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For remote sensing-assisted natural resource inventories, the effects of spatial resolution in the form of pixel size and the effects of subpixel information on estimates of population parameters were evaluated by comparing results obtained using Landsat 8 and RapidEye auxiliary imagery. The study area was in Burkina Faso, and the response variable of interest was firewood volume (m 3 /ha). A sample consisting of 160 field plots was selected from the population following a two-stage sampling design. Models were fit using weighted least squares; the population mean, μ , and the variance of the estimator of the population mean, V μ ̂ , were estimated using two inferential frameworks, model-based and model-assisted, and compared. For each framework, V μ ̂ was estimated both analytically and empirically. Empirical variances were estimated using bootstrapping that accounted for the two-stage sampling. The primary results were twofold. First, for the effects of spatial resolution and subpixel information, four conclusions are relevant: (1) finer spatial resolution imagery indeed contributed to greater precision for estimators of population parameter, but despite the finer spatial resolution of RapidEye, the increase was only marginal, on the order of 10% for model-based variance estimators and 36% for model-assisted variance estimators; (2) subpixel information on texture was marginally beneficial for inference of large area population parameters; (3) RapidEye did not offer enough of an improvement to justify its cost relative to the free Landsat 8 imagery; and (4) for a given plot size, candidate remote sensing auxiliary datasets are more cost-effective when their spatial resolutions are similar to the plot size than with much finer alternatives. Second, for the comparison between estimators, three conclusions are relevant: (1) sampling distribution for the model-based V ̂ μ ̂ was more concentrated and smaller on the order of 42% to 59% than that for the model-assisted V ̂ μ ̂ , suggesting superior consistency and efficiency of model-based inference to model-assisted inference; (2) bootstrapping is an effective alternative to analytical variance estimators; and (3) prediction accuracy expressed by RMSE is useful for screening candidate models to be used for population inferences. [ABSTRACT FROM AUTHOR]

International organizations increasingly require estimates of forest parameters to monitor the state of and changes in forest resources, the sustainability of forest practices and the role of forests in the carbon cycle. Most countries rely on data from their national forest inventories (NFI) to produce these estimates. However, because NFI survey years may not match the required reporting years, techniques for updating NFI-based estimates are necessary. The main aim was to develop an unbiased method to update NFI estimates of mean growing stock volume (m 3 /ha) using models to predict annual plot-level volume change, and to estimate the associated uncertainties. Because the final large area volume estimates were based on plot-level model predictions rather than field observations, hybrid inference was necessary to accommodate both model prediction uncertainty and sampling variation. Specific objectives were to compare modelling approaches, to assess the utility of Landsat data for increasing model prediction accuracy, to select the most accurate method, and to compare model-based and design-based uncertainty components. For four monospecific forest types, data from the 2nd and 3rd Spanish NFI surveys together with site variables and Landsat images were used to construct models to predict NFI information for the year of the 4th NFI survey. Data from the 3rd and 4th surveys were used to assess the accuracy of the model predictions at both plot-level and large area spatial scales. The most accurate method used a set of three models: one to predict the probability of volume removals, one to predict the amount of removed volume, and one to predict gross annual volume. Incorporation of Landsat-based variables in the models increased prediction accuracy. Differences between large area estimates based on plot-level field observations for the 4th NFI survey and estimates based on the model predictions were minimal for all four forest types. Further, the standard errors of the estimates based on the model predictions were only slightly greater than standard errors based on the field observations. Thus, model predictions of plot-level growing stock volume based on field and satellite image data as auxiliary information can be used to update large area NFI estimates for reporting years for which spectral data are available but field observations are not. Finally, variances of means are under-estimated unless hybrid inferential methods are used to incorporate both model prediction uncertainty and sampling variation. For the two forest types for which the two sources of uncertainty were of the same order of magnitude, the under-estimation was non-negligible. [ABSTRACT FROM AUTHOR]

Remotely sensed data have been widely used in recent years for mapping and estimating biomass. However, the characterization of the uncertainty of mapped or estimated biomass in previous studies was either based on ad-hoc approaches (e.g., using model fitting statistics such root mean square errors derived from purposive samples) or mostly limited to the analysis of mean biomass for the whole study area. This study proposed a novel uncertainty analysis method that can characterize biomass uncertainty across multiple spatial scales and multiple spatial resolutions. The uncertainty analysis method built on model-based inference and can propagate errors from trees to field plots, individual pixels, and small areas or large regions that consist of multiple pixels (up to all pixels within a study area). We developed and tested this method over northern Minnesota forest areas of approximately 69,508 km 2 via a unique combination of several datasets for biomass mapping and estimation: wall-to-wall airborne lidar data, national forest inventory (NFI) plots, and destructive measurements of tree aboveground biomass (AGB). We found that the pixel-level AGB prediction error is dominated by lidar-based AGB model residual errors when the spatial resolution is near 380 m or finer and by model parameter estimate errors when the spatial resolution is coarser. We also found that the relative error of AGB predicted from lidar can be reduced to approximately 11% (or mean 5.1 Mg/ha; max 43.6 Mg/ha) at one-hectare scale (or at 100 m spatial resolution) over our study area. Because our uncertainty analysis method uses model-based inference and does not require probability samples of field plots, our methodology has potential applications worldwide, especially over tropics and developing countries where NFI systems are not well-established. [ABSTRACT FROM AUTHOR]

We report on the operational use of remotely sensed data by national forest inventory (NFI) programmes in 45 countries representing approximately 65% of the world's forest area. The analysis is based on responses to a questionnaire prepared under the auspices of COST Action FP1001 “Improving Data and Information on the Potential Supply of Wood Resources: A European Approach from Multisource National Forest Inventories (USEWOOD)”. Responses were received from NFI remote sensing experts from both European and non-European countries. Three major conclusions were drawn from the study: (1) remote sensing now plays an essential role in many NFI programmes and provides data that can be used to enhance estimates for the most meaningful and commonly reported forest resource parameters; (2) a wide spectrum of remote sensing methods are currently used by NFI teams; and (3) although substantial effort and attention has been focused on the use of aerial photography and spaceborne sensor data for mapping and enhancing estimation, integration of uncertainly estimation requires additional attention. The operational use of remotely sensed data by NFI programmes is illustrated for three case studies: a case study for Switzerland focuses on digital aerial photography, a case study for Finland focuses on spaceborne sensor data for small area estimation, and a case study for the USA focuses on spaceborne sensor data for increasing the precision of large area estimates. Although use of remotely sensed data by NFI programmes may remain region-specific and some approaches are not readily transferable, generally applicable good practice guidelines were formulated on the basis of the questionnaire responses and the case studies. These guidelines are intended to promote better use of limited financial resources and to increase the accuracy and precision of NFI estimates. [ABSTRACT FROM AUTHOR]

Due to the availability of good and reasonably priced auxiliary data, the use of model-based regression-synthetic estimators for small area estimation is popular in operational settings. Examples are forest management inventories, where a linking model is used in combination with airborne laser scanning data to estimate stand-level forest parameters where no or too few observations are collected within the stand. This paper focuses on different approaches to estimating the variances of those estimates. We compared a variance estimator which is based on the estimation of superpopulation parameters with variance estimators which are based on predictions of finite population values. One of the latter variance estimators considered the spatial autocorrelation of the residuals whereas the other one did not. The estimators were applied using timber volume on stand level as the variable of interest and photogrammetric image matching data as auxiliary information. Norwegian National Forest Inventory (NFI) data were used for model calibration and independent data clustered within stands were used for validation. The empirical coverage proportion (ECP) of confidence intervals (CIs) of the variance estimators which are based on predictions of finite population values was considerably higher than the ECP of the CI of the variance estimator which is based on the estimation of superpopulation parameters. The ECP further increased when considering the spatial autocorrelation of the residuals. The study also explores the link between confidence intervals that are based on variance estimates as well as the well-known confidence and prediction intervals of regression models. [ABSTRACT FROM AUTHOR]

Remote sensing-based change estimation typically takes two forms. Indirect estimation entails constructing models of the relationship between the response variable of interest and remotely sensed auxiliary variables at two times and then estimating change as the differences in the model predictions for the two times. Direct estimation entails constructing models of change directly using observations of change in the response and the remotely sensed auxiliary variables for two dates. The direct method is generally preferred, although few statistically rigorous comparisons have been reported. This study focused on statistically rigorous, indirect and direct estimation of biomass change using forest inventory and airborne laser scanning (ALS) data for a Norwegian study area. Three sets of statistical estimators were used: simple random sampling estimators, indirect model-assisted regression estimators, and direct model-assisted regression estimators. In addition, three modeling approaches were used to support the direct model-assisted estimators. The study produced four relevant findings. First, use of the ALS auxiliary information greatly increased the precision of change estimates, regardless of whether indirect or direct methods were used. Second, contrary to previously reported results, the indirect method produced greater precision for the study area mean than the traditional direct method. Third, the direct method that used models whose predictor variables were selected in pairs but with separate coefficient estimates and models whose predictor variables were selected without regard to pairing produced the greatest precision. Finally, greater emphasis should be placed on the effects of model extrapolations for values of independent variables in the population that are beyond the range of the variables in the sample. [ABSTRACT FROM AUTHOR]

For remote and inaccessible forest regions, lack of sufficient or possibly any sample data inhibits estimation and construction of confidence intervals for population parameters using familiar probability- or design-based inferential methods. Although maps based on remotely sensed data may provide information on the distribution of resources, map-based estimates are subject to classification and prediction error, and map accuracy measures do not directly inform the uncertainty of the estimates. Model-based inference does not require probability samples and when used with synthetic estimation can circumvent small or no-sample difficulties associated with probability-based inference. The study focused on estimating proportion forest area using Landsat data for a study area in Minnesota, USA, and aboveground biomass using airborne laser scanning data for a study area in Hedmark County, Norway. For both study areas, model-based inference was used to estimate the components necessary for constructing confidence intervals for population means for non-sampled areas. The estimates were compared to simple random sampling, model-assisted, and model-based estimates that would have been obtained if the areas had been sampled. All estimates were within two simple random sampling standard errors of each other, thereby illustrating the utility of model-based inference for non-sampled areas. [ABSTRACT FROM AUTHOR]

For most national forest inventories, the variables of primary interest to users are forest area and growing stock volume. The precision of estimates of parameters related to these variables can be increased using remotely sensed auxiliary variables, often in combination with stratified estimators. However, acquisition and processing of large amounts of remotely sensed data can be costly and laborious, and stratified estimation requires construction of strata and satisfaction of within-stratum sample size constraints. An alternative to both challenges is to use an existing remote sensing-based, spatial product with the model-assisted estimators. The latter estimators use continuous auxiliary information directly rather than their aggregation into strata and are not subject to such severe sample size constraints. The objective of the study was to compare estimates of mean proportion forest area and mean growing stock volume per unit area obtained using both stratified and model assisted estimators with a remote sensing-based percent tree canopy cover map as auxiliary information. For a study area in Minnesota, USA, the primary conclusion was that estimates obtained with both sets of estimators were acceptably precise, but that the model-assisted estimators were easier to implement and facilitated aggregation of estimates from smaller sub-areas to estimates for larger areas. [ABSTRACT FROM AUTHOR]

Multiple remote sensing-based approaches to estimating gross afforestation, gross deforestation, and net deforestation are possible. However, many of these approaches have severe data requirements in the form of long time series of remotely sensed data and/or large numbers of observations of land cover change to train classifiers and assess the accuracy of classifications. In particular, when rates of change are small and equal probability sampling is used, observations of change may be scarce. For these situations, post-classification approaches may be the only viable alternative. The study focused on model-assisted and model-based approaches to inference for post-classification estimation of gross afforestation, gross deforestation, and net deforestation using Landsat imagery as auxiliary data. Emphasis was placed on estimation of variances to support construction of statistical confidence intervals for estimates. Both analytical and bootstrap approaches to variance estimation were used. For a study area in Minnesota, USA, estimates of net deforestation were not statistically significantly different from zero. [ABSTRACT FROM AUTHOR]

Abstract: Statistical inference requires expression of an estimate in probabilistic terms, usually in the form of a confidence interval. An approach to constructing confidence intervals for remote sensing-based estimates of net deforestation is illustrated. The approach is based on post-classification methods using two independent forest/non-forest classifications because sufficient numbers of observations of forest/non-forest change were not available for direct classification. Further, the approach uses a model-assisted estimator with information from a traditional error matrix for the forest/non-forest classifications to compensate for bias as the result of classification errors and to estimate variances. Classifications were obtained using a logistic regression model, forest inventory data, and two dates of Landsat imagery, although the approach to inference can be used with multiple classification approaches. For the study area in northeastern Minnesota, USA, overall pixel-level accuracies for the year 2002 and 2007 forest/non-forest classifications were 0.85–0.88, and estimates of proportion net deforestation for the 2002–2007 interval were less in absolute value than 0.015. However, standard errors for the remote sensing-based estimates of net deforestation were on the order of 0.02–0.04, meaning that the estimates were not statistically significantly different from zero. Particular attention is directed to the potentially severe sample size and classification accuracy requirements necessary for estimates of net deforestation to be detected as statistically significantly different from zero. [Copyright &y& Elsevier]

New model-based estimators of the uncertainty of pixel-level and areal k-nearest neighbour (k nn) predictions of attribute Y from remotely-sensed ancillary data X are presented. Non-parametric functions predict Y from scalar ‘Single Index Model’ transformations of X . Variance functions generated estimates of the variance of Y. Three case studies, with data from the Forest Inventory and Analysis program of the U.S. Forest Service, the Finnish National Forest Inventory, and Landsat ETM+ ancillary data, demonstrate applications of the proposed estimators. Nearly unbiased k nn predictions of three forest attributes were obtained. Estimates of mean square error indicate that k nn is an attractive technique for integrating remotely-sensed and ground data for the provision of forest attribute maps and areal predictions. [Copyright &y& Elsevier]

Abstract: Strategic forest inventory programs produce forest resource estimates for large areas such as states and provinces using data collected for a large number of variables on a relatively sparse array of field plots. Management inventories produce stand-level estimates to guide management decisions using data obtained with sampling intensities much greater than for strategic inventories. The costs associated with these greater sampling intensities have motivated investigations of alternatives to traditional sample-based management inventories. This study focused on a relatively inexpensive alternative to management inventories that uses strategic forest inventory plot data, Landsat Thematic Mapper (TM) satellite imagery, and the k-Nearest Neighbors (k-NN) technique. The approach entailed constructing stem density and basal area per unit area maps from which stand-level means were estimated as averages of k-NN pixel predictions. The study included investigations of the benefits of selecting optimal combinations of k-NN feature space variables derived from the TM imagery and the benefits of modifying the k-NN technique to eliminate spurious nearest neighbors. For both the stem density and basal area per unit area training data, the selection of optimal feature space covariates produced less than 1.5% improvement in root mean square error relative to using all covariates. The k-NN modification improved the sum of mean squared deviations for stand-level stem density and basal area per unit area estimates by 7–20% depending on the k-NN feature space covariates. For the best combination of feature space covariates, estimates of stand-level means were within confidence intervals for validation estimates for 11 of 12 stands for stem density and for 10 of 12 stands for basal area per unit area. [Copyright &y& Elsevier]

The k-Nearest Neighbor (k-NN) technique has become extremely popular for a variety of forest inventory mapping and estimation applications. Much of this popularity may be attributed to the non-parametric, multivariate features of the technique, its intuitiveness, and its ease of use. When used with satellite imagery and forest inventory plot data, the technique has been shown to produce useful estimates of many forest attributes including forest/non-forest, volume, and basal area. However, variance estimators for quantifying the uncertainty of means or sums of k-NN pixel-level predictions for areas of interest (AOI) consisting of multiple pixels have not been reported. The primary objectives of the study were to derive variance estimators for AOI estimates obtained from k-NN predictions and to compare precision estimates resulting from different approaches to k-NN prediction and different interpretations of those predictions. The approaches were illustrated by estimating proportion forest area, tree volume per unit area, tree basal area per unit area, and tree density per unit area for 10-km AOIs. Estimates obtained using k-NN approaches and traditional inventory approaches were compared and found to be similar. Further, variance estimates based on different interpretations of k-NN predictions were similar. The results facilitate small area estimation and simultaneous and consistent mapping and estimation of multiple forest attributes. [Copyright &y& Elsevier]

Imagery from the Landsat Program has been used frequently as a source of auxiliary data for modeling land cover, as well as a variety of attributes associated with tree cover. With ready access to all scenes in the archive since 2008 due to the USGS Landsat Data Policy, new approaches to deriving such auxiliary data from dense Landsat time series are required. Several methods have previously been developed for use with finer temporal resolution imagery (e.g. AVHRR and MODIS), including image compositing and harmonic regression using Fourier series. The manuscript presents a study, using Minnesota, USA during the years 2009–2013 as the study area and timeframe. The study examined the relative predictive power of land cover models, in particular those related to tree cover, using predictor variables based solely on composite imagery versus those using estimated harmonic regression coefficients. The study used two common non-parametric modeling approaches (i.e. k -nearest neighbors and random forests) for fitting classification and regression models of multiple attributes measured on USFS Forest Inventory and Analysis plots using all available Landsat imagery for the study area and timeframe. The estimated Fourier coefficients developed by harmonic regression of tasseled cap transformation time series data were shown to be correlated with land cover, including tree cover. Regression models using estimated Fourier coefficients as predictor variables showed a two- to threefold increase in explained variance for a small set of continuous response variables, relative to comparable models using monthly image composites. Similarly, the overall accuracies of classification models using the estimated Fourier coefficients were approximately 10–20 percentage points higher than the models using the image composites, with corresponding individual class accuracies between six and 45 percentage points higher. [ABSTRACT FROM AUTHOR]

Area estimates of land cover and land cover change are often based on reference class labels determined by analysts interpreting satellite imagery and aerial photography. Different interpreters may assign different reference class labels to the same sample unit. This interpreter variability is typically not accounted for in variance estimators applied to area estimates of land cover. A simple measurement model provides the basis for an estimator of the total variance (V Total) that takes into account both sampling variance and interpreter variance. This method requires two or more reference class interpretations (i.e., repeated measurements) obtained by analysts, working independently of each other, for the full sample or a random subsample of the full sample. Estimators of the total variance (V ̂ Total) and the variance component attributable to interpreters (V ̂ 1) were obtained for the case of two reference class interpretations per repeated sample unit. To evaluate the effect of interpreter variability on variance estimation, we used land cover reference data interpreted by seven analysts who each interpreted the same 300 sample pixels from a region of the Pacific Northwest of the United States. From these data, we estimated the contribution of interpreter variance to the total variance (i.e., V ̂ 1 / V ̂ Total) and the relative bias of the standard simple random sampling variance estimator (V ̂ stand) as an estimator of V Total , defined as 100%*(V ̂ stand − V ̂ Total)/ V ̂ Total. For each of five land cover classes, we computed V ̂ 1 , V ̂ Total , and V ̂ stand using the sample data from each of the 21 possible pairwise combinations of the seven interpreters, and then calculated the mean of V ̂ 1 / V ̂ Total and the mean of the estimated relative bias of V ̂ stand over these 21 pairs. Based on the mean of V ̂ 1 / V ̂ Total per class, interpreter variance contributed from 25% (cropland) to 76% (grass/shrub) of the total variance, indicating that interpreter variance was a non-negligible component of the total variance. Typically, the standard variance estimator, V ̂ stand , underestimated the total variance with the mean estimated relative bias ranging from −3% (cropland) to −33% (grass/shrub). Classes with greater inconsistency between pairs of interpreters had larger contributions of interpreter variance to the total variance (V ̂ 1 / V ̂ Total) and larger negative estimated relative bias of V ̂ stand. Given that interpreter variance can contribute substantially to the total variance, the repeated measurements approach offers a practical way to incorporate this variability into an estimator of the total variance. • Interpreter variability in reference data arises when interpreters disagree. • A simple measurement model is used to obtain an estimator of total variance. • Interpreter variability may contribute substantially to the total variance. • The standard variance estimator underestimates total variance. • Protocols to ensure consistency among interpreters are critical. [ABSTRACT FROM AUTHOR]

Data assimilation (DA) has a broad category of mathematical procedures for updating and calibrating existing predictions or parameter estimates using new observations. Typical DA procedures such as the Kalman filter require that the observations of a variable of interest used in a forecast of this variable to be collected just prior to the updating procedure and that they continue to be collected over time, a requirement that is not always practical for forest inventory problems. Distinct from the Kalman filter, the best linear unbiased predictor (BLUP) circumvents this time constraint, because it can calibrate the predicted values of a variable of interest using observations from other variables correlated with this variable of interest. Remote sensing played a major role in this study by providing the latter observations. The objective of this study was threefold: (1) to propose and illustrate a DA calibration procedure that incorporates simultaneous predictions and BLUP to improve prediction accuracy; (2) to expand this procedure in the framework of model-based inference; and (3) to compare the inferential properties before and after DA calibration for multiple scenarios. Four major conclusions are relevant. First, the prediction accuracies for all variables of interest were consistently increased by 10%–74% after implementing the DA procedure. Second, the DA procedure supported simultaneous inference, and the precision of the simultaneously estimated population means for the variables of interest were increased by 55%–76% after implementing this procedure. Third, the parametric bootstrap procedures used to estimate the inferential precisions for this complex estimation problem were effective and converged rapidly. In addition, this DA calibration procedure is universally applicable for DA calibrations using other data sources such as airborne or terrestrial laser scanning and spectral data, given that cross-model correlations exist. Overall, the proposed procedure demonstrated considerable potential for better serving forest inventory with respect to both simultaneous inference and inferential precision. • We proposed a remote sensing-assisted model-based calibration procedure. • This procedure incorporated data assimilation and simultaneous inference. • Multiple forest attributes were simultaneously predicted, calibrated and estimated. • Remote sensing played a major role to provide observations for the calibration. • Considerable improvements in efficiency and estimation precision greater than 55%. [ABSTRACT FROM AUTHOR]

Remote sensing aims to provide precise information on forest ecosystems under climate and land use changes, much of which is in the form of parameters estimated for biotic and abiotic variables for various official reporting instruments. Model-assisted estimation (MA) that harnesses remote sensing has demonstrated a surpassing ability to balance the tradeoff between robustness and efficiency. However, (1) MA has to unfold in a way complying with rather than overriding a sampling design because modification to sample size and field protocol is usually not allowed for an established setup, thus impeding further increases to inventory precision; and (2) it is inefficient to predict multiple forest attributes with many individual models, producing inconsistencies in the estimates due to lack of preserving the correlations, and offsetting the gains in inventory precision with the cost spent on modeling. Consequently, within the statistical framework of MA, this study proposes a remotely sensed data assimilation procedure, DAMA, to support high-precision multivariate forest inventory. Based on populations in China and Burkina Faso, promising results indicate that (1) the DAMA estimator proposed is approximately design-unbiased with its variance affected by the sampling design, the prediction accuracy, and the type of remotely sensed auxiliaries involved in DA, in descending order; (2) with simple random sampling, DAMA estimator increases the inferential precision on average 14% and 7% for Horvitz-Thompson and MA counterparts; and (3) with two-stage sampling, remarkably, 180% and 57%. Overall, DAMA demonstrates considerable efficiency that would better serve natural resource observation and management. • We develop a statistical procedure for calibrating model-assisted estimation (MA). • This procedure, DAMA, incorporates remote sensing (RS) and data assimilation. • Multiple forest attributes are simultaneously predicted, calibrated and estimated. • RS plays a key role to provide wall-to-wall observations for implementing DAMA. • DAMA is asymptotically unbiased and more efficient than HT and MA counterparts. [ABSTRACT FROM AUTHOR]

The k-Nearest Neighbors (k-NN) technique is a popular method for producing spatially contiguous predictions of forest attributes by combining field and remotely sensed data. In the framework of Working Group 2 of COST Action FP1001, we reviewed the scientific literature for forestry applications of k-NN. Information available in scientific publications on this topic was used to populate a database that was then used as the basis for a meta-analysis. We extracted qualitative and quantitative information from 260 experimental tests described in 148 scientific papers. The papers represented a geographic range of 26 countries and a temporal range from 1981 to 2013. Firstly, we describe the literature search and the information extracted and analyzed. Secondly, we report the results of the meta-analysis, especially with respect to estimation accuracies reported for k-NN applications for different configurations, different forest environments, and different input information. We also provide a summary of results that may reasonably be expected for those planning a k-NN application using remotely sensed data from different sensors and for different forest attributes. Finally, we identify some methodological publications that have advanced the state of the science with respect to k-NN. [ABSTRACT FROM AUTHOR]