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The gain-loss approach for greenhouse gas inventories requires estimates of areas of human activity and estimates of emissions per unit area for each activity. Stratified sampling and estimation have emerged as a popular and useful statistical approach for estimation of activity areas. With this approach, a map depicting classes of activity is used to stratify the area of interest. For each map class used as a stratum, map units are randomly selected and assessed with respect to an attribute such as forest/non-forest or forest land cover change. Ground observations are generally accepted as the most accurate source of information for these assessments but may be cost-prohibitive to acquire for remote and inaccessible forest regions. In lieu of ground observations, visual interpretations of remotely sensed data such as aerial imagery or satellite imagery are often used with the caveat that the interpretations must be of greater quality than the map data. An unresolved issue pertains to the effects of interpreter error on the bias and precision of the stratified estimators of activity areas. For a 7500-km 2 study area in north central Minnesota in the United States of America, combinations of forest inventory plot observations, visual interpretations of aerial imagery, and two forest/non-forest maps were used to assess the effects of interpreter error on stratified estimators of proportion forest and corresponding standard errors. The primary objectives related to estimating the bias and precision of the stratified estimators in the presence of interpreter errors, identifying factors and the levels of those factors that affect bias and precision, and facilitating planning to circumvent and/or mitigate the effects of bias. The primary results were that interpreter error induces bias into the stratified estimators of both land cover class proportion and its standard error. Bias increased with greater inequality in stratum weights, smaller map and interpreter accuracies, fewer interpreters and greater correlations among interpreters. Failure to account for interpreter error produced stratified standard errors that under-estimated actual standard errors by factors as great as 2.3. Greater number of interpreters mitigated the effects of interpreter error on proportion forest estimates, and a hybrid variance estimator accounted for the effects on standard errors. [ABSTRACT FROM AUTHOR]

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]

Abstract: Estimation of large area forest attributes, such as area of forest cover, from remote sensing-based maps is challenging because of image processing, logistical, and data acquisition constraints. In addition, techniques for estimating and compensating for misclassification and estimating uncertainty are often unfamiliar. Forest area for the state of Santa Catarina in southern Brazil was estimated from each of four satellite image-based land cover maps, and an independent estimate was obtained using observations of forest/non-forest for more than 1000 points assessed as part of the Santa Catarina Forest and Floristic Inventory. The latter data were also used as an accuracy assessment sample for evaluating the four maps. The map analyses consisted of identifying classification errors, constructing error matrices, calculating associated accuracy measures, estimating bias, and constructing 95% confidence intervals for proportion forest estimates using a model-assisted regression estimator. Overall accuracies for the maps ranged from 0.876 to 0.929. The standard errors of the estimates were all smaller than the standard error of the simple random sampling estimate by factors ranging from approximately1.23 to approximately 1.69. The model-assisted regression estimator lends itself to easy implementation for adjusting for estimated classification bias and for constructing confidence intervals. [Copyright &y& Elsevier]

Abstract: The scientific method has been characterized as having two distinct components, Discovery and Justification. Discovery emphasizes ideas and creativity, focuses on conceiving hypotheses and constructing models, and is generally regarded as lacking a formal logic. Justification begins with the hypotheses and models and ends with a valid scientific inference. Unlike Discovery, Justification has a formal logic whose rules must be rigorously followed to produce valid scientific inferences. In particular, when inferences are based on sample data, the rules of the logic of Justification require assessments of bias and precision. Thus, satellite image-based maps that lack such assessments for parameters of populations depicted by the maps may be of little utility for scientific inference; essentially, they may be just pretty pictures. Probability- and model-based approaches are explained, illustrated, and compared for producing inferences for population parameters using a map depicting three land cover classes: non-forest, coniferous forest, and deciduous forest. The maps were constructed using forest inventory data and Landsat imagery. Although a multinomial logistic regression model was used to classify the imagery, the methods for assessing bias and precision can be used with any classification method. For probability-based approaches, the difference estimator was used, and for model-based inference, a bootstrap approach was used. [ABSTRACT FROM AUTHOR]

Abstract: Satellite image-based maps of forest attributes are of considerable interest and are used for multiple purposes such as international reporting by countries that have no national forest inventory and small area estimation for all countries. Construction of the maps typically entails, in part, rectifying the satellite images to a geographic coordinate system, observing ground plots whose coordinates are obtained from Global Positioning System (GPS) receivers that are calibrated to the same geographic coordinate system, and then matching ground plots to image pixels containing the centers of the ground plots. Errors in rectification and GPS coordinates cause observations of ground attributes to be associated with spectral values of incorrect pixels which, in turn, introduces classification errors into the resulting maps. The most important finding of the study is that for common magnitudes of rectification and GPS errors, as many as half the ground plots may be assigned to incorrect pixels. The effects on areal estimates obtained by aggregating class predictions for individual pixels are deviation of the estimates from their true values, erroneous confidence intervals, and incorrect inferences. Results are reported in detail for both probability-based (design-based) and model-based approaches to inference for proportion forest area using maps constructed from Landsat imagery, forest inventory plot observations and a logistic regression model. [Copyright &y& Elsevier]

Abstract: Estimates of forest area are among the most common and useful information provided by national forest inventories. The estimates are used for local and national purposes and for reporting to international agreements such as the Montréal Process, the Ministerial Conference on the Protection of Forests in Europe, and the Kyoto Protocol. The estimates are usually based on sample plot data and are calculated using probability-based estimators. These estimators are familiar, generally unbiased, and entail only limited computational complexity, but they do not produce the maps that users are increasingly requesting, and they generally do not produce sufficiently precise estimates for small areas. Model-based estimators overcome these disadvantages, but they may be biased and estimation of variances may be computationally intensive. The study objective was to compare probability- and model-based estimators of mean proportion forest using maps based on a logistic regression model, forest inventory data, and Landsat imagery. For model-based estimators, methods for evaluating bias and reducing the computational intensity were also investigated. Four conclusions were drawn: the logistic regression model exhibited no serious lack of fit to the data; all the estimators produced comparable estimates for mean proportion forest, except for small areas; probability-based inferences enhanced using maps produced increased precision; and the computational intensity associated with estimating variances for model-based estimators can be greatly reduced with no detrimental effects. [Copyright &y& Elsevier]

Nearest neighbors techniques have been shown to be useful for predicting multiple forest attributes from forest inventory and Landsat satellite image data. However, in regions lacking good digital land cover information, nearest neighbors selected to predict continuous variables such as tree volume must be selected without regard to relevant categorical variables such as forest/non-forest. The result is that non-zero volume predictions may be obtained for pixels predicted to be non-forest, and volume predictions for pixels predicted to be forest may be erroneously small due to non-forest nearest neighbors. For users who wish to circumvent this discrepancy, a two-step algorithm is proposed in which the class of a relevant categorical variable such as land cover is predicted in the first step, and continuous variables such as volume are predicted in the second step subject to the constraint that all nearest neighbors must come from the predicted class of the categorical variable. Nearest neighbors, multinomial logistic regression, and discriminant analysis techniques were investigated for use in the first step. The results were generally similar for the three techniques, although the multinomial logistic regression technique was slightly superior. The k-Nearest Neighbors technique was used in the second step because many continuous forest inventory variables do not satisfy the distributional assumptions necessary for parametric multivariate techniques. The results for six 15-km×15-km areas of interest in northern Minnesota, USA, indicate that areal estimates of tree volume, basal area, and density obtained from pixel predictions are comparable to plot-based estimates and estimates by conifer and deciduous classes are also comparable to plot-based estimates. When a mixed conifer/deciduous class was included, predictions for the mixed and deciduous class were confused. [Copyright &y& Elsevier]

Nearest neighbors techniques are non-parametric approaches to multivariate prediction that are useful for predicting both continuous and categorical forest attribute variables. Although some assumptions underlying nearest neighbor techniques are common to other prediction techniques such as regression, other assumptions are unique to nearest neighbor techniques. Graphical diagnostic tools are proposed to evaluate the assumptions and to address issues of bias, homoscedasticity, influential observations, outliers, and extrapolations. The tools are illustrated using results obtained from applying the k-Nearest Neighbors technique with Landsat imagery and forest inventory ground observations. [Copyright &y& Elsevier]

Forest inventory programs report estimates of forest variables for areas of interest ranging in size from municipalities, to counties, to states or provinces. Because of numerous factors, sample sizes are often insufficient to estimate attributes as precisely as is desired, unless the estimation process is enhanced using ancillary data. Classified satellite imagery has been shown to be an effective source of ancillary data that, when used with stratified estimation techniques, contributes to increased precision with little corresponding increase in cost. Stratification investigations conducted by the Forest Inventory and Analysis program of the USDA Forest Service are reviewed, and a new approach to stratification using satellite imagery is proposed. The results indicate that precision may be substantially increased for estimates of both forest area and volume per unit area. [ABSTRACT FROM AUTHOR]

For two large study areas in Minnesota, USA, stratified estimation using classified Landsat Thematic Mapper satellite imagery as the basis for stratification was used to estimate forest area. Measurements of forest inventory plots obtained for a 12-month period in 1998 and 1999 were used as the source of data for within-stratum estimates. These measurements further served as calibration data for a k-Nearest Neighbors technique that was used to predict forest land proportion for image pixels. The continuum of forest land proportion predictions was separated into strata to facilitate stratified estimation. The k-Nearest Neighbors technique is carefully explained, five precautions are noted, and a plea is made for an objective approach to calibrating the technique. The variances of the stratified forest area estimates were smaller by factors as great as 5 than variances of the arithmetic mean calculated under the assumption of simple random sampling. In addition, when including all plots over a 5-year plot measurement cycle, the forest area precision estimates may be expected to satisfy national standards. [Copyright &y& Elsevier]

This paper presents a nationwide application of k-nearest neighbors (k-NN) to estimate growing stock volume per hectare for the Irish National Forest Estate using optical satellite imagery and field inventory data from the second National Forest Inventory (NFI). Two approaches are tested: an unweighted k-NN and an improved version (ik-NN) that is optimised using a genetic algorithm. The performance of the models is assessed in terms of the root mean square error (RMSE) and prediction error. From the simulations, it was found that the optimal value of k was 3, and the smallest pixel-level RMSE for growing stock was 126 m3·ha–1 when ik-NN was used. Comparisons with estimates from the NFI show that the ik-NN technique can enhance the Irish NFI. These improvements include a total estimate of growing stock volume of 102 million m3 with a confidence interval of ±3%, which is smaller than the NFI-reported confidence interval of ±5%. In addition, while total county-level estimates of growing volume estimated using ik-NN were consistent with those published from the NFI, their corresponding confidence intervals were much narrower, in the range of a two- to four-fold reduction in the width of the confidence interval. [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]

Highlights • Landsat data are used to estimate broadleaf encroachment in Irish forests. • A stratified estimator is used to estimate the area and CIs from the error matrix. • Total affected area of encroachment is 20,003 ha (±20%). • Results used by forest managers to revise operational forest management plans. Abstract In recent years, several critical issues have been identified concerning the performance of recently established spruce forest plantations in Ireland, in particular coniferous reforestation sites. More specifically, the reforestation of peatland areas in the midlands of Ireland have been subject to encroachment by broadleaf species, such as birch, and willow. These species regenerate naturally and compete with, and outgrow, the coniferous species (commonly Norway spruce) that were planted. In many cases, the growth of these trees is faster than the spruce, resulting in stands being completely encroached by approximately 15 years of age. Given the widespread nature of this problem coupled with the fragmented nature of the Irish forest estate, a project was established to use Earth observation data to predict the spatial distribution and species composition of the affected sites. The spatial distribution and associated area estimates of broadleaf encroachment within State owned spruce forests were assessed using multi-temporal Landsat satellite imagery. The overall accuracy of the encroachment map was 85.23% and a Kappa Index of Agreement of 0.58. The associated area of encroached or broadleaf dominated forests was 20,003 ha with a confidence interval of ±20% calculated using a sample-based estimator. [ABSTRACT FROM AUTHOR]

The k-Nearest Neighbour (k-NN) estimation and prediction technique is widely used to produce pixel-level predictions and areal estimates of continuous forest variables such as area and volume, often by sub-categories such as species. An advantage of k-NN is that the same parameters (e.g., k-value, distance metric, weight vector for the feature space variables) can be used for all variables, whether continuous or categorical. An obvious question is the degree to which accuracy can be improved if the k-NN estimation parameters are tailored for specific variable groups such as volumes by tree species or categorical variables. We investigated prediction of categorical forest attribute variables from satellite image spectral data using k-NN with optimisation of the weight vector for the ancillary variables obtained using a genetic algorithm. We tested several genetic algorithm fitness functions, all derived from well-known accuracy measures. For a Finnish test site, the categorical forest attribute variables were site fertility and tree species dominance, and for an Italian test site, the variables were forest type and conifer/broad-leaved dominance. The results for both test sites were validated using independent data sets. Our results indicate that use of the genetic algorithm to optimize the weight vector for prediction of a single forest attribute variable had a slight positive effect on the prediction accuracies for other variables. Errors can be further decreased if the optimisation is done by variable groups. [Copyright &y& Elsevier]