Background & Summary

Numerous stand size-density metrics exist to guide forest monitoring, management, and modeling1. One of the most robust and comprehensive metrics is relative density (RD)1,2, which is defined as the proportion of absolute number of trees per unit area compared to an empirically derived maximum size-density relationship (MSDR) estimate3,4,5,6,7,8. RD is specifically based on the stand’s current stand density index (SDI) and its maximum SDI (SDIMAX; RD = SDI/SDIMAX). Due to its generality, robustness, and high interpretability, the predictions and quantification of RD imply that there is strong potential in anticipating current or future competition, growth and mortality, which can be useful for guiding forest management decisions9,10,11. RD objectively quantifies a forest’s current size-density when compared against a maximum value with key biological objectivity from broad ecological and policy perspectives depending on spatial scale being evaluated, ranging from local to regional or even national-levels10. Therefore, the expression of RD is relevant for determining stand development stages, dynamic processes, and potential disturbance susceptibility at strategic spatial and temporal scales3,4,5,6,7,8,11,12,13. RD can be used for various management objectives such as fiber production and net carbon sequestration. RD can quantify key stand development processes that drive gross tree carbon accretion and depletion like canopy closure and mortality, disturbance re-growth, and the overall degree of tree-to-tree competition. These processes can significantly influence the future development of forest ecosystems and associated carbon pools. Density-dependent mortality from self-thinning plays a crucial role in the formation of snags and down woody material (DWM) which transfers carbon from the live to the dead pool. Therefore, metrics that assess size-density relationships, like SDI and RD, have the potential to contribute to a broader understanding of carbon dynamics, particularly DWM. In addition, scientists and policy makers dealing with carbon accounting programs may need to be informed by the best available science to address potential shortcomings of using potentially subjective ecological baselines such as minimum carbon stocks14. Data availability and analysis are important to recalibrate the current ecological thresholds for carbon offset project baselines, development stages of forests, biological potential for sequestration and emission and potential risk from climate change induced natural disturbances11. For example, the use of RD to optimize carbon sequestration in the context of adaptive silviculture has been suggested1,11, because of the ability to better account for and minimize density-dependent mortality15. In order to meet the different applications of RD, a nationally consistent and spatially explicit yet a robust dataset of key size-density metrics is needed.

Globally, national forest inventories and monitoring databases assess key attributes and variables over large land areas16. The Forest Inventory and Analysis (FIA) program under the United States Department of Agriculture (USDA) Forest Service conducts national inventories. FIA determines the condition, extent, trends and status of forest resources across different land ownership classes in the United States (US)17,18,19. FIA inventories are annually sampled at a national base sample intensity of 1 plot per ~ 2,428 forested hectares with a specific remeasurement cycle of 5–10 years depending on states. This may limit the planning and management of forest resources based solely on FIA data when considering stand-level management needs in the context of error propagation20. To provide for key technological challenges of providing spatially contiguous estimates, there has been the development and application of varying statistical approaches that relate FIA plot data and environmental variables to cover forest areas not directly inventoried21. The availability of medium-resolution remotely sensed data from Landscape Fire and Resource Management Planning Tools (LANDFIRE) presents an opportunity for improved regular monitoring of size-density metrics when fused with conventional forest inventory datasets such as FIA. In particular, spatially-explicit imputation allows a few highly detailed observations to be assigned to unmeasured locations, which provides high-resolution and spatially contiguous information21. For example, Riley, Grenfell, Shaw, and Finney20 modified a random forest approach together with LANDFIRE variables to impute FIA plot data to a 30 m gridded dataset TREEMAP2016 (hereafter referred to as “TREEMAP”). Similar methodology was used to develop subsequent generations of TREEMAP2020[22](https://www.nature.com/articles/s41597-025-06012-6#ref-CR22 “Zimmer, S. N. et al. TreeMap 2020 CONUS: A Tree-Level Model of the Forests of the Conterminous United States circa 2020. https://doi.org/10.2737/RDS-2025-0031

(2025).“) and TREEMAP2022[23](https://www.nature.com/articles/s41597-025-06012-6#ref-CR23 “Houtman, R. M. et al. TreeMap 2022 CONUS: A Tree-Level Model of the Forests of the Conterminous United States circa 2022. https://doi.org/10.2737/RDS-2025-0032

(2025).“).TREEMAP provides the opportunity for the quantification and validation of ground-based size-density dynamics at spatial resolutions not achievable when using traditional methodologies alone1. The availability of gridded vegetation raster maps such as LANDFIRE and TREEMAP20 provides a unique opportunity to produce landscape-level metrics of key forest attributes that drive forest planning and management (e.g. carbon, density, diversity, stand structure). Specifically, TREEMAP allows data collected from FIA plots to be presented at 30 m × 30 m pixel resolution. In this data description, we have linked SDI, SDIMAX and RD attributes derived from FIA plot-level records to the publicly available TREEMAP raster attribute table to produce medium-resolution, wall to wall, and spatially contiguous maps for CONUS.

Importance of RD in policy/management decision making across spatial scales

Recently, there has been increased interests in the national scale quantification of size-density metrics like SDI and RD across CONUS9,10 in the context of large-scale forest planning and management, potential fuel loading24,25,26, and carbon stock analyses11,27,28. In particular, an estimation of the RD at the national scale allows for the prediction of future carbon stocks based on the identification of loss, gain or stagnation in forest growth9 as well as disentangling the gross components of net forest carbon change29.

Forest data produced by FIA is used by different partners for information, planning, and management purposes, especially in the context of biomass and carbon estimation, fire monitoring, and habitat utilization20,30. However, FIA data may be limited for certain infrequent forest types, species groups and ecoregions. This limits the general availability of high resolution size-density spatial products like RD, which would assist and allow for analyses at smaller scales not covered not adequately covered by -base national inventory sample intensity20. The potential of developing and refining size-density spatial products based on the available TREEMAP data is an interesting and potentially valuable leveraging of datasets, which could allow for the production of wall-to-wall coverage of size-density metrics like RD in space and time, while also supporting state- to national-level efforts for biomass/carbon estimation, fuel treatment, revision of forest plans and large-scale forest dynamics20.

Size-density metrics like RD can be used for projecting future competition and stand dynamics, which is a key input into management decisions with some limited subjectivity in biological and management interpretations of the metrics10. Forest management treatments are premised on quantifying the observed stand density when compared to either an optimal, desired, or maximum density7 for input into strategic-scale inventory assessments. At a stand-level, RD is used to inform silvicultural operations like pre-commercial or commercial thinning to improve growth and quality of trees. RD can also be used to assess the risk to potential disturbances like fire, drought or insect outbreak as high RD forest stands can have increased vulnerability and reduced resilience2,3,11,29,30,31,32. At a national-level, RD can be used to inform large-scale forest management and planning decisions in the view of climate change to restore ecological integrity and resiliency of forest landscapes. In short, RD is a useful metric that could be used during policy and management action development to increase resilience of forests at broad scales. Increased resilience can be done to maximize productivity and/or minimize the effects of disturbances, which will ultimately help forests to achieve multiple ecosystem services and persist during climate change.

Knowledge of the RD in a stand can be critical to guiding and optimizing management decisions, which has led to the development of decision-making tools such as size-density management charts (SDMCs)2. Incorporation of RD in SDMCs, allows visualization and anticipation of stand development through stages of competition in space and time2. Often SDMCs rely on regional size-density values, which may limit applicability in certain locations and applications. The use of more local size-density metrics could help refine and increase applicability of SDMCs, which could broaden their use beyond traditional forest management applications33,34.

At a national-level, RD estimates may provide a useful baseline for assessing the potential long-term impacts of alternative disturbances or management regimes across contrasting forest types at meaningful spatial scales relevant for refining the understanding of current and future forest dynamics9. Stand-level data on size-density estimation is relevant for determining the biological capacity of a given species when determining site-specific management decision, whereas large scale data is generally needed for evaluating the underlying variability of density for certain management purposes35. At a national level, a robust and spatially-contiguous estimation of RD is useful for the development of policy-oriented frameworks for activities such as reforestation, optimizing density management for a variety of forest carbon management objectives. The carbon management activities may include avoided future catastrophic emissions and mitigation activities in service to a greater goal of enhanced forest carbon stewardship10.

This article introduces 30 m resolution, spatially contiguous, and nationally consistent size-density metrics for CONUS. The article further presents the developed datasets and associated methods, evaluating key relationships across methods. Further the article summarizes the primary attributes across various metrics and spatial scales. In particular, two primary methods of estimating size-density metrics are evaluated across selected forest types, counties, and states across CONUS.

Methods

FIA Inventory data

Data used in the study was taken from the publicly available database of the Forest Inventory Analysis (FIA) program under the United States Department of Agriculture (USDA) Forest Service[36](https://www.nature.com/articles/s41597-025-06012-6#ref-CR36 “Nelson, M. D. et al. Defining the United States Land Base: A Technical Document Supporting the USDA Forest Service 2020 RPA Assessment. https://doi.org/10.2737/NRS-GTR-191

(U.S. Department of Agriculture, Forest Service, Northern Research Station, Madison, WI, 2020).“). From around 2000, FIA conducted annual forest inventories in the US of forestland. Forestland is defined as an area with live trees occupying about 10% canopy cover or having capabilities of supporting 10% cover if having undergone harvesting or disturbances and having an area of ~0.4 ha and width of ~36.6 m37. The National Forest Inventory (NFI) design establishes a single plot in every 24 km2 of forest38. Fixed area plots are nested within a cluster with large subplots with a radius of 17.95 m in which all trees 12.7 cm in diameter at breast height (dbh) and greater are measured. The small plots have a radius of 2.07 m and all trees >2.54 cm dbh are measured. A single inventory plot has a cluster of four subplots, specifically there is a central subplot and the other three subplots have an orientation of 0, 120, and 240° from the central subplot37. The subplots are 36.58 m away from the central subplot where live trees and snags are counted. In each plot, variables such as tree height, species, tree form, dbh, forest type, forest type group, stand age, ownership, slope, elevation, and aspect are recorded. For this particular analysis, SDI, were estimated at the subplot-level to provide multiple independent estimates for a given plot to ensure proper estimation of the plot-level random effects10.

Estimating SDIMAX and RD

FIA data is highly hierarchical and nested in structure, which poses a challenge in determining SDIMAX estimates at various scales like the subplot-, plot-, county- and-/ or state-levels. In order to address and effectively leverage the nested nature of the data, a number of statistical methods have been used to estimate SDIMAX across national levels1. Prior analyses have primarily used linear quantile mixed model (lqmm)13 in the calculation of Reineke (1933)39 relationship based on the number of trees per unit area and a given reference size metric like quadratic mean diameter (QMD):

$$ln(TPH)=({b}_{10}+{\upsilon }_{i})+({b}_{11}+{\gamma }_{i})\ast ln(QMD)+{\varepsilon }_{i}$$

(1)

where TPH is the number of trees per hectare (# ha−1), QMD is the quadratic mean diameter (cm), bi are the fixed effects parameters, εi is the residual for the ith plot and ʋi and ɣi are random effects for the ith plot. For this analysis, Bayesian hierarchical quantile regression methods were used to achieve more robust estimates and determine plot-level uncertainty in the derived values (Fig. 1). To do this, the Bayesian Multilevel Models using Stan (BRMS) package40 in R v4.2.3 was used. A unique identifier for each FIA subplot was created and used as a hierarchical effect on both the slope and intercept. BRMS default values for the number of chains (4) and iterations (2,000) were used. Consistent with Woodall and Weiskittel (2021), a 95% quantile was specified, while normal priors based on their model fits were used. Based on the derived coefficients in Eq. (1), plot-level estimates of SDIMAX were estimated from the FIA subplot data similar to Woodall and Weiskittel10. The SDIMAX for each plot was estimated using a standard reference diameter (25.4 cm) in the following equation:

$${{SDI}}_{{MAX}}={\exp }\left(\left({b}_{10}+{\upsilon }_{i}\right)+\left({b}_{11}+{\gamma }_{i}\right)\ast {ln}\left(25.4\right)\right)$$

(2)

where all attributes are previously defined. RD is the proportion of absolute stem density in a stand relative to the maximum theoretical stem density achievable in a stand based on the maximum size-density relationship3,4,5,6,7,8. Plot-level estimates of RD were determined using estimates from both Eqs. (1, 2) as follows:

$${RD}=\frac{{SDI}}{{{SDI}}_{{MAX}}}$$

(3)

Fig. 1

The workflow used in this study. Plot and subplot represent the different scales of FIA data measurement. CN: sequence number; BAPA: Basal area per acre; QMD: quadratic mean diameter; TPA: trees per acre (see R code for the conversion from imperial to metric units).

Currently, generally accepted RD threshold values for critical stand developmental stages are available, namely crown closure and initiation of mortality (RD = 0.15–0.30), optimum growth (RD = 0.30–55), and zone of imminent mortality (RD = 0.55–1.0).

TREEMAP

The development of TREEMAP has been extensively described by the authors of TREEMAP20,21,30,41, therefore, we will briefly describe it here. TREEMAP is a tree level model for forests in the US which is a product of two datasets from FIA and gridded data from LANDFIRE database20. TREEMAP uses machine learning algorithm such as random forest (RF) in the yimpute package in R software to impute plot data measured by FIA to landscape level gridded maps (disturbance, vegetation and biophysical parameters) in the LANDFIRE database30. Imputation is an estimation method where non-sampled measurements from the target dataset are replaced with observations with similar characteristics from the reference dataset42. In the context of TREEMAP, imputation was used to assign FIA plots (reference) to the target data (LANDFIRE database)30. A set of filters were applied to the reference data from FIA: measurements should come from single condition and accessible plots. The target data was from a LANDFIRE for a 2016 project and data included attributes predictor variables such as topography, latitude and longitude, vegetation, disturbance and biophysical characteristics which are needed to be available both in the reference and target dataset. Resultantly, the measured forest attributes available in raster format at a medium resolution of 30 × 30 m. Each forested FIA plot is assigned to the most similar forested pixels in the LANDFIRE database thereby producing a medium resolution data for forest characteristics20. The TREEMAP raster has an attribute table which allow for linkages between FIA data allowing users to make summarize of the variables and produce maps in a Geographic Information System (GIS)20. In this study we leveraged on the characteristics of the TREEMAP raster to link, summarize and produce maps of SDI, SDIMAX and RD across CONUS.

The TREEMAP dataset has FIA tree level attributes measured at subplot level. In order to keep the observed variability and to produce robust estimates, tree level estimates of SDI were determined using the additive summation method and aggregated to plot level following10 (Fig. 1). Plot-specific SDIMAX estimates were derived using hierarchical Bayesian quantile modelling similar to the methods used by Woodall and Weiskittel10 with RD derived from SDI and SDIMAX. We leveraged on the common fields (TREEMAP record number (tm.id)), to join the TREEMAP raster and the FIA data. The joining of the two datasets allowed us to make summaries and comparisons between size-density estimates across forest types, Environmental Monitoring and Assessment Program (EMAP) hexagons, counties, and states (Fig. 1). Due to mismatch between the FIA and TREEMAP tm.id and RD > 1, (684 NULL observations were deleted), resulting in a total of 54,925 observations being used. In this study, SDI, SDIMAX and RD were mapped at 30 × 30 m spatial resolution. We compared summaries of TREEMAP and FIA based size-density estimates across forest types, counties, state, and US EMAP 64.8 km2 hexagons in CONUS. Several filters were applied to maintain national consistency and robustness, for example dealing with potential influential values, such as where RD exceeded 1 as this is not biologically feasible. In cases where FIA based estimates of RD exceeded 1, it was reset to 1 and this accounted for approximately 1,305 observations or 2.4% of the data. Preliminary analysis showed that this greatly skewed the overall distribution of RD and these observations were removed from subsequent analysis as most of the observations were located in uncommon forest types and/or ecoregions, which likely led to the initial imprecise estimate for the size-density metrics. For TREEMAP, 684 observations or approximately 1.2% of the data were removed as they had RD = 1 or had null observations, thus, we remained with 54,925 observations.

Summarizing RD across space/time

TREEMAP derived estimates of SDI, SDIMAX and RD were centered on 2016 were compared with FIA estimates from 2013–2020. We graphically compared the distributions of SDI, SDIMAX, and RD derived from TREEMAP and FIA plot-based estimates across multiple scales (Fig. 1). Primary scales of comparison were from specific FIA forest types, counties, states and EMAP hexagons to illustrate key similarities and differences across data products (Fig. 1). General trends and patterns are briefly highlighted and discussed below.

Data Records

The data records cited in this work are stored at FigShare, which is a public access repository for publishing research data[43](https://www.nature.com/articles/s41597-025-06012-6#ref-CR43 “Chivhenge, E., Weiskittel, A. R., Woodall, C. W., D’amato, A. W. & Daigneault, A. Geospatial Estimation of Forest Relative Density across the Continental US. FigShare https://doi.org/10.6084/m9.figshare.28127525

(2024).“). This data set consists of 8 separate files. Descriptions of these data records are as follows:

FIA SDIMAX plot file

This file provides the FIA SDIMAX estimates determined using BRMS for plots across the CONUS[44](https://www.nature.com/articles/s41597-025-06012-6#ref-CR44 “Chivhenge, E., Weiskittel, A. R., Woodall, C. W., D’Amato, A. W. & Daigneault, A. Plot level estimates of maximum stand density index (SDImax) for the United States. FigShare https://doi.org/10.6084/m9.figshare.28112171

(2025).“).

FIA SDI subplot file

This file provides the subplot estimates of the stand density index (SDI) and the associated tm_id and the unique control number (CN) used to identify a survey record in the FIADB[45](https://www.nature.com/articles/s41597-025-06012-6#ref-CR45 “Chivhenge, E., Weiskittel, A. R., Woodall, C. W., D’Amato, A. W. & Daigneault, A. TM.subp.sum. FigShare https://doi.org/10.6084/m9.figshare.28112198

(2025).“).

Treemap tree table

This file provides the TREEMAP tree table list with the CN, tm.id, trees per acre and diameter at subplot level[46](https://www.nature.com/articles/s41597-025-06012-6#ref-CR46 “Riley, K. L., Greenfield, I. C., Finney, M. A. & Shaw, J. D. A Tree-Level Model of the Forests of the Conterminous United States circa 2016. https://doi.org/10.2737/RDS-2021-0074

(2021).“).

TREEMAP SDI Raster

This file is the 30 m × 30 m resolution TREEMAP derived SDI estimates for forested areas of the CONUS in 2016[47](https://www.nature.com/articles/s41597-025-06012-6#ref-CR47 “Chivhenge, E., Weiskittel, A. R., Woodall, C. W., D’Amato, A. W. & Daigneault, A. TREEMAP SDI. FigShare https://doi.org/10.6084/m9.figshare.28119677

(2024).“).

TREEMAP SDIMAX Raster

This file is the 30 m × 30 m resolution TREEMAP derived SDIMAX estimates for forested areas of the CONUS in 2016[48](https://www.nature.com/articles/s41597-025-06012-6#ref-CR48 “Chivhenge, E., Weiskittel, A. R., Woodall, C. W., D’Amato, A. W. & Daigneault, A. Plot SDImax. FigShare https://doi.org/10.6084/m9.figshare.28119920

(2025).“).

TREEMAP RD Raster

This file is the 30 m × 30 m TREEMAP derived RD estimates for forested areas of the CONUS in 2016[49](https://www.nature.com/articles/s41597-025-06012-6#ref-CR49 “Chivhenge, E., Weiskittel, A. R., Woodall, C. W., D’Amato, A. W. & Daigneault, A. TREEMAP RD. FigShare https://doi.org/10.6084/m9.figshare.28119680

(2025).“).

TREEMAP 2016 raster

This is an updated version of the original TREEMAP 2016 raster and the associated files for CONUS. The new additions to the TREEMAP raster attribute table are the SDI, SDIMAX and RD estimates[50](https://www.nature.com/articles/s41597-025-06012-6#ref-CR50 “Chivhenge, E., Weiskittel, A. R., Woodall, C. W., D’Amato, A. W. & Daigneault, A. This is an updated version of the original TREEMAP 2016 raster and the associated files for CONUS. The new additions to the TREEMAP raster attribute table are the SDI, SDIMAX and RD estimates. FigShare https://doi.org/10.6084/m9.figshare.30170902.v1

(2025).“).

R code

This file has the R code that was used to calculate SDI from the TREEMAP 2016 tree table. The code permanently merged the SDI, SDIMAX and RD csv files to the original TREEMAP 2016 raster attribute table.

Data comparisons

Forest type size-density comparisons

TREEMAP and FIA SDI estimates were skewed towards fewer trees (≈500 tph) (Fig. 2a). The SDI distributions showed significant differences in the FIA (459 ± 272 tph) and TREEMAP based estimate (444 ± 234 tph; Fig. 2b also see Figure S1 for the comparison of SDI densities of all forest types according to TREEMAP and FIA datasets). There were no significant differences in the distributions of SDIMAX across forest types based on the TREEMAP (844 ± 366 tph) and FIA datasets (845 ± 359 tph, Fig. 3b and also see Figure S2). For FIA, distributions of SDI were skewed towards lower values, which created distinct differences in the RD distributions across forest types (Fig. 4a, also s