Comparison of some annual forest inventory estimators

Van Deusen P.C.

Flexible models are proposed for assessing trend in annual forest survey data with increasing levels of generality. The models can be fit to the data using a mixed estimator and compared using the Akaike or Schwarz information criterion. The models also provide smoothed estimates of annual means.

Van Deusen P.C.

Le mesurage annuel d'un sous-ensemble de parcelles permanentes fournit une information a jour sur la ressource forestiere. Plusieurs methodes d'analyse des donnees d'un inventaire annuel sont discutees sans pretendre couvrir toutes les methodes possibles. Les methodes considerees vont des procedures standard d'echantillonnage systematique aux methodes plus elaborees des suites temporelles. La majeure partie de la discussion est consacree aux procedures d'analyse des series de donnees imputees de facon unique ou multiple, lesquelles contiennent des donnees fictives pour les parcelles non mesurees pendant l'annee en cours. Cela est accompagne d'une breve discussion des methodes d'imputation.

Affleck D.L., Gaines G.C.

The mixed estimator (ME) for annual forest inventory proposed by van Deusen (1999; Can. J. For. Res. 29: 1824–1828) is reformulated as a linear mixed model. This equivalent structure admits an interpretation of the ME as a polynomial regression on year with correlated year-specific random effects. It also uncovers the necessary criterion for maximum likelihood (ML) estimation. The improved performance of the ME under ML estimation is illustrated through simulations and application to inventory data from Montana, USA. Limitations of the ME relating to model-misspecification are also discussed.

Bontemps J., Bouriaud O.

Abstract Key message International forest reporting processes and increasing forest disturbances delineate new requirements regarding the information delivered by national forest inventories (NFI), with implications on their sampling strategies. An original comparative review of the sampling designs of 6 pioneer NFI programs being both annual and 5-year periodic evidences a set of common principles used to meet these demands, but also marked implementation differences, and open questions. Bases for a common framework and persisting research needs are highlighted. Developing virtual forest sampling simulation facilities at large scale is a critical challenge. Context National forest inventories (NFI) rely on diverse sampling strategies. In view of international forest reporting processes, these surveys are increasingly adopting a 5-year periodicity (their bar). The increased need for delivering updated representative statistics in the context of the environmental crisis is making annual forest inventory (their beat) a growing standard of the forest monitoring approach. To meet both objectives, spatially balanced sampling designs resulting in samples that can be split into yearly systematic subsamples have been devised. They ground the grid-based interpenetrating panel design principle that has generated various ingenious designs, however never presented nor reviewed to date. Aims The purpose of this review was to explore how the interpenetrating panel design principle has been implemented by the NFIs that have turned annual. The aims were to describe and frame the diversity of their designs, highlight their common bases and differences, and compare their ability to address new reporting needs. A special emphasis was placed on the graphical representation of these sampling designs. The NFI programs of France, Norway, Poland, Romania, Sweden, and of the USA were considered. Results The interpenetrating panel design principle is effective in reviewed inventories and is associated with the 5-year moving-window estimator. Original and creative design developments were identified, causing substantial variations in its implementation. They concern panel geometry, unaligned sampling options, sampling unit status, and estimation methods, making no-two inventory designs identical among those reviewed. In these inventories, the notions of annual and cyclic inventory do not substitute for each other, but appear to complement themselves to serve distinct reporting purposes. Also, negative coordination among annual samples is observed, questioning their adequacy for trend monitoring purposes. Conclusions The review evidences that a core sampling design principle, used to simultaneously operate annual and 5-year periodic forest inventory, has given rise to a diversity of implementation options. While it offers an original benchmark for any survey transition toward an annual frequency, it demonstrates the absence of a standardized framework. Developing simulation facilities for the comparison and optimization of associated designs appears as a critical priority, especially in the context of the EC forest monitoring perspective.

Bouriaud O., Morneau F., Bontemps J.

AbstractAimsSpatially balanced sampling is the most efficient method for surveying continuous and spatially structured populations. The spatial sampling of large‐scale surveys is mostly based on grids whose properties drive and potentially limit the possibility of building flexible samples. Periodicity causes high sampling constraints when an increase in the frequency of information delivery is sought. The sampling stratification of the adaptive sampling intensity also conflicts with the grid‐based approach. Although some surveys seemingly exploit these properties, no formal developments have been made available in the survey sampling literature across the fields of application.MethodsWe define and demonstrate the geometric properties of square grids, demonstrate how they can be used to produce nested hierarchical grids compatible with multiple periodicity values of interest for natural monitoring, and adapt the sampling intensity across space and time. A simulation study was conducted to quantify how spatial balance can be traded slowly for sample size reduction.ResultsWe showed that square grids have geometric properties that can be exploited to cope with spatial flexibility in the sampling effort and the spatiotemporal coordination of samples. We also provide an original extension of this framework intended to tune the sampling effort gradually while preserving spatial systematicity. The simulation study showed that a nested hierarchical grid can be used to progressively reduce the sampling intensity while preserving regularity in the spatial arrangement of units.ConclusionsWe demonstrate the flexibility and diversity of sampling schemes that can be implemented with square grids, answering the need for periodicity and the coordination of multiple samples and the limits of their use.

Chen F., Hou Z., Saarela S., McRoberts R.E., Ståhl G., Kangas A., Packalen P., Li B., Xu Q.

Remote sensing (RS) has enhanced forest inventory with model-based inference, that is, a family of statistical procedures rigorously estimates the parameter of a variable of interest (VOI) for a spatial population, e.g., the mean or total of forest carbon for a study area. Upscaling in earth observation, alias to this estimation, aggregates VOI from a finer spatial resolution to a coarser one with reduced uncertainty, serving decision making for natural resource management at larger scales. However, conventional model-based estimation (CMB) confronts a major challenge: it only supports RS wall-to-wall data, meaning that remotely sensed data must be available in panorama and non-wall-to-wall but quality data such as lidar or even cloud-masked satellite imagery are not supported due to incomplete coverage, impeding precise upscaling with cutting-edge instruments or for large scale applications. Consequently, this study aims to develop and demonstrate the use and usefulness of RS non-wall-to-wall data for upscaling with Hierarchical model-based estimation (HMB) which incorporates a two-stage model for bridging RS non– and wall-to-wall data; and for optimizing cost-efficiency, to evaluate the effects of non-wall-to-wall sample size on upscaling precision. Three main conclusions are relevant: (1) the HMB is a variant of the CMB estimator through trading in the uncertainty of the second-stage model to enable estimation using RS non-wall-to-wall data; (2) a quality first-stage model is key to exerting the advantage of HMB relative to the CMB estimator; (3) the variance of the HMB estimator is dominated by the first-stage model variance component, indicating that increasing the sample size in the first-stage is effective for increasing the overall precision. Overall, the HMB estimator balances tradeoffs between cost, efficiency and flexibility when devising a model-based upscaling in earth observation.

Edgar C.B., Westfall J.A.

An analysis of United States national forest inventory observations in the Laurentian Mixed Forest reveals a marked increase in forest disturbance between 1999 and 2015. The Laurentian Mixed Forest Province ecological subregion spans the northern sections of Michigan, Minnesota, and Wisconsin and includes forest area of between 16.7 and 17.5 million hectares depending on the year. Forest disturbance ranges from a low of 0.13 million hectares (0.8% of forest area) in 2000 to a high of 2.09 million hectares (11.9% of forest area) in 2014. The year 2015 is notable for being the first year since 2000 where forest disturbance declines, albeit modestly (11.4% of forest area). The marked increase is attributable to disturbances occurring continuously over time between remeasurement. Disturbances with the highest annual averages are insect damage to trees, disease damage to trees, and deer/ungulate at 291 thousand, 189 thousand, and 126 thousand hectares per year, respectively. Disturbances occurring in a specific year, what we term discrete disturbances, show no discernible trend during the period. The most extensive discrete disturbances are wind in 1999, 2011, and 2012 at 108 thousand, 62 thousand, and 61 thousand hectares, respectively. Standard estimates from national forest inventory lack specificity as to the actual year of the disturbance. The estimates reported here are actual annual estimates of disturbance that apply estimation methods accounting for the retrospective nature of the disturbance observation. The timing (year) and location (ecological section) of the two most extensive wind events coincide with historical records.

Hou Z., Domke G.M., Russell M.B., Coulston J.W., Nelson M.D., Xu Q., McRoberts R.E.

• We propose a data assimilation procedure for updating estimates with USFS FIA data. • This procedure incorporates the design-based and model-based inferences. • Updated estimates are comparable with estimates requiring 5+ years pooled FIA data. • This procedure is 100% compatible with the FIA database that is publicly available. • This procedure is unbiased and efficient, suitable for official reporting instruments. The United Nations Framework Convention on Climate Change requires annual estimates for forestry and ecological indicators to monitor the change in forest resources, the sustainability of forest management, and the emission and sink of forest carbon. It is particularly important to update estimates of forestland area in a timely fashion and at flexible geographical scales, not only for its value in monitoring biological diversity at the ecosystem scale, but also because of its close association with other indicators such as forest biomass and carbon. However, in the US, the Forest Survey Handbook advises that the sampling error should not exceed 3% per 404686 ha (one million acres) of forestland area, a demanding standard barely met by pooling the Forest Inventory and Analysis (FIA) panel data measured in an inventory cycle of 5–10 years. Consequently, this study aims to propose and illustrate an updating procedure using data assimilation that integrates a design-based estimator with a model-based mixed estimator for updating annual estimates at two population levels, the state- and county-levels. The three states in the USA, Minnesota (MN), Georgia (GA) and California (CA), representing the Northern, the Southern and the Pacific Northwest FIA programs, constitute the study areas. FIA data collected were based on a 5-year inventory cycle for MN (2006–2010) and GA (2005–2009), and a 10-year cycle for CA (2001–2010). The total number of sample plots was 17764 for MN, 6323 for GA, and 16740 for CA. Distinguishing features attribute to this procedure include: (1) unbiasedness: the integration of design-based estimates into the mixed estimator introduces a favorable property – unbiasedness, which could be the property national forest inventories concern the most; (2) efficiency: considerable improvements in estimation precision greater than 55%, achieving sampling errors as small as those relying on using 5–10 years pooled FIA data; (3) time: compared with the temporal trends reflected by design-based estimates, the updated trends were of much smoother trend lines and narrower confidence intervals that would better depict temporal changes for a population at flexible spatial scales; (4) space: this procedure is scale-invariant, meaning its efficiency is not affected by an inventory employing either a large- or small-area estimation, which was demonstrated at the two population levels; and (5) generalizability: this procedure is unbiased and efficient, 100% compatible with the FIA database which is readily available to the public, and thus suitable for various official reporting instruments.

Edgar C.B., Westfall J.A., Klockow P.A., Vogel J.G., Moore G.W.

Understanding the impacts of large-scale disturbances on forest conditions is necessary to support forest management, planning, and policy decision making. National forest inventories (NFIs) are an important information source that provide consistent data encompassing large areas, covering all ownerships, and extending through time. Here we compare how temporal aggregation approaches with NFI data affects estimates of standing dead trees as these respond to extreme disturbance events. East Texas was selected for this study owing to the occurrence of three significant disturbance events in a short span: Hurricane Rita in 2005, Hurricane Ike in 2008, and a historic drought in 2011. Wide-spread tree damage and mortality were reported after each disturbance and estimates of standing dead trees were used as the inventory variable for assessment. In the NFI of the US, the plot network is systematically divided into panels and one panel is measured each year. A measurement cycle is completed when all panels have been measured, which varies between 5 and 10 years depending on the region. Using the standard estimation approach of the US NFI, we computed population estimates using data from the full set of panels (FSP), multiple sets of panels (MSP), and single set of panels (SSP). For estimation, a single plot observation is computed from the most recent measurement of the plot that does not exceed the estimate year. Because one panel is measured per year, FSP and MSP estimates will necessarily consist of plot observations whose measurements were collected over a number of years. The SSP estimate is computed from one panel and thus all the plot observations are based on measurements collected over one year. We found that interpretations of disturbance event impacts varied depending on which sets of estimates were considered. All sets of estimates suggested a large and significant drought impact. However, differences existed among the estimates in the timing and magnitude of the impacts. The FSP estimates showed clear lag bias and smoothing of trends relative to the SSP estimates. MSP estimates were intermediate between FSP and SSP estimates. Differences in Hurricane Rita impacts were also observed between sets of estimates. Evidence of a net impact on standing dead trees following Hurricane Ike was weak among all sets of estimates. Given the potential for lag bias and smoothing, we recommend that SSP and MSP estimates be considered along with FSP estimates in assessments of large-scale disturbance impacts on forest conditions.

Coulston J.W., Westfall J.A., Wear D.N., Edgar C.B., Prisley S.P., Treiman T.B., Abt R.C., Smith W.B.

Understanding roundwood production in the United States at fine spatial and temporal scales is needed to support a range of analyses for decision making. Currently, estimates of county-level roundwood production are available at various time intervals for different regions of the country and for different products. Here we present our reasoning for moving to an annual timber products monitoring program and further present a comparison of sample designs to facilitate an annual program without increased effort. We found that both probability proportional to size and stratified simple random sampling designs were viable options, but the stratified simple random sampling design provided more flexibility. This flexibility was deemed important to target emerging markets and to enable sampling with certainty of specific firms. Our results lay the foundations for moving to an annual timber products output monitoring design in support of market, sustainability, and policy analyses as well as projections.

Gschwantner T., Lanz A., Vidal C., Bosela M., Di Cosmo L., Fridman J., Gasparini P., Kuliešis A., Tomter S., Schadauer K.

The increment estimation methods of European NFIs were explored by means of 12 essential NFI features. The results indicate various differences among NFIs within the commonly acknowledged methodological frame. The perspectives for harmonisation at the European level are promising. The estimation of increment is implemented differently in European National Forest Inventories (NFIs) due to different historical origins of NFIs and sampling designs and field assessments accommodated to country-specific conditions. The aspired harmonisation of increment estimation requires a comparison and an analysis of NFI methods. The objective was to investigate the differences in volume increment estimation methods used in European NFIs. The conducted work shall set a basis for harmonisation at the European level which is needed to improve information on forest resources for various strategic processes. A comprehensive enquiry was conducted during Cost Action FP1001 to explore the methods of increment estimation of 29 European NFIs. The enquiry built upon the preceding Cost Action E43 and was complemented by an analysis of literature to demonstrate the methodological backgrounds. The comparison of methods revealed differences concerning the NFI features such as sampling grids, periodicity of assessments, permanent and temporary plots, use of remote sensing, sample tree selection, components of forest growth, forest area changes, sampling thresholds, field measurements, drain assessment, involved models and tree parts included in estimates. Increment estimation methods differ considerably among European NFIs. Their harmonisation introduces new issues into the harmonisation process. Recent accomplishments and the increased use of sample-based inventories in Europe make perspectives for harmonised reporting of increment estimation promising.

Massey A., Mandallaz D., Lanz A.

In 2009, the Swiss National Forest Inventory (NFI) turned from a periodic into an annual measurement design in which only one-ninth of the overall sample of permanent plots is measured every year. The reduction in sample size due to the implementation of the annual design results in an unacceptably large increase in variance when using the standard simple random sampling estimator. Thus, a flexible estimation procedure using two- and three-phase regression estimators is presented with a special focus on utilizing updating techniques to account for disturbances and growth and is applied to the second and third Swiss NFIs. The first phase consists of a dense sample of systematically distributed plots on a 500 m × 500 m grid for which auxiliary variables are obtained through the interpretation of aerial photographs. The second phase is an eightfold looser subgrid with terrestrial plot data collected from the past inventory, and the third and final phase consists of the three most recent annual subgrids with the current state of the target variable (stem volume). The proposed three-phase estimators reduce the increase in variance from 294% to 145% compared with the estimator based on the full periodic sample while remaining unbiased.