a

Net Change in Forest Density, 1873-2001: 

Using Historical Maps to Monitor 

Long-term Forest Trends

United States Research Map NRS-4

Department of Agriculture

Forest 

Service
b

Abstract

European settlement of the United States and utilization of forests are inextricably linked. Forest products 

fueled development, providing the building blocks for railroads, bridges, ships, and homes. Perhaps 

because of the importance of its forests, the United States has a rich cartographic history documenting its 

resources. Long-term, broad-scale monitoring efforts for forests focus on relatively simple measures, such 

as forest area, change in forest area over time, and proportion of forest land. We demonstrate how historical 

cartographic products could be effectively used to produce information about the change of forests over 

time at regional or national scales. We georeferenced and digitized a map of U.S. woodland density circa 

1873 produced for the first national atlas. Using a contemporary digital forest layer derived from MODIS 

satellite imagery, we developed density categories that matched the historical map and calculated changes 

since 1873. A process is presented for combining historical maps with modern data. We discuss challenges 

with georeferencing of scanned images, lack of metadata, thematic misclassification, and inconsistent 

definitions, all of which require that historical maps should be used with caution for the purpose of broadscale monitoring of resources. 

Published by: For additional copies:

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May 2013

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Manuscript received for publication May 2011

Printed on recycled paper
1

Greg C. Liknes, Mark D. Nelson, and Daniel J. Kaisershot

Greg C. Liknes is a research 

physical scientist with the Forest 

Inventory and Analysis (FIA) 

program, Northern Research 

Station, St. Paul, MN.

Mark D. Nelson is a research 

forester with the Forest Inventory 

and Analysis (FIA) program, 

Northern Research Station, St. 

Paul, MN.

Daniel J. Kaisershot is a natural 

resource specialist with the 

Forest Inventory and Analysis 

(FIA) program, Northern Research 

Station, St. Paul, MN.

Net Change in Forest Density, 

1873-2001: Using Historical 

Maps to Monitor Long-term 

Forest Trends

The Authors
2

INTRODUCTION

The development of the United States during the era of 

European settlement depended on the availability of wood 

as a raw material. The collective “forest culture” (Cox 1985, 

Kollmorgen 1969) utilized trees on abundant forest land 

to build homes, ships, bridges, railroads, and furniture. In 

addition to harvesting natural resources for raw materials, 

land was converted for agriculture resulting in the clearing of 

vast stretches of forest land in the United States. Wood also 

served as a primary fuel for heating, cooking, and steambased locomotion. Kellogg (1907) estimated the U.S. annual 

cut rate to be 20 billion cubic feet (156 million cords) of 

wood in the beginning of the 20th century. Concerns about 

the sustainability of such practices began in the late 19th to 

early 20th century, leading to the acquisition and reporting of 

tabular lumber statistics in a variety of outlets.

In addition to these historical statistical reports, there is also 

a rich cartographic history related to the natural resources of 

North America and the United States. Joseph Henry (1858) 

developed a nationwide map titled “The Forest and Prairie 

Lands of the United States” depicting broad categories of 

evergreen and deciduous forests, and arable and dry prairies. 

James Cooper (1860) depicted a series of provinces in his 

North American map titled “Map of the Distribution of 

North American Forests.” William H. Brewer developed 

an 1873 map of forest density resulting from the ninth U.S. 

Census (Walker 1874), and Charles Sargent later presented a 

forest density map based on the tenth census (Sargent 1884). 

Shantz and Zon (1924) produced a map of natural vegetation 

in the United States. Each of these maps covers a large spatial 

extent (national or continental) and represents a temporal 

snapshot of resources.

Today there is a variety of monitoring and reporting efforts 

related to forests and the environment that rely on past 

information to inform current analyses. For example, the 

Food and Agriculture Organization of United Nations 

produces a Global Forest Resources Assessment at 5- to 

10-year intervals. In the United States, the Forest and 

Figure 1.—Woodland density map (circa 1873) produced by William H. Brewer for the “Statistical Atlas of the United States...” based on results from the ninth 

census (Walker 1874). Image source: United States Library of Congress.
3

Rangeland Renewable Resources Planning Act (RPA) of 1974 

mandates that an assessment be prepared every 10 years. 

In fulfillment of the RPA, a forest resource assessment was 

most recently published in 2009 (Smith et al. 2009), which 

also includes a compilation of 22 maps of contemporary 

U.S. forest resources. These broad-scale, long-term forest 

resource monitoring efforts generally rely on relatively simple 

measures, such as forest area and change in forest area over 

time. The United Nations’ Seventh Millennium Development 

Goal (environmental sustainability) will use the proportion 

of land area covered by forests as a primary indicator, and 

it will be assessed over time (http://millenniumindicators.

un.org). To support these applications of trend information 

in sustainability efforts, we need information on past or 

baseline conditions.

Our objective was to demonstrate how historical cartographic 

products can be effectively used to produce information about 

the change of forests over time at regional or national scales. 

We georeferenced a scanned image of William H. Brewer’s 

1873 U.S. map of woodland density, digitized polygons of 

density classes, and converted the results into a nationwide 

raster dataset. Using a forest probability layer derived from 

recent MODIS satellite imagery and in situ data from the U.S. 

Forest Service’s Forest Inventory and Analysis (FIA) program, 

we replicated the mapping unit and categories of woodland 

density from the 1873 map to facilitate the calculation of change 

between historical and current dates.

HISTORICAL WOODLAND DENSITY MAP

William H. Brewer produced a U.S. map of woodland1

density (Fig. 1) in 1873 that was included in the “Statistical 

Atlas of the United States...” (Walker 1874). Brewer reported 

that for the eastern United States, the map was largely based 

on statistics from the ninth census of 1870. He developed 

density categories based on the ratio of agricultural acreage 

to forested acreage. For the western United States, Brewer felt 

the census statistics were inadequate, so he pieced together 

information from 

“various reports and documents, from the General, State, 

and Territorial Governments, reports of surveys of every 

kind, public and private, journals and narratives of travel, 

reports of various expeditions, explorations and voyages, 

various journals, reports and opinions of botanists, the 

publications of learned societies, scientific periodicals, journals 

devoted to special industries dependent on wood and lumber, 

and other published information not necessary here to be 

enumerated.” 

With regard to the definition of the mapped categories, Brewer 

writes that he attempted to portray 

“the relative proportions of surface occupied by woodlands 

and by lands not occupied by trees, so far as the scale chosen 

will allow, it takes no account of the species which make up the 

tree-covering of the soil, nor of the density of the forests—that 

is, of the relative numbers of trees per acre—nor of their size 

or economic value, or their fitness for sawing or other use or 

manufacture.” 

It is worth emphasizing density portrayed on the map is a 

macro-scale measure rather than the more familiar trees per 

acre or basal area per acre. Brewer mapped density in five 

categories according to the number of 40-acre blocks per 

square mile (640 acres) that were wooded. The map reflects the 

cover of the land rather than its use.

A scanned image of the map was acquired from the U.S. Library 

of Congress (http://memory.loc.gov) in JPEG2000 format. 

While the map is quite readable (Fig. 1), the original document 

is not without defects. A line is visible down the center of the 

map (likely from a fold), and a tear is visible near the bottom 

center of the map (Fig. 2). Additionally, information about the 

projection or coordinate system is not provided. In short, the 

scanned image inherited flaws in the original map and is not 

accompanied by thorough metadata, a familiar scenario for 

those working with maps of this vintage.

MODERN FOREST DENSITY MAP

To match the mapping unit and density categories of the 

1873 map, a modern geospatial dataset was needed with A) 

full coverage of the United States as of 1873; B) sufficient 

spatial detail to determine the number of 40-acre blocks per 

square mile that currently are forested; and C) a flexible forest 

definition. A forest probability data layer derived primarily 

from MODIS satellite data and information collected on tens 

of thousands of ground plots by the FIA program was selected. 

Figure 2.—Examples of flaws in a scanned map: a fold line near the top of 

the map (left) and a tear in the map (right).

1

 Although Brewer uses the term woodland in his map, the description of 

the categories indicates he is referring to what we would generically now 

call forest. For clarity, we use only the term forest hereafter unless the term 

woodland is used in a direct quote.
4

While the MODIS imagery was primarily from 2001, the 

resulting product will be referred to as the modern- or presentday map or geospatial dataset This dataset has nationwide 

coverage (CONUS + Alaska), 250-m spatial resolution (pixel 

size), and values ranging from 0 to 1 indicating the probability 

each pixel is forested. The dataset was produced as a forest/

nonforest mask in support of a nationwide biomass dataset 

(Blackard et al. 2008) and is accessible from the Oak Ridge 

National Laboratory Distributed Active Archive Center 

(http://webmap.ornl.gov/biomass/biomass.html). It should 

be noted that while remote sensing approaches focus on land 

cover, the FIA data used for model training is based primarily 

on a land use definition of forest land, although both data 

sources include elements of land cover and land use. Therefore, 

it is possible some pixels assigned a high forest probability may 

be in the early stage of forest regeneration and thus have 

sparse forest cover.

PREPARATION OF DATA FOR CHANGE DETECTION

The initial step in preparing the historical density map was to 

georeference it to real-world coordinates. The first attempt at 

georeferencing involved the use of state boundary intersections 

as reference points (i.e., ground control points) and a thirdorder polynomial model. This resulted in a reasonably 

well-registered map, but there were a few large discrepancies, 

particularly at the U.S.-Canada border. A second attempt was 

made that involved the creation of a reference graticule layer, 

since a large number of graticule intersections (2 degree x 2 

degree intervals of longitude and latitude) are visible on the 

map. In this second attempt, a piece-wise polynomial model 

(a.k.a., rubber sheeting) was used and resulted in a reasonable 

product. The final output product employed a combination of 

these two georeferencing approaches and was an improvement 

on the first two attempts.

The first step in the preparation process was the division of 

the 1873 forest density map into three separate, rectangular 

pieces (Fig. 3) and the removal of extraneous geographic 

extents (oceans, Canada, Mexico) and the map surround. 

Because the desired output was a map of changes based on 

derived data rather than a visually-appealing georeferenced 

historical map, maintaining the map surround and a 

seamless appearance was not a requirement. Furthermore, 

by isolating the center of the image where the map fold and 

tear existed, the overall georeferencing was improved. The 

western and eastern subset images were georeferenced using 

primarily state intersections as references with a thirdorder polynomial model. The center image utilized rubber 

sheeting and latitude/longitude intersections as reference 

points. Polynomial transformations are the most flexible 

of georeferencing options while rubber sheeting should be 

reserved for the most severely distorted images (Gao 2008).

Once the georeferencing was completed, the density areas 

on the map were heads-up digitized2

 via a geographic 

information system while displayed on a computer monitor, 

and labeled according to their density class as defined on the 

original map (Fig. 4 on pg. 9). The resulting vector layer of 

density class polygons (Liknes et al. 2013) was then converted 

to a raster dataset for subsequent comparison with the 

modern forest density map.

To prepare a modern map for the comparison, pixels were 

resampled from approximately 15 acres (250 m x 250 m 

pixel resolution) to 40 acres, with a weighted average of the 

associated forest probabilities assigned to the new, larger 

pixels. A probability threshold of 0.5 was then applied 

in order to assign each pixel to a “forest” or “nonforest” 

category. Lastly, a block statistics operation was used to 

determine the count of forested 40-acre pixels per square 

mile, simulating the geographic scale and attributes of 

the 1873 map (Fig. 5 on pg. 9).

(Text continues on pg. 10).

Figure 3.—Three geographic extents clipped from a scanned image of the 

1873 Brewer map (outlined in black, red, and blue) to facilitate improved 

georeferencing. The central extent, outlined in red, contained few woodland 

areas and had the most distortion due to a fold in the center of the page; it was 

georeferenced with a rubber sheeting model while the western and eastern 

extents used a third-order polynomial model.

2

 Here we use the term heads-up digitized to refer to the fact geographic 

features displayed on a computer monitor were traced using a mouse rather 

than using a digitizing table or similar device.
5

Forest Ranger locating distance to forest fire on map by means of compass. Cabinet National Forest, 

Montana. Photo courtesy of Forest History Society, Durham, NC.

Fire tower on Gila National Forest, New Mexico. 

Photo by E.S. Shipp, U.S. Forest Service.

5

Load of logs, Clam River, Minnesota, 1902. Photo courtesy of Forest 

History Society, Durham, NC.

Measuring a ponderosa pine (bottom right) on Gila National Forest, New Mexico. 

Photo by I.B. Nash, U.S. Forest Service.

Forest surveyors and engineers in camp, South Dakota, circa 1889. Photo on file at Library of Congress, 

photographer John Grabill collection.

Ranger on the Jefferson National Forest is pointing out 

a tree peeled to make a huckleberry bucket , circa 1940. 

Photo courtesy of Forest History Society, Durham, NC.
6

Net Change in Forest 

Density, 1873-2001: 

Using Historical 

Maps to Monitor 

Long-term Forest 

Trends 

Forest Density Net Change

Major decrease

Moderate decrease

Slight or no changes

Moderate increase

Major increase

Greg C. Liknes, Mark D. Nelson, 

and Daniel J. Kaisershot

1,000

 Miles

West East
7

Scale: 1:15,000,000

Projection: Albers Equal Area Conic

Central Meridian: 96° W

Latitude of Origin: 23° N

Datum: NAD83

0 125 250 500

2501250 500 750 1,000

750 1,000

 Miles

 Kilometers

Scale: 1:15,000,000

Projection: Albers Equal Area Conic

Central Meridian: 96° W

Latitude of Origin: 23° N

Datum: NAD83

2501250 500 750 1,000

 Kilometers
8

Map Description

This map depicts the net change in forest density across 

the conterminous United States (CONUS) from 1873 to 

2001. In this case, density is defined as the number of 

forested 40-acre blocks per square mile.

A scanned image of a 1873 map by William H. Brewer 

(Walker 1874) depicting six categories of density (in acres 

per square mile: 0-40; 40-120; 120-240; 240-360; 360-560; 

560+) was georeferenced and digitized (Liknes et al. 2013). 

The same density categories were replicated for 2001 

using data derived from MODIS satellite data and ground 

observations from the Forest Inventory and Analysis 

program (Blackard et al. 2008). The difference in forest 

density between the two time periods was then calculated 

using a geographic information system. The change class 

labels on the map are defined as follows: an increase 

or decrease of four or five density categories is a major 

change, a difference of two or three density categories is a 

moderate change, and a difference in zero or one category 

is slight or no change. 

The pie charts on the inset map indicate the relative 

proportions of the change categories for the western and 

eastern United States. In the West, roughly half of the 

forested area has experienced slight or no net density 

change during the time interval, and increases and 

decreases are approximately equal. In the East, slight or no 

change has occurred on a little less than half of the forested 

area, and more areas have experienced increases than 

those that have experienced decreases. 

The map is generally applicable at a national scale and does 

agree to some extent with what we know of the history of 

forests in the United States. It should be noted the change 

results are influenced by errors in both the 1873 and 2001 

data sources. Net change does not capture all changes that 

may have occurred during intervening periods. The map 

provides a spatial portrayal of long-term forest change in 

the U.S. that has otherwise been depicted only with tabular 

statistics. 

8

Data Sources

The map is a bitemporal change map derived from two sources. 

The time 1 data source is a scanned image of William H. 

Brewer’s 1873 map of woodland density which was obtained 

from the U.S. Library of Congress. The time 2 map is derived 

from 2001 MODIS imagery and ground observations from the 

Forest Inventory and Analysis program. Political boundaries 

are from Environmental Systems Research Institute (ESRI) 

Data & Maps.
9

Figure 4.—Woodland density map derived from an 1873 William H. Brewer map via georeferencing and heads-up digitization. (Liknes et al. 2013). Please see 

footnote 1 on page 3.

Woodland Density

(acres per square mile)

Forest Density

(acres per square mile)

Figure 5.—Modern day forest density map derived from MODIS satellite imagery and ground based data from the U.S. Forest Service Forest Inventory and Analysis 

program (Blackard et al. 2008). Forest density refers to the number of 40 acre blocks per square mile that are forested.
10

NET CHANGE MAP

Once the final datasets from 1873 and the present were 

complete, a simple difference was calculated, and a map of 

net forest density change was produced (Fig. 6 and centerfold 

map). The results of the density difference calculation were 

aggregated but still depict different degrees of change. Areas 

increasing or decreasing by four or five density classes were 

labeled as major change, areas increasing or decreasing by two 

or three density classes were labeled as moderate change, and 

areas that remained in the same density class or changed by 

only one class were labeled as slight or no change. The map 

has been deliberately labeled as net change because the time 

interval is sufficient to mask widespread forest loss followed by 

recovery. Consider the predominance of slight or no change in 

the Lakes States (Minnesota, Wisconsin, and Michigan) and 

the Pacific Northwest. Heavy logging did not begin in these 

states until after 1873 (Williams 1989) and forests have since 

recovered to the point the areas show little net change. 

Several regional patterns are apparent. The eastern United 

States is a very patchy mix of loss, gain, and no change with 

slightly more increase than decrease overall (see inset map, 

Fig. 6). Conversely in the western United States, areas of loss 

slightly exceed areas of density gain. Areas in the central 

United States, including portions of Ohio and Indiana, have 

experienced losses in density. As previously mentioned, 

much of the Pacific Northwest and the Lakes States have 

experienced no net change. In addition to regional patterns, 

a few subregional features are apparent, such as slight or no 

net change in Adirondack Park in northeastern New York, 

slight or no net change in the Yellowstone National Park area 

in northwestern Wyoming, and a major decrease in the Great 

Black Swamp in northwestern Ohio. Areas of major change 

appear to be concentrated in transition zones between forest 

and nonforest, such as in the eastern Rocky Mountains, along 

the prairie/forest boundary in central Minnesota, and southcentral Florida. 

MAP UNCERTAINTY

The map of net forest density change is the cumulative result 

of actual change (or stasis), thematic misclassification at time 

1 and/or time 2, positional errors, and differences in thematic 

definitions between time 1 and time 2. Determining the 

total impact of these errors and the relative contributions of 

each component is always a challenge in change detection. 

We have attempted to match the density attribute from the 

1873 map, and have noted the possible discrepancies in 

forest definition related to confusion between land cover and 

land use. Significant time was spent attempting to minimize 

locational errors in the 1873 map during the georeferencing 

process, yet error remains. However, because the map is 

intended for a broad-scale (regional to national) analysis, 

the importance of positional accuracy is somewhat reduced. 

Carmel (2004) reports a significant decrease in error in 

vegetation classification when pixels are aggregated to 3-10 

times the size of locational error. Because a density class has 

been assigned to 640-acre blocks, some benefit of aggregation 

is realized in this case. While aggregation may lessen the 

impact of registration errors, we also acknowledge the 

drawbacks, such as reduced ability to represent local variance 

Figure 6.—Net change in forest 

density since 1873. Classes are 

based on density categories defined 

in an 1873 woodland density map by 

William H. Brewer. Change classes 

are labeled as follows: an increase 

or decrease of four or five density 

categories is a major change, a 

difference of two or three density 

categories is a moderate change, and 

a difference in zero or one category 

is slight or no change. The pie charts 

on the inset map indicate the relative 

proportions of the change categories 

for the western and eastern United 

States. For a larger version of this 

map, see pages 6-7.
11

(Goodchild 2001) and overrepresentation of land cover 

classes where cover is dense and underrepresentation where 

sparse (e.g., Nelson et al. 2009). Thus, it is difficult to separate 

offsetting positive and negative effects of the map scale, which 

can vary by density class.

Given the sources of uncertainty, we evaluated the validity of 

the net change dataset by asking the question, “Does the map 

make sense?” In some regions, the patterns agree with what 

we know of history. For example, there is evidence to suggest 

a large amount of unsuitable farmland reverted to forest in 

the eastern United States during the change interval. In fact, 

Brown et al. (2005) report a 22 percent decline in cropland 

area (much of which reverted to forest) east of the Mississippi 

River between 1950 and 2000. In the central United States, 

we noted areas of forest loss, and these correspond with 

the agricultural conversion of these lands in the late 19th 

century. Much of the West (including the Pacific Northwest) 

experienced no net change or has gained in density. This could 

be reflective of widespread conservation efforts that began 

early in the 20th century. However, the increases in density 

in the southeastern United States are difficult to corroborate. 

Estimates of forest land presented by Kellogg (1907) can be 

extrapolated backward in time using U.S. Census land-clearing 

records, resulting in a forest density in many areas that is 

substantially higher than the 1873 map (W. Brad Smith, U.S. 

Forest Service, personal communication). Thus, the 1873 map 

is questionable in the southeast, and the resulting net change 

may be suspect. The large area of major decrease in western 

Wyoming/Montana is also difficult to corroborate, and this 

could be the result of an overly generalized forest boundary 

line in the eastern Rocky Mountains on the 1873 map. We 

also noted the presence of smaller-scale features on the net 

change map; each has a plausible explanation. For example, 

it is reasonable to expect little change in Adirondack Park or 

Yellowstone National Park due to restrictions on logging. The 

Great Black Swamp in northwestern Ohio, which contained 

stands of oak, hickory, and sycamore trees, was drained for 

agriculture in the late 1800s (Mollenkopf 1999), resulting in a 

major decrease in forest density.

CONCLUSION

We examined whether historical maps provide meaningful 

baseline information for broad-scale monitoring of forest 

resources. In the process of converting an historical 

map to digital data, we found it valuable to use different 

georeferencing approaches for different geographic extents of 

a single map. Additionally, we took the approach of mimicking 

categories on the original map in the modern dataset to 

facilitate change detection. These findings may be helpful 

with similar data reconstructions. Though the map of forest 

density change is generally informative, challenges related to 

sparse metadata, incompatible definitional changes, thematic 

misclassifications, and positional accuracy resulted in a forest 

density change map that contains patterns inconsistent with 

other sources of information in some parts of the country. 

Additional research can be done to quantify real change 

indicated by the map as well as errors.

Brewer said this about the nature of mapping resources on such 

a broad scale: 

“It is not possible to portray on one map all the characters of 

woodlands. The scale of this map is too small to show more than 

a very general distribution. Nor is it possible to convey the same 

idea to all persons by shades of density, especially not to persons 

whose observations have been restricted to limited areas widely 

separate, nor is it possible to convey by this means a correct 

idea of the character of the forests themselves. We cannot thus 

satisfactorily compare the grand forests of Puget Sound and 

Mendocino with the oak openings of Texas and the mesquite 

groves of Arizona; the hills clothed with a dense growth of small 

hardwood trees in New England, with the open forests of the pine 

barrens farther south; the fringe of willows and cottonwoods 

skirting a river of the plains, with the tangled growth of the coast 

ranges of the Pacific; or the scattered cedars on the ridges of 

Dakota, with the intricate forests of Florida. The map, therefore, 

is a compromise, on which I have tried to show as far as is 

possible what is known of our woodlands. As it is the first, it is 

to be hoped that the work will ultimately be more satisfactorily 

done from fuller data and in a series of maps...each to illustrate 

some separate character.” 

Like Brewer, we, too, attempted to portray what is known 

of our forests and have arrived at a compromise in order to 

spatially portray changes over a large area and a long time 

interval. Over the course of many decades and at national 

or regional scales, cartographic products can provide useful 

information for sustainability reporting efforts, even with the 

inherent flaws and challenges, but should be corroborated 

with other data sources wherever possible. 

ACKNOWLEDGMENTS

We thank Brad Quayle and Adrian Grell (U.S. Forest Service) 

for their ideas and assistance regarding georeferencing. We 

also thank W. Brad Smith (U.S. Forest Service) for his insights 

regarding changes to U.S. forests over time.
12

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European settlement of the United States and utilization of forests are inextricably 

linked. Forest products fueled development, providing the building blocks for railroads, 

bridges, ships, and homes. Perhaps because of the importance of its forests, the United 

States has a rich cartographic history documenting its resources. Long-term, broadscale monitoring efforts for forests focus on relatively simple measures, such as forest 

area, change in forest area over time, and proportion of forest land. We demonstrate 

how historical cartographic products could be effectively used to produce information 

about the change of forests over time at regional or national scales. We georeferenced 

and digitized a map of U.S. woodland density circa 1873 produced for the first national 

atlas. Using a contemporary digital forest layer derived from MODIS satellite imagery, we 

developed density categories that matched the historical map and calculated changes 

since 1873. A process is presented for combining historical maps with modern data. We 

discuss challenges with georeferencing of scanned images, lack of metadata, thematic 

misclassification, and inconsistent definitions, all of which require that historical maps 

should be used with caution for the purpose of broad-scale monitoring of resources. 

KEYWORDS: historical map, William H. Brewer, georeferencing, sustainability, forest 

resources

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