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There is a wide variety of biodiversity monitoring systems. In this chapter we outline a number of important steps that should be considered when developing a new system or redesigning an old system, from the questions and objectives at the start, through formulating important aspects such as the target population to be monitored, relevant time span for monitoring, and which sources of bias and error different types of monitoring systems might suffer from. Most of the time it is more efficient to focus monitoring efforts on detailed survey of a sample, rather than trying to survey a phenomenon in its entirety. How a sample is selected is important and design-based sampling can be used to avoid selection bias, which otherwise can distort the results of monitoring.

Presence–absence sampling is an important method for monitoring state and change of both individual plant species and communities. With this method, only the presence or absence of the target species is recorded on plots and thus the method is straightforward to apply and less prone to surveyor judgement compared to other vegetation monitoring methods. However, in the basic setting, all plots must be equally large or otherwise it is unclear how data should be analysed. In this study, we propose and evaluate five different methods for estimating plant density based on presence–absence registrations from surveys with variable plot sizes. Using artificial plant population data as well as empirical data from the Swedish National Forest Inventory, we evaluated the performance of the proposed methods. The main analysis was conducted through sampling simulation in artificial populations, whereby bias and variance of density estimators for the different methods were quantified and compared. Both for state and change estimation of plant density, we found that the best method to handle variable plot size was to perform generalized least squares regression, using plot size as an independent variable. Methods where plots smaller than a certain threshold were excluded or their registrations recalculated were, however, almost as good. Using all registrations as if they were obtained from plots with the nominal plot size resulted in substantial bias. Our findings are important for plant population studies in a wide range of environmental monitoring programmes. In these programmes, plots are typically randomly laid out and may be located across boundaries between different land‐use or land‐cover classes, resulting in subplots of variable size. Such splitting of plots is common when large plots are used, for example, with the 100 m2 plots used in the Swedish National Forest Inventory. Our methods overcome problems to estimate plant density from presence–absence data observed in plots that vary in size.

Inventories of plant populations are fundamental in ecological research and monitoring, but such surveys are often prone to field assessment errors. Presence/absence (P/A) sampling may have advanta ...

Thin, hair-like lichens (Alectoria, Bryoria, Usnea) form conspicuous epiphyte communities across the boreal biome. These poikilohydric organisms provide important ecosystem functions and are useful indicators of global change. We analyse how environmental drivers influence changes in occurrence and length of these lichens on Norway spruce (Picea abies) over 10 years in managed forests in Sweden using data from >6000 trees. Alectoria and Usnea showed strong declines in southern-central regions, whereas Bryoria declined in northern regions. Overall, relative loss rates across the country ranged from 1.7% per year in Alectoria to 0.5% in Bryoria. These losses contrasted with increased length of Bryoria and Usnea in some regions. Occurrence trajectories (extinction, colonization, presence, absence) on remeasured trees correlated best with temperature, rain, nitrogen deposition, and stand age in multinomial logistic regression models. Our analysis strongly suggests that industrial forestry, in combination with nitrogen, is the main driver of lichen declines. Logging of forests with long continuity of tree cover, short rotation cycles, substrate limitation and low light in dense forests are harmful for lichens. Nitrogen deposition has decreased but is apparently still sufficiently high to prevent recovery. Warming correlated with occurrence trajectories of Alectoria and Bryoria, likely by altering hydration regimes and increasing respiration during autumn/winter. The large-scale lichen decline on an important host has cascading effects on biodiversity and function of boreal forest canopies. Forest management must apply a broad spectrum of methods, including uneven-aged continuous cover forestry and retention of large patches, to secure the ecosystem functions of these important canopy components under future climates. Our findings highlight interactions among drivers of lichen decline (forestry, nitrogen, climate), functional traits (dispersal, lichen colour, sensitivity to nitrogen, water storage), and population processes (extinction/colonization).

When conducting firm-level surveys, a relevant aspect in sampling design is to guarantee that the selected sample of business units is representative of the population. Stratified sampling design i...

The boreal forest floor vegetation is critical for ecosystem functioning and an important part of forest biodiversity. Given the ongoing global change, knowledge on broad-scale changes in the composition and abundance of different plant species and species groups is hence important for both forest conservation and management. Here, we analyse permanent plot data from the National Forest Inventory (NFI) on changes in the vegetation over a 10-year period in four regions of Sweden. To limit the direct and relatively well-known effects of forest management and associated succession, we only included mature forest stands not influenced by forestry during the 10 years between inventories, and focused on vegetation change mainly related to other factors. Results show strong decrease among many species and species groups. This includes dominant species such as Vaccinimum myrtillus and Deschampsia flexuosa as well as several forest herbs. The only species increasing are some mosses in the southern regions. Our data do not allow for a causal interpretation of the observed patterns. However, the changes probably result from latent succession in combination with climate change and nitrogen deposition, and with time lags complicating the interpretation of their relative importance. Regardless of the cause, the observed changes are on a magnitude that suggest impacts on ecosystem functioning and hence highlight the need for more experimental work.

New ways to combine data from multiple environmental area frame surveys of a finite population are being introduced. Environmental surveys often sample finite populations through area frames. However, to combine multiple surveys without risking bias, design components (inclusion probabilities, etc.) are needed at unit level of the finite population. We show how to derive the design components and exemplify this for three commonly used area frame sampling designs. We show how to produce an unbiased estimator using data from multiple surveys, and how to reduce the risk of introducing significant bias in linear combinations of estimators from multiple surveys. If separate estimators and variance estimators are used in linear combinations, there’s a risk of introducing negative bias. By using pooled variance estimators, the bias of a linear combination estimator can be reduced. National environmental surveys often provide good estimators at national level, while being too sparse to provide sufficiently good estimators for some domains. With the proposed methods, one can plan extra sampling efforts for such domains, without discarding readily available information from the aggregate/national survey. Through simulation, we show that the proposed methods are either unbiased, or yield low variance with small bias, compared to traditionally used methods.

A new sampling strategy for design-based environmental monitoring is proposed. It has the potential to produce superior estimators for totals of environmental variables and their changes over time. In the strategy, we combine two concepts known as spatially balanced sampling and coordination of samples. Spatially balanced sampling can provide superior estimators of totals, while coordination of samples over time is often used to improve estimators of change. Compared with reference strategies, we show that the new strategy can improve the precision of the estimators of totals and their change simultaneously. A forest inventory application is used to illustrate the new strategy and the results can be summarized as (i) using auxiliary information to spread the sample can improve the estimators of totals; (ii) a positive coordination of the samples reduced the variance of the estimator of change by more than 37% compared with independent samples; and (iii) a high overlap between successive samples does not guarantee a good estimator of change. The presented strategy can be used to develop more efficient environmental monitoring programs.

When sampling from a continuous population (or distribution), we often want a rather small sample due to some cost attached to processing the sample or to collecting information in the field. Moreover, a probability sample that allows for design‐based statistical inference is often desired. Given these requirements, we want to reduce the sampling variance of the Horvitz–Thompson estimator as much as possible. To achieve this, we introduce different approaches to using the local pivotal method for selecting well‐spread samples from multidimensional continuous populations. The results of a simulation study clearly indicate that we succeed in selecting spatially balanced samples and improve the efficiency of the Horvitz–Thompson estimator.

Large-scale surveys, such as national forest inventories and vegetation monitoring programs, usually have complex sampling designs that include geographical stratification and units organized in clusters. When models are developed using data from such programs, a key question is whether or not to utilize design information when analyzing the relationship between a response variable and a set of covariates. Standard statistical regression methods often fail to account for complex sampling designs, which may lead to severely biased estimators of model coefficients. Furthermore, ignoring that data are spatially correlated within clusters may underestimate the standard errors of regression coefficient estimates, with a risk for drawing wrong conclusions. We first review general approaches that account for complex sampling designs, e.g. methods using probability weighting, and stress the need to explore the effects of the sampling design when applying logistic regression models. We then use Monte Carlo simulation to compare the performance of the standard logistic regression model with two approaches to model correlated binary responses, i.e. cluster-specific and population-averaged logistic regression models. As an example, we analyze the occurrence of epiphytic hair lichens in the genus Bryoria; an indicator of forest ecosystem integrity. Based on data from the National Forest Inventory (NFI) for the period 1993–2014 we generated a data set on hair lichen occurrence on >100,000 Picea abies trees distributed throughout Sweden. The NFI data included ten covariates representing forest structure and climate variables potentially affecting lichen occurrence. Our analyses show the importance of taking complex sampling designs and correlated binary responses into account in logistic regression modeling to avoid the risk of obtaining notably biased parameter estimators and standard errors, and erroneous interpretations about factors affecting e.g. hair lichen occurrence. We recommend comparisons of unweighted and weighted logistic regression analyses as an essential step in development of models based on data from large-scale surveys.

A new sampling strategy for forest inventories is presented. The most important difference from the traditional sampling strategies is that auxiliary variables from remote sensing are incorporated into the sampling design. The sample is selected to match population distributions of the auxiliary variables as well as possible. This is achieved by a double sampling approach, where auxiliary variables are extracted for a large first-phase sample. The second selection is done by the local pivotal method and produces an even thinning of the first-phase sample. Thus, we make sure that the selected second-phase sample becomes much more representative of the population than what is possible by the use of traditional designs. The potential of implementing the new strategy for the temporary clusters within the Swedish national forest inventory is evaluated with five auxiliary variables: the geographical coordinates, elevation, predicted tree height, and predicted basal area. The increased representativity that we achieve with the new strategy induces up to 95% reduction of the variance of the sample means of the remote sensing auxiliary variables compared with traditional designs. For this reason, we conclude that the new strategy that will be implemented in the forthcoming Swedish national forest inventory has a great potential to achieve large improvements in estimation of many important forest attributes.

This study presents an approach for predicting stand-level forest attributes utilizing mobile laser scanning data collected as a nonprobability sample. Firstly, recordings of stem density were made at point locations every 10th metre along a subjectively chosen mobile laser scanning track in a forest stand. Secondly, kriging was applied to predict stem density values for the centre point of all grid cells in a 5 m x 5 m lattice across the stand. Thirdly, due to nondetectability issues, a correction term was computed based on distance sampling theory. Lastly, the mean stem density at stand level was predicted as the mean of the point-level predictions multiplied with the correction factor, and the corresponding variance was estimated. Many factors contribute to the uncertainty of the stand-level prediction; in the variance estimator, we accounted for the uncertainties due to kriging prediction and due to estimating a detectability model from the laser scanning data. The results from our new approach were found to correspond fairly well to estimates obtained using field measurements from an independent set of 54 circular sample plots. The predicted number of stems in the stand based on the proposed methodology was 1366 with a 12.9% relative standard error. The corresponding estimate based on the field plots was 1677 with a 7.5% relative standard error.

The statistical framework of data assimilation provides methods for utilizing new data for obtaining up-to-date forest data: existing forest data are forecasted and combined with each new remote sensing data set. This new paradigm for updating forest database, well known from other fields of study, will provide a framework for utilizing all available remote sensing data in proportion to their quality to improve prediction. It also solves the problem that not all remote sensing data sets provide information for the entire area of interest, since areas with no remote sensing data can be forecasted until new remote sensing data become available. In this study, extended Kalman filtering was used for assimilating data from 19 TanDEM-X InSAR images on 137 sample plots, each of 10-meter radius at a test site in southern Sweden over a period of 4 years. At almost all time points data assimilation resulted in predictions closer to the reference value than predictions based on data from that single time poi...

Forest resource assessments utilizing remotely sensed auxiliary data are becoming increasingly important due to their ability to provide precise estimates of forest parameters at low cost. In presenting results from such surveys, it is important to provide not only estimates of the target parameters, but also their confidence intervals, which provide the range of values wherein the true value is located with a certain level of confidence. If such an interval is narrow the point estimates from the survey can be considered very reliable. In estimating the confidence interval the variance of an estimator must first be estimated. Unbiasedness, i.e. that an estimator on average coincides with the true value, is an important property also for variance estimators. Another important property is that the variance estimator itself has low variance, not least in cases when the variance estimates obtained with the estimator may not be strictly positive. One such important case is when two-stage designs are used to first allocate sample clusters in the form of strips from which auxiliary data, such as metrics derived from airborne laser scanning, are obtained; field data are then derived from sample plots beneath each sample strip in a second stage. In this article we compare two variance estimators for such surveys. The first estimator is a standard estimator suggested in reference textbooks on model-assisted sampling. The second estimator is proposed by the authors, and utilizes the auxiliary data to a larger extent. Through Monte Carlo simulation we show that both variance estimators are approximately unbiased, but that the new estimator is more stable (i.e., has lower empirical variance) and provides empirical confidence interval coverage rates that coincide more closely with the nominal coverage rates.

Specially designed forest damage inventories, directed to areas with potential or suspected damage, are performed in many countries. In this study, we evaluate a new approach for damage inventories in which auxiliary data are used for the sample selection with the recently introduced local pivotal sampling design. With this design, a sample that is well spread in the space of the auxiliary variables is obtained. We applied Monte Carlo sampling simulation to evaluate whether this sampling design leads to more precise estimates compared with commonly applied baseline methods. The evaluations were performed using different damage scenarios and different simulated relationships between the auxiliary data and the actual damages. The local pivotal method was found to be more efficient than simple random sampling in all scenarios, and depending on the allocation of the sample and the properties of the auxiliary data, it sometimes outperformed two-phase sampling for stratification. Thus, the local pivotal method may be a valuable tool to cost-efficiently assess the magnitude of forest damage once outbreaks have been detected in a forest region.

Positional errors may cause problems when field and remotely sensed data are combined in connection with forest surveys. In this study we evaluated the effects of such errors on statistical estimates of growing stock volume using model-assisted and model-based estimation. With model-assisted estimation, positional errors affect the model parameter estimates for the models that are used as part of the estimation framework. In addition, positional errors affect the estimators, since the deviations between model predictions and field measurements are often larger than they would have been without positional errors. Using model-based estimation positional errors affect the model parameter estimates and thus the estimators. We compared the effects of positional errors in model-assisted and model-based estimation through Monte Carlo sampling simulation in a simulated study area resembling the forest conditions in Kuortane, western Finland. The forest population was created using a copula modelling approach based on field, Landsat and LiDAR data. We found that positional errors led to slightly biased estimators, and estimators with larger variances compared to the cases where data were perfectly geo-located. The relative increase of the variances of the estimators was of equal magnitude for model-assisted and model-based estimation, when models were developed and applied to data with geopositional errors. Further, the variance estimators were always more precise for the model-based estimators compared to the model-assisted estimators. When the models were developed based on perfectly geo-located data but applied to data with positional errors, model-based estimation was superior to model-assisted estimation.

Sample coordination seeks to maximize or to minimize the overlap of two or more samples. The former is known as positive coordination, and the latter as negative coordination. Positive coordination is mainly used for estimation purposes and to reduce data collection costs. Negative coordination is mainly performed to diminish the response burden of the sampled units. Poisson sampling design with permanent random numbers provides an optimum coordination degree of two or more samples. The size of a Poisson sample is, however, random. Conditional Poisson (CP) sampling is a modification of the classical Poisson sampling that produces a fixed-size πps sample. We introduce two methods to coordinate Conditional Poisson samples over time or simultaneously. The first one uses permanent random numbers and the list-sequential implementation of CP sampling. The second method uses a CP sample in the first selection and provides an approximate one in the second selection because the prescribed inclusion probabilities are not respected exactly. The methods are evaluated using the size of the expected sample overlap, and are compared with their competitors using Monte Carlo simulation. The new methods provide a good coordination degree of two samples, close to the performance of Poisson sampling with permanent random numbers.

1. Plant communities are attracting increased interest in connection with forest and landscape inventories due to society’s interest in ecosystem services. However, the acquisition of accurate information about plant communities poses several methodological challenges. Here, we investigate the use of presence-absence sampling with the aim to monitor state and change in plant density. We study what plot sizes are informative, i.e. the estimators should have as high precision as possible. 2. Plant occurrences were modelled through different Poisson processes and tests were developed for assessing the plausibility of the model assumptions. Optimum plot sizes were determined by minimizing the variance of the estimators. While state estimators of similar kind as ours have been proposed in previous studies, our tests and change estimation procedures are new. 3. We found that the most informative plot size for state estimation is 1.6 divided by the plant density, i.e. if the true density is 1 plant per square metre the optimum plot size is 1.6 square metres. This is in accordance with previous findings. More importantly, the most informative plot size for change estimation was smaller and depended on the change patterns. We provide theoretical results as well as some empirical results based on data from the Swedish National Forest Inventory. 4. Use of too small or too large plots resulted in poor precision of the density (and density change) estimators. As a consequence, a range of different plot sizes would be required for jointly monitoring both common and rareplants using presence-absence sampling in monitoring programmes. Statistical methods for ecological research on data from national monitoring programs. Funded by the Swedish Research Council. Grant Number 340-2013-5076.

By using more sophisticated sampling designs in forest field inventories, it is possible to select more representative field samples. When full cover auxiliary information is available at the planning stage of a forest inventory, an efficient strategy for sampling is formed by making sure that the sample is well spread in the space spanned by the auxiliary variables. We show that by using such a sampling design, we can improve not only design-based estimation, but also estimation based on nearest neighbour techniques. A new technique to select well-spread probability samples, in multidimensional spaces, from larger populations is introduced. As an application, we illustrate how this strategy can be applied to a forest field inventory. We use an artificial dataset corresponding to a full cover forest remote sensing inventory of a 30 000 ha area of Kuortane, western Finland. The target variable (growing stock volume) has been generated for the entire area by a copula technique. The artificial population has been validated by utilizing the Finnish National Forest Inventory.

An interesting alternative to wall-to-wall mapping approaches for the estimation of landscape metrics is to use sampling. Sample-based approaches are cost-efficient, and measurement errors can be reduced considerably. The previous efforts of sample-based estimation of landscape metrics have mainly been focused on data collection methods, but in this study, we consider two estimation procedures. First, landscape metrics of interest are calculated separately for each sampled image and then the image values are averaged to obtain an estimate of the entire landscape (separated procedure, SP). Second, metric components are calculated in all sampled images and then the aggregated values are inserted into the landscape metric formulas (aggregated procedure, AP). The national land cover map (NLCM) of Sweden, reflecting the status of land cover in the year 2000, was used to provide population information to investigate the statistical performance of the estimation procedures. For this purpose, sampling simulation with a large number of replications was used. For all three landscape metrics, the second procedure (AP) produced a lower relative RMSE and bias than the first one (SP). A smaller sample unit size (50 ha) produced larger bias than a larger one (100 ha), whereas a smaller sample unit size produced a lower variance than a larger sample unit. The efficiency of a metric estimator is highly related to the degree of landscape fragmentation and the selected procedure. Incorporating information from all of the sampled images into a single one (aggregated procedure, AP) is one way to improve the statistical performance of estimators.

We give a formal definition of a representative sample, but roughly speaking, it is a scaled-down version of the population, capturing its characteristics. New methods for selecting representative ...

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

Hair lichens are strongly influenced by forest structure at local scales, but their broad-scale distributions are less understood. We compared the occurrence and length of Alectoria sarmentosa (Ach.) Ach., Bryoria spp., and Usnea spp. in the lower canopy of > 5000 Picea abies (L.) Karst. trees within the National Forest Inventory across all productive forest in Sweden. We used logistic regression to analyse how climate, nitrogen deposition, and forest variables influence lichen occurrence. Distributions overlapped, but the distribution of Bryoria was more northern and that of Usnea was more southern, with Alectoria's distribution being intermediate. Lichen length increased towards northern regions, indicating better conditions for biomass accumulation. Logistic regression models had the highest pseudo R-2 value for Bryoria, followed by Alectoria. Temperature and nitrogen deposition had higher explanatory power than precipitation and forest variables. Multiple logistic regressions suggest that lichen genera respond differently to increases in several variables. Warming decreased the odds for Bryoria occurrence at all temperatures. Corresponding odds for Alectoria and Usnea decreased in warmer climates, but in colder climates, they increased. Nitrogen addition decreased the odds for Alectoria and Usnea occurrence under high deposition, but under low deposition, the odds increased. Our analyses suggest major shifts in the broad-scale distribution of hair lichens with changes in climate, nitrogen deposition, and forest management. Statistical methods for ecological research on data from national monitoring programs. Funded by the Swedish Research Council. Grant Number 340-2013-5076.

A new spatial sampling method is proposed in order to achieve a double property of balancing. The sample is spatially balanced or well spread so as to avoid selecting neighbouring units. Moreover, the method also enables to satisfy balancing equations on auxiliary variables available on all the sampling units because the Horvitz–Thompson estimator is almost equal to the population totals for these variables. The method works with any definition of distance in a multidimensional space and supports the use of unequal inclusion probabilities. The algorithm is simple and fast. Examples show that the method succeeds in using more information than the local pivotal method, the cube method and the Generalized Random-Tessellation Stratified sampling method, and thus performs better. An estimator of the variance for this sampling design is proposed in order to lead to an inference that takes the effect of the sampling design into account. Copyright © 2012 John Wiley & Sons, Ltd.

A new method for sampling from a finite population that is spread in one, two or more dimensions is presented. Weights are used to create strong negative correlations between the inclusion indicators of nearby units. The method can be used to produce unequal probability samples that are well spread over the population in every dimension, without any spatial stratification. Since the method is very general there are numerous possible applications, especially in sampling of natural resources where spatially balanced sampling has proven to be efficient. Two examples show that the method gives better estimates than other commonly used designs.

A simple method to select a spatially balanced sample using equal or unequal inclusion probabilities is presented. For populations with spatial trends in the variables of interest, the estimation can be much improved by selecting samples that are well spread over the population. The method can be used for any number of dimensions and can hence also select spatially balanced samples in a space spanned by several auxiliary variables. Analysis and examples indicate that the suggested method achieves a high degree of spatial balance and is therefore efficient for populations with trends.

Over the past quarter century, the incidence of tick-borne encephalitis (TBE) has increased in most European nations. However, the number of humans stricken by the disease varies from year to year. A method for predicting major increases and decreases is needed.We assembled a 25-y database (1984-2008) of the number of human TBE victims and wildlife and climate data for the Stockholm region of Sweden, and used it to create easy-to-use mathematical models that predict increases and decreases in the number of humans stricken by TBE.Our best model, which uses December precipitation and mink (Neovison vison, formerly Mustela vison) bagging figures, successfully predicted every major increase or decrease in TBE during the past quarter century, with a minimum of false alarms. However, this model was not efficient in predicting small increases and decreases.Predictions from our models can be used to determine when preventive and adaptive programmes should be implemented. For example, in years when the frequency of TBE in humans is predicted to be high, vector control could be intensified where infested ticks have a higher probability of encountering humans, such as at playgrounds, bathing lakes, barbecue areas and camping facilities. Because our models use only wildlife and climate data, they can be used even when the human population is vaccinated. Another advantage is that because our models employ data from previously-established databases, no additional funding for surveillance is required.

Sampford's (1967) unequal probability sampling method is extended to the case that the inclusion probabilities do not sum to an integer. In this case the sampling outcome is left open for exactly o ...

In real-time sampling, the units of a population pass a sampler one by one. Alternatively the sampler may successively visit the units of the population. Each unit passes only once and at that time it is decided whether or not it should be included in the sample. The goal is to take a sample and efficiently estimate a population parameter. The list sequential sampling method presented here is called correlated Poisson sampling. The method is an alternative to Poisson sampling, where the units are sampled independently with given inclusion probabilities. Correlated Poisson sampling uses weights to create correlations between the inclusion indicators. In that way it is possible to reduce the variation of the sample size and to make the samples more evenly spread over the population. Simulation shows that correlated Poisson sampling improves the efficiency in many cases.

There exist many designs for unequal probability sampling. In this paper entropy, which is a measure of randomness, is used to compare eight designs. Both old and commonly used designs and more rec ...

Sampford sampling is a method for unequal probability sampling. There exist several implementations of the Sampford sampling design which all are rejective methods, i.e. the sample is not always accepted. Thus the existing methods can be time consuming or even infeasible in some situations. In this paper, a fast and non-rejective list-sequential method, which works in all situations, is presented. The method is a modification of a previously existing rejective list-sequential method. Another list-sequential implementation of Sampford sampling is also presented.

The repeated Poisson sampling design is a new design for selecting a sample of fixed size with unequal inclusion probabilities. The design is very close to the conditional Poisson sampling design, but the implementation of the RP-design is much more efficient.

Data assimilation techniques were used to estimate forest stand data in 2011 by sequentially combining remote sensing based estimates of forest variables with predictions from growth models. Estimates of stand data, based on canopy height models obtained from image matching of digital aerial images at six different time-points between 2003 and 2011, served as input to the data assimilation. The assimilation routines were built on the extended Kalman filter. The study was conducted in hemi-boreal forest at the Remningstorp test site in southern Sweden (lat. 13°37′ N; long. 58°28′ E). The assimilation results were compared with two other methods used in practice for estimation of forest variables: the first was to use only the most recent estimate obtained from remotely sensed data (2011) and the second was to forecast the first estimate (2003) to the endpoint (2011). All three approaches were validated using nine 40 m radius validation plots, which were carefully measured in the field. The results showed that the data assimilation approach provided better results than the two alternative methods. Data assimilation of remote sensing time series has been used previously for calibrating forest ecosystem models, but, to our knowledge, this is the first study with real data where data assimilation has been used for estimating forest inventory data. The study constitutes a starting point for the development of a framework useful for sequentially utilizing all types of remote sensing data in order to provide precise and up-to-date estimates of forest stand parameters.

In this study, we investigate the use of model-based inference in forest surveys in which auxiliary data are available as a probability sample. We evaluate the effects of model form and sample size on estimators of growing stock volume, based on different types of remotely sensed auxiliary data. The study was performed through Monte Carlo sampling simulation using a two-phase sampling design within a simulated study area resembling the conditions in mid-western Finland. We show that the choice of model has a minor to moderate effect on the precision of model-based estimators. Similarly, the choice of estimator of the variance–covariance matrix of model parameter estimates, which is at the core of uncertainty assessment in model-based inference, was also found to have a minor to moderate effect on the precision of model-based estimators. Regarding sample sizes, the model error contribution to the total variance remains the same regardless of the sample size of the first phase (i.e., the size of the sample of auxiliary data); to reduce the model-error contribution, there is a need to increase the sample size of the second phase (i.e., the size of the sample of field plots for developing regression models). As a baseline for comparisons, model-assisted estimators were applied and found to be about equally precise as the model-based estimators, in accordance with the theory for the case when models are estimated from the sample data.

An extended theoretical framework for the continuous population approach to forest inventories is derived. Here, we treat a simultaneous selection of sample points with any prescribed sampling intensity over a continuous population. Different ways to use available auxiliary information, for example, from remote sensing, by selection of approximately balanced or spatially balanced samples are considered. A large data set of spatially continuous individual tree‐level data is used to demonstrate the potential of these theoretical approaches. This study shows new ways to integrate remote sensing information in designs for forest inventory applications, which can significantly reduce the variance of the Horvitz–Thompson estimator for target variables related to the auxiliary information.

Airborne Light Detection and Ranging (LiDAR) and Landsat data were evaluated as auxiliary information with the intent to increase the precision of growing stock volume estimates in field-based forest inventories. The aim of the study was to efficiently utilize both wall-to-wall Landsat data and a sample of LiDAR data using model-assisted estimation. Variables derived from the Landsat 7 ETM + satellite image were spectral values of blue, green, red, near infra-red (IR), and two shortwave IR (SWIR) bands. From the LiDAR data twenty-six height and density based metrics were extracted. Field plots were measured according to a design similar to the 10th Finnish National Forest Inventory, although with an increased number of plots per area unit. The study was performed in a 30 000 ha area of Kuortane, Western Finland. Three regression models based on different combinations of auxiliary data were developed, analysed, and applied in the model-assisted estimators. Our results show that adding auxiliary Landsat and LiDAR data improves estimates of growing stock volume. Very precise results were obtained for the case where wall-to-wall Landsat data, LiDAR strip samples, and field plots were combined; for simple random sampling of LiDAR strips the relative standard errors (RSE) were in the range of 1–4%, depending on the size of the sample. With only LiDAR and field data the RSEs ranged from 4% to 25%. We also showed that probability-proportional-to-size sampling of LiDAR strips (utilizing predicted volume from Landsat data as the size variable) led to more precise results than simple random sampling.

More than 50 methods have been developed to draw unequal probability samples with fixed sample size. All these methods require the sum of the inclusion probabilities to be an integer number. There are cases, however, where the sum of desired inclusion probabilities is not an integer. Then, classical algorithms for drawing samples cannot be directly applied. We present two methods to overcome the problem of sample selection with unequal inclusion probabilities when their sum is not an integer and the sample size cannot be fixed. The first one consists in splitting the inclusion probability vector. The second method is based on extending the population with a phantom unit. For both methods the sample size is almost fixed, and equal to the integer part of the sum of the inclusion probabilities or this integer plus one.