Gap models and their individual-based relatives in the assessment of the consequences of global change

One collection of approaches to developing a scientific basis for recalibrating yield tables was statistical. This focused on regularly spaced plantations of trees of the same species and age. Clutter (1963), Clutter et al (1983) parsed this problem into one of statistically deriving the parameters of two coupled derivatives: one for the change in the natural lobvolume of wood in a forest stand over the age of the stand (dlnV/dA) and a second for the change in basal area (the sum of the cross-sectional area of all the trees at a reference height) with age (dB/dA). Helpfully, if trees in the stand are all the same size, the basal area of the stand is simply the basal area of each tree times the density of trees, essentially the Normalbaum concept of Carlowitz. Empirical relations amongst tree height, the volume of a tree as a function of its diameter, changes in the increment of diameter as functions of tree density, or the local site conditions promoting tree growth to differing degrees make this a daunting mathematical estimation problem. This approach has the capability of ingesting records of forest plantation performance to obtain forest yield tables and to change these tables with changes in the growth rates of individual trees. It and its subsequent improvements are standard tools for plantation forestry (Burkhart and Sprinz 1984, Burkhart 1990). Embedded in these models are assumptions that all the trees in a stand are identical and that the stand density is fixed. These assumptions are appropriate for plantations but not so much for trees growing under more natural conditions.

Japanese forest ecologists tackled same problem of understanding patterns in the growth in diameters of trees in even-aged forest stands and the resultant change in stand volume (or biomass). Yoda et al (1963) developed a 'thinning law' to predict mortality in growing even-aged forests. Shinozaki et al (1964) produced the 'pipe model' concept that implied the sapwood cross-sectional area per unit of land provided a limit to growth and yield by relating the distributions of sizes and numbers of trees. Suzuki and Umemura (1974) visualized the prediction of growth and yield as a matter of understanding the change in the average size of a tree (tree growth) and the changes of the numerical distribution around the average tree for stands in which the trees were competing and eliminating weaker competitors (thinning). As smaller trees were overtopped and suppressed by the dominant canopy trees, the shape of the numbers distribution around the average tree changed in skewness and kurtosis around the average tree size change as a function of the population processes.

This Japanese-approach was applied to simulate the change in the distribution of tree sizes for the cohorts of trees in the gap left from the death of a large tree in temperate rainforests on Yakushima Island in southern Japan (Kohyama 1992) and subsequently to tropical rainforests in Borneo (Kohyama 1993). This latter approach was subsequently used as the computational engine for the ecosystem demography or ED model (Moorcroft et al 2001), which has been applied as a regional or global model for better understanding the dynamical role of forests in the global carbon cycle. This will be discussed below as a method to scale-up gap-model dynamics.

Kohyama's (1992, 1993) models represent a transition from the plantation modeling of growth and yield to the approximation of dynamics of forest mosaics. In general, yield tables have not worked well in forests comprised of trees of different ages (or sizes) or of different species. The problem of predicting change over time and managing for such forests generated an alternate approach to forest modeling that emphasized the growth and interaction of each individual tree in a simulated forest stand. The Normalbaum concept at the dawn of scientific forestry can be interpreted as an individual-tree-based modeling approach, and these new models were explicitly based on individual trees.

The first such model (Newnham 1964) was developed for Douglas-fir (Pseudotsuga menziesii) forests and predicted tree growth and stand yield for forest in which trees had non-regular spacing and were of different sizes. The subsequent development of similar models, developed in the doctoral dissertations at several Schools of Forestry, are archived in Forest Science, which at that time published the abstracts of forestry doctoral dissertations. These early forest IBMs were complex and large for the computers that were then being used to solve them.

For example, the competition among individual trees was typically simulated by crown interactions involving the three-dimensional geometry of each individual tree crown for all the trees in a stand (Newnham 1964); the growth of the tree trunks of each tree were often simulated at multiple heights (Hegyi 1974); tree mortality was related to two- or three-dimensional crown pruning among trees (Mitchell 1969, 1975). The most detailed early model, FOREST (Ek and Monserud 1974), also considered multiple tree species. In FOREST, tree competition derived from the interactions among the three-dimensional crown geometries (different idealized-shaped canopies were used for different species). FOREST mapped the exact locations of trees, calculated the dispersion pattern of seed-fall based on seed morphology, etc. It exceeds the complexity of virtually all modern forest IBMs.

This history of development of forest landscape models and their origins starting with forestry growth and yield models to more models operating at the landscape scales has recently been reviewed by Shifley et al (2017). They and we see the increased mechanistic complexity and physical dimension represented in spatial forest-landscape models developing over time as a consequence of the increase in computational power over the past decades. The effect arises can be related to the so-called Moore's Law, that the number of components in integrated circuits doubles about every two years (Moore 1965). In the case of landscape models, this increase in computational capability, has allowed the fusion of increasingly larger data sets into the models. Much of the functional complexity was found even in very early forest IBMs.

In 1972, Botkin et al 1972 produced an important simplification of the earlier forestry work using IBMs, which they called the JABOWA model for the initials of its developers. A model (Siccama et al 1969) presented at the annual meeting of the Ecological Society of America has been cited as an earlier version of this model but based on its short description, it seems to be a different, more statistical approach. From a forest inventory plot, JABOWA annually computed diameter increment of each tree, it stochastically killed trees and planted new trees. Botkin et al (1972) did not cite any of the antecedent forestry models. Because the forestry IBMs were mostly, but certainly not entirely, in sources not frequently read by forest ecologists, the earlier forestry work remained sub rosa to most ecologists. Additionally, some of the forestry IBMs drifted into the realm of 'industrial secrets' as their developers found employment in the timber industry.

In 1980, Shugart and West introduced the term 'gap model,' to describe this class of models. The gap model designation emphasized that a principal simplifying assumption in these models (the assumption that the competition among individual trees on a small patch of land was homogeneous in the horizontal dimension across a small area but spatially explicit in the vertical dimension) related to the classic 'gap dynamics' concept of A.S. Watt (1925, 1947). Implied in this formulation was an underlying idea that a small plot, near the size of the influence zone of a large tree was an appropriate scale to include the gap generation and recovery seen in Watt's classic work. In practice, the plot size used in these models has been around 0.04 to 0.10 hectares depending on sizes and heights of trees. Gap models formulated at larger or smaller spatial scales can demonstrate dynamic responses that are anomalous to those of Watt's basic 'pattern-and-process' concept for forests (Shugart and West 1979). The ratio of height of a gap to its width changes the direct-light illumination zone of the forest floor as a function of latitude (Kuuluvainen 1992). In agreement with Kuuluvainen, the spatial unit used in gap models for models from the tropics to temperate to boreal zones have smaller plot sizes towards the equator matching the higher average sun angles there.

A generation of forest ecologists have made numerous extensions of 'gap models' and the term, nowadays, refers to a broad class of IBMs for forests and other ecosystems of a 'natural' character (mixed-age, mixed-species, natural disturbance regimes, etc). Modeling forest growth has been reviewed several times and it is our intention to recognize but not rehash this well-done work. Liu and Ashton (1995) reviewed gap models and tabulated the phylogeny of about 20 of these models springing from the JABOWA and FORET models. Porté and Bartelink (2002) used a hierarchical search algorithm to the papers in several abstracting data sets and found about 700 papers involving modeling mixed-forest stands published up to 2000. They produced a thoughtful review of the common issues of successes and needs across 199 of these models, including many gap models. Bugmann (2001) review presented and investigated details of model assumptions and formulations. Xi et al (2009) reviewed forest landscape models and placed gap models in the context of 'other, landscape-level simulators of forest dynamics'. Shugart and Woodward (2011) reviewed a large set of gap models and tabulated the testing of these against a wide range of forest data at different time and space scales. More recently, Larocque et al (2016) reviewed forest succession models, which simulate the long-term dynamic change of mixed-age, mixed-species forests and tabulated the significant functions and applications of each.

We searched the Web of Science for citations to 12 different early gap models (or model series) that each had more than one hundred citations since their publication. The three books in this collection were searched on Google Scholar and were also included in this analysis as is indicated in the legend of figure 1. Citations to these models show two strong peaks, one in the interval 1995–1996 and a second stronger peak in 1999–2001 (figure 1). The total number of publications that cite these articles totaled 6500 (up until the end of the year 2016). Some of these models show substantial 'longevity' and are still being cited regularly 30+ years after their initial publications. One would expect a transition to more recent papers, perhaps with revisions in the models, in the citation pattern over time. The decline in citations after 2001 in figure 1 appears to arise from the substitution citation of new versions of the original models or of more recently derived second-generation models derived from these early 12 gap models. Model developers of almost any ecological model tend to differentiate their creations from those developed by others.

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Currently, there are hundreds of gap models in use for a wide array of local-to-regional applications. This is potentially confusing for non-model-oriented scientists trying to read across this literature. These models have more in common than many suspect. These gap models endorse the fundamental premise that the structure of forests promotes a remarkable control of ecosystem dynamics that is lost in more aggregated modelling approaches. This class of models has a surprising capability to predict responses of real forests over longer-than-annual time scales. Exercising the models has also produced useful theory on how forests could be expected to respond to change and what factors determine these patterns of change.

The issue of model complexity invariably arises in the development of forest IBMs. In general, an increase in model 'complexity' including number of parameters in a model, the amount of data needed to initialize the models, or the additional to functional couplings in a model has increased with computation power. Multi-level models, such as gap models with individual plant → plot → landscape → region → continent scaling are relatively simple when seen across one of the levels, but are complex when seen through multiple levels. Most ecological modelers realize that there is a trade-off between model simplicity and model complexity that results in a 'sweet-spot', the so-called Medawar zone (see: Medawar 1967, Grimm et al 2005). Differences in objectives in a given study preclude the universal acceptance of any one model approach as always being the most appropriate choice, even when restricted to the case of individual-based models simulating forests.

Gap models intentionally feature relatively simple protocols for estimating the model parameters (Shugart 1984, Shugart and Woodward 2011). For many of the more common temperate and boreal forest trees, there is a considerable body of information on the performance of individual trees (growth rates, establishment requirements and height/diameter relations) that can be used directly in estimating the parameters of such models. Parameter estimation is aided by many of the parameters in the model being tangible attributes of tree species: their maximum growth rate, their maximum heights, their tolerance of shading, drought, nutrient stress, etc.

One obvious approach to simplifying this class of models would be to represent the species in the models with some reduced number of 'functional types' of plants. Since the computation burden in the models stems from the processing of individual trees, the main advantage is in the reduction of the demands for parameter estimation for each species of tree considered. Hartmut Bossel and colleagues (Bossel 1991–1996, Bossel and Krieger 1991–1994, Köhler et al 2000, Huth and Ditzer 2000–2001) pioneered this approach for tropical rain forests. Such models have subsequently found wide applications in Borneo, French Guiana and in several other tropical ecosystems, as well as for forest at the global scale. Two examples will be discussed in more detail in the sections below for the FORMIND model (Fischer et al 2016, Köhler and Huth 1998) and the FORCCHN (Ma et al 2017) model.

Gap models have simple rules for interactions among individuals (e.g. shading, competition for limiting resources, etc) and equally simple rules for birth, death and growth of individuals. The simplicity of the functional relations in the models has positive and negative consequences. The positive aspects are largely involved in the ease of estimating model parameters for a large number of species; the negative aspects with a desire for more physiologically or empirically 'correct' functions. An earlier synthesis (Shugart 1984) was entitled 'A Theory of Forest Dynamics' with the 'A' intended to emphasize that the theoretical implications of these models are necessarily special theories—the theoretical implications and practical applications are constrained by the underlying gap-model assumptions.

To elucidate some of these assumptions, figure 2 outlines the general features in gap models. The essential modelling functions of a gap model resemble those of other IBMs for forests. In most gap models, the diameter of each tree is updated annually and the parameters of the diameter growth equation vary with species. The original JABOWA and FORET models incremented volume of wood and used allometric equations derived from species' maximum heights and diameters to include a species' geometry in the diameter increment equation. Others have used other methods of incorporating tree geometry in the parameterization. For examples, FORSKA (Leemans and Prentice 1987, 1989) and FAREAST (Yan and Shugart 2005) models used a diameter-increment equation based on a pipe-model approach (Shinozaki et al 1964). OVALIS (Harrison and Shugart 1990) simulated tree form with both the heights and diameters dynamically changing in the model. Larocque et al (2016) provides a summary of these and other functions used across a large set of gap models and should be consulted for those interested in more details on these functions and the relationships that are discussed here and immediately below. They present a six-page table summarizing the internal functions for tree growth, competition, etc in 23 gap models as well as the trade-offs in the use of the different functions.

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The species' growth equations (one equation per tree) invariably contain individual tree size as one important variable and are implemented as a differential or difference equations. The coupling of these equations is based on decreased individual growth in response of species specific responses to environmental factors (the vertical light profile, the nutrient availability for the plot, soil moisture, etc, see figure 2). These factors are computed at the plot level and require the implementation of biogeochemical models for nutrient elements, hydrological models of evapotranspiration, light extinction as a function of overhead light, etc.). The interaction among trees are a consequence of each tree's effect on the plot environment and the feedback of these environmental changes on each tree. Some gap models (e.g. FORMIND, FORCCHN) explicitly calculate each tree's biomass growth determined on the basis of a carbon balance including photosynthesis and respiration. Carbon-balanced-based tree growth is implicit in the formulation of most gap models. Mortality and establishment are also consequences of the mutually-modified and mutually-shared environment of the simulated plot.

In developing IBMs, one would like to avoid n-body problems, in which each individual interacts with each other individual, because the number of interactions then varies as a function of n². For example, determining the shading of each tree on every other tree for hundreds of trees on a plot demands much, much more computation than simply computing the vertical profile of photosynthetically active radiation and then registering each tree against the computed light profile, as is done in most gap models. When spatially deriving the interactions of trees on a large landscape, n in the n-body problem becomes enormous, outstripping the capabilities of modern computers. Gap models are based on the assumption that the interactions among neighbours near the scale of a canopy gap are the dominant interactions (Watt 1947).

When averaged, the standard protocol for Monte Carlo simulation with stochastic models, gap models basically simulate landscape dynamics. In the simplest case (figure 2(a)), one simulates a large number of plots, which can be initialized by the species and diameters of each tree on sample plots with a matching spatial scale. As is the case in typical survey design, these plots are independent of one another (although they may share the same annual weather conditions, and perhaps large-scale disturbance events). The expected average of the landscape is the average of these simulated plots over time.

Because gap models are stochastic, comparisons between a single simulated plot to an actual re-measured sample plot are generally neither fruitful nor useful. After initialization with actual tree sizes and species from an actual forest sample plot, random events in the simulated plot, such as the death of a very large tree for example, would not be expected to occur in coordination those on the actual plot. An actual long-term reconstruction of plot-level field data would require a remarkably deep and detailed history of the sample plot. By analogy, a stochastic model of a pair of dice could predict the average proportions of numbers thrown over time. Indeed, it could be used to determine that real dice are 'loaded', but one would not expect the model to predict the next throw of the dice.

Perhaps for this reason, gap-model developers have generally had an interest in testing their models at the landscape- and larger-scale data. Shugart and Woodward (2011), chapter 5, provide numerous examples of such tests including:

• With a priori parameter estimation for species, predict forest-level features (total biomass, leaf area, stem density, average tree diameter, etc).
• Run model for a long period of time, predict mature forests preserved in a region.
• Calibrate model on stands of a given age, predict structure on stands of a different age(s).
• Use introduction of disease or change in conditions (e.g. fire frequency, droughts, disease such as the Chestnut Blight (Cryphonectria parasitica, etc) as 'natural' experiments.
• Predict independent tree diameter increment data, forestry yield tables, forest composition change along single environmental gradients, and forest composition response to multiple environmental gradients.

These tests of the models in cases involving gradient responses simulations are performed by placing clusters of simulation runs at grid locations across a landscape (figure 2(b)). Examples include tests against mountain altitudinal gradients (Kercher and Axelrod 1984, Bugmann 1996, Bugmann and Solomon 2000, Gutiérrez et al 2016, Yan and Shugart 2005, Foster et al 2017)

In more spatial applications, one can simulate a landscape as a tessellation with the land surface covered with adjacent plots of land. Applications have included dispersal of seeds from one cell to another or the spread of wildfire or other disturbances across the landscape (figure 2(c)). Finally, the ZELIG model (Urban et al 1991) simulates stem maps of tree (size and species) across a landscape map. The model is implemented by computationally 'dropping' a gap model on a small overlapping subsections of a stem map and then using the gap model to update the map. This is repeated to produce the next year's stem map, etc. The spatial resolution of the stem map spring from the overlap of the subsections. This computational procedure is called 'windowing' (figure 2(d)) and is a common general implementation for IBMs largely to reduce computational inefficiencies of spatially explicit models.

The ZELIG approach has been implemented in time plus three spatial dimensions and tested on its ability to reproduce fine-scale patterns in the autocorrelation structure of Douglas fir forests as measured by high-spatial resolution remote sensing (Weishampel et al 1992). More recently, Brazhnik and Shugart (2016) used a gap model with explicit spatial representation of the positions of the individual trees account for the effects of the flatter angles of direct light at high latitudes. This simulation includes the spatial effects of topographic shading (tall mountains to the south shading an area, the shadiness of steep valleys, etc) as well as the significant differences in north- and south-facing slopes along altitudinal gradients. Foster et al (2017) presents a similar investigation forest composition change with slope and aspect patterns as a gap model test in the USA Rocky Mountains. Spatial effects such as wildfire have also been represented in spatial forest IBMs (Brazhnik et al 2017).

Gap models can also be used to investigate questions related to biodiversity. In a case study, a gap model simulated the forest dynamics of a tropical rainforest with more than 400 tree species (Köhler and Huth 2004). It was shown that recruitment limitation and disturbance intensity are important for maintaining species richness (Köhler and Huth 2004). Besides species richness, forest management can play an important role for the development of forests. Logging has been included in forest gap models, allowing to simulate different logging strategies and to explore their long-term impacts on forest dynamics (Kammesheidt et al 2001, Köhler and Huth 2004).

It was shown that long logging cycles >60 years in combination with reduced-impact logging strategies could significantly reduce the negative long-term impact of logging on forest carbon stocks (Köhler and Huth 2004, Brazhnik et al 2017, Huth et al 2004). This strategy might be applied as a compromise between economic and ecological interests.

The individual-based approach of gap models is the key driver for their successful application for questions on forest management. Beside this, other types of disturbances, such as landslides, forest wildfires, and windstorms, have been investigated with gap models (e.g. Gutiérrez and Huth 2012, Dislich and Huth 2012, Brazhnik et al 2017).

To provide the reader with some more tangible examples of the diversity of general questions that have been approached with gap models, consider the following examples:

Feedbacks among canopy processes, succession and atmospheric chemistry—IBMs are a potentially powerful tool in elucidating the role of biodiversity in feedbacks between the biosphere and air quality that are integral to the complex biosphere-atmosphere interactions. The terrestrial biosphere is a large emitter of volatile organic compounds (VOCs; Guenther et al 2006), which are highly reactive and involved in complex photochemical reactions with oxidants of hydroxyl radical (OH⁻) and nitrate radical (NO₃⁻) in the troposphere to form ozone (O₃) and secondary organic aerosols (SOA) that influence air quality (Atkinson and Arey 2003). These pollutants can, in turn, affect the vegetation both directly and indirectly. In particular, O₃ forms a strong oxidative pressure over the biosphere, to which species show a varying sensitivity (Wang et al 2016). Moreover, VOCs emissions are highly species-dependent in an ecosystem (Lerdau and Slobodkin 2002). Implications of such widespread species-level heterogeneity for ecosystem functions are neglected largely because of methodological limitations.

Recent explorations with forest gap models clearly suggest the capacity of IBMs in tackling this issue. Wang et al (2017) developed an individual-based forest VOCs emission model, UVAFME-VOC (v1.0), from the gap model, University of Virginia Forest Model Enhanced (UVAFME), the latest version of the FORET gap model (Shugart and West 1977). UVAFME-VOC was used to investigate the impacts of surface O₃ pollution on forest dynamics simulated for the Walker Branch Watershed research facility at Oak Ridge National Laboratory in Oak Ridge, Tennessee, USA (Wang et al 2016, figures 3(a)–(b)). This model simulates isoprene emissions at an hourly time step on the basis of demographic processes at a yearly time step. Elevated O₃ significantly altered forest dynamics by favoring species that are O₃-resistant, many of which are producers of isoprene, which is the largest source of non-methane VOCs. Because of the compensation arising from the increased proportion of O₃-resistant species (figure 3(a)), compositional changes ameliorated an expected simulated suppression both of forest productivity and carbon stock.

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This finding contradicts previous studies based on models that lack an explicit simulation of the species-specific sensitivity to O₃ (e.g. Sitch et al 2007). With more isoprene production arising from increased presence of isoprene-emitting species, there is a positive feedback between tropospheric O₃ and forest (figure 3(b)). Additionally, UVAFME-VOC was also applied to study climate warming impacts on forest isoprene emissions (Wang et al 2018). This latter study found that, unlike previous studies with aggregated models (Guenther et al 2006), climate warming will not always stimulate isoprene emissions. In addition to its direct enhancing effect, warming simultaneously reduces isoprene emissions by causing a decline in the abundance of isoprene-emitting species (figure 3(c)). This ecological effect eventually outweighs the physiological one, and reduces the overall emissions over time (figure 3(d)). These findings have significant implications for the understanding of complex climate-biosphere-air quality feedbacks. Results from an individual-based gap model are not congruent with those produced by more aggregated ecosystem models, and demonstrate the capability of gap models in addressing feedbacks between biosphere and atmospheric chemistry.

Estimating Amazon-wide biomass with local gap models—Linking remote sensing and forest modelling for large scale applications is a promising field in forest ecology (Shugart et al 2015). There are two options to link forest simulations with remote sensing: either by using remote sensing products to initialize existing forest models (e.g. using forest cover maps) or alternatively, using first forest models to explore relationships between different forest attributes (e.g. forest height and biomass) and apply them to remote sensing to derive hidden forest attributes that cannot be measured directly by remote sensing (like forest productivity or forest structure, Knapp et al 2018). The advantage of using an individual-based forest model is that it brings along information on forest structure (Fischer et al 2016). This structural realism can be used to link simulated and remotely sensed information on forest structure at different levels (e.g. canopy height). Rödig et al (2017) used remote sensing data to establish large-scale applications of forest gap models and to derive maps of forest carbon stocks and fluxes at the continental scale.

They used the forest gap model, FORMIND (Fischer et al 2016), which is normally applied at stand levels, to simulate forest dynamics at a much larger scale, here the Amazonian rainforest (figure 4). This large-scale application required two steps: (1) the technical implementation and (2) the regionalization approach. The technical application took advantage of modern high-performance computers and ran simulations with parallel computation. The regionalization approach involved the regional modification of model parameters for which a process-based description is often missing (e.g. mortality rates change in different regions, for example due to changes in environmental factors). With this parameter adaptation, simulation of heterogeneous forest dynamics can be achieved for the Amazon region. However, the estimation of these model parameters is a complex process and only a limited amount of forest site observations is available. Therefore, an inverse modeling technique for forest models was developed (Lehmann and Huth 2015).

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This technique has been used to calibrate model parameters against field inventory data, but it is potentially also applicable to automatically calibrate forest models with remote sensing data. To derive biomass maps and forest productivity maps across large landscapes with a fine resolution, they linked the forest gap model with Amazon-wide forest height maps from remote sensing, in the current case, the forest height map of Simard et al (2011). These canopy heights are used to identify successional stages of forests. The result was a map of forest biomass in the Amazon rainforest at 40 m resolution (Rödig et al 2017, figure 4). Beside forest biomass, gap models also provide information on the relations among successional stage, disturbance state and carbon fluxes (Fischer et al 2016). These findings highlight the capability of deriving high-resolution maps of carbon fluxes, as well as biomass, across large landscapes such as the Amazon forests system.

Additional carbon releases due to tropical-wide forest fragmentation—Another approach of large scale applications of forest gap models focuses on the influence of land use on tropical forests (figure 5). By combining remote sensing data and a forest gap model, Brinck et al 2017) calculated long-term carbon losses due to forest fragmentation. They analyzed the impact of edge effects on different forest-stand carbon fluxes using the FORMIND model (Pütz et al 2011). These results are combined with high-resolution forest cover maps. In detail, each forest fragment in the tropics was counted and analyzed using such tree cover maps (Landsat with 30 m resolution). Forest area lying within 100 m of a forest edge was evaluated, as wherein this forest edge area trees suffer increased mortality. The impact of this increased mortality on forest structure and dynamics was analyzed by field data (Laurance 2000, Laurance et al 2011) and by forest gap models (Pütz et al 2014). Combining high-resolution forest cover analysis with results of gap model simulations provides important findings, notably tropical forest fragmentation increases carbon loss significantly and should be accounted for in the global carbon cycle (Brinck et al 2017).

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Using gap models to simulate global carbon fluxes from forests—The FORCCHN model (FORest ecosystem carbon-budget model for CHiNa model, Ma et al 2017) is a gap model designed for global applications involving forest structural change (tree height, leaf area index, size distributions of trees, successional dynamics, etc) and its influence on biogeochemical fluxes from forests. Its simulations are based on a plot-scale gap model, which plants, grows and kills the individual trees categorized into functional types rather than species.

The FORHCHN model assumes that net photosynthate is allocated to the tree growth, leaf litter and fine roots. Any remaining photosynthate is stored in a so-called 'buffer carbon pool' on a daily basis. At the end of the year, this cumulative 'buffer carbon pool' is primarily used to support the growth of canopy height and basal diameter increment of each tree on each simulated plot. As a preamble to applying the FORCCHN model to estimate global carbon uptake by forest ecosystems, Ma et al (2017) used the CO₂ flux measurements from 37 eddy covariance flux sites located between ∼38°S to ∼70°N to examine the FORCCHN's performance. In these initial tests, model simulated higher correlations in gross primary production (GPP) for the 37 sites (correlations averaging 0.72 across predicted and observed daily across the 37 sites), ecosystem respiration (ER, average correlations of 0.70) and net ecosystem production (NEP, average correlations of 0.53) across all forest biomes.

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Ma and his colleagues then applied the FORCCHN model to estimate the carbon fluxes on global scale with the satellite-derived data from IGBP-DIS land cover classification system and Global Land Surface Satellite LAI products. The simulated results are comparable to and reinforce estimates reported in other studies. More generally, these results also indicate that gap models, notably the FORCCHN model, have application in global carbon modeling. Figure 6 illustrates the performance of the FORCCHN model simulating the net ecosystem production for global forests over the interval 1970–2008. One significant pattern seen in this analysis is the region in the Eurasian boreal forest region where red colors indicate landscape- to regional-scale negative NEP across the very part of Eurasia that has been significantly warming over this time interval (Serreze et al 2000). One can also see similar negative NEP in tropical regions undergoing clearing that has yet to be offset by recovery.

When available, forest inventory data (i.e. tree height and basal diameter of individual tree on survey plots of an appropriate size.) are used as the initial conditions to start the FORCCHN model. As was just mentioned for Amazonian estimation of the components of biomass dynamics at the regional scale, in global applications a significant difficulty lies in the lack of availability of extensive plot-based inventory data. For this reason, satellite-derived LAI products (along with information on forest types, latitude, and elevation for a given plot area) are used to initialize the stand structure in the initial year of the simulation. For the FORMIND application for the Amazon (above) the procedures used are outlined in Rödig et al (2017) and Lehmann and Huth (2015). For the FORCHHN model, procedures in Zhao et al (2012) are used for initialization the states of the individual trees on plots. These applications could likely be improved by perfecting an observational basis for the initialization data. The availability of synoptic individual-tree inventory data for the world's forest at large scales is essentially non-existent and there are relatively few good national-scale examples. One can expect that with the deployment of LiDAR and RaDAR satellites by multiple international space agencies, the availability of better characterizations of forest physical structure will serve to improve initialization of spatially extensive gap-model applications.

Some of the parameters of some ecological process models embedded in the FORCCHN model have been applied globally. For example, to simulate vertical light distributions and soil conditions, FORCCHN is coupled with a forest-canopy-height radiation sub-model and a CENTURY (Parton et al 1988 and 1995) sub-model. These sub-models play a key role in photosynthesis and decomposition in the FORCCHN model. FORCCHN model uses such physiological and ecological functions along with the forest structure to describe the productivity of global forests. High-quality global-meteorological databases are imperative to construct the estimates of the local environmental factors for the global simulations.

Technological advances in remote sensing should improve the climate observations used in the FORCCHN model and other gap models. For the testing of these models more observation stations have established and can provide more extensive observational data, particularly for carbon flux data. The FORCCHN model can also consider the influence of CO₂ concentration in the atmosphere on vegetation growth. The current FORCCHN simulation results can be compared directly with the station carbon flux data at the site scale directly, and is its basic validation for global modelling.

The global-scale modeling with IBMs and associated gap models does present have several challenges for data collection at different scales. Some of this regards a better characterization of species parameters and better functional representations of ecological process. These represent a continuation of ongoing silvicultural and biogeochemical research agendas. One hopes that the relative success in gap models when tested against a spectrum of forest properties can inspire a increased interest in these research areas.

Despite the advances in remote sensing technology, uncertainties remain and directly influence the vegetation initialization. For example, the FORCCHN model is initialized with two different sorts on information. First, the model requires individual-tree information—tree species, diameter, height, etc of each tree on a sample plot or alternatively a set of rules allowing the model to spin-up a theoretical forest landscape of a given age. Second, plot information is required—the tree numbers on the plot, leaf area index, available nutrients.

Since the impact of environmental change on forest ecosystem fluxes is not only limited to CO₂ enrichment and climate change, but also to the cycling of different elements. Nitrogen (N) is a key element to photosynthesis process, which generates a corresponding problem of determining ecosystem-N fluxes and initializing N-storage. C and N are interactive and many studies have shown that atmospheric nitrogen deposition can affect the uptake of CO₂ in the subtropical, temperate and boreal forests. The understanding of these interactive processes at multiple scales remains a challenge.