Sören Holm

Model-based inference for biomass estimation in a LiDAR sample survey in Hedmark County, Norway

In forest inventories, regression models are often applied to predict quantities such as biomass at the level of sampling units. In this paper, we propose a model-based inference framework for combining sampling and model errors in the variance estimation. It was applied to airborne laser (LiDAR) data sets from Hedmark County, Norway, where the model error proportion of the total variance was found to be large for both scanning (airborne laser scanning) and profiling LiDAR when biomass was estimated. With profiling LiDAR, the model error variance component for the entire county was as large as 71% whereas for airborne laser scanning, it was 43% of the total variance. Partly, this reflects the better accuracy of the pixel-based regression models estimated from scanner data as compared with the models estimated from profiler data. The framework proposed in our study can be applied in all types of sample surveys where model-based predictions are made at the level of individual sampling units. Especially, it should be useful in cases where model-assisted inference cannot be applied due to the lack of a probability sample from the target population or due to problems of correctly matching observations of auxiliary and target variables.

A forest inventory method based on density‐adapted circular plot size

A method using sample plots with “fixed number of stems, random circular plot size”; in the stand‐description phase was studied both theoretically and empirically in several regards; it was also developed for practical purposes. We call this inventory method “the density‐adapted method”;. The advantage of this method, compared with the currently employed method, is that the work per sample plot is proportional to the amount of useful information gathered per sample plot. In simulation studies, “forests”; are simulated, and the density‐adapted method is then used in these “forests”;. Generally speaking, the bias amounts to a few percent in the realistic forests that are simulated. The bias is sometimes positive and sometimes negative. Positive bias results from a high degree of clustering, negative from high evenness. In actual stand structures, the density‐adapted method has been proven to produce an insignificant amount of bias. Long‐term prognoses in conjunction with timber assessment calculations have ...

On the potential of Kriging for forest management planning

Forest management planning aims at fulfilling the goals of the forest owner. Scheduling treatments of forest stands, both in time and space, have been well investigated previously. Usually, however, these studies have assumed spatially discrete stands, representing imagined treatment units. Furthermore, the stands have been inventoried using ocular methods with varying and unknown precision. As an alternative to this conventional way of describing the forest, an objective circular plot inventory method was used, in the present investigation, to represent the forest on a 400 ha estate. Kriging was used to estimate spatially continuous forest characteristics from the georeferenced inventory plots. Spatial discontinuity, for example, between young and old forests, was handled by making an initial stratification of the forest into age‐classes. This approach enabled several spatially continuous variables, of interest to forest management planning, to be estimated at all locations. The stratification made it po...

Use of models in large-area forest surveys: comparing model-assisted, model-based and hybrid estimation

This paper focuses on the use of models for increasing the precision of estimators in large-area forest surveys. It is motivated by the increasing availability of remotely sensed data, which facilitates the development of models predicting the variables of interest in forest surveys. We present, review and compare three different estimation frameworks where models play a core role: model-assisted, model-based, and hybrid estimation. The first two are well known, whereas the third has only recently been introduced in forest surveys. Hybrid inference mixes design-based and model-based inference, since it relies on a probability sample of auxiliary data and a model predicting the target variable from the auxiliary data..We review studies on large-area forest surveys based on model-assisted, model-based, and hybrid estimation, and discuss advantages and disadvantages of the approaches. We conclude that no general recommendations can be made about whether model-assisted, model-based, or hybrid estimation should be preferred. The choice depends on the objective of the survey and the possibilities to acquire appropriate field and remotely sensed data. We also conclude that modelling approaches can only be successfully applied for estimating target variables such as growing stock volume or biomass, which are adequately related to commonly available remotely sensed data, and thus purely field based surveys remain important for several important forest parameters.

Estimating forest characteristics in scanned aerial photographs with respect to requirements for economic forest management planning

The objective of forest management planning is often expressed as maximum sustainable economic yield. Methods used to collect information for forestry planning should, therefore, include variables significant for economic evaluations of management alternatives. It is important to be able to differentiate mature stands with respect to timber volumes and species mixture. In this study, digital high‐altitude aerial photographs are tested as a data source for planning. Circular plot data from a forest estate in northern Sweden were used as reference material. Global positioning system (GPS) measurements, with differential correction, were used to georeference the plots. Harvesting priorities were calculated for each plot using the Forest Management Planning Package. Volumes, species mixture and harvest priorities were estimated using regression analysis based on textural and spectral information from aerial photographs. The results show that the dependent variables could be estimated fairly well using only sp...

Using digital image projections to visualize forest landscape changes due to management activities and forest growth

A pedagogic problem in forestry and landscape management is to visualize future landscape effects of forest growth and current management activities in the forest. This paper presents a method for forecasting digital image projections of forest landscape dynamics. Static nonlinear regression functions estimate the digital numbers in a Landsat Thematic Mapper image. Regressors used are forest stand variables. By estimating the future forest stand data, based on intermediate treatment and growth, future satellite digital images are created. In a case study example, the future landscape of a forest block in the province of Västernorrland, Sweden, is projected to demonstrate the application of this visualization technique.

Hierarchical model-based inference for forest inventory utilizing three sources of information

Abstract∙ Key messageThe study presents novel model-based estimators for growing stock volume and its uncertainty estimation, combining a sparse sample of field plots, a sample of laser data, and wall-to-wall Landsat data. On the basis of our detailed simulation, we show that when the uncertainty of estimating mean growing stock volume on the basis of an intermediate ALS model is not accounted for, the estimated variance of the estimator can be biased by as much as a factor of three or more, depending on the sample size at the various stages of the design.∙ ContextThis study concerns model-based inference for estimating growing stock volume in large-area forest inventories, combining wall-to-wall Landsat data, a sample of laser data, and a sparse subsample of field data.∙ AimsWe develop and evaluate novel estimators and variance estimators for the population mean volume, taking into account the uncertainty in two model steps.∙ Methods Estimators and variance estimators were derived for two main methodological approaches and evaluated through Monte Carlo simulation. The first approach is known as two-stage least squares regression, where Landsat data were used to predict laser predictor variables, thus emulating the use of wall-to-wall laser data. In the second approach laser data were used to predict field-recorded volumes, which were subsequently used as response variables in modeling the relationship between Landsat and field data.Results∙ The estimators and variance estimators are shown to be at least approximately unbiased. Under certain assumptions the two methods provide identical results with regard to estimators and similar results with regard to estimated variances.∙ Conclusion We show that ignoring the uncertainty due to one of the models leads to substantial underestimation of the variance, when two models are involved in the estimation procedure.

A cost function estimating the loss due to extended rotation age

A method for estimating the economic loss in timber production resulting from extending the rotation age was studied. Basically, optimal rotation age depends on the stated objectives. If the objective comprises only timber production, the rotation age is derived from maximizing the net present value (PV) of timber production. If, on the other hand, the objective function includes, for example, the maintenance of biodiversity and scenic values, the optimal rotation age is likely to be extended. In the present study, PVs from successively extended rotation ages were estimated for a sample of economically mature stands. The PVs were based on no thinning allowed (case A), and thinning allowed in the first 5‐yr period (case B). By using regression analysis, functions were estimated that predict the inoptimality loss from extending the rotation age for both cases. Stand data collected by subjective (ocular) inventory methods were the regressors. Only the problem of economic loss in timber production from extend...

Using airborne & space lidars for large-area inventory

NASA plans to launch two space lidar missions over the next decade, and at least one proposal for a space lidar is being considered by the European Space Agency. All designs call for single-beam or multi-beam profiling systems. These space ranging systems, like the ICESat/GLAS lidar that collected over 1.91 billion waveforms between January 2003 and October 2009, must necessarily be used as sampling tools to characterize vegetation cover and to estimate forest volume, biomass, and carbon globally. Recent investigations conducted by these authors have centered on developing, testing, and refining statistical approaches that can incorporate airborne and space lidar acquisitions to inventory large areas.

Assessing uncertainty: Sample size trade-offs in the development and application of carbon stock models

Many parties to the United Nation’s Framework Convention on Climate Change (UNFCCC) base their reporting of change in Land Use, Land-Use Change and Forestry (LULUCF) sector carbon pools on national forest inventories. A strong feature of sample-based inventories is that very detailed measurements can be made at the level of plots. Uncertainty regarding the results stems primarily from the fact that only a sample, and not the entire population, is measured. However, tree biomass on sample plots is not directly measured but rather estimated using regression models based on allometric features such as tree diameter and height. Estimators of model parameters are random variables that exhibit different values depending on which sample is used for estimating model parameters. Although sampling error is strongly influenced by the sample size when the model is applied, modeling error is strongly influenced by the sample size when the model is under development. Thus, there is a trade-off between which sample sizes to use when applying and developing models. This trade-off has not been studied before and is of specific interest for countries developing new national forest inventories and biomass models in the REDD context. This study considers a specific sample design and population. This fact should be considered when extrapolating results to other locations and populations.