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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]

When probability samples are not available, the model-based framework may be the only option for constructing inferences in the form of prediction intervals for population means. Further, for machine learning and some non-parametric and nonlinear regression prediction techniques, resampling methods such as the bootstrap may be the only option for obtaining the standard errors necessary for constructing those prediction intervals. All bootstrap approaches entail repeatedly sampling from the original sample, estimating the parameter of interest for each replication, and estimating the standard error of the estimate of the parameter as the standard deviation of the bootstrap estimates over replications. The objective of the study was to develop a procedure for terminating resampling such that the resulting number of replications assures, at least in probability, that the estimate of the standard error stabilizes to the standard error corresponding to one million replications. The analyses used a variety of datasets: five forest inventory datasets with either volume or aboveground biomass as the dependent variable and metrics from either airborne laser scanning or Landsat as independent variables, three from Europe, one from Southwest Asia, and one from Africa; and two forest/non-forest versus Landsat datasets, one from Minnesota and one from Wisconsin, both in the USA. The primary contribution of the study was development and demonstration of a procedure that specifies criteria for terminating resampling that assure in probability that the bootstrap estimate of the standard error stabilizes to the estimate obtained with one million replications. • Proposes and demonstrates criteria for terminating bootstrap resampling. • Assures in probability that the bootstrap standard error stabilizes. • Minimizes the uncertainty of a bootstrap standard error-based prediction interval. • Results are demonstrated for seven international forest inventory datasets. [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]

Forest cover maps were produced for the Gabonese Agency for Space Studies and Observations (AGEOS) for 1990, 2000 and 2010 for an area of approximately 102,000 km 2 corresponding to 38% of the total area of Gabon and representative of the range of human pressure on forest resources. The maps were constructed using a combination of a semi-automated classification procedure and manual enhancements to ensure the greatest possible accuracy. A two-stage area frame sampling approach was adopted to collect reference data for assessing the accuracy of the forest cover maps and to estimate proportion forest cover and net proportion deforestation. A total of 251 2 × 2 km segments or primary sample units (PSUs) were visually interpreted by a team of photo-interpreters independently from the map production team to produce a reference dataset representing about 1% of the study area. Paired observations were extracted from the forest cover map and the reference data for a random selection of 50 secondary sample units (SSUs) in the form of pixels within each PSU. Overall map accuracies were greater than 95%. PSU and SSU outputs were used to estimate proportion forest cover and net proportion deforestation using both direct expansion and model-assisted regression (MAR) estimators. All proportion forest cover estimates were similar, but the variances of the MAR estimates were smaller than variances for the direct expansion estimates by factors as great as 50. In addition, SSU-level estimates had standard errors slightly greater than those of PSU-level estimates, but the differences were small, particularly when auxiliary variables were obtained from forest cover maps. Therefore, a two-stage sampling approach was justified for collecting a reliable forest cover reference dataset for estimating proportion forest cover area and net proportion deforestation. Finally, despite large overall map accuracies, net proportion deforestation estimates obtained from the maps alone can be misleading as indicated by the finding that the MAR estimates, which included adjustment for bias estimates, were twice the non-adjusted map estimates for the periods 1990–2000 and 1990–2010. The results confirmed the expected generally small level of net deforestation for Gabon. However, loss of forest cover appears to have almost stopped in the last 10 years. One explanation could be the creation of national parks and the implementation of forest concession management plans from 2000 onward, but this should be further explored. [ABSTRACT FROM AUTHOR]

Abstract: National forest inventories report estimates of parameters related to forest area and growing stock volume for geographic areas ranging in size from municipalities to entire countries. Landsat imagery has been shown to be a source of auxiliary information that can be used with stratified estimation to increase the precision of estimates, although the increase is greater for estimates of forest area than for estimates of growing stock volume. The objective of the study was to assess the utility of lidar-based stratifications for increasing the precision of mean proportion forest area and mean growing stock volume per unit area. Stratifications based on nonlinear logistic regression model predictions of volume obtained from lidar data reduced variances of mean growing stock volume estimates by factors as great as 3.2 and variances of mean proportion forest area estimates by factors as great as 1.5. [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]

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]

One of the benefits of model-based inference relative to design-based inference is that probability samples are not required which means that models can be constructed using data external to the area of interest. Although “external” usually means spatially or geographically external, it could also be used in the temporal sense that the model is constructed using data whose dates are temporally external to the dates of the data to which the model is applied. This study focuses on assessing the effects of such temporally external application data on model-based inference using remotely sensed auxiliary information. The study area was in Burkina Faso, and the variable of interest was firewood volume (m 3 /ha). A sample of 160 field plots was selected from the population and measured, and auxiliary datasets from Landsat 8 were acquired. Models were fit using weighted least squares; the population mean, μ , was estimated; and the variance of the population mean, Var μ ̂ , was estimated using both an analytical variance estimator, V ̂ − μ ̂ an , and an empirical bootstrap estimator, V μ ̂ boot . The estimates, μ ̂ and Var ̂ μ ̂ , were compared for models constructed using calibration and application data of the same date and models constructed using calibration and application data whose dates differed. The primary results were twofold. First, for cases for which the dates of the model calibration and application data were the same, μ ̂ , V ̂ − μ ̂ an , V μ ̂ boot and Bias ̂ μ ̂ were similar across datasets. These results suggest that the particular date of the dataset from which the calibration and application data are obtained may be mostly arbitrary assuming the relation between the dependent and independent variables does not change over time. Second, for a model for which the calibration and application data were obtained from temporally different datasets, V ̂ − μ ̂ an , V μ ̂ boot , and Bias ̂ μ ̂ were all greater than when the calibration and application data were not temporally different. Further, the criterion for screening candidate models must be based on estimation of μ ̂ and Var ̂ μ ̂ rather than the model prediction accuracy or goodness of fit. The adverse effects of differing dates for the calibration and application data were exacerbated as the difference in dates increased. Finally, because the temporal differences also affected the analytical variance calculation, the bootstrapping procedure is recommended. [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]