This paper focuses on the use of models for increasing the precision of estimators in large-area forest surveys. It is motivated by the increasing availability of remotely sensed data, which facilitates the development of models predicting the variables of interest in forest surveys. We present, review and compare three different estimation frameworks where models play a core role: model-assisted, model-based, and hybrid estimation. The first two are well known, whereas the third has only recently been introduced in forest surveys. Hybrid inference mixes designbased and model-based inference, since it relies on a probability sample of auxiliary data and a model predicting the target variable from the auxiliary data..We review studies on large-area forest surveys based on model-assisted, modelbased, and hybrid estimation, and discuss advantages and disadvantages of the approaches. We conclude that no general recommendations can be made about whether model-assisted, model-based, or hybrid estimation should be preferred. The choice depends on the objective of the survey and the possibilities to acquire appropriate field and remotely sensed data. We also conclude that modelling approaches can only be successfully applied for estimating target variables such as growing stock volume or biomass, which are adequately related to commonly available remotely sensed data, and thus purely field based surveys remain important for several important forest parameters.

Trees outside forests (TOFs) are an important natural resource that contributes substantially to national biomass and carbon stocks and to the livelihood of people in many regions. Over the last decades, decision makers have become increasingly aware of the importance of TOF, and as a consequence, this tree resource is nowadays often considered in forest monitoring systems. Our review shows that in many cases, TOF are included in national forest inventories, applying traditional methodologies with relatively sparse networks of field sample plots. Only in some countries, such as India, the design of the inventories has considered the special features of how TOFs occur in the landscape. Several research studies utilising remote sensing for monitoring TOF have been conducted lately, but very few studies include comparative studies to optimise sampling strategies for TOF. Our review indicates that methods combining remote sensing and field surveys appear to be very promising, especially when remote sensing techniques that assess both the horizontal and vertical structures of tree resources are applied. For example, two-phase sampling strategies with laser scanning in the first phase and a field survey in the second phase appear to be effective for assessing TOF resources. However, TOFs often exhibit different characteristics than forest trees. Thus, to improve TOF monitoring, there is often a need to develop models, e.g. for biomass assessment, that are specifically adapted to this tree resource. Alternatively, field-based remote sensing methods that provide structural information about individual trees, notably terrestrial laser scanning, could be further developed for TOF monitoring applications. This also would have a potential to reduce the problem of accessing TOF during field surveys, which is a problem, for example, in countries where TOF are present on intensively utilised private grounds like gardens and agricultural fields.

Key messageThe 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.

In contrast to forest trees, trees outside forests (TOF) often are not included in the national monitoring of tree resources. Consequently, data about this particular resource is rare, and available information is typically fragmented across the different institutions and stakeholders that deal with one or more of the various TOF types. Thus, even if information is available, it is difficult to aggregate data into overall national statistics. However, the National Forest Monitoring and Assessment (NFMA) programme of FAO offers a unique possibility to study TOF resources because TOF are integrated by default into the NFMA inventory design. We have analysed NFMA data from 11 countries across three continents. For six countries, we found that more than 10% of the national above-ground tree biomass was actually accumulated outside forests. The highest value (73%) was observed for Bangladesh (total forest cover 8.1%, average biomass per hectare in forest 33.4 t ha(-1)) and the lowest (3%) was observed for Zambia (total forest cover 63.9%, average biomass per hectare in forest 32 t ha(-1)). Average TOF biomass stocks were estimated to be smaller than 10 t ha(-1). However, given the large extent of non-forest areas, these stocks sum up to considerable quantities in many countries. There are good reasons to overcome sectoral boundaries and to extend national forest monitoring programmes on a more systematic basis that includes TOF. Such an approach, for example, would generate a more complete picture of the national tree biomass. In the context of climate change mitigation and adaptation, international climate mitigation programmes (e.g. Clean Development Mechanism and Reduced Emission from Deforestation and Degradation) focus on forest trees without considering the impact of TOF, a consideration this study finds crucial if accurate measurements of national tree biomass and carbon pools are required.

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.