arXiv subjects

Arne Nothdurft

Publications and source records attributed to Arne Nothdurft.

7 recordsLinked to original sources

arXiv2026

A Bayesian Magnitude-Composition Model for Tree-Size Distributions and Stand-Tables

Sparse forest inventories often provide too few plots to estimate species-specific tree-size distributions for individual stands. We develop a general Bayesian magnitude-composition model that separates overall abundance from its allocation among categories. A negative-binomial model describes total counts, while multinomial models describe how those counts are allocated among categories. In forest inventory, this construction allocates trees among species and then size classes within species, without imposing a parametric form on the tree-size distribution. Covariates inform both abundance and composition. Shared latent factors represent residual spatial and group-level dependence among categories using relatively few processes, while smoothing priors on regression coefficients borrow information across neighboring size classes. Nearest-neighbor Gaussian processes support efficient spatial computation. Joint posterior prediction and area-weighted aggregation yield stand-tables---tree densities by species and size class---and derived measures such as size-class diversity, with associated uncertainty. Simulations show small estimation errors and near-nominal predictive-interval coverage for forest and stand summaries. An application combining field plots and light detection and ranging (LiDAR) covariates illustrates estimation of species-specific distributions of diameter at breast height and size-class diversity in sampled and unsampled stands.

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arXiv2026

Evaluating LiDAR Data Sources, Predictor Resolution, and Spatial Random Effects in Bayesian Change-of-Support Models for Forest Inventory

Forest managers need timely stand-level information to support operational planning, particularly in mixed-species, structurally heterogeneous forests facing climate-related disturbance. Model-based estimation combines sparse field data with remotely sensed predictors to estimate growing stock volume (GSV) for small areas. While uncrewed aerial vehicle laser scanning (ULS) offers flexible, high-resolution LiDAR acquisition, its advantages over conventional airborne laser scanning (ALS) remain unclear. We compared publicly available ALS and newly acquired ULS data using Bayesian change-of-support models to estimate GSV in a mixed-species forest in north-eastern Germany. We evaluated distributional LiDAR metrics and spatial random effects. ULS consistently outperformed ALS, achieving cross-validated RMSPEs of 68.5 m^3/ha and 79.5 m3/ha, respectively-a 13.8 % reduction in prediction error. Distributional metrics improved ULS models more strongly, reducing RMSPE by up to 10.1 %; spatial effects provided only minor gains at substantially higher computational cost. ULS also produced lower uncertainty in latent stand-mean GSV estimates. The ULS advantage may reflect both finer-scale canopy information and closer temporal alignment with field measurements. Timely, information rich LiDAR may therefore be more valuable for stand-level GSV estimation than increasingly complex spatial models. Temporally matched ALS-ULS comparisons are needed to isolate platform effects.

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arXiv2025

Small area estimation of growing stock timber volume, basal area, mean stem diameter, and stem density for mountain forests in Austria

Regression models were evaluated to estimate stand-level growing stock volume (GSV), quadratic mean diameter (QMD), basal area (BA), and stem density (N) in the Brixen im Thale forest district of Austria. Field measurements for GSV, QMD, and BA were collected on 146 inventory plots using a handheld mobile personal laser scanning system. Predictor variables were derived from airborne laser scanning (ALS)-derived normalized digital surface and terrain models. The objective was to generate stand-level estimates and associated uncertainty for GSV, QMD, BA, and N across 824 stands. A unit-level small area estimation framework was used to generate stand-level posterior predictive distributions by aggregating predictions from finer spatial scales. Both univariate and multivariate models, with and without spatially varying intercepts, were considered. Predictive performance was assessed via spatially blocked cross-validation, focusing on bias, accuracy, and precision. Despite exploratory analysis suggesting advantages of complex multivariate spatial models, simpler univariate spatial -- and in some cases, non-spatial -- models exhibited comparable predictive performance.

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arXiv2025

Leveraging national forest inventory data to estimate forest carbon density status and trends for small areas

National forest inventory (NFI) data are often costly to collect, which inhibits efforts to estimate parameters of interest for small spatial, temporal, or biophysical domains. Traditionally, design-based estimators are used to estimate status of forest parameters of interest, but are unreliable for small areas where data are sparse. Additionally, design-based estimates constructed directly from the survey data are often unavailable when sample sizes are especially small. Traditional model-based small area estimation approaches, such as the Fay-Herriot (FH) model, rely on these direct estimates for inference; hence, missing direct estimates preclude the use of such approaches. Here, we detail a Bayesian spatio-temporal small area estimation model that efficiently leverages sparse NFI data to estimate status and trends for forest parameters. The proposed model bypasses the use of direct estimates and instead uses plot-level NFI measurements along with auxiliary data including remotely sensed tree canopy cover. We produce forest carbon estimates from the United States NFI over 14 years across the contiguous US (CONUS) and conduct a simulation study to assess our proposed model's accuracy, precision, and bias, compared to that of a design-based estimator. The proposed model provides improved precision and accuracy over traditional estimation methods, and provides useful insights into county-level forest carbon dynamics across the CONUS.

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arXiv2024

Bayesian Modeling of Incompatible Spatial Data: A Case Study Involving Post-Adrian Storm Forest Damage Assessment

Modeling incompatible spatial data, i.e., data with different spatial resolutions, is a pervasive challenge in remote sensing data analysis. Typical approaches to addressing this challenge aggregate information to a common coarse resolution, i.e., compatible resolutions, prior to modeling. Such pre-processing aggregation simplifies analysis, but potentially causes information loss and hence compromised inference and predictive performance. To avoid losing potential information provided by finer spatial resolution data and improve predictive performance, we propose a new Bayesian method that constructs a latent spatial process model at the finest spatial resolution. This model is tailored to settings where the outcome variable is measured on a coarser spatial resolution than predictor variables -- a configuration seen increasingly when high spatial resolution remotely sensed predictors are used in analysis. A key contribution of this work is an efficient algorithm that enables full Bayesian inference using finer resolution data while optimizing computational and storage costs. The proposed method is applied to a forest damage assessment for the 2018 Adrian storm in Carinthia, Austria, that uses high-resolution laser imaging detection and ranging (LiDAR) measurements and relatively coarse resolution forest inventory measurements. Extensive simulation studies demonstrate the proposed approach substantially improves inference for small prediction units.

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arXiv2023

Spatial prediction of diameter distributions for the alpine protection forests in Ebensee, Austria, using ALS/PLS and spatial distributional regression models

A spatial distributional regression model is presented to predict the forest structural diversity in terms of the distributions of the stem diameter at breast height (DBH) in the protection forests in Ebensee, Austria. In total 36,338 sample trees were measured via a handheld mobile personal laser scanning system (PLS) on 273 sample plots each having a 20 m radius. Recent airborne laser scanning (ALS) data was used to derive regression covariates from the normalized digital vegetation height model (DVHM) and the digital terrain model (DTM). Candidate models were constructed that differed in their linear predictors of the two gamma distribution parameters. Non-linear smoothing splines outperformed linear parametric slope coefficients, and the best implementation of spatial structured effects was achieved by a Gaussian process smooth. Model fitting and posterior parameter inference was achieved by using full Bayesian methodology and MCMC sampling algorithms implemented in the R-package BAMLSS. Spatial predictions of stem count proportions per DBH classes revealed that regeneration of smaller trees was lacking in certain areas of the protection forest landscape.

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arXiv2021

Estimating timber volume loss due to storm damage in Carinthia, Austria, using ALS/TLS and spatial regression models

A spatial regression model framework is presented to predict growing stock volume loss due to storm Adrian which caused heavy forest damage in the upper Gail valley in Carinthia, Austria, in October 2018. Model parameters were estimated using growing stock volume measured with a terrestrial laser scanner on 62 sample plots distributed across five sub-regions. Predictor variables were derived from high resolution vegetation height measurements collected during an airborne laser scanning campaign. Non-spatial and spatial candidate models were proposed and assessed based on fit to observed data and out-of-sample prediction. Spatial Gaussian processes associated model intercepts and regression coefficients were used to capture spatial dependence. Results show a spatially-varying coefficient model, which allowed the intercept and regression coefficients to vary spatially, yielded the best fit and prediction. Two approaches were considered for prediction over blowdown areas: 1) an areal approach that viewed each blowdown as a single prediction unit indexed by its centroid; and 2) a block approach where each blowdown was partitioned into smaller prediction units to better align with sample plots' spatial support. Joint prediction was used to acknowledge spatial dependence among block units. Results demonstrated the block approach is preferable as it mitigated change-of-support issues encountered in the areal approach. Despite the small sample size, predictions for 55% of the total 564 blowdown areas, accounting for 93% of the total loss, had a coefficient of variation less than 25%. Key advantages of the proposed regression framework are the ability to quantify uncertainty in spatial covariance parameters, propagate parameter uncertainty through to prediction, and provide statistically valid prediction point and interval estimates for individual blowdowns and collections of blowdowns.

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