Ozone is a phytotoxic air pollutant which enters plants mainly through the leaf stomata, where reactive oxygen species (ROSs) are formed that can injure essential leaf functioning . Ozone-induced declines in net photosynthesis have been observed as the result of injury of the photosynthetic apparatus and increased respiration rates caused by investments in the repair of injury, as well as the production of defence compounds . At the leaf-scale, ozone injury occurs and accumulates when the instantaneous stomatal ozone uptake of leaves surpasses the ability of the leaf to detoxify ozone . These effects are likely the primary cause for reduced rates of net photosynthesis and a decreased supply of carbon and energy for growth and net primary production (NPP), which contributes to the commonly observed ozone-induced reductions in leaf area and plant biomass . Changes in tropospheric ozone abundance and associated changes in ozone-induced injury thus have the potential to affect the ability of the terrestrial biosphere to sequester carbon . However, a quantitative understanding of the effect of ozone pollution on forest growth and carbon sequestration at the regional scale is still lacking. Terrestrial biosphere models can be used to obtain regional or global estimates of ozone damage based on an understanding of how ozone affects plant processes leading to C assimilation and growth. Modelling algorithms to estimate regional or global impacts of ozone on gross primary production (GPP) have been developed for several of these terrestrial biosphere models . However, simulated reductions in GPP due to ozone-induced injury vary substantially between models and model versions .

This uncertainty is predominantly due to the different approaches that these models use to relate ozone uptake (or ozone exposure) to reductions in whole-tree biomass and in the exact parameterisation of the injury functions and dose–response relationships applied . The injury functions employed by current terrestrial biosphere models differ decidedly in their slope (i.e. the change in injury per unit of time-integrated ozone uptake), intercept (ozone injury at zero time-integrated ozone uptake) and their assumed threshold, below which the ozone uptake rate is considered sufficiently low that ozone will be detoxified before any injury occurs . For example, relates the instantaneous ozone uptake exceeding a flux threshold to net photosynthetic injury via an empirically derived factor. An alternative approach has been to relate ozone injury to net photosynthesis in response to the accumulated ozone uptake rather than to the instantaneous ozone uptake as in , e.g. by using the CUOY, which refers to the cumulative canopy O3 uptake above a flux threshold of Y nmol m-2 s-1 .

The effect of ozone on plant growth has been investigated by ozone filtration/fumigation experiments either at the individual experimental level or by pooling data from multiple experiments that have been conducted according to a standardised experimental method. These experiments typically rely on young trees because of their small size. A challenge in developing and testing process-based models of ozone damage from these ozone fumigation experiments is that often only the difference in biomass accumulation between plants grown in an ozone treatment and in ambient or charcoal-filtered air at the end of the experiment are reported. Data from these studies provide evidence for a linear, species-specific relationship between accumulated ozone uptake and reductions in plant biomass e.g.. for instance calibrated their instantaneous leaf-level injury function between ozone uptake and photosynthesis by relating simulated annual net primary production and accumulated ozone uptake to observed biomass dose–response relationships developed by and , where biomass/yield damage is related to the phytotoxic ozone dose (PODy). The PODy refers to the accumulated ozone uptake above a flux threshold of y nmol m-2 s-1 by the leaves representative of the upper-canopy leaves of the plant. Such an approach applies biomass dose–response relationships of young trees to mature trees. However, the effects of ozone on leaf physiology (e.g. net photosynthesis and stomatal conductance) or plant carbon allocation may differ between juvenile and adult trees . Whether or not biomass dose–response relationships can be used to calibrate injury functions for mature trees is uncertain.

An alternative approach is to directly simulate ozone injury to photosynthesis, which may have been a major cause for the observed decline in plant biomass production . Possible injury targets in the simulations can be, for example, the net photosynthesis or leaf-specific photosynthetic activity (such as represented by the maximum carboxylation capacity of Rubisco, Vcmax). For instance, based their injury function on an experimental study involving a single forest tree species, whereas more recent publications (e.g. and ) have used injury functions from meta-analyses of a far larger set of filtration/fumigation studies. Meta-analyses have attempted to summarise the responses of plant performance to ozone exposure across a wider range of experiments and vegetation types and to develop injury functions for plant groups that might provide an estimate of mean plant group responses to ozone. However, these meta-analyses suffer from a lack of consistency in the derivation of either plant injury or ozone exposure and generally report a large amount of unexplained variance. A further complication in the meta-analyses of ozone injury e.g. is that they have to indirectly estimate the cumulative ozone uptake underlying the observed ozone injury based on a restricted amount of data, which causes uncertainty in the derived injury functions.

provides an independent data set of whole-tree biomass plant responses to ozone uptake which is independent of data sets that were used to describe injury functions by and . This data set has been collected from experiments that follow a more standardised methodology to assess dose–responses and has associated meteorological and ozone data at a high time resolution that allow more accurate estimates of modelled ozone uptake to be made. These dose–response relationships describe whole-tree biomass reductions in young trees derived from standardised ozone filtration/fumigation methods for eight European tree species at 10 locations across Europe see Table  for details;. These data thus provide an opportunity to evaluate simulations of biosphere models that use leaf-level injury functions (describing the effect of ozone uptake on photosynthetic variables) to estimate C assimilation, growth and ultimately whole-tree biomass against these robust empirical dose–response relationships that relate ozone exposure directly to whole-tree biomass response.

Here we test four alternative, previously published ozone injury functions that target either net photosynthesis or the leaf carboxylation capacity (Vcmax), which have been included in state-of-the-art terrestrial biosphere models against these new biomass dose–response relationships by . We incorporate these injury functions into a single modelling framework, the O-CN model . To reduce model–data mismatch, we test the functions in simulations that mimic to the extend possible the conditions of each of the experiments in the data set, in particular the young age, such that we can directly compare the simulated to the observed whole-tree biomass reductions in the empirically derived dose–response relationships. This allows us to identify the contribution of these alternative injury function formulations on the simulated whole-tree biomass response. The simulated biomass dose–response relationships are then compared to the data from the experiments to evaluate the capability of the different model versions to reproduce observed dose–response relationships. Based on these comparisons we use a similar approach to that of and develop alternative parameterisations of the injury functions to improve the capability of the O-CN model to simulate the whole-tree biomass responses observed in the fumigation experiments, with the notable exception that we explicitly simulate in-fumigation experiments and the approximate age of the trees. Finally, we explore whether or not there is a substantial difference in the biomass response to ozone of young or mature trees by using a sequence of model simulations and comparing the response both in terms of whole-tree biomass as well as net primary production.

We use the O-CN terrestrial biosphere model , which is an extension of the ORCHIDEE model to simulate conditions of the ozone fumigation experiments described in . The O-CN model, an average–individual dynamic vegetation model, simulates the terrestrial coupled carbon (C), nitrogen (N) and water cycles for up to 12 plant functional types and is driven by climate data and atmospheric composition.

O-CN simulates a multilayer canopy with up to 20 layers with a thickness of up to 0.5 leaf area index each. Net photosynthesis is calculated according to a modified Farquhar scheme for shaded and sunlit leaves considering the light profiles of diffuse and direct radiation . Leaf nitrogen concentration and leaf area determine the photosynthetic capacity. Increases in the leaf nitrogen content increase Vcmax and Jmax (nitrogen-specific rates of maximum light harvesting, electron transport) and hence maximum net photosynthesis and stomatal conductance per leaf area. The leaf N content is highest at the top of the canopy and exponentially decreases with increasing canopy depth . Following this net photosynthesis, stomatal conductance and ozone uptake are generally highest in the top canopy and decrease with increasing canopy depth.

Canopy-integrated assimilated carbon enters a labile non-structural carbon pool, which can either be used to fuel maintenance respiration (a function of tissue nitrogen), storage (for seasonal leaf and fine-root replacement and buffer of inter-annual variability in assimilation) or biomass growth. The labile pool responds within days to changes in GPP; the long-term reserve has a response time of several months, depending on its use to support seasonal foliage and fine-root development or sustain growth in periods of reduced photosynthesis. After accounting for reproductive production (flowers and fruits), biomass growth is partitioned into leaves, fine roots and sapwood according to a modified pipe model , accounting for the costs of biomass formation (growth respiration). In other words, changes in leaf-level productivity affect the build-up of plant pools and storage and thereby feed back on the ability of plants to acquire C through photosynthesis or nutrients through fine-root uptake.

Injury functions that relate accumulated ozone uptake to fundamental plant processes such as photosynthesis are a key component for models that aim to estimate the potential impacts of ozone pollution on forest productivity, growth and carbon sequestration. We tested four published injury functions for net photosynthesis and Vcmax within the framework of the O-CN model to assess their ability to reproduce the empirical whole-tree biomass dose–response relationships derived by . The biomass dose–response relationships calculated from the O-CN simulations show that the parameterisation of the injury functions included in the model has a large impact on the simulated whole-tree biomass: the published injury functions either substantially over- or substantially underestimated whole-tree biomass reduction compared to the data presented by . Our results highlight the importance for improved evaluation of injury functions applied in the simulation of ozone damage for large-scale risk assessments, and we discuss a number of important considerations for an improved parameterisation below.

The simulation results from the O-CN version applying an injury function based on a single, ozone-sensitive species to a range of European tree species leads to a strong overestimation of the simulated biomass damage compared to the observations used in this study. The problem of using such injury parameterisations based on short-term experiments of ozone-sensitive species is further highlighted when applying them in simulations of multiple season fumigation experiments and/or high ozone concentrations. Under such conditions, fumigation with high O3 concentrations can lead to lethal doses, which might not be observed in field experiments due to restricted experiment lengths. Previous studies have suggested that in large areas of Europe, the eastern US and southeast Asia average growing season values of CUOY for recent years range between 10 and 100 mmol O3 m-2 . The injury relationships L12PS and L12VC by assume a 100 % injury to net photosynthesis or Vcmax at accumulation values of about 5 mmol O3 m-2. This would imply that in these large geographic regions, photosynthesis would have been completely impaired by ozone, which is clearly not the case. This result highlights the need for a representative set of species for the development of injury functions for large-scale biosphere models. Overall, our results suggest that the estimates by of global GPP reduction as a result of ozone pollution are strongly overestimated.

Meta-analyses are designed to minimise the effect of species-specific ozone sensitivities and provide estimates of the average species response. However, we found that the relationships derived by these meta-analyses substantially underestimate biomass damage. Technically, the reasons for this are a weak or non-existent increase in the ozone injury with increased ozone uptake (shallow or non-existent slopes) and/or high ozone injury at zero accumulated ozone uptake (intercept lower than 1). Apparently, the diversity of species responses and experimental settings that are assembled in the meta-analyses by and , together with uncertainties in precisely estimating accumulated ozone uptake in these databases preclude the identification of injury functions that are consistent with the damage estimates by . The high intercepts in the meta-analyses by and , which assume a considerable injury fraction even when no ozone is taken up at all, seem to be ecologically illogical and suggest that an alternative approach is necessary to simulate ozone injury. As a consequence of these points, the Europe-wide GPP reduction estimates by , which have been based on the injury function by , may substantially underestimate actual GPP reduction. Similarly, global estimates as well as spatial variability in ozone damage to GPP by , based on , are virtually independent of actual ozone concentrations or uptake for all tree plant functional types and should be interpreted with caution.

A crucial aspect in forming dose–response relationships is the calculation of the accumulated ozone uptake (e.g. PODy or CUOY). The calculation of accumulated ozone uptake is realised in different ways in the meta-analyses and the study by as well as in our approach here. Experiments synthesised in the meta-analyses generally do not have access to stomatal conductance values at high resolution measured throughout the experiment, which impedes precise determination of O3 uptake. The uncertainty in the necessary approximations of accumulated ozone uptake can be assumed to be considerable, and it is thus highly recommendable to measure and report required observations in future ozone fumigation experiments. use the DO3SE model to simulate ozone uptake and accumulation in a similar way as in our model here. These modelled values for ozone uptake and accumulation can be assumed to be more reliable since both models simulate processes that determine ozone uptake continuously for the entire experiment length at high temporal resolution. They account for diurnal changes in stomatal conductance as well as climate factors restricting stomatal conductance and hence ozone uptake. However, both models vary in their complexity of the simulated plants, carbon assimilation and growth processes, which will also impact the estimates of ozone accumulation (PODy) and hence their suggested biomass dose–response relationships.

The meta-analyses do not account for non-stomatal ozone deposition (e.g. to the leaf cuticle or soil), which imposes a bias towards overestimating ozone uptake and accumulation, contrary to the DO3SE model used by , which accounts for this. The O-CN model in principle can simulate non-stomatal ozone deposition from the free atmosphere to ground level (see ). The leaf boundary layer is implicitly included in the calculation of the aerodynamic resistance of O-CN and included in . However, for the simulation of the chamber experiments we used the observed chamber O3 concentrations, rather than estimating the canopy-level O3 concentration based on the free atmosphere (approximately 45 m above the surface) and atmospheric turbulence. This required not accounting for aerodynamic resistance and therefore also the leaf-boundary layer resistance as it prevented the calculation of the non-stomatal deposition, which may lead to a slight overestimation of ozone uptake and accumulation in our simulations.

The calibration of injury functions to net photosynthesis and Vcmax shows that, in principle, the linear structure of Eq. () is sufficient to simulate biomass dose–response relationships comparable to in O-CN. An advantage of the injury functions derived here compared to previously published injury functions is the intercept of 1, implying that simulated ozone injury is zero at zero accumulated O3 and steadily increases with increased ozone accumulation. The flux threshold used in the simulations is 1 nmol m-2 (leaf area) s-1 as suggested by the . Since the tuned injury functions are structurally identical to previously published injury functions based on accumulated ozone uptake, they can be directly compared to them. Slopes of the tuned injury functions lie in between the values proposed by and and thus take values in an expected range. We did not find any significant difference in simulated biomass responses between the use of net photosynthesis or leaf-specific photosynthetic capacity (Vcmax) as a target for the ozone injury function, although we do note that the slopes were slightly lower for the net photosynthesis-based functions. The simulation of ozone effects on leaf-specific photosynthetic capacity (Vcmax) seems preferable over the adjustment of net photosynthesis because Vcmax and Jmax are parameters in the calculation of net photosynthesis and thus are likely more easily transferable between models. Models with different approaches to simulate net photosynthesis might obtain better comparable results by using injury relationships that target Vcmax instead of net photosynthesis.

All injury functions included in the O-CN model base injury calculations on the injury index CUOY (canopy value) rather than PODy, as used by some other models, e.g. the DO3SE model . We tested the effect of basing the injury calculation on POD1 rather than CUO1 and found that these produced comparable biomass dose–response relationships as the injury relationships based on CUO1 presented in Fig.  (results not shown). The slopes of injury functions based on POD1 are approximately two-thirds and half compared to the slopes based on CUO1 for broadleaved and needleleaf species, respectively. The difference in the slope values associated with POD1 and CUO1 results from the different calculation and application of them. PODy is calculated in the top canopy layer and the respective injury fraction is then applied uniformly to all canopy layers. CUOY and the associated injury fraction is calculated separately for each canopy layer and varies with the canopy profile of stomatal conductance and therefore the distribution of light and photosynthetic capacity (other factors such as vertical gradients of temperature or ozone are currently not represented in O-CN). More analysis of the gradients of ozone injury within deep canopies are required to evaluate whether the scaling of top-of-the-canopy injury to whole-canopy injury is appropriate or if alternative simulation approaches need to be developed. Higher-frequency data on the ozone injury incurred by plants are required to disentangle whether an ozone injury parameterisation based on instantaneous (e.g. similar to the approach by ) or accumulated ozone uptake results in a more accurate simulation of the seasonal effects of ozone fumigation.

Further aspects that determine ozone sensitivity and damage to the carbon gain of plants, like leaf morphology , different sensitivity of sunlit and shaded leafs , early senescence , and costs for the detoxification of ozone and/or the repair of ozone injury that likely increases the plant's respiration costs , are not considered by either approach. observed an ozone-induced reduction in biomass but no significant reduction in physiological parameters like Vcmax. They suggest that the reduced growth is caused by higher energy investments and reducing power for the detoxification of ozone whereas the photosynthetic apparatus remained uninjured .

Species within the same plant functional type are known to exhibit different sensitivities to ozone . This suggests that the application of a single injury function for a large set of species and plant functional types may not be sufficient to yield reliable estimates of large-scale damage estimates. Species interaction and competition, differing genotypes, and individuals ontogeny may further alter ozone impacts on plants and ecosystems . For instance, a modelling study using an individual-based forest model showed that ozone may not reduce the carbon sequestration capacity in forests if at the ecosystem level the reduced carbon fixation of ozone-sensitive species is compensated for by an increased carbon fixation of less ozone-sensitive species . First-generation dynamic global vegetation models such as O-CN do not simulate separate species but are based on plant functional types, which combine a large set of species. This restricts per se the ability of global models to simulate ozone-induced community dynamics and may therefore lead to overestimates of the net ozone impact if the parameterisation of the damage functions is entirely based on ozone-sensitive species. In our study, we have presented an approach to use the existing experimental evidence to parameterise a globally applicable model in a simple design to generate injury functions which are based on a relevant range of species rather than relying on species-specific injury functions as a first step towards a more reliable parameterisation of large-scale ozone damage.

Some studies have found that ozone-affected stomata respond much more slowly to environmental stimuli than unaffected cells , which can delay closure and trigger stomatal sluggishness, an uncoupling of stomatal conductance and photosynthesis and thus impact transpiration rates and the plant's water use efficiency . The O-CN model is able to directly impair stomatal conductance, by uncoupling injury to net photosynthesis from the subsequent injury to stomatal conductance. In this version of the O-CN model, both net photosynthesis and stomatal conductance can directly be injured by individual injury functions. The simulation of this kind of direct injury to stomatal conductance additional to the injury of net photosynthesis, both according to the injury functions by , have a negligible impact on biomass production compared to not accounting for direct injury to the stomata (results not shown). However, our above-mentioned concerns regarding the structure of the injury relationships by should be taken into account when considering this result.

A key challenge for the use of fumigation experiments to parameterise ozone injury in models is that trees (as opposed to grasses fumigated from seeds) typically possess a certain amount of biomass at the beginning of the fumigation experiment. Even at lethal ozone doses, the relative biomass thus cannot decline to zero, and tree death may occur at values of a relative biomass greater than zero. The relative biomass is positive even if carbon fixation is fully reduced and the plants survive due to the use of stored carbon. The higher the initial biomass and the slower the annual biomass growth rate of the tree is, the harder it is to obtain low values of RB. When comparing RB values obtained from trees with substantially different initial biomass and tree species with different growth rates, proportionate damage rates thus cannot be directly inferred. This indicates that the explanatory value of the relative biomass between a control and a treatment to estimate long-term plant damage at a given O3 concentration is limited. This is particularly the case when evaluating the damage of more mature forests. The simulated biomass dose–response relationships of adult trees are much more shallow than dose–response relationships of young trees (see Fig. ) because of the high initial biomass prior to fumigation. This suggests that the use of biomass injury functions derived from experiments with young trees to parameterise the biomass loss of adult trees, as done in , will likely lead to an overestimation of plant damage and loss of carbon storage. Dose–response relationships based on biomass increments or growth rates might be better transferable between young and mature trees and hence better suitable for parameterising global terrestrial biosphere models.

Our approach to overcome this challenge was to alter the vegetation model to simulate the ozone damage of young trees, where we could directly compare simulated biomass reductions to observations. Since we used injury relationships that are based on the calculation of leaf-level photosynthesis, we are able to apply the calibrated model also for mature stands. Our simulations have demonstrated that despite the different sizes of young and mature trees and associated changes in the wood growth rate and the available amount of non-structural carbon reserves to repair incurred injury, the simulated effect of ozone on the net annual biomass production (NPP) was very similar when using an injury function associated with leaf-level photosynthesis. Overall our findings support the idea that the photosynthesis-based injury relationships developed here and evaluated against fumigation experiments of young trees might be useful to estimate effect on forest production of older trees. Monitoring approaches of ozone damage that are either capable of measuring the actual increment of biomass or quantify at the leaf and canopy level the change in net photosynthesis over the growing season would allow us to develop injury/damage estimates that could be more readily translated into modelling frameworks.

The extrapolation of results from short-term experiments with young trees to estimate responses of adult trees grown under natural conditions is subject to several issues, e.g. due to the differing environmental conditions and changing ozone sensitivities with increasing tree size or age . It is still uncertain whether the simulation of injury to photosynthesis based on experiments with young trees can indeed be transferred to adult trees to yield realistic biomass damage estimates. The sparse knowledge of ozone effects on the biomass of adult forest trees prevents an evaluation of simulated ozone damage of adult trees. Ozone fumigation is mostly found to reduce the biomass or diameter of adult trees (e.g. for an overview), but this is not always the case . Results from phytotron and free-air fumigation studies suggest that in natural forests, a multitude of abiotic and biotic factors exist that have the potential to impact the plants ozone effects . If more data become available, e.g. regarding the changes in ozone sensitivity between young and mature trees, a more realistic damage parameterisation of mature forests in terrestrial biosphere models might become possible.

Terrestrial biosphere models in general assume that plant growth is primarily determined by carbon uptake. However, an alternative concept proposes that plant growth is more limited by direct environmental controls (temperature, water and nutrient availability) than by carbon uptake and photosynthesis . The O-CN model provides a first step into this direction because it separates the step of carbon acquisition from biomass production, both in terms of a non-structural carbon buffer as well as a stoichiometric nutrient limitation on growth independent of the current photosynthetic rate. This would in principle allow us to account for ozone effects on the carbon sink dynamics within plants. However, it is not clear that data readily exist to parameterise such effects. Instead of targeting net photosynthesis as done in our approach here, ozone injury might be better simulated by targeting biomass growth rates or processes that limit these, e.g. stomatal conductance, which impacts the plants' water balance, assuming that suitable data to parameterise a large-scale model become available.

All in all, a multitude of aspects that impact ozone damage to plants has not yet been incorporated into global terrestrial biosphere models. The ongoing discussion of which processes are major drivers for observed damage, how they interact and impact different species and plant types, and the lack of suitable data needed to parameterise a global model are reasons why the simulation of ozone damage has up to now focussed only on a few aspects where suitable data are available, as presented in our study.

The inclusion of previously published injury functions in the terrestrial biosphere model O-CN led to a strong over- or underestimation of simulated biomass damage compared to the biomass dose–response relationship by . Injury functions included in terrestrial biosphere models are a key aspect in the simulation of ozone damage and have a great impact on the estimated damage in large-scale ozone risk assessments. The calibration of injury functions performed in this study provides the advantage of calculating ozone injury close to where the actual physiological injury might occur (photosynthetic apparatus) and simultaneously reproduces observed biomass damage relationships for a range of European forest species used by . The calibration of ozone injury functions similar to our approach here in other ozone sub-models of terrestrial biosphere models might improve damage estimates compared to previously published injury functions and might lead to better estimates of terrestrial carbon sequestration. The comparison of simulated biomass dose–response relationships of young and mature trees shows strongly different slopes. This suggests that observed biomass damage relationships from young trees might not be suitable for estimating the biomass damage of mature trees. The comparison of simulated NPP dose–response relationships of young and mature trees shows similar slopes and suggests that they might more readily be transferred between trees differing in age.