Descriptions and Maps

The USDA, Economic Research Service's (ERS) Area and Road Ruggedness Scales data product provides measures of topographic variation, or "ruggedness," for census tracts across 50 States and Washington, DC. The data product provides continuous and categorical measures of topographic variation for vintage 2010 census tracts, offering end-users the flexibility to utilize measures of rugged terrain that meet their unique needs.

This page provides basic definitions as well as tables and maps that summarize the data. For more details on the background and creation of the Area and Road Ruggedness Scales, see the Documentation. Much of the information here is excerpted or adapted from the August 2023 report, Characterizing Rugged Terrain in the United States (ERR-322).

Definitions

  • Terrain Ruggedness Index (TRI): A grid-cell-level measure of elevation change between a grid cell and its adjacent grid cells. TRIs were used as a building block to create the categorical scales.
  • Area Ruggedness Scale (ARS): A six-category classification of the relative ruggedness of land within U.S. census tracts. The scale was calculated using the mean (average) Area TRI, which measures the change in elevation for grid cells across all terrain.
  • Road Ruggedness Scale (RRS): A five-category classification of the relative ruggedness of the land along roads within U.S. census tracts. The scale was calculated using the mean (average) Road TRI, which measures the change in elevation for grid cells that contain roads.

The Area Ruggedness Scale

The ARS is a classification of topographic variation within census tracts. Each of the land-based census tracts from the 2010 decennial census was classified into one of six ARS categories based on its mean (average) Area TRI. The census tracts with the lowest mean TRI values have the least topographic variation, whereas the census tracts with the highest mean TRI values have the most topographic variation. The six ARS categories are:

  1. Level, with mean Area TRI values of 0.000–18.519 meters;
  2. Nearly level, with mean Area TRI values of 18.520–41.469 meters;
  3. Slightly rugged, with mean Area TRI values of 41.470–71.699 meters;
  4. Moderately rugged, with mean Area TRI values of 71.700–103.864 meters;
  5. Highly rugged, with mean Area TRI values of 103.865–134.430 meters; and
  6. Extremely rugged, with mean Area TRI values of 134.431–242.804 meters.

Summary statistics for the mean Area TRI values of the census tracts in each ARS category are available in the table below. Most census tracts have very little topographic variation, with 71.0 percent of census tracts being classified as category 1–level in the ARS. However, this category has the smallest range of mean Area TRI values (18.5 meters). The next largest category is 2–nearly level with 19.4 percent of census tracts. This results in 9.6 percent of census tracts being classified as at least slightly rugged (categories 3–6) and only 0.5 percent being classified as extremely rugged (category 6). The top category has the largest range of mean Area TRI values, with a difference of about 108 meters between the largest and smallest values.

Vintage 2010 census tract mean Area Terrain Ruggedness Index values by Area Ruggedness Scale category
ARS category Category values (meters) Number of census tracts Mean (meters) Standard deviation (meters)
1–Level 0.000–18.519 51,639 9.131 4.341
2–Nearly level 18.520–41.469 14,125 26.485 6.280
3–Slightly rugged 41.470–71.699 4,478 53.577 8.517
4–Moderately rugged 71.700–103.864 1,572 85.373 9.249
5–Highly rugged 103.865–134.430 559 117.549 8.871
6–Extremely rugged 134.431–242.804 392 158.504 21.458
U.S. total 0.000–242.804 72,765 18.520 21.410
Note: The Area Ruggedness Scale (ARS) is an ordinal scale of topographic variation within census tracts in the United States, ranging from category 1–level to category 6–extremely rugged.
Source: USDA, Economic Research Service, Area and Road Ruggedness Scales data product.

In the ARS map below, light orange represents category 1, which has the most level land, while dark orange represents the highest level of ruggedness, category 6. The geographic patterns illustrated by the ARS categories are similar to those of a topographic relief map. The Appalachian Mountains, Rocky Mountains, Pacific Mountain System, and Sierra Nevada are all clearly visible in the ARS. The Southern Coastal, Great Plains, and Corn Belt regions are relatively level. However, prominent exceptions to this observation are the Ozark and Ouachita Mountains in Arkansas, southern Missouri, and eastern Oklahoma; the Black Hills in western South Dakota; and the Driftless Area in western Wisconsin along the borders with Minnesota and Iowa. Other well-known topographic features in these areas can also be identified, such as the Badlands in North and South Dakota and the Sandhills in Nebraska.

The Road Ruggedness Scale

The RRS is a classification of topographic variation along roads within census tracts. Each of the land-based census tracts from the 2010 decennial census was classified into one of five RRS categories based on its mean (average) Road TRI. The census tracts with the lowest mean TRI values have the least topographic variation, whereas the census tracts with the highest mean TRI values have the most topographic variation. The five RRS categories are:

  1. Level, with mean Road TRI values of 0.000–13.650 meters;
  2. Nearly level, with mean Road TRI values of 13.651–26.209 meters;
  3. Slightly rugged, with mean Road TRI values of 26.210–40.553 meters;
  4. Moderately rugged, with mean Road TRI values of 40.554–54.949 meters; and
  5. Highly rugged, with mean Road TRI values of 54.950–134.656 meters.

Summary statistics for the mean Road TRI values of the census tracts in each RRS category are available in the table below. Most census tracts have very little topographic variation, with 65.6 percent of census tracts classified as category 1–level in the RRS. The next largest category is 2–nearly level, with 22.4 percent of census tracts. This results in 12.0 percent of census tracts being classified as slightly to highly rugged (categories 3–5) and only 4.4 percent being classified as moderately or highly rugged (categories 4 and 5). The top category has the largest range of Road TRI values, with a difference of nearly 80 meters between the largest and smallest values, while the other four categories have a range of about 13 to 14 meters.

Vintage 2010 census tract mean Road Terrain Ruggedness Index values by Road Ruggedness Scale category
RRS category Category values (meters) Number of census tracts Mean (meters) Standard deviation (meters)
1–Level 0.000–13.650 47,740 7.068 3.055
2–Nearly level 13.651–26.209 16,297 18.528 3.461
3–Slightly rugged 26.210–40.553 5,518 32.178 4.082
4–Moderately rugged 40.554–54.949 1,956 46.569 4.137
5–Highly rugged 54.950–134.656 1,254 68.022 12.189
U.S. total 0.000–134.656 72,765 13.651 12.368
Note: The Road Ruggedness Scale (RRS) is an ordinal scale of topographic variation along roads in the United States, ranging from category 1–level to category 5–highly rugged.
Source: USDA, Economic Research Service, Area and Road Ruggedness Scales data product.

In the RRS map below, the light-yellow color represents category 1, which has the most level land, whereas dark brown represents category 5, the highest level of ruggedness. As with the ARS, the geographic patterns illustrated by the RRS categories are similar to those of a topographic relief map. In the eastern United States, the Appalachian Mountains are clearly visible, stretching from western Maine down to northeastern Alabama. There are clusters of census tracts with roads on very rugged land in the Appalachian Mountains, particularly along the Tennessee-North Carolina border and along the Kentucky-Virginia border into southwestern West Virginia.

In the western United States, parts of the Rocky Mountains are clearly visible. In particular, there are clusters of census tracts with roads on very rugged land in western Montana and the Idaho panhandle, east of the Great Salt Lake in Utah, and in west-central Colorado roughly coinciding with the Colorado Mineral Belt. The Pacific Mountain System is also clearly visible along the Pacific Coast in Washington, Oregon, northern California, and southeast Alaska. The Sierra Nevada range in eastern California and many of the Hawaiian Islands also have roads on rugged land.

In contrast, the roads of the coasts of the Atlantic Ocean and Gulf of Mexico, as well as the Great Plains and the Corn Belt, are on relatively level land. However, prominent exceptions to this statement are the Ozark and Ouachita Mountains in Arkansas, southern Missouri, and eastern Oklahoma; the Black Hills in western South Dakota; and the Driftless Area in western Wisconsin along the borders with Minnesota, Iowa, and Illinois. However, some topographic features that were identifiable in the ARS are no longer visible in the RRS. This is because the roads through these features, such as the Badlands in North and South Dakota and the Sandhills in Nebraska, are located on more level land.