natural resources, land parcels for development, and recreation. A metric of roadless space is needed for monitoring the balance between these ecological costs and societal benefits. We introduce a metric, roadless volume (RV), which is derived from the calculated distance to the nearest road. RV is useful and integrable over scales ranging from local to national. The 2.1 million cubic kilometers of RV in the conterminous United States are distributed with extreme inhomogeneity among its counties.

The road network of the United States exceeds 6.3 million km in aggregate length (1) and fills the national landscape so fully that, except in Alaska, one can get no farther from a road than 35 km (2). This extensive road network provides societal benefits by bringing natural resources to consumers, linking workers to jobs, and connecting people to urban services. It is in the spaces between the roads that valuable natural resources are present and ecosystem services are rendered. Road encroachment affects ecological resources, primarily in negative ways (1, 38), usually by fragmenting habitats and introducing chemical contaminants and exotic species to the ecosystem. Roads have been demonstrated to have dozens, if not hundreds, of effects on ecosystems and watersheds (1, 35, 711). Physical, chemical, and biological processes transmit influences from roads to their surroundings in a mélange of deterministic, stochastic, and chaotic processes that are made even more complex through their interactions with the variability of the landscape. The span of documented effects ranges from a few meters to many kilometers (1) and depends not only on the roads themselves but also on the volume and types of traffic that they carry. These complexities make it impractical to measure or estimate the area of influence without extensive local observation. Our work is aimed at bridging these details in order to answer two questions: (i) how much space is there between the roads, and (ii) how much is lost as new roads are added to the network, penetrating roadless space? These questions cannot be answered by measuring either the length or surface area of roads because these metrics do not respond to road placement. We sought a metric that would have a greater response to a road penetrating deeply into otherwise roadless space than to a road of similar length lying close to other roads.

We introduce a metric called roadless volume (RV). RV calculation begins with the computation of the horizontal distance to the nearest road (DTR), which is most accurately done with fast-marching methods (12) or adequately done with network methods (13); the network computation method is available in many geographic information systems. In practice, DTR is computed for points on a square grid (we used a 30-m grid); grid size does not bias results, but it affects accuracy. RV for an area is the integral of DTR over the area, which is estimated to be the total of the DTR cell values multiplied by cell area, with resulting units of cubic meters or cubic kilometers. Calculation accuracy depends on cell size, the quality of the road data set used for DTR computation, the sinuosity of roads, and (to a small degree) the method of calculation. RV is objective; there are no arbitrary factors.

RV can be described and visualized as follows: Substitute DTR for elevation to create a pseudotopographic surface (real topography plays no role in our definition of RV). RV of a footprint area is the volume of the pseudotopography above that footprint (Fig. 1). Roads of equal length produce different RV changes, depending on their alignments with respect to other roads (Fig. 2). RV responds simultaneously to footprint area, footprint shape, and the alignment of roads within the footprint. Compact footprints with no internal roads produce maximum RV. Meandering boundaries and internal roads diminish RV. The greatest reduction comes from roads that penetrate places that otherwise would be most remote from roads. Roads placed close to other roads only modestly reduce RV.

Fig. 1.

RV is calculated by substituting DTR for elevation and then calculating the volume beneath the pseudotopographic surface. Two examples are shown, with perimeter roads in blue (there is a hidden road along the back of each volume). (Left) For a 1-km-square road pattern, the pyramid has a height of 0.5 km and a volume of 0.167 km3. (Right) The elongated pyramid measures 0.333 by 3 km and therefore has the same footprint area as the square pyramid, but its volume is 47% of the square pyramid volume. RV simultaneously accounts for area and shape.

Fig. 2.

(Left) A square road pattern produces a pyramid of roadless volume. (Center) Four added roads, each of length = 0.5 × (the length of one pyramidside) and intersecting at the center (the two roads parallel to the long side of the image are mostly hidden), reduce the pyramid volume by 50%. (Right) Four roads of the same length, starting at the corners and angled slightly toward the center (tan divergence angle = 0.1), diminish the pyramid volume by only 13.5%.

We calculated DTR for the entire United States on a 30-m grid aligned with the National Land Cover Dataset (NLCD), thus enhancing a national geospatial resource that is used for a wide variety of ecological and land-use analyses (6, 14, 15). RV for any footprint is A<DTR>, where A is the area of the footprint and <DTR> is its mean DTR. With this definition, footprints need not be bounded by roads, enabling calculations of RV for counties (16). By summing county RV values, we estimated the RV of the conterminous United States to be 2.1 × 106 km3. Maps inherently provide visual weighting by area, so we color-coded county results (Fig. 3) by <DTR> values rather than by RV, thus avoiding double emphasis of county size.

Fig. 3.

Map of <DTR> by county in the conterminous United States. DTR legend classes are of approximately equal area, and color rendering closely follows area-adjusted county rank.

Roadless space is an asset that is unequally distributed by county and further unequally distributed among the population. Residents of two counties with equal RV have different per-capita shares of the roadless-space resource in inverse proportion to the county populations. Figure 4 shows per-capita RV by county, which can also be interpreted as the pressure of population against the counties' roadless spaces. Comparing Figs. 3 and 4, one sees that some counties with high DTR, and therefore high RV, have low per-capita RV. Prominent examples occur on the Pacific coast, along the Wasatch Front in Utah, along the Front Range in Colorado, and at the southern tips of Nevada and Florida; all these counties have metropolitan areas closely juxtaposed with mountains, deserts, or (in Florida) extensive wetlands. In contrast, low county populations create high per-capita RV in a band of counties stretching from the Dakotas to western Texas, in spite of relatively low DTR in most of these counties.

Fig. 4.

Per-capita RV by county for the conterminous United States. Legend classes are of approximately equal area, and color rendering closely follows area-adjusted county rank.

The county with the lowest per-capita RV is Kings County in New York (Brooklyn; roughly 4000 m3 per capita, giving each person the equivalent of a 45° pyramid that is 30 m long on aside) (17), and the county with the highest per-capita RV is Hinsdale County in southern Colorado (11.9 km3 per capita, giving each person a pyramid that is 4.1 km long on a side). The contrast in ecological conditions between these counties is extreme: One county is a dense urban area; the other is largely wilderness. The ratio of least to greatest roadless space per person in the conterminous United States, measured at the county scale, is approximately 1:3 × 106: a greater dynamic range than that of other common socioeconomic statistics at the county scale, such as population density (1:7 × 105) (18) or mean income (1:7.8) (19). This large dynamic range implies that counties with low population densities also have few roads, large values of <DTR>, and large RV.

Socioeconomic processes add roads, diminishing DTR and RV. An assessment of changes in RV requires detailed and consistent maps on multiple dates, which are available in only a few places. One such place is the Front Range in Colorado, for which we made a movie of the change of RV from 1937 to 1997 (20). Here, nearly half of the initial RV was lost during the 60-year study period, as a result of urban expansion, growth of small towns, and housing dissemination—all occurring on agricultural land.

It is reasonable to postulate that distance from roads, on average, diminishes road influences, an application of a geographic law introduced by Tobler (21). Thus, although we cannot trace the details of road-induced effects, it may nevertheless be useful to know the extent to which we are diminishing the space where these effects are least likely and least intense. RV is a sensitive indicator that summarizes the status of this space.

Supporting Online Material

www.sciencemag.org/cgi/content/full/316/5825/736/DC1

Materials and Methods

SOM Text

Tables S1 and S2

References

Movie S1

References and Notes

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