Volume 10, Issue 1 p. 91-105
Research Article
Open Access

Mapping tree cover expansion in Montana, U.S.A. rangelands using high-resolution historical aerial imagery

Scott L. Morford

Corresponding Author

Scott L. Morford

Numerical Terradynamic Simulation Group, University of Montana, Missoula, Montana, 59812 USA


Scott L. Morford, Numerical Terradynamic Simulation Group, ISB 418, University of Montana, Missoula, MT 59812, USA. Tel: (406) 461-4910; E-mail: [email protected]

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Brady W. Allred

Brady W. Allred

University of Montana, W. A. Franke College of Forestry and Conservation, Missoula, Montana, 59812 USA

Google, Mountain View, California, 94043 USA

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Eric R. Jensen

Eric R. Jensen

Numerical Terradynamic Simulation Group, University of Montana, Missoula, Montana, 59812 USA

Desert Research Institute, Reno, Nevada, 89512 USA

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Jeremy D. Maestas

Jeremy D. Maestas

United States Department of Agriculture, Natural Resources Conservation Service, Portland, Oregon, 97232 USA

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Kristopher R. Mueller

Kristopher R. Mueller

Numerical Terradynamic Simulation Group, University of Montana, Missoula, Montana, 59812 USA

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Catherine L. Pacholski

Catherine L. Pacholski

United States Department of Agriculture, Natural Resources Conservation Service, Bozeman, Montana, 59715 USA

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Joseph T. Smith

Joseph T. Smith

Numerical Terradynamic Simulation Group, University of Montana, Missoula, Montana, 59812 USA

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Jason D. Tack

Jason D. Tack

United States Fish and Wildlife Service, Habitat and Population Evaluation Team, Missoula, Montana, 59812 USA

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Kyle N. Tackett

Kyle N. Tackett

United States Department of Agriculture, Natural Resources Conservation Service, Bozeman, Montana, 59715 USA

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David E. Naugle

David E. Naugle

University of Montana, W. A. Franke College of Forestry and Conservation, Missoula, Montana, 59812 USA

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First published: 19 July 2023

Editor: Mat Disney

Associate Editor: Jin Wu

Preprint server: bioarxiv.org; CC-BY-NC-ND 4.0.

Funding Information

This work was made possible by the USDA-Natural Resources Conservation Service's (NRCS) Conservation Collaboration Grant (Agreement NR200325XXXXC002). NVIDIA provided hardware used in this analysis through their Academic Hardware Grants program. The findings and conclusions in the publication are those of the authors and should not be construed to represent the views of the USDA, U.S. Fish and Wildlife Service, or the U.S. Government. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.


Worldwide, trees are colonizing rangelands with high conservation value. The introduction of trees into grasslands and shrublands causes large-scale changes in ecosystem structure and function, which have cascading impacts on ecosystem services, biodiversity, and agricultural economies. Satellites are increasingly being used to track tree cover at continental to global scales, but these methods can only provide reliable estimates of change over recent decades. Given the slow pace of tree cover expansion, remote sensing techniques that can extend this historical record provide critical insights into the magnitude of environmental change. Here, we estimate conifer expansion in rangelands of the northern Great Plains, United States, North America, using historical aerial imagery from the mid-20th century and modern aerial imagery. We analyzed 19.3 million hectares of rangelands in Montana, USA, using a convolutional neural network (U-Net architecture) and cloud computing to detect tree features and tree cover change. Our bias-corrected results estimate 3.0 ± 0.2 million hectares of conifer tree cover expansion in Montana rangelands, which accounts for 15.4% of the total study area. Overall accuracy was >91%, but the producer's accuracy was lower than the user's accuracy (0.60 vs. 0.88) for areas of tree cover expansion. Nonetheless, the omission errors were not spatially clustered, suggesting that the method is reliable for identifying the regions of Montana where substantial tree expansion has occurred. Using the model results in conjunction with historical and modern imagery allows for effective communication of the scale of tree expansion while overcoming the recency effect caused by shifting environmental baselines.


Tree cover expansion (hereafter, tree expansion) is a widespread global change phenomenon that alters rangeland ecosystems' structure, function, and biodiversity (Nackley et al., 2017; Van Auken, 2009). Tracking local and regional tree expansion has been an active area of remote sensing research for more than 20 years, but only recently have operational products been developed to track tree cover change in rangelands at continental to global scales (Allred et al., 2021; Asner et al., 2003; Brown et al., 2022). Renewed concern regarding the accelerating degradation of global rangelands and loss of rangeland-obligate fauna highlights the need for tools and approaches to better track and communicate the extent to which tree expansion is modifying grassland and shrubland ecosystems (Bardgett et al., 2021; Lees et al., 2022).

Addressing tree and shrub encroachment in rangelands (defined as grasslands, shrublands, savannas, and open woodlands) is a globally important strategy for climate adaptation and biodiversity protection (Buisson et al., 2022; Smith et al., 2022). In temperate zones of the northern hemisphere, managing grassland tree expansion also helps mitigate climate change by maintaining or restoring high land-surface albedo (Ge & Zou, 2013; Mykleby et al., 2017; Nuñez et al., 2021). Yet, the broader global change community shows sparse awareness of how increasing tree cover impacts the function and biodiversity of grasslands. This awareness gap is perhaps best illustrated by recent calls for afforestation of global grasslands to enhance land carbon sequestration (Bastin et al., 2019; Veldman et al., 2019).

This awareness gap extends to the wider public. Tree encroachment unfolds slowly over decades, and humans have difficulty perceiving incremental environmental change (Essl et al., 2015). Evolutionary or cultural esthetic preferences for trees in the landscape may also limit human recognition of potential consequences for rangelands as tree cover proliferates (Cook & Cable, 1995; Han, 2007). Further, numerous high-profile environmental campaigns promote tree planting as a simple and universal solution to climate change and environmental challenges, hindering recognition that tree cover can harm the function of native grasslands and their biodiversity. (Holl & Brancalion, 2020).

Providing scientists, land managers, and the public with a tool to visualize tree expansion is a powerful conservation communication strategy to overcome the recency effect associated with shifting environmental baselines (Jones et al., 2020; Soga & Gaston, 2018). While time-series analysis of satellite data provides robust spatiotemporal estimates of tree expansion, these moderate-resolution data products do little to visually convey how tree expansion is reorganizing the structure of grasslands as they are converted to woodlands and forests. In contrast, using historical aerial imagery allows users to see how tree cover expansion has unfolded at resolutions in-line with modern aerial and satellite mapping technologies.

This work builds upon recent innovations in photogrammetry, deep learning, and cloud-based geospatial processing to analyze tree cover change at previously impossible spatial and temporal scales. New photogrammetry techniques that utilize Structure from Motion and MultiView Stereo algorithms can efficiently orthorectify thousands of historical images with relatively little user intervention (Hirschmuller, 2008; Toldo et al., 2015). Deep learning approaches, such as convolutional neural networks, are now widely used across disciplines for labeling objects and performing semantic segmentation (Ma et al., 2019). For example, The U-Net architecture and its variations are readily used in biomedical and environmental applications to segment images pixel by pixel (Ronneberger et al., 2015; Wagner et al., 2019). Fusing and processing these data in cloud geospatial platforms, such as Google Earth Engine, provide efficient and scalable computing power that allow for these data to be analyzed by scientists without extensive expertise in high-performance computing.

Recent tree expansion work from the United States (U.S.) shows that tree cover in grasslands has increased by 85% over the past 30 years, resulting in 147 700 km2 of tree-free grasslands being converted to woodlands (Morford et al., 2022). These changes to ecosystem structure rival the impacts from cropland conversion and drive significant losses of habitat for sagebrush- and grassland-obligate birds such as greater sage-grouse (Centrocercus urophasianus) and lesser prairie chickens (Tympanuchus pallidicinctus) (Baruch-Mordo et al., 2013; Lautenbach et al., 2017). The broader impacts of tree expansion on ecosystem services and biodiversity have been widely documented across the southern U.S. Great Plains where tree expansion has expanded rapidly over the past century. However, tree expansion has received relatively little attention in the northern Great Plains (Symstad & Leis, 2017). Current satellite observations and dynamic vegetation modeling report that tree expansion is rapidly increasing across the northern Great Plains and will continue to accelerate the conversion of grassland to woodlands in the coming decades as a result of climate change (Klemm et al., 2020; Shafer et al., 2015).

Here, we analyze tree expansion over a period of 70+  years across 19.2 million hectares of rangelands in the state of Montana, United States of America. We use high-resolution (<2-m ground sampling distance) historical and modern imagery to quantify the aerial extent of tree expansion since the mid-20th century. We also provide complementary estimates for rangeland tree cover losses to help understand the magnitude and direction of ecosystem evolution between grasslands, woodlands, and forests.

We focus on Montana U.S.A. rangelands because they are a focal area for ongoing multinational conservation efforts to protect North American grasslands and their biodiversity (Epstein et al., 2021). Grasslands in this region are critical habitat for collapsing North American grassland bird populations, many species of which are highly sensitive to even low abundances of trees (Rosenberg et al., 2019). Additionally, tree encroachment in this region can lead to losses in forage production, which can exacerbate economic stress on small ranching operations and further promote land use conversion to row-crop agriculture, residential sub-division, and fossil-fuel energy development (Allred et al., 2015; Lark, 2020; Morford et al., 2022).

Materials and Methods

We used high-resolution historical aerial imagery sourced from the United States Geological Survey (USGS), modern aerial imagery from the National Agricultural Inventory Program (NAIP), and auxiliary land cover data to analyze tree expansion in Montana rangelands. The extent of Montana rangelands was taken from the LANDFIRE Biophysical Settings (BPS, v1.4.0) layer which represented the dominant vegetation cover prior to Euro-American settlement (LANDFIRE, 2017). Conceptually, we first perform semantic segmentation of the historical and modern imagery at their native resolutions to identify treed pixels in the two sets of aerial imagery. We then used kernel averaging to calculate a continuous tree cover model at a scale of 0.40 hectares (one acre) for both modern and historical imagery. Finally, we calculated the difference between the historical and modern continuous tree cover models to identify areas of tree expansion or tree cover loss in Montana rangelands (Fig. 1). Detailed information regarding data sources used in this analysis is provided in Table S1.

Details are in the caption following the image
Conceptual workflow for identifying areas of tree encroachment using historical and modern aerial imagery. Median year for the historical imagery was 1954 (range: 1946–1977) and 2019 for the Modern imagery (range 2019–2020). U-Net was used to identify pixels with conifers. Conifer cover was calculated using a kernel method, and conifer expansion was calculated by differencing the historical and modern cover models. Tree detection and conifer cover model were performed at the native imagery resolutions (0.6–1.0 m) and the expansion map was aggregated at 30-m pixels to reduce pixel-to-pixel noise.

We acquired historical aerial images from the USGS single-frame archive collected by the U.S. Army between 1946 and 1977 (USGS, 2018). The median year for imagery acquisition was 1954. The images were scanned by the USGS at a resolution of 25 micron (1000 dots per inch) in 8-bit grayscale. Images with cloud cover were not included in the analysis. Depending on acquisition altitude, these images produced digital orthoimagery with a ground sampling distance (GSD) between 0.8 and 2.0 m. The modern aerial imagery was sourced from 2019 and 2020 and was provided by NAIP as pre-rectified 4-band (RGB-IR) 8-bit images with a GSD of 0.6 m.

Figure 2 presents the data-processing pipeline. The pipeline is segmented into three distinct workflows including alignment and orthorectification, tree cover modeling, and spatial analysis.

Details are in the caption following the image
Data processing workflow. Our approach comprises of three modules: orthorectification of historical imagery, feature detection and mapping using U-Net neural network, and spatial analysis of tree cover expansion and loss. GEE labeled processes used Google Earth Engine.

Alignment and orthorectification

We used MATLAB, Metashape, and QGIS to produce the historical orthoimage for Montana. Images from individual USGS flight projects were processed together and then projects were merged into a final seamless orthoimage product for all of Montana. In MATLAB, we cropped the images to remove the film borders and applied a dehazing and low light filter to reduce vignetting and enhance image contrast. In Metashape, preliminary image alignment was performed using image coordinates provided by USGS metadata, and internal and external calibration parameters were determined by the software. Image-to-image overlap was approximately 30% which was sufficient to produce an elevation model. Orthorectification used a DEM derived from dense-point-cloud processing of the imagery in Metashape.

After generating a preliminary orthoimage, we imported the imagery into QGIS and identified common features in historical and modern aerial imagery for use as ground control points (GCP). We used solitary trees, building corners, and rock outcrops as the primary invariant objects to place GCP; road intersections and fence corners at property lines were also used sparingly for GCP if more permanent objects were unavailable. We used XY coordinates in the modern imagery as the reference; Z (elevation) coordinates were taken from the USGS elevation point query service. We spaced GCPs at intervals of <20 km in relatively flat terrain and <10 km intervals in areas of higher relief. GCPs and XYZ coordinates were added to Metashape, and the project was realigned using GCP coordinates only. Candidate orthoimagery products were then re-evaluated in a GIS to assess map alignment. If needed, additional GCPs were added, and the imagery was reprocessed until the horizontal (XY) offset between the historical and modern aerial imagery was on the order of 5–10 m based on visual inspection by the photogrammetry technician and the error metrics provided by Metashape. The final merged orthoimage was exported with a GSD of 1.0 m.

Following the generation of the final merged orthoimage, we performed a post hoc evaluation of the XY offset between the historical and modern aerial imagery in QGIS. To assess the XY offset error, we overlaid a regular grid (n = 380, cell size = 1000 km2) on the historical imagery in QGIS and identified common features in both the historical and modern aerial image that were as close as possible to the cell center and measured the linear distance between the features.

Tree cover modeling

We applied the U-Net convolutional neural network architecture described in Ronneberger et al. (2015) to detect tree pixels in historical and modern aerial imagery. U-Net performed semantic segmentation, classified each pixel as a tree or non-tree, and output a binary tree segmentation model at the native resolution of 1.0 and 0.6 m for the historical and modern imagery, respectively. Using the approach developed by Falkowski et al. (2017), we then applied a box-linear kernel filter to convert the binary tree model into continuous tree cover models representing percent tree cover over a scale of 0.4 ha (1 acre). We exported the historical and continuous tree cover models at a GSD of 1.0 m.

The tree cover modeling approach was similar for both the historical and modern imagery, but there were some important differences in processing due to variations in image quality and band depth between the historical and modern imagery sources. Table 1 summarizes model implementation, input bands, and hyperparameter selection in the two models with additional details provided in the following sections.

Table 1. Tree feature detection model and performance metrics.
Historical imagery Contemporary imagery
Tree feature detection
Architecture U-Net U-Net
Input image dimensions 256 × 256 × 4 bands 1024 × 1024 × 4 bands
Input bands Grayscale image Red band
GLCM variance Green band
BPS vegetation class Blue band
Modern tree cover NDVI
Ground sampling distance 1.0 m 0.6 m
Total model parameters 31 126 785 31 138 305
Training images 8245 10 690
Training pixels 540 million 11.2 billion
Optimizer Adam RMSProp
Loss Dice coefficient Dice coefficient
Performance metrics from validation dataset
Dice 0.9018 0.8141
Jacard (IoU) 0.8669 0.7311
Sensitivity 0.9858 0.9314
Specificity 0.9855 0.9769

Training data development

Utilizing QGIS and Google Earth Engine, we created training data by manually annotating historical and modern imagery. Field data were not used. Pixels were visually evaluated at 1:1000 to 1:5000 scale to classify conifer species as the model target. We attempted to constrain our tree model detection to conifer trees because tree expansion in the northern Great Plains is driven by conifer species, primarily Douglas Fir (Pseudotsuga menziesii), Eastern Red Cedar (Juniperus virginiana) and Rocky Mountain Juniper (Juniperus scopularum). In modern aerial imagery, visually distinguishing between conifer and deciduous trees was relatively easy owing to differences in texture and color. Marking the historical imagery was more difficult because distinguishing between conifer and deciduous trees relied primarily on detecting textural differences in imagery and reliance on auxiliary data such as landscape position and vegetation classification.

We limited our training data to upland grassland and forested locations and omitted riparian, wetland, cropland, and urban areas using modern land cover classification from the USDA NASS, USGS NLCD, and Montana Natural Heritage Land Cover products. Locations for training data were stratified roughly equally among primary forests, woodlands, and rangeland cover classes, with an emphasis on capturing the transition between these cover types. For modern imagery, we labeled trees in a total of 10 690 (1024 × 1024 pixel) tiles; for historical imagery, we labeled 8245 tiles (256 × 256 pixel). We used an 80–20% training validation split during model fitting.

Data preparation and fusion

To create the model for detecting trees in modern imagery, we used NAIP images from 2019 and 2020. We substituted the near-infrared band (band 4) with NDVI calculated from red and near-infrared bands.

Inputs to the historical tree cover model were more diverse due to differences in image quality and image-to-image variance in contrast and lighting. To develop a successful segmentation model, we included the historical imagery from the orthorectification step (band 1), gray-level co-occurrence matrix (GLCM) variance derived from the historical imagery (band 2), historical vegetation cover type data (band 3), and the continuous tree cover model developed from the analysis of modern imagery (band 4, see Section “6”).

For input band 2, we calculated GLCM variance from the historical orthoimage using the ee.Image.glcmTexture function in Google Earth Engine (5-pixel neighborhood, averaging over all four directions). GLCM variance is presented in Equation 1, and represents the dispersion of pixel value intensity relative to the surrounding neighborhood, where p(i, j) are coordinates of the spatial-dependence matrix and μ represents the mean of the neighborhood values (Haralick et al., 1973). We rescaled and clamped the GLCM values from [200, 2000] to [0, 1] floating point values.
GLCM variance = i = 1 N g j = 1 N g i μ 2 p i , j (1)

The band 3 input variable was vegetation type from LANDFIRE BPS. These data were included to inform the network about coarse differences in vegetation structure. We used an ordinal encoding approach to sort vegetation types in two 12 groups based on vegetation structure (e.g., hardwood forest, conifer forest, grassland, shrubland, etc). These classes were then rescaled from [1, 12] to [0, 1] floating point values for inclusion in the neural network.

For band 4, we used the continuous tree cover layer from the modern imagery processing. We included these data to help reduce false-positive detections of trees in open grasslands and shrublands in areas where high soil moisture, herbaceous productivity, and shrub cover contribute to image mottling. We integrated these data as pixel-wise fractional tree cover (%) scaled from 0 to 1.

Neural network training and inference of binary tree cover model

Figure 3 presents the U-Net architecture used for semantic segmentation of the historical imagery data with an input array (tile size) of size 256 × 256 pixels × 4 bands (256 × 256 × 4). The output was an array of 256 × 256 pixels × 1 band (256 × 256 × 1). We used a sigmoid activation function in our final network layer. The U-Net model used for modern imagery takes the same form, but includes additional down-sampling and up-sampling steps due to its larger input array size (1024 × 1024 × 4). We used different input array sizes for the modern and historical models because of computational limits imposed by calculating GLCM variance for the historical model in Google Earth Engine.

Details are in the caption following the image
U-Net architecture used for tree feature detection in historical imagery, adapted from Ronneberger et al. (2015). The architecture consists of encoding blocks (blue) and decoding blocks (green). The encoding pathway serves to learn tree features from the input dataset and the decoder pathway enables pixel-level prediction for tree and non/tree classes. Data are also transmitted from the encoder to decoder blocks using copy and concatenate skip connections which help with the localization of global-level feature detection at each pixel. Terminology used here is specific to implementing the model in TensorFlow (https://tensorflow.org, Abadi et al., 2016).
We used the TensorFlow 2.5 Python API for training and inference accelerated with an NVIDIA A100 Tensor Core GPU. For training, we used the Dice Coefficient for our loss function (Equation 2). We evaluated 3 standard optimizers provided in TensorFlow (RMSProp, ADAM, and SGD) using grid search over 200 epochs and achieved the best validation Dice score using the ADAM and RMSProp for the historical and modern tree detection models, respectively (Yang & Shami, 2020). Data augmentation was limited to random rotations of the imagery during training. We also report the Jaccard index (Intersection over Union), sensitivity, and specificity of the model using validation data (Table 1).
Dice coefficient = 2 TP 2 TP + FP + FN (2)
Jaccard coefficient IoU = TP TP + FP + FN (3)
Sensitivity = TP TP + FN (4)
Specificity = TN TN + FP (5)

Where TP equals true positive, FP equals false positive, TN equals true negative, and FN equals false negative in a binary classification system. For training and inference, we used a binary threshold value of 0.5.

Inference was performed in TensorFlow 2.5 (Abadi et al., 2016) and the exported image tiles were processed in GDAL 3.4.1 (GDAL Contributors, 2020) to remove tile buffers and apply affine transformations for reprojection prior to re-ingestion into Google Earth Engine.

Kernel filter and continuous tree cover model

To convert our binary tree segmentation models of continuous tree cover, we applied the Falkowski et al. (2017) moving window approach that is widely used to map tree cover across U.S. rangelands. We used the ee.Image.reduceNeighborhood tool in Google Earth Engine to apply a box linear filter (square kernel, radius = 31.8 m) over an area of 0.40 ha (1 US acre) to the historical and modern models produced in Section “5”. The filter is applied at each pixel so that the model output represents the weighted mean of all pixels in the 0.40 ha neighborhood window. We multiply the output raster by 100 to approximate the percent tree cover; GSD of the resulting model is 1.0 m for both the historical and modern products.

Mapping areas of tree cover expansion in rangelands

To identify areas of tree cover increase and decrease in rangelands, we first subtracted the historical continuous tree cover model from the modern continuous tree cover model to produce a difference image at 1 m GSD. We then aggregated the difference image to a GSD of 30 × 30 m in Earth Engine using the ee.Image.reduceResolution tool with ee.Reducer.mean to more closely match the scale of the kernel operations and to reduce pixel-to-pixel variability observed at the 1.0 m GSD data. Finally, we applied two filters to identify areas of tree encroachment and tree cover loss. For pixels to score as tree encroachment (grassland/shrubland conversion to woodland), they needed to have <2% cover in the historical imagery and >4% in the modern imagery. To score as tree cover loss (woodland to grassland/shrubland conversion), the pixels needed to have >10% cover in the historical imagery and <4% in the modern imagery. The 4% threshold was defined operationally, as it was observed to negatively impact tree-sensitive wildlife (Baruch-Mordo et al., 2013). The 10% threshold was chosen because this is the standard tree cover level used by the United States Forest Service (USFS) to define woodlands or forest lands (Brohman & Bryant, 2005). Finally, the tree expansion and tree cover loss images were masked to include only lands identified as rangelands in the LANDFIRE BPS layer. Rangelands that had been converted to row-crop agriculture were also excluded using USDA NASS data.

Calculating tree expansion area and mapping accuracy

To calculate the area of tree expansion in Montana rangelands, we used the best practice guidelines outlined in Olofsson et al. (2014) to assess classification accuracy and develop unbiased areal estimates for tree expansion and tree cover loss. We used a random stratified sampling design to evaluate 3500 pixels based on the relative prevalence in the classified map (1000, 500, 2000; 30 × 30 m pixels in areas classified as increasing, decreasing tree cover, or no change, respectively). An analyst not involved in the modeling or development of the training data visually assessed tree cover in historical imagery (1–2 m GSD), 2019 NAIP imagery (0.6 m GSD), and Google Maps base imagery (0.15 m GSD) in a GIS to evaluate class agreement/disagreement in tree encroachment map. The analysis classified each pixel into one of three classes (tree expansion, tree cover loss, and no change\other). We approximated 4% tree cover as being 3–4 mature conifer trees or approximately 6–8 juvenile trees per acre.

We developed a count error matrix from the data to calculate bias-corrected areal estimates and confidence intervals. The data presented in this main text represent bias-corrected estimates; performance metrics based solely on the validation data (what is usually reported for ML modeling) are presented in the supplemental.

Following the development of the sampling error (confusion) matrix, we calculated the unbiased estimator ( p ̂ ij ) for each cell in the count matrix (Equation 6). Here, i refers to the map classification and j refers to the reference classification. Each cell classification is weighted by the fractional mapped area for each class ( W i ). Here, n ij represents the count data for a cell in the original error matrix.
p ̂ ij = W i n ij n i · (6)
Next, we developed an error-adjusted area estimate for each class ( A ̂ j ) that accounts for omission errors and commission errors over the total map area ( A tot ). Here, q refers to the number of classes used in the accuracy assessment. This estimate allowed us to estimate the true area of tree expansion after accounting for misclassification in the map product.
A ̂ j = A tot i = 1 q p ̂ ij (7)
The standard error S A ̂ j of the error-adjusted estimated area is presented in Equation 8, with q representing the number of classes in our map. The approximate 95% CI is calculated by multiplying S A ̂ j by the z-score (z = 1.96 at 95th percentile).
S A ̂ j = A tot i = 1 q W i 2 n ij n i · 1 n ij n i · n i · 1 (8)
Error-adjusted user's accuracy ( U ̂ i ) was calculated directly from the estimated error matrix, where p ̂ ii represents the true positive estimator for class i in the map (Equation 9).
U ̂ i = p ̂ ii p ̂ i · (9)
Similarly, error-adjusted producer accuracy ( P ̂ j ) was calculated directly from the estimated-error matrix where p ̂ jj represents the true positive estimator for the reference class.
P ̂ j = p ̂ jj p ̂ j · (10)
Overall accuracy ( O ̂ )is estimated by summing the true-positive estimators across q classes.
O ̂ = j = 1 q p ̂ jj (11)

Finally, we conducted a hotspot analysis using the Getis-Ord Gi algorithm (Getis & Ord, 1992) to understand if classification errors were spatially clustered and to identify regions with high rates of misclassification. We aggregated our point-based misclassification rate into a 0.5 × 0.5-° grid to identify hotspots at the 95% CI.


We processed 17 942 high-resolution historical aerial images for this project. The resulting historical orthoimage product covers 380 832 km2; <10 km2 of imagery was missing from the final product due to missing imagery or processing errors. A total of 1422 ground control points were placed to assist with georectification. In the final product, we found that the median horizontal (XY) spatial offset was 10 m between historical and modern aerial imagery (Figure S1).

The feature detection models used in this analysis segmented trees in rangelands, woodlands, and most forested ecosystems in both modern and historical imagery. For the historical imagery model, sensitivity and specificity in our validation dataset were found to be 0.9858 and 0.9855, respectively (Table 1). We found that the U-Net architecture appeared to have had difficulty with false positive classifications in agricultural areas, more mesic (wet) sites, and areas of higher textural complexity (e.g., rock outcrops with shadows) in the historical imagery (Figure S2). However, these areas of misclassification generally had little impact on the overall analysis; agricultural areas and wetlands were masked in the final analysis, and mesic sites in uplands generally did not result in tree cover estimates >10%.

The U-Net model for the modern NAIP imagery performed similarly to the historical model (sensitivity: 0.9314, specificity: 0.9769), but had difficulty in areas of complete and uniform tree cover (e.g. Pinus contorta stands) where false negative detections were common (Figure S2). However, because primary forests were omitted from our analysis of tree expansion in rangelands, this misclassification had little impact on identifying tree expansion among rangelands. Alpine areas in deep shadow and on high slope also showed higher rates of commission errors, but these areas were uncommon among mapped rangelands.

Figure 4 shows the extent of tree expansion (conversion of grasslands and shrublands to woodlands or forests) and tree cover loss (conversion of woodlands/forests to shrublands and grasslands) across the historical extent of rangelands in Montana. Map user's accuracy was 88% for tree expansion, indicating that the extent of tree encroachment identified in Figure 4 is robust. Producer's accuracy was lower (60%), indicating that some tree expansion pixels were missed during mapping. User's and producer's accuracy for woodland loss were 95% and 32%, respectively. Areas mapped as no change/other had similar user's accuracy (92%) and producer's accuracy (99%). Tables S2 and S3 present error matrices from our accuracy assessment for the raw, and area-corrected assessment.

Details are in the caption following the image
Model results for tree cover expansion and loss across Montana rangelands. Forests, agricultural lands, wetlands, and the built environment were excluded from the analysis.

Tree encroachment in Montana grasslands totaled 2 965 587 ± 195 976 hectares between the mid-20th century and 2019, comprising 15.4% of the total modern rangeland area within Montana. The analysis also identified 378 947 ± 86 703 hectares of tree cover loss, covering 2.0% of the rangeland area (Table 2). Importantly, the total area estimates and CI for tree encroachment and woodland loss account for classification error, and thus represent unbiased estimates of land cover change.

Table 2. Tree encroachment in Montana grasslands and shrublands determined from analysis of historical and modern aerial imagery. Model accuracy assessment was performed using visual inspection of historical imagery, modern NAIP imagery, and modern Google Map imagery.
No change in land cover classification Grassland/shrubland conversion to woodland Woodland conversion to grassland/shrubland
Area (ha) 15 927 228 2 965 587 378 947
95% CI (ha) 210 722 195 976 86 703
Standard error (ha) 107 511 99 988 44 236
User's accuracy 0.92 0.88 0.95
Producer's accuracy 0.99 0.60 0.32
Dice coefficient (F1 score) 0.95 0.71 0.47

We summarize tree expansion and tree cover loss by ecosystem type in Table 3. Grasslands were most impacted by acreage (1 416 665 ± 93 618 ha, 11.3% of area), but we saw greater impacts to shrublands and woodlands (20.7 and 33.1% tree expansion by area, respectively). Tree cover loss was found to be occurring across 1.0% of grasslands and shrublands, but losses were much higher in open woodlands (16.3% of area).

Table 3. Tree cover change metrics by ecosystem type. Ecosystem classification is from LANDFIRE BPS and represents dominant vegetation classes prior to European settlement of western North America.
Area (ha) CI (ha) % area
Tree cover expansion
Grasslands 1 416 665 93 618 11.3
Shrublands 1 144 909 75 659 20.7
Woodlands 404 013 26 699 33.1
Tree cover loss
Grasslands 125 167 28 638 1.0
Shrublands 57 492 13 154 1.0
Woodlands 196 287 44 911 16.1

To identify areas of tree expansion and woodland loss not captured by our model, we performed a hot spot analysis to identify and investigate areas where model errors were spatially clustered. Figure 5 displays the spatial distribution of points used in our accuracy assessment, as well as the misclassification of hot spots (clusters) identified by the Getis-Ord Gi algorithm. The algorithm identified seven potential hot spot clusters at the 95% confidence level (Fig. 5, left panel). Misclassified points within these hot spot clusters represented 2.8% of the points used in the accuracy assessment.

Details are in the caption following the image
Accuracy assessment. Left panel shows 3500 points analyzed for model accuracy. Right panel shows areas identified as misclassification hotspots using the Getis-Ord Gi algorithm; Post hoc analysis of hotspots found two areas of gross misclassification due to localized failure of the tree-detection algorithm due to over-exposed historical imagery (identified with an asterisk)

After visual examination, we found that two of the seven hot spot clusters had classification errors that would result in significant misinterpretation of land cover change in the map product. These areas had tree expansion commission error rates exceeding 15%. In the remaining five clusters, we found classification error rates ranging from 6 to 10%, but these errors did conceal the dominant patterns of tree expansion and woodland loss in the map product at watershed to regional scales. Notably, the areas with gross tree expansion commission errors were located in southeast Montana and are marked with an asterisk in Figure 5 (left panel). These model errors were attributable to the failure of the U-Net model to identify tree cover in the historical imagery due to low-contrast (over-exposed) source imagery.

Overall, the primary source of tree expansion commission errors in our map product was due to horizontal (XY) spatial offset between the historical and modern aerial imagery. We observed these errors primarily along boundaries between rangelands and forests where the XY offset was >25–30 m (Figure S1).


We found that more than 15% of Montana's rangelands have experienced tree expansion since the mid-20th century, with the majority of expansion occurring among grassland and shrubland sites (2.56 million ha). These findings are consistent with other analyses of tree expansion in the western United States and the recent acceleration of tree expansion in the northern Great Plains (Filippelli et al., 2020; Morford et al., 2022). Roughly 33% of woodlands were experiencing tree expansion, but these sites also saw relatively higher tree cover loss (16.1% of area), suggesting that climate-driven disturbance mechanisms (fire, drought, and beetle kill, see Loehman et al., 2018) were more effective at regulating tree expansion among these sites vs. grasslands and shrublands. Considering expansion and loss processes together, Montana's shrubland ecosystems appear most impacted by tree expansion, aligning with broader, biome-wide analyses showing rapid declines in the extent of intact sagebrush habitats across the western United States (Doherty et al., 2022).

Multiple factors contribute to the occurrence of tree encroachment, including global change impacts and local management practices like overgrazing and fire suppression. The complex interaction of these factors influences where and how quickly tree encroachment occurs (Archer et al., 2017). Disentangling these controls is beyond the scope of this work, but some landscape-level patterns are of note. For instance, Montana shrublands may be more susceptible to tree encroachment than grasslands due to their proximity to seed sources in forests and woodlands. In Montana, shrublands are typically located at the ecotone between forests, woodlands, and grasslands, and much of the observed tree cover expansion in western Montana extends away from primary forest edges into sagebrush shrublands and then further into grasslands. In central and eastern Montana, where grasslands dominate, these spatial patterns are likely more complex given the footprint of row-crop agriculture which dissects the landscape, and the prevalence of tree seed sources that are concentrated in networks of coulees.

Compared to satellite-based analyses, a baseline from the mid-20th century captures an additional four decades of ecosystem change. Using this earlier baseline, we quantified nearly twice as much tree expansion in Montana grasslands and shrublands as can be quantified using more recent satellite data (Fig. 6, Morford et al., 2022). These two independent estimates point to woodland expansion rates in Montana of 46.7 and 58.2 thousand hectares per year when using the 1954 and 1990 baselines, respectively. However, these rates are likely conservative because tree cover expansion has accelerated in the northern Great Plains over the past decade, consistent with exponential growth and spread dynamics observed in biological invasions (Morford et al., 2022; Shigesada & Kawasaki, 1997). Overall, we found similar broad spatial patterns of tree expansion using aerial and satellite imagery, implying that satellite-based methods are similarly effective at identifying where tree expansion is occurring on the landscape—albeit with a later baseline.

Details are in the caption following the image
Comparison of tree cover expansion estimates using historical imagery (this analysis) and satellite imagery (Morford et al., 2022). The historical imagery approach identified nearly double the amount of tree cover expansion in grasslands and shrublands. These differences are attributable to differences in baselines (1954 vs. 1990) and improved detection of tree recruitment using aerial imagery

Wildfire was responsible for most of the tree cover loss in Montana's rangelands. We intersected our tree cover loss map with fire perimeter data from 1984 to 2019 and found that 81.3% of tree cover loss corresponded to lands burned in large wildfires (Eidenshink et al., 2007). Visual comparison of pre- and post-fire imagery frequently revealed the persistence of standing dead trees (snags) after fire, even where fire had successfully prevented subsequent tree recruitment. These snags may offer hunting perches for predators, potentially hindering the recolonization of obligate grassland and shrubland species post-fire (Howe et al., 2014). As a result, increasing fire frequency in the western United States may not immediately improve biodiversity outcomes in rangeland ecosystems where tree expansion has occurred, even if other ecosystem functions and biogeochemical cycling recover as a result of fire disturbance (Burke et al., 2021; Williams et al., 2020).

Mapping landscape-scale tree expansion using deep learning models and historical aerial imagery was an effective strategy for quantifying change over time periods that are unavailable with satellite data. However, because of variability in data quality and inconsistent imagery orthorectification, this approach introduces additional modeling challenges that do not exist when using curated satellite imagery, such as Landsat Collection 2 (Micijevic et al., 2020). Differences in contrast and vignetting in the historical imagery cause issues with tree feature detection during inference that are difficult to detect and mitigate using our semi-automated approach. For example, some source imagery was over-exposed, which resulted in poor contrast between trees and the background. Furthermore, XY offset in historical imagery orthorectification (due to poor principal point determination) contributes to tree expansion commission errors, particularly near forest edges (Figure S1). Our XY offset errors averaged 10 meters or less, which is a higher error rate compared to modern digital imagery sources, but is in line with other attempts is semi-automated orthorectification of historical imagery (Slonecker et al., 2009). These issues, however, can likely be addressed with improved imagery restoration and deep learning-assisted georectification (Feng et al., 2021; Su et al., 2022).

Our findings have implications for conservation-focused tree encroachment management in U.S. grasslands and shrublands. Given the scope and extent of this environmental change, our results suggest that management strategies that fail to consider the landscape-level trajectory for tree encroachment will likely be ineffective at achieving durable grassland conservation. Small-scale, isolated, tree removal projects in highly encroached areas contribute little to grassland conservation if trees and tree seed sources persist nearby (Twidwell et al., 2021). Instead, managers should prioritize addressing early tree expansion in vulnerable and intact grasslands and shrublands of high conservation value (Maestas et al., 2022; Morford et al., 2022; Yokomizo et al., 2009). For example, combining our tree expansion maps with conservation priority area maps can help prioritize where conservation funds should be invested to have the greatest likelihood of achieving desired outcomes at a landscape scale (Fig. 7).

Details are in the caption following the image
Conservation strategies should leverage historical imagery with an understanding of where core-intact grassland and shrubland biomes intersect areas of tree expansion. Conserving intact biomes should be prioritized, with management activities focused first on removing invading trees and seed sources from intact core areas rather than removing trees from highly invaded areas. Sagebrush Core Habitat from Doherty et al. (2022). The arrows show management should start within the core areas removing small seedlings and progressively move toward the encroachment front.

The tree expansion map and historical imagery provide a compelling conservation tool for communicating how tree expansion reorganizes the structure of rangeland ecosystems. The slow pace of tree expansion and its impacts on ecosystem function and biodiversity are difficult to observe directly, especially in the early stages of tree colonization when conservation management is most effective. Presenting a visual landscape-level view of tree expansion in an easy-to-use mapping decision support tool can help overcome some of the limitations of shifting baseline syndrome (Soga & Gaston, 2018). Notably, historical imagery does not represent reference conditions at every location, so caution should be exercised when attempting to infer localized process-level change. We propose combining historical imagery with land use and disturbance history data to make informed management decisions that integrate landscape-level tree expansion trajectories with local-scale site conditions and conservation priorities. We provide a web application to visualize historical imagery and tree expansion in Montana rangelands to facilitate the far-reaching use of these data.


Tree expansion is rapidly altering the structure of grasslands and shrublands in Montana. More than 15% of Montana's historical grasslands and shrublands have been converted to woodlands and forests over the past 70 years, with a conversion rate now exceeding 58 000 hectares a year. These findings underscore the urgent need for effective conservation strategies to address this environmental challenge and mitigate the impacts of tree expansion on biodiversity loss. Our mapping product provides a novel tool for visually and numerically conveying the extent of tree encroachment and its effects on ecosystem structure, enabling management practitioners to develop targeted conservation plans. Furthermore, our modeling approach demonstrated the utility of neural network models for image segmentation applications of noisy historical aerial imagery (overall accuracy of 91.3%). We suggest that future work to improve model performance should consider additional image preprocessing approaches to improve scene-to-scene contrast and address principal point calculation of scanned historical aerial images in photogrammetric processing.


This work was made possible by the USDA-Natural Resources Conservation Service's (NRCS) Conservation Collaboration Grant (Agreement NR200325XXXXC002). NVIDIA provided hardware used in this analysis through their Academic Hardware Grants program. The findings and conclusions in the publication are those of the authors and should not be construed to represent the views of the USDA, U.S. Fish and Wildlife Service, or the U.S. Government. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.

    Author Contributions

    SLM and BWA conceived the analysis. SLM developed the project framework, performed the modeling and analysis, and wrote the paper. EJ assisted with photogrammetric processing. KM performed the accuracy assessment and assisted with figure preparation. All authors assisted in evaluating and interpreting the results and provided input on the manuscript draft.

    Conflict of Interest

    The authors declare no conflicts of interest.

    Data Availability Statement

    Data available from Zenodo https://doi.org/10.5281/zenodo.8083547 and Google Earth Engine https://smorford.users.earthengine.app/view/montana-conifer-expansion. Historical imagery can be downloaded from the University of Montana http://rangeland.ntsg.umt.edu/data/rap/historical-imagery/.