Estimating global carbon uptake by lichens and bryophytes

Lichens and bryophytes are abundant globally and they may even form the dominant autotrophs in (sub)polar ecosystems, in deserts and at high altitudes. Moreover, they can be found in large amounts as epiphytes in old-growth forests. Here, we present the first process-based model which estimates the net carbon uptake by these organisms at the global scale, thus assessing their significance for biogeochemical cycles. The model uses gridded climate data and key properties of the habitat (e.g. disturbance intervals) to predict processes which control net carbon uptake, namely photosynthesis, respiration, water uptake and evaporation. It relies on equations used in many dynamical vegetation models, which are combined with concepts specific to lichens and bryophytes, such as poikilohydry or the effect of water content on CO 2 diffusivity. To incorporate the great functional variation of lichens and bryophytes at the global scale, the model parameters are characterised by broad ranges of possible values instead of a single, globally uniform value. The predicted terrestrial net uptake of 0.34 to 3.3 Gt yr −1 of carbon and global patterns of productivity are in accordance with empirically-derived estimates. Considering that the assimilated carbon can be invested in processes such as weathering or nitrogen fixation, lichens and bryophytes may play a significant role in biogeochemical cycles.


Introduction
Lichens and bryophytes are different from vascular plants: Lichens are no real plants, 20 but a symbiosis of a fungus and at least one green alga or cyanobacterium, whereas bryophytes, such as mosses or liverworts, are plants which have no specialised tissue such as roots or stems. Both groups are poikilohydrous, which means that they cannot actively control their water content because they do not have an effective epidermal tissue, a cuticle or stomata. Mainly due to their ability to tolerate dessication, combined global biogeochemical cycles has been examined only by a few studies. The work of Elbert et al. (2012), for instance, suggests a significant contribution of cryptogamic covers, which largely consist of lichens and bryophytes, to global cycles of carbon and nitrogen. They use a large amount of data from field experiments or lab measurements to estimate characteristic mean values of net carbon uptake and nitrogen fixation for 10 each of the world's biomes. By multiplying these mean values with the area of the respective biome they arrive at global numbers for uptake of carbon and nitrogen. While their estimate for global net carbon uptake amounts to 7 % of terrestrial net primary productivity (NPP), the derived value of nitrogen fixation corresponds to around 50 % of the terrestrial uptake, representing a large impact on the global nitrogen cycle. 15 Lichens and bryophytes may have also played an important role with respect to biogeochemical cycles in the geological past. From the early Paleozoic on, the predecessors of today's lichens and bryophytes have likely contributed to the enhancement of surface weathering rates (Lenton et al., 2012). The organisms accelerate chemical weathering reactions of the substrate by releasing organic acids, complexing agents, and bryophytes in the model. These properties depend on the location of growth, which is either the canopy or the ground, as well as the surrounding vegetation, which is described by a biome classification.

Model processes
In the following, we describe the physiological processes implemented in the model. 5 First, we name the effects of the living environment on lichens and bryophytes. Then, we explain how water content and climatic factors relate to physiological properties of the organism. Finally, we describe the exchange flows between the organism and its environment.
For simplicity, we will not present any equations. All equations used in the model can 10 be found in Appendix B and are explained there. The parameters associated with the equations are listed in Tables B7 to B13 in the Appendix.

Living environment
In the model, lichens and bryophytes can be located either in the canopy or on the ground. The location of growth is important for the radiation and precipitation regime 15 the organism is exposed to (see Fig. 2). Lichens and bryophytes living in the upper part of the canopy, for example, may receive more shortwave radiation than those living beneath the canopy. Additionally, the location of growth determines the available area for growth. The available area in the canopy is assumed to be the sum of Leaf Area Index (LAI) and Stem Area Index (SAI). The available area on the ground depends on Introduction control water loss, evaporation is not affected by the activity status of the organism. Water uptake takes place via the thallus surface. Where water input exceeds maximum storage capacity, surplus water is redirected to runoff. The water balance of the lichen or bryophyte is thus determined by evaporation and water uptake.

Model parameters 5
The equations that describe physiological processes in the model are parameterised and the parameters can be subdivided into two categories: properties of lichens and bryophytes and characteristics of the environment of the organisms. Since lichens and bryophytes have a large functional variation, the parameters that represent their properties, such as specific area or photosynthetic capacity, are characterised by large ranges of possible values. To incorporate the functional variation of lichens and bryophytes into the model, many physiological strategies are generated by randomly sampling the ranges of possible parameter values. We call these parameterisations "strategies" and not "species", because they do not correspond exactly to any species that can be found in nature. Nevertheless, these strategies are assumed to represent the physiological 15 properties of real lichen and bryophyte species in a realistic way. Hence, the functional variation of the organisms can be simulated without knowing the exact details of each species. The model is then run with all strategies, but not every strategy is able to maintain a positive biomass in each grid cell, which is necessary to survive. The results are com-20 puted by averaging only over the surviving strategies of each grid cell. Thus, climate is used as a filter to narrow the ranges of possible parameter values in each grid cell and therefore to make the results more accurate (see Fig. 4).
The studies of Bloom et al. (1985) and Hall et al. (1992) analyse from a theoretical perspective the relations between the "strategy" of an organism and the success of this 25 organism regarding natural selection in a certain environment. Follows and Dutkiewicz (2011) apply this approach to marine ecosystems while Kleidon and Mooney (2000) use it to predict biodiversity patterns of terrestrial vegetation. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | method to modelling biogeochemical fluxes of terrestrial vegetation has been successfully demonstrated by the JeDi-DGVM (Pavlick et al., 2012). The 15 model parameters which are included in the random sampling method are listed in Table B9 in the appendix. They represent structural properties of the thallus of a lichen or bryophyte, such as specific area or water storage capacity. They also describe 5 implications of the thallus structure, such as the relation between water content and water potential. Furthermore characteristics of the metabolism are considered, such as optimum temperature. Also parameters which have categorical values are used: a lichen or bryophyte can either live in the canopy or at the soil surface (see Sect. 2.1.1). Another categorical parameter determines if the organism has a carbon concentration mechanism (CCM) or not. Although regulation of the CCM has been observed (Miura et al., 2002), the model contains a fixed representation of the CCM for simplicity. Some of the 15 parameters mentioned above are related to further lichen or bryophyte parameters. The respiration rate at a certain temperature, for instance, is assumed to be related to Rubisco content and turnover rate. Hence, the parameters 15 "Rubisco content" and "turnover rate" are not sampled from ranges of possible values, but determined by the value of the parameter "respiration rate". The reason for this relationship is an underlying physiological constraint, in this case, maintenance costs of enzymes. A lichen or bryophyte with a high concentration of Rubisco, for example, has to maintain these enzymes and therefore also shows a high respiration rate and a high 20 turnover rate. These relationships are called tradeoffs. The parameters which describe the tradeoffs are assumed to have constant values.
Six tradeoffs are implemented in the model. The first tradeoff describes the relation between Rubisco content, respiration rate and turnover rate explained above. The second tradeoff relates the diffusivity for CO 2 to the metabolic activity of the lichen or 25 bryophyte via its water content. This means that a high diffusivity is associated with a low water content which results in a low activity. The third tradeoff describes the positive correlation between the maximum electron transport rate of the photosystems (J max ) and the maximum carboxylation rate (V C, max  Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | organism and photosynthesis is the minimum of the two, it would be inefficient if they were independent from each other. The fourth tradeoff is associated with the carbon concentration mechanism (CCM). In case a lichen or bryophyte possesses a CCM, a part of the energy acquired by the photosystems is not used to fix CO 2 , but to increase the CO 2 concentration in the photobionts. If the organism is limited by low CO 2 or high 5 photorespiration but enough light is available, a CCM can lead to higher productivity. The fifth and sixth tradeoffs concern the Michaelis-Menten constants of the carboxylation and oxygenation reactions of Rubisco. They relate these constants to the molar carboxylation and oxygenation rates of Rubisco. One tradeoff is usually associated with more than one parameter. The model parameters that describe tradeoffs are listed in 10   Table B10. The model contains several additional lichen or bryophyte parameters which are not directly associated with tradeoffs, but which represent physiological or physical constraints. Therefore, they are assumed to have constant values. They can be found in Table B11. 15 In addition to the parameters that describe properties of the lichens and bryophytes, the model contains parameters that represent environmental conditions. They describe the extinction of light as a function of LAI, the interception efficiency for precipitation of the canopy, characteristics of the snow cover, thermal properties of the upper soil layer, roughness of the surface regarding wind and the time intervals for disturbance Introduction

Simulation setup
The model runs on a global rectangular grid with a resolution of 2.8125 degrees (T42), hence all input data are remapped to this resolution. The land mask and the climate forcing are taken from the WATCH data set (Weedon et al., 2011). This data set comprises shortwave radiation, downwelling longwave radiation, rainfall, snowfall, air temperature at 2 m height, wind speed at 10 m height, surface pressure and specific humidity. The latter two variables are used to compute relative humidity. The temporal resolution of the data is 3 h and the years 1958 to 2001 are used. Since the model runs on an hourly time step, the data is interpolated. In addition to the climate forcing, the model uses maps of LAI and SAI in a monthly resolution and a temporally constant 10 map of bare soil area, which are taken from the Community Land Model (Bonan et al., 2002). They are used to provide estimates for the available area for growth and the light environment. A biome map which is taken from Olson et al. (2001) is used to represent disturbance by assigning characteristic disturbance intervals to each biome (see Table B3). Furthermore, surface roughness is determined as a function of the biome. 15 The model provides output for each surviving strategy in a grid cell independently. Hence, to obtain an average output value for a certain grid cell the different strategies have to be weighted. Since ecological interactions between species are not considered in the model, it is not possible to determine the relative abundance and thus the weight of each strategy. Therefore, the uncertainty due to the unknown weights of the 20 strategies has to be included into the results. As lower bound for net carbon uptake in a certain grid cell we assume that all strategies are equally abundant and the estimate thus corresponds to equal weights for all surviving strategies. This weighting method is called "average". Since strategies that do not grow much are probably not as abundant as strongly growing strategies, the true net carbon uptake is probably underestimated Introduction species would have to be very strong to reduce diversity to such an extent. The upper and lower bounds derived from the two weighting methods are then used for the evaluation of the model. The model is evaluated by comparing model estimates to observational data on a biome basis. Hence, data from several field study sites located in a certain biome are 5 compared to the simulated net carbon uptake averaged over all grid cells of this biome. Only studies which report estimates of net carbon uptake based on surface coverage of lichens or bryophytes are used for evaluating the model. This facilitates a direct comparison of model estimates and observations. The estimates from these studies show a large variability, even for the same site they differ by more than an order of 10 magnitude. Moreover, the number of studies is quite limited. Only 4 out of 14 biomes are represented in the field studies: Tundra, boreal forest, desert and tropical rainforest. For both forest biomes only one study site is available, respectively, making reliable estimates of net carbon uptake difficult. Nevertheless, we think that the data from the field studies is suitable to give a rough idea of the mean net carbon uptake in a certain 15 biome.
The model is run for 2000 yr with an initial number of 3000 strategies. The simulation length of 2000 yr is sufficient to reach a dynamic steady state regarding the carbon balance of every strategy, which also implies that the number of surviving strategies has reached a constant value. Furthermore, the initial strategy number of 3000 is high Introduction average numbers. Additionally, further properties of lichens and bryophytes estimated by the model are presented to illustrate the large range of possible predictions. To assess the quality of the predictions, the model estimates are compared to observational data. Since this study is the first process-based approach to quantify the productivity of lichens and bryophytes at the global scale, comparison of the results with other mod-5 els is not possible. To estimate the effect of uncertain model parameter values on the predictions of the model, a sensitivity analysis is performed.

Modelled net carbon uptake
The global estimate of net carbon uptake by lichens and bryophytes amounts to 0.34 (Gt C) yr −1 for the "average" weighting method and 3.3 (Gt C) yr −1 for the "maxi-10 mum" weighting method (for a description of the weighting methods see Sect. 2.3). The global biomass is 4.0 (Gt C) (average) and 46 (Gt C) (maximum), respectively. Note that we use a capital "C" to abbreviate carbon throughout the manuscript. To avoid confusion with unit symbols, we put C and the associated unit in brackets. We show maps of the global net carbon uptake by lichens and bryophytes, biomass, 15 surface coverage, number of surviving strategies and two characteristic parameters, the optimum temperature of gross photosynthesis and the fraction of organisms with a Carbon Concentration Mechanism (CCM). These maps are created from time averages over the last 100 yr of the simulation described in Sect. 2.3. The maps are based on the "average" weighting method. The "maximum" weighting shows very similar patterns 20 and the corresponding maps are shown in Fig. A1a to d. The net carbon uptake by lichens and bryophytes is shown in Fig. 5a. In some areas, such as Greenland and the driest parts of deserts, no strategy is able to survive and net carbon uptake is equal to zero there. The biomes differ largely with respect to carbon uptake. While dry areas are characterised by the lowest productivity, the highest values 25 are reached in forested areas. In the tropical rainforest the high productivity is mainly due to the high carbon uptake by epiphytic lichens and bryophytes (see Fig. 5c). In the boreal zone, lichens and bryophytes in the canopy as well as on the ground contribute 3749 Introduction significantly to carbon uptake (see Fig. 5d). Biomass (Fig. 5b) exhibits a global pattern similar to carbon uptake. At high latitudes, however, the ratio of biomass to carbon uptake seems to be slightly higher than in the tropics. Figure 6a shows the global absolute cover of lichens and bryophytes in m 2 projected surface area of the organisms per m 2 ground. Since the available area can be higher 5 than one in the canopy, high values of absolute cover do not necessarily mean high fractional cover. On the contrary, the fractional cover is highest in regions with low absolute cover, especially grasslands and agricultural areas, since the available area in these regions is very small. A map of fractional cover is shown in Fig. A2. Figure 6b shows the number of surviving strategies at the end of the simulation. The global pat-10 tern is slightly different from the pattern of carbon uptake. Although forested regions show the highest number of strategies, the high latitudes are richer in strategies than the tropics. Figure 6c and 6d shows the global patterns of two characteristic lichen and bryophyte parameters. As described in Sect. 2.2 these parameters are sampled randomly from 15 ranges of possible values to create many artificial strategies. Thus, at the start of a simulation possible values from the range of a certain parameter are present in equal measure in each grid cell. During the simulation, however, parameter values from certain parts of the range might turn out to be disadvantageous in a certain climate and the corresponding strategies might die out. This leads to a narrowing of the range 20 and consequently to global patterns of characteristic parameters. These patterns reflect the influence of climate on properties of surviving strategies. Figure 6c shows the optimum temperature of gross photosynthesis of lichens and bryophytes living on the ground. The optimum temperature shows a latitudinal pattern, with high values in the tropics and low values towards the poles or at high altitudes. In Fig. 6d the fraction of 25 organisms on the ground is shown which have a Carbon Concentration Mechanism (CCM). Also this parameter is characterised by a latitudinal pattern. The fraction of organisms with a CCM is almost one in the tropics, while it is approximately 0.5 in polar regions. Lichens and bryophytes living in the canopy exhibit global patterns of optimum temperature and CCM fraction similar to those living on the ground. The corresponding maps are shown in Fig. A2. Figure 7 shows a comparison between model estimates and observational data with regard to net carbon uptake for 4 biomes. Considering the order of magnitude and 5 the large scale patterns of net carbon uptake, the model results agree well with the observations. There are, however, large uncertainties due to variability in the data, the difference between "average" and "maximum" estimate and the climatic differences between the grid cells of a certain biome. Furthermore, there a too few data points to make any definitive statements. More detailed comparisons between modelled and observed carbon uptake, however, are beyond the scope of this study (as discussed in Sect. 4). The field studies corresponding to the data points in Fig. 7 are listed in Table 1.

Sensitivity analysis
As described in Sect. 2.2 model parameters that describe tradeoffs, physiological con-15 straints or environmental properties are assumed to have constant values. Some of these parameter values have already been estimated in other studies and thus they can be taken directly from the literature. Others, however, have yet to be determined. A reliable estimate of these unknown parameter values would require a considerable amount of experimental data, which is beyond the scope of this study. Therefore, the 20 parameter values were derived by "educated guess" using the available information from the literature (see Appendix B). To assess the impact of these parameter values on the model result we perform a sensitivity analysis (see Table 2). Note that some of the parameters tested in the sensitivity analysis are aggregated into a single process. For a detailed overview of the parameters see Tables B8 and B10 In general, the model is not very sensitive to the parameter values which applies both for the "average" and "maximum" weighting methods. Regarding the environmental parameters a change by 50 % leads to a 10 % or less change in the modelled net carbon uptake in most cases. Only disturbance interval and rain interception efficiency have a slightly larger influence. The parameters that describe tradeoffs have a larger impact.

5
Changing the relation of water content to diffusivity for CO 2 by 50 %, for instance, leads to a change in "average" net carbon uptake by almost 50 %. The effect of the respiratory costs associated with Rubisco content is similarly strong. The climate forcing has only a moderate influence on the simulated net carbon uptake. Note that the variation in climate forcing is only 20 % compared to 50 % for the parameters. This is done to 10 avoid generating unrealistic climatic regimes.
The turnover parameter affects "maximum" and "average" net carbon uptake in opposite ways. Moreover, the effects of the parameters J max /V C, max , light extinction and surface roughness on carbon uptake are not straightforward to explain. These points are discussed in Sect. 4. For reasons of computation time we used a different simula- 15 tion setup (400 yr, 300 strategies) for the sensitivity analysis. Therefore, the net carbon uptake values for the control run (Table 2) differ from the ones presented above. The pattern of productivity, however, is very similar to those of the longer run with more strategies (see Fig. A2). We thus assume that the sensitivity of the model does not change significantly with increased simulation time and number of initial strategies.

Discussion
In this study we estimate global net carbon uptake by lichens and bryophytes using a process-based model. In the following, we discuss the plausibility of the model estimates with respect to the patterns and the absolute values. Furthermore, we give an overview of the limits regarding the accuracy of the predictions as well as the certainty 25 of parameter values. The model predicts plausible patterns of productivity and biomass (see Fig. 5) as well as cover, number of surviving strategies and characteristic parameters (see Fig. 6). The productivity of lichens and bryophytes in deserts seems to be generally limited by low water supply while forested areas are characterised by high values of productivity. The vertical pattern of productivity in tropical forests is different from the one in boreal 5 forests and it probably can be attributed to forest structure and temperature: The boreal forests have a relatively open canopy with large, sunlit areas in between that allow for lichen or bryophyte growth. Since this is not the case in the dense tropical lowland forests carbon uptake on the ground is lower than in the boreal zone. Furthermore, in the moist lowland forest, high temperatures at night together with high humidity near 10 the soil surface cause high respiratory losses for lichens and bryophytes and therefore constrain their growth (Nash III, 1996). This is also reflected in the ratio of biomass to carbon uptake, which is slightly lower in the tropics than at high latitudes. Tropical cloud forests, however, which also exist in the lowland (Gradstein, 2006), may facilitate high productivity of lichens and bryophytes near the ground. The spatial resolution of 15 the climate data and the biome map, however, is not high enough to represent these ecosystems. Hence, at a large spatial scale, the climate of the high latitudes seems to be more favourable for a large range of lichen and bryophyte growth strategies than the tropical climate, which is also illustrated by the higher number of strategies of the boreal forest zone compared to the tropical one. Nevertheless, the potential for productivity 20 seems to be highest in the moist tropics, although survival in this region is more difficult.
The surface coverage shows a plausible range of values. In deserts, it is in the order of 10 % or lower and in (sub)polar regions, it is around 30 %, which seems realistic. In forested regions, it ranges from 40 to 65 %, which is plausible since the available area is larger than 1 m 2 per m 2 ground for lichens and bryophytes living in the canopy.

25
The latitudinal pattern of the optimum temperature of gross photosynthesis is realistic, since the mean climate in the tropics is warmer than in polar regions or at high altitudes. The fact that the edges of the parameter range are not represented in the map can be explained as follows: extreme climatic conditions, which could be associated with extreme values of the optimum temperature of gross photosynthesis, often do not persist for long time periods. Lichens and bryophytes are usually inactive during these periods and are therefore not affected by them. Extreme temperatures that last for longer periods of time are probably only present at the microclimatic scale and are therefore absent from the grid cell climate. Same as optimum temperature, also the lat-5 itudinal pattern of the fraction of organisms with a CCM makes sense. A CCM is useful in situations where CO 2 is limited, either due to low supply from the atmosphere or due to high photorespiration. These conditions are met in the tropics. The moist climate in the rainforest generally leads to high water content of the thallus, which results in a low diffusivity for CO 2 . Additionally, the high temperatures in the tropics result in high photorespiration, further reducing the available CO 2 in the pore space. Although the global pattern is plausible, the fraction of lichens and bryophytes with a CCM seems to be generally too high. The reason for this could be that the metabolic costs of a CCM are underestimated in the model. As mentioned in Sect. 3.3, the parameters describing the costs of the CCM are not very well known. Although the global patterns of 15 optimum temperature and CCM probably cannot be evaluated on a quantitative basis, these patterns help to assess qualitatively the plausibility of the model results.
The model results are in good agreement with observational data (see Fig. 7). There are, however, relatively large uncertainties associated with this comparison, mainly due to the large variability in the observational data. One reason for this variability in 20 productivity might be differences in microclimate at the study sites. These differences can be considerable, although the sites belong to the same large-scale mean climate. Another reason for the variability in the observations might be the effect of biodiversity on net carbon uptake. While one site might be dominated by a species that is very well adapted to the local climate and thus exhibits a high productivity, another Introduction productivity between the grid cells with the most and the least favourable climate of a certain biome is substantial. Another source of uncertainty is the spatial resolution of the model. Even if the number of field studies was high enough to reliably estimate a mean productivity for each biome, comparing the study sites to the model grid cells is not straightforward. Due 5 to the much larger spatial scale, the climate of a grid cell represents a mean state of the local climates that can be found in the cell. Hence, the climatic variability derived from the grid cells belonging to a certain biome might be smaller than the corresponding microclimatic variability in this biome. Depending on the degree of nonlinearity in the relation between climate and net carbon uptake, an estimate of mean net carbon uptake based on the climate of grid cells might be biased compared to the mean of the observed values. Since the relation between climate and net carbon uptake is a complex function of many variables, quantifying its nonlinearity is difficult. Reducing the spatial resolution of the model down to the microclimatic scale, however, is virtually impossible. While the limited amount of observational data and the coarse spatial 15 resolution of the model are issues that cannot be resolved easily, a significant improvement in the accuracy of the model predictions could be achieved by quantifying the abundance of the strategies as described in Sect. 2.3. By implementing a scheme that simulates competition between lichen or bryophyte strategies, the large difference between the "average" and the "maximum" estimate ( Fig. 7) could be reduced. Such a 20 scheme would be a promising perspective for extending the model.
Considering the sensitivity analysis, the general behaviour of the model is plausible. Increasing the Rubisco content per base respiration rate, for example, leads to an increase in net carbon uptake and vice versa (see Table 2). Some effects, however, require further explanation: Introduction content, but we found only one study that quantified the diffusivity for CO 2 as a function of water content. The latter, however, is much more useful for modelling CO 2 diffusion through the thallus on a process basis. Hence, accumulating more empirical data that is suitable to determine the values of the parameters that describe tradeoffs with higher accuracy would be a very efficient way to improve the model. One example of a such 5 a study is the work of Wullschleger (1993) which analyses the ratio between J max and V C, max . For a large number of vascular plants this ratio is approximately 2. The reason for this constant ratio is the fact, that a high J max is not useful if the V C, max is low and vice versa, since productivity is the minimum of the two rates. As both rates are associated with metabolic costs, a tradeoff emerges.
To summarise, the model is able to produce realistic global patterns of net carbon uptake by lichens and bryophytes. The uncertainty concerning the absolute value of carbon uptake is relatively high, but the observational data available to evaluate the model also show large variability. Given that this study is supposed to be a first order estimate of global lichen and bryophyte productivity, the outcomes are satisfying. Re- 15 garding possible improvements of the model it would be useful to implement competition between the strategies. In this way, the uncertainty due to the unknown abundance of the strategies could be eliminated. Furthermore, it would be beneficial if values of model parameters that describe tradeoffs could be determined more accurately. 20 In this paper, we present the first process-based model of global net carbon uptake by lichens and bryophytes. The model explicitly simulates processes such as photosynthesis and respiration to quantify exchange flows of carbon between organisms and environment. The predicted global net carbon uptake of 0.34 to 3.3 (Gt C) yr −1 has a realistic order of magnitude compared to empirical studies (Elbert et al., 2012). The values of productivity correspond to approximately 1 to 6 % of the global terrestrial Net Primary Productivity (NPP) (Ito, 2011). Furthermore, the model represents the large Introduction functional variation of lichens and bryophytes by simulating many different physiological strategies. The performance of these strategies under different climatic regimes is used to narrow the range of possible values of productivity. This method is an efficient way to incorporate the effects of biodiversity on productivity into a vegetation model (Pavlick et al., 2012). The predicted global patterns of surviving strategies are plausi-5 ble from a qualitative perspective. To further reduce the number of possible values for productivity, competition between the different strategies could be implemented. This would also make the representation of functional variation of lichens and bryophytes in the model more realistic. The uptake of carbon is only one of many global biogeochemical processes where 10 lichens and bryophytes are involved. They probably also play an important role in the global nitrogen cycle due to the ability of some lichens to fix nitrogen (around 50 % of terrestrial uptake) (Elbert et al., 2012). The fixation of nitrogen, however, is relatively expensive from a metabolic viewpoint. It would be interesting to quantify the costs of this process at the global scale and its relation to nutrient limitation. 15 While nitrogen can be acquired from the atmosphere, phosphorus usually has to be released from rocks by weathering. Thus, lichens and bryophytes might increase their access to phosphorus or other important nutrients by enhancing weathering rates at the surface through exudation of organic acids and complexing agents. Since weathering rates control atmospheric CO 2 concentration on geological time scales, lichens and 20 bryophytes might have influenced global climate considerably throughout the history of the earth (Lenton et al., 2012).

Conclusions and outlook
Lichens and bryophytes have to invest carbon in order to fuel nitrogen fixating enzymes or produce organic acids necessary for weathering. Hence, these investments could be implemented as a cost function into the model, making it possible to quantify 25 the associated processes at the global scale. Quantifying the carbon budget of lichens and bryophytes can thus be seen as a first step towards estimating the impact of these organisms on other biogeochemical cycles. values and the units of the parameters and variables used in the model equations are tabulated in Sects. "Model parameters" and "Model variables" (see Tables B6 to B15). The tables contain references to the respective equations. To make the equations more easily readable, characteristic prefixes are added to the model parameters and the associated tables are structured accordingly. The prefixes, the type of parameter and the 15 associated table(s) can be found in Table B1. For further details on the implementation of parameters and equations in the model we refer to the source code of the model which is available on request (pporad@bgcjena.mpg.de). 20 To account for the large functional variability of lichens and bryophytes, many strategies are generated in the model which differ from each other in 15 characteristic parameters (see Sect. 2.2). To create the strategies, these 15 characteristic parameters are assigned through randomly sampling ranges of possible values. The parameters and 3759 Introduction

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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | the corresponding ranges are listed in Table B9. Assignment of parameter values is performed in two steps: (a) for each strategy, a set of 15 random numbers uniformly distributed between 0 and 1 is sampled. The random numbers are generated by a Latin Hypercube algorithm (McKay et al., 1979). This facilitates an even sampling of the 15-dimensional space of random numbers, since the space is partitioned into equal subvolumes from which the random numbers are then sampled. (b) The 15 random numbers are mapped to values from the ranges of the parameters. Since the purpose of the sampling is to represent the whole range of a parameter as evenly as possible, two different mapping methods are used, a linear one for parameters that have only a small range of possible values, and an exponential one for parameters that span more 10 than one order of magnitude. If the possible values of a parameter x span a relatively small range, a random number between 0 and 1 is linearly mapped to this range according to: where N is a random number between 0 and 1. x max and x min are the maximum and 15 the minimum value from the range of possible values for the parameter x. To ensure that the ranges are sufficiently broad, more extreme values than those found in the literature are used as limits. For this purpose, the mean of the literature based parameter values is computed. x min is then calculated by subtracting the distance between the mean and the lowest value found in the literature from this lowest value. x max is 20 calculated by adding the distance between mean and highest value found in the literature to this highest value. A precondition for this procedure is that the parameter values span a relatively small range, as mentioned above. Otherwise, subtracting the above mentioned distance from the mean would result in negative values. If the possible values of a parameter span a large range, the mapping from a random 25 number between 0 and 1 to this range is exponential and written as: where the symbols have the same meaning as in Eq. (B1). The exponential function is used to represent each order of magnitude of the range equally. If the limits of the range were 1 and 10 000, for instance, using Eq. (B1) would result in 90 % of the values lying between 1000 and 10 000. Hence, values from the range 1 to 1000 would be strongly underrepresented. By using Eq. (B2) this problem is avoided, which is 5 particularly important if the model is run with low numbers of strategies. In this case, the underrepresentation of strategies with parameter values from the lower end of the range could lead to unrealistic model results. To be consistent with the exponential mapping, the limits of the range are also calculated differently than for Eq. (B1): x min is assumed to be half the lowest value found in the literature, while x max is set to the 10 double of the highest value found in the literature. Additionally random numbers can be transformed into categorical values. This is done by assigning a lichen or bryophyte to a certain category if the corresponding random number is below a threshold, and otherwise to another category. The threshold is a number between 0 and 1. 15 In the following, each of the 15 strategy parameters is shortly described together with references for the range of possible values.

B1.1 Albedo
The albedo x α of a lichen or bryophyte is assumed to vary from 0 to 1. The reason for this assumption is that lichens and bryophytes show a large variety of colors and 20 therefore a large range of possible values for the albedo (Kershaw, 1975). For simplicity, each strategy has a fixed value of x α . In reality, species can adapt their albedo to different environmental conditions. This can be represented in the model by strategies differing only in the value of x α .
A linear mapping is used for the parameter range since we found no reason to as-25 sume a priori that a certain value of the albedo is more frequent than the others.

B1.2 Specific water storage capacity
The specific water storage capacity x Θ max represents the maximum amount of water per gram carbon a lichen or bryophyte can store (Fig. B1). An exponential mapping is used for the range of possible values.

5
The specific projected area x A spec represents the surface area per gram carbon of a lichen or bryophyte projected onto a plane (Fig. B2). An exponential mapping is used for the range of possible values.

B1.4 Location of growth
The location of growth x loc of a lichen or bryophyte is a categorical variable. Two cat-10 egories are possible: canopy and ground. Since no data could be found about the relative abundance of lichens and bryophytes living in the canopy and the ones living on the ground, the probability for each location of growth is 50 %.

B1.5 Threshold saturation and shape of water potential curve
As described in Sect. 2.1.2 the water potential Ψ H 2 O is an increasing function of the 15 water saturation of the thallus, Φ Θ , which is described below in Sect. B3.1. Ψ H 2 O has a value of −∞ at zero water content and reaches a maximum value of 0 at a certain threshold saturation (see Fig. B3). This threshold saturation represents the partitioning between water stored in the cells of the thallus and extracellular water. It is described by the parameter x Φ Θ, sat . The theoretical limits of x Φ Θ, sat are 0 and 1, where 0 would mean 20 that the lichen or bryophyte stores all its water extracellularly and 1 would mean that no extracellular storage capacity exists. A lower limit of 0 is physiologically unrealistic. Some mosses have, however, a relatively large capacity to store water extracellularly (Proctor, 2000). Hence, the lower limit of x Φ Θ, sat is set to 0.3. An upper limit of 1.0 seems 3762 Introduction

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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | realistic, since significant amounts of extracellular water do not seem to occur in many lichens under natural conditions (Nash III, 1996, p. 161). Due to the small range of possible values for x Φ Θ,sat a linear mapping is used for this parameter. A second parameter, x Ψ H 2 O , determines the shape of the water potential curve from zero water content to the threshold saturation. Given a certain value of x Φ Θ, sat , the 5 parameter x Ψ H 2 O controls the water content of the thallus in equilibrium with a certain atmospheric vapour pressure deficit. Since the range of possible values of x Ψ H 2 O is quite limited a linear mapping is used. The limits for this range are estimated using the data points in Fig. B3 and are set to 5.0 and 25.0, respectively. The calculation of the water potential Ψ H 2 O is given below in Sect. B3.3. 10 Furthermore, the relation between water content and water potential influences the tradeoff between CO 2 diffusivity and metabolic activity. This is explained in detail below in Sect. B3.5.

B1.6 Molar carboxylation rate of Rubisco
The molar carboxylation rate of Rubisco x V C, max represents the maximum carboxylation 15 velocity of a Rubisco molecule (Fig. B4). The data are taken from a study that analyses a broad range of photoautotrophs. An exponential mapping is used for the range of possible values.

B1.7 Molar oxygenation rate of Rubisco
The molar oxygenation rate of Rubisco x V O, max represents the maximum oxygenation 20 velocity of a Rubisco molecule (Fig. B5). The data are taken from a study that analyses a broad range of photoautotrophs. A linear mapping is used for the range of possible values. 10,2013 Estimating global carbon uptake by lichens and bryophytes P. Porada et al.

B1.8 Reference maintenance respiration rate and Q 10 value of respiration
The specific respiration rate of lichens and bryophytes, R spec , is controlled by two parameters: the reference respiration rate at 10 • C, x R ref , and the Q 10 value of respiration, x Q 10 . The distributions of these parameters are shown in Figs. B6 and B7. For x R ref an exponential mapping is used while for x Q 10 a linear mapping is used. The limits of 5 x Q 10 are not calculated by the method described for Eq. (B1), since the resulting range would be physiologically unrealistic. Instead, the values were rounded to the nearest integer. The influences of the two parameters on respiration rate are shown in Fig. B8. Moreover, the respiration rate is related to Rubisco content and turnover rate of the thallus, as described in Sect. 2.2. The details of these relationships are explained below in Sects. B5.2 and B5.6.

B1.9 Optimum temperature of photosynthesis
The optimum temperature of photosynthesis x T opt, PS represents the temperature at which gross photosynthesis shows a maximum (Fig. B9). A linear mapping is used for the range of possible values. The range is not calculated by the method described 15 for Eq. (B1) since the resulting values would be physiologically unrealistic. Instead, the limits derived from the data were extended by 10 and 5 Kelvin, respectively.

B1.10 Enzyme activation energy of K C and K O
K C and K O are the Michaelis-Menten constants of the carboxylation and oxygenation reactions of Rubisco. The enzyme activation energies x E a , K C and x E a , K O control the 20 temperature response of K C and K O . The available data (see Table B2) are not sufficient to estimate the shapes of the ranges of x E a , K C and x E a , K O . We assume that the parameters do not span several orders of magnitude and hence apply a linear mapping. The limits of the parameter ranges are calculated according to the method described for Eq. (B1). Introduction

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B1.11 Carbon Concentration Mechanism (CCM)
The parameter x CCM is a categorical variable. It controls if a lichen or bryophyte possesses a Carbon Concentration Mechanism (CCM) or not. If a CCM is present, a part of the energy acquired by the photosystems is not used to fix CO 2 , but to increase the CO 2 concentration in the photobionts. Since no data could be found about the rela-5 tive abundance of lichens and bryophytes with and without a CCM, the probability to possess a CCM is set to 50 %.

B1.12 Fraction of carbon allocated to growth
The parameter x alloc represents the fraction of the sugar reservoir that is allocated to growth each day. x alloc therefore describes the partitioning of assimilated carbon 10 between storage pools and biomass. Since we found no reason for a fixed value of x alloc for all strategies, the possible values are assumed to range from 0 to 1 and a linear mapping is used.

B2 Living environment
The location of growth of a lichen or bryophyte strongly influences its radiation and 15 precipitation regime and the available area for growth (Sect. 2.1.1). The equations describing these influences are listed and explained below in Sects. B2.1 and B2.2. Further environmental effects on lichens and bryophytes depend not only on the location of growth but also on the biome. These are disturbance frequency, aerodynamic resistance to heat transfer and soil thermal properties as well as ground heat flux. The 20 equations related to these effects can be found below in Sects. B2.3 to B2.5.

B2.1 Radiation and precipitation regime
Radiation and precipitation flows are partitioned between the canopy and the ground. This partitioning is described by factors which represent the fraction of the flow that 3765 Introduction reaches the surface of a lichen or bryophyte. For the partitioning of radiation, Beer's law is used (Bonan, 2008, p. 254) and the associated factors for shortwave radiation φ rad S and longwave radiation φ rad L are calculated by: where x α is the albedo of a lichen or bryophyte for shortwave radiation and p is the emissivity of an organism for longwave radiation. p λ, s and p λ, l are extinction coefficients for short-wave radiation (Bonan, 2008, p. 254) and longwave radiation (Kustas and Norman, 2000), respectively. A LAI and A SAI are Leaf Area Index (LAI) and Stem Area 10 Index (SAI). The partitioning of precipitation is assumed to be a linearly decreasing function of LAI and the fraction of precipitation that reaches a lichen or bryophyte is: where p η rain is the interception efficiency of the canopy for precipitation, A LAI is Leaf 15 Area Index and p LAI max is the maximum LAI in the data set, both derived from Bonan et al. (2002).

B2.2 Available area
The available area for growth of a lichen or bryophyte per m 2 ground depends on its location of growth, which is either the ground or the canopy (see Sect. 2.1.1). The 20 BGD 10,2013 Estimating global carbon uptake by lichens and bryophytes P. Porada et al. available area on the ground, A ground, max , is determined by two factors: (a) the amount of bare soil, which means soil surface that is not occupied by herbaceous vegetation, such as grasses or crops. Bare soil area is highest in non-vegetated areas such as deserts or mountain tops, but also in forested areas, since the ground is not per se occupied there. For simplicity, the area occupied by tree trunks is neglected. (b) Leaf Area Index (LAI), which affects the available area on ground through leaf fall by trees: under dense canopies (high LAI), a constantly renewed litter layer impedes the growth of lichens and bryophytes. Under open canopies (low LAI), a certain fraction of the soil surface is not affected by leaf fall, thus providing area for growth. The available area on the ground is calculated according to: where A baresoil is the area of soil not occupied by herbaceous vegetation derived from Bonan et al. (2002). A LAI is Leaf Area Index and p LAI max is the maximum LAI in the data set.
The available area in the canopy, A canopy, max is assumed to be the sum of LAI and 15 Stem Area Index (SAI). This means that the strategies are assumed to grow on all parts of the canopy, which means stems (i.e. trunks and twigs) and leaves. Growth on leaves, however, is assumed to be possible only for evergreen vegetation (see Sect. B2.3 for details). Thus the available area for growth is written as: where A SAI is SAI. The surface area of a lichen or bryophyte per m 2 ground, A thallus , is calculated according to: where x A spec is the specific area of a lichen or bryophyte, s B is the biomass per m 2 ground and A canopy, max and A ground, max are the available area in the canopy and on the ground, respectively. This means that A thallus is limited by the available area. Since biomass is related to surface area via the specific area, also biomass is limited by available area.

5
The fraction of available area that is covered by a lichen or bryophyte is described by the variable Φ area . This variable is necessary to obtain flows per m 2 ground instead of m 2 lichen or bryophyte. If the respiration flow per m 2 thallus is known, for instance, multiplication by Φ area gives the respiration flow per m 2 ground. This is important because the purpose of the model is to predict global flows of carbon and water per m 2 10 ground. Φ area is calculated according to: where A thallus is the surface area of a lichen or bryophyte and A canopy, max is the available area in the canopy. The maximum function is used in Eq. (B9) to ensure that the reference for the exchange flows is a m 2 ground, not a m 2 of lichen or bryophyte. If, for 15 example, the available area in the canopy was 0.8 m 2 per m 2 ground and the thallus area was 0.6 m 2 per m 2 ground, the exchange flows per m 2 ground should be multiplied by a Φ area of 0.6, and not by 0.6/0.8.

B2.3 Disturbance interval
The disturbance interval τ veg is assigned according to biome and location of growth 20 (see Table B3). Disturbance leads to an instantaneous loss of biomass. The following processes are represented in the model: Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 1. Fire or treefall. In this case the biomass of a strategy is set back to the initial value each time a disturbance takes place. Fire and treefall are assumed to affect both strategies living on the ground as well as those living in the canopy.
2. Leaf fall, which affects only strategies living in the canopy. As described in Sect. B2.2, strategies in the canopy are assumed to live on trunks and twigs as 5 well as on leaves. If leaf fall takes place, the biomass of a strategy is reduced to the fraction that is sustained by stem area, while the fraction that was growing on the leaf area is set to zero. Growth on leaves from deciduous forests is precluded, since the leaves are all shed at the same time of year. Although leaf fall is not a disturbance, its effect on biomass is represented similarly to a disturbance event 10 in the model. Hence, leaf fall is listed here.
3. Herbivory, which is restricted in the model to large-scale grazing by herds of animals. It is thus assumed to affect only strategies living on the ground of savanna, grassland, desert or tundra. Other types of herbivory, which take place on smaller scales and also more frequently, are included in the biomass loss term (e.g. epi-15 phytic herbivory by snails).
The implementation of disturbance used here leads to an oscillation of biomass over time, with a slow build-up between disturbance events and an instantaneous reduction during the event. Such an oscillation is unrealistic on the scale of a grid cell where the ecosystem is usually in a "shifting mosaic steady state". This means, fires, treefall and 20 leaf fall do not affect the whole grid cell, but only a small fraction of it. The purpose of the model, however, is to predict mean biomass. It does not matter if this mean value is derived by averaging over many individuals in a grid cell which are in different states of a disturbance cycle or if the mean is derived by the time average over a whole cycle for just one individual. Hence, if the averaging period is at least as long as one disturbance 25 interval, the mean value is correct.

B2.4 Aerodynamic resistance to heat transfer
The aerodynamic resistance to heat transfer, r H , controls exchange flows of heat between the surface of lichens or bryophytes and the atmosphere. It is calculated according to Allen et al. (1998): where p κ is the von Karman constant, u is near surface wind speed, p ∆ u is the measurement height for wind speed, ∆ d is the displacement height for wind speed and z 0 and z 0, h are the roughness length of momentum and humidity, respectively. The stability corrections which are used in some cases to make Eq. (B10) more accurate (Liu et al., 2007) are neglected here for simplicity. 10 The roughness length z 0 describes the impact of the surface on the flow of air above it. z 0 is parameterised as one of three possible values (Stull, 1988, p. 380): Note that this parameterisation implies that large-scale structures such as forests dominate the aerodynamic properties of the surface. The shape of lichens or 15 bryophytes growing on that surface is assumed to have only a small impact on the roughness length and is consequently neglected in the model. z 0 is related to z 0, h according to: where p z 0 , mh is the ratio between the roughness length of humidity and momentum 20 (Allen et al., 1998 The displacement height is related to roughness length via: where p z 0 , d is the ratio between displacement height and roughness length. The value of p z 0 , d is derived from the relations ∆ d = 2/3 vegetation height and z 0 = 0.123 vegetation height. These relations are adapted from (Allen et al., 1998) and represent 5 rough approximations. Determining average values for displacement height for the each biome, however, would be beyond the scope of this study.

B2.5 Soil thermal properties
The ground heat flux f G affects the energy balance of a lichen or bryophyte if the organism is living on the ground. Typically, the soil temperature is lower than the surface 10 temperature during the day and higher during the night, leading to heat exchange between thallus and soil. If a lichen or bryophyte is living in the canopy, heat exchange with the soil is neglected, since it is assumed that thallus of the organism is in a thermal equilibrium with the canopy layers below. The effect of location of growth on f G is represented by the variable χ G : The ground heat flux is not only affected by the temperature gradient between thallus and soil, but also by soil properties. These are the soil heat capacity C soil and the thermal conductivity of the soil k soil (Lawrence and Slater, 2008;Anisimov et al., 1997;Peters-Lidard et al., 1998). Since they depend on the average water content of the soil, 20 desert soils are parameterised differently from non-desert soils in the model:

B3.1 Water saturation
The water storage capacity Θ max describes how much water a lichen or bryophyte can store per m 2 ground. Θ max is assumed to be proportional to biomass per m 2 ground: where x Θ max is the specific water storage capacity, s B is the biomass of a lichen or bryophyte and c ρ H 2 O is the density of liquid water. The water saturation Φ Θ is then calculated as the ratio of the actual water content s Θ and the water storage capacity:

B3.2 Diffusivity for CO 2 15
The diffusivity of the thallus for CO 2 is represented by the variable D CO 2 . It decreases from a maximum value to a minimum value with increasing water saturation (see Fig. B10) and it is calculated according to: where w D CO 2 , min is the minimum value of CO 2 diffusivity, w D CO 2 , max is the maximum value of CO 2 diffusivity, Φ Θ is the water saturation of the thallus and w D CO 2 is a parameter that determines the shape of the diffusivity curve. w D CO 2 is estimated using the data points in Fig. B10, while w D CO 2 , min and w D CO 2 , max are taken from the literature (Cowan et al., 1992).

5
The relation between D CO 2 and Φ Θ is an important component of the tradeoff between CO 2 diffusivity and metabolic activity. This is explained below in Sect. B3.5.

B3.3 Water potential
The water potential Ψ H 2 O is an increasing function of water saturation and it is calculated according to: where Φ Θ is the water saturation. The parameter x Φ Θ, sat is the threshold saturation. If Φ Θ is above this threshold, all cells in the thallus are fully turgid. Additional water is assumed to be stored extracellularly. x Ψ H 2 O is a parameter that determines the shape of the water potential curve. The parameters of the water potential curve are discussed 15 in further detail in Sect. B1.5 and the curve is shown in Fig. B3. The influence of the relation between water saturation and water potential on the tradeoff between CO 2 diffusivity and metabolic activity is explained below in Sect. B3.5.

B3.4 Metabolic activity
The metabolic activity of a lichen or bryophyte is represented by the variable Φ act . It is 20 assumed to increase linearly from 0 at zero water content to 1 at the threshold saturation (Fig. B11). This assumption is based on the fact, that metabolic activity of lichens and bryophytes increases with their water content (Nash III, 1996, p. 157 shape of this relation is not known, but it should be proportional to the relation between dark respiration and water content at constant temperature. We thus approximate this relation by a linear one. Φ act is written as: where Φ Θ is the water saturation of the thallus and x Φ Θ, sat is the threshold saturation.

5
The relation between Φ act and Φ Θ is an important component of the tradeoff between CO 2 diffusivity and metabolic activity. This is explained below in Sect. B3.5.

B3.5 Tradeoff between CO 2 diffusivity and metabolic activity
The CO 2 diffusivity of the thallus, D CO 2 , decreases with increasing water saturation Φ Θ (see Sect. B3.2). The metabolic activity of a lichen or bryophyte Φ act , however, 10 increases with Φ Θ (see Sect. B3.4). This leads to a tradeoff: at low Φ Θ the potential inflow of CO 2 in the thallus and thus potential productivity are high, but the low Φ act limits the actual productivity. At high Φ Θ productivity is limited by low D CO 2 , although the lichen or bryophyte is active. Since both the relation between D CO 2 and Φ Θ and the relation between Φ act and Φ Θ are controlled by underlying physiological constraints, 15 the associated parameters, such as w D CO 2 , are assumed to have constant values (see Sect. 2.2).
The tradeoff is illustrated in Fig. B12: to maximise productivity, a lichen or bryophyte should try to spend most of the time near the optimum water saturation. It can achieve this goal through appropriate values of the characteristic parameters which control 20 water content. These are mainly x Φ Θ, sat , x Ψ H 2 O and x Θ max , but also parameters that indirectly influence water content of the thallus, such as x α , x A spec and x loc . 10,2013 Estimating global carbon uptake by lichens and bryophytes

B4 Climate relations
The climate forcing (air temperature, wind speed, relative humidity, precipitation and downwelling short-and longwave radiation) influences almost all physiological processes of lichens and bryophytes (see Fig. 3). Furthermore, it determines potential evaporation and surface temperature. In the following sections the relations between 5 potential evaporation (Sect. B4.3), surface temperature (Sect. B4.4) and climate forcing are described. The factors necessary for the calculation of these relations are: 1. Net radiation (see Sect. B4.1).

Relative humidity.
Also snow affects physiological processes of lichens and bryophytes. The dynamics of the snow layer are explained in Sect. B4.5 while the effects of the snow layer on physiological processes are described in the sections related to these processes. 15 Net radiation is the sum of downwelling short-and longwave radiation, upwelling longwave radiation and the ground heat flux. Ingoing short-and longwave radiation are derived from the climate forcing data.

B4.1 Net radiation
Outgoing longwave radiation f rad LW↑ is calculated as a function of surface temperature and air temperature: where T air is air temperature, T surf is surface temperature and c σ is the Stefan-Boltzmann constant. Equation (B22)  power emitted by the surface of a black body (Stefan-Boltzmann law). It is taken from Monteith (1981). The factor Φ area is the fraction of available area that is covered by the thallus (see Eq. B9). This factor thus converts f rad LW↑ to Watts per m 2 ground.
The ground heat flux f Q soil is written as a function of the temperature difference between the thallus of a lichen or bryophyte and the soil: where k soil is the thermal conductivity of the soil (see Eq. B16), T surf is the surface temperature of the thallus, s T soil is soil temperature and p ∆ z is the damping depth of the soil for a diurnal cycle (Bonan, 2008, p. 134). Φ area is the fraction of available area that is covered by the thallus. χ G is a switch to set f Q soil to zero if a lichen or bryophyte is living in the canopy (see Eq. B14).
To compute soil temperature s T soil , the balance for the soil heat reservoir is used: where f Q soil is the ground heat flux, C soil is soil heat capacity, Φ area is the fraction of available area covered by a lichen or bryophyte, p ∆ z is the damping depth of the soil 15 for a diurnal cycle and p ∆ t is the time step of the model. Net radiation f H is written as: where φ rad S is a conversion factor for shortwave radiation (see Eq. B3) and φ rad L is a conversion factor for longwave radiation (see Eq. B4). f rad SW↓ and f rad LW↓ are the down-20 welling shortwave and longwave radiation flows derived from the climate forcing data. Φ area is a factor to reduce the radiation flows to the fraction per m 2 ground that reaches the thallus of a lichen or bryophyte (see Eq. B9). f rad LW↑ is already multiplied by Φ area in Eq. (B22), the same applies for f Q soil in Eq.
where p e s, 1 , p e s, 2 and p e s, 3 are empirical parameters and T air, C is the air temperature in 5 degree Celsius, calculated as T air, If the water saturation of a lichen or bryophyte is below the threshold saturation x Φ Θ,sat (see Sects. B1.5 and B3.3), the water potential at the surface of the thallus becomes negative. Hence the saturation vapour pressure is reduced by the factor φ e sat which is calculated according to Nikolov et al. (1995): where Ψ H 2 O is the water potential of the thallus, c M H 2 O is the molar mass of water, c R gas is the universal gas constant, T air, C is the air temperature, c ρ H 2 O is the density of liquid water and the factor 1.0E6 is used to convert from MPa to Pa. Hence the saturation vapour pressure above the thallus of a lichen or bryophyte, e sat , 15 is written as (Nikolov et al., 1995): The slope of the saturation vapour pressure curve, d e sat , is calculated by differentiating e sat after T air, C :

B4.3 Potential evaporation
The potential evaporation E pot above the thallus of a lichen or bryophyte is written as the sum of two independent potential flows: One driven by net radiation and another one driven by the vapour pressure deficit of the atmosphere (Monteith, 1981): where f H is net radiation, d e sat is the slope of the saturation vapour pressure curve, e sat is saturation vapour pressure and Φ RH is relative humidity. c C air is the heat capacity of air, r H is the aerodynamic resistance to heat transfer, c γ is the psychrometric constant, c ∆H vap, H 2 O is the enthalpy of vaporisation and c ρ H 2 O is the density of liquid water. The factor Φ area reduces the part of E pot related to vapour pressure deficit to the fraction 10 per m 2 ground covered by the thallus of a lichen or bryophyte. The part of E pot driven by net radiation is already corrected for surface coverage in Eq. (B25). Note that both parts of E pot can be negative. If net radiation is negative, the thallus emits more energy to the ground or the atmosphere than it receives. Consequently, dew forms on the thallus surface. This process can be an important source of moisture 15 for lichens or bryophytes, especially in deserts (Nash III, 1996, p. 6). If relative humidity is larger than one and therefore the vapour pressure deficit is negative, fog forms above the thallus surface. Also this process can contribute to the water supply of a lichen or bryophyte.

B4.4 Surface temperature
Lichen surface temperature T surf is derived from the same factors as potential evaporation. It is written according to Monteith (1981) as: where T air is air temperature, e sat is saturation vapour pressure, Φ RH is relative humid-5 ity, d e sat is the slope of the saturation vapour pressure curve and c γ is the psychrometric constant. φ rad S and φ rad L are conversion factors for shortwave and longwave radiation, f rad SW↓ and f rad LW↓ are the downwelling shortwave and longwave radiation flows and c σ is the Stefan-Boltzmann constant. k soil is the thermal conductivity of the soil, p ∆ z is the damping depth of the soil for a diurnal cycle, s T soil is soil temperature and χ G is a 10 switch to set f Q soil to zero if a lichen or bryophyte is living in the canopy. c C air is the heat capacity of air and r H is the aerodynamic resistance to heat transfer.

B4.5 Snow layer
The snow cover leads to a reduction of light input for lichens and bryophytes. Furthermore, it changes the dynamics of the water supply and the temperature regime 15 compared to a situation without snow cover. It is assumed in the model that lichens and bryophytes are not able to photosynthesise if the snow cover above them exceeds a certain critical thickness p ∆ snow (Pannewitz et al., 2003). Since it is impractical to simulate the water content of the organisms under snow, also dark respiration is assumed to be negligible in this situation. This means that no metabolic activity takes place except BGD 10,2013 Estimating global carbon uptake by lichens and bryophytes P. Porada et al. To calculate the thickness of the snow cover a mass balance is used. It consists of input by snowfall and output by snowmelt and slow, lateral movement of the snow pack due to gravity. The latter term has only a negligible effect on a seasonal snow cover. The snow balance for Greenland, however, would be always positive without ice moving laterally towards the ocean in form of glaciers.

5
Snowmelt f snowmelt is calculated as a function of air temperature (Bergström, 1992): where T air is air temperature and c T melt, H 2 O is the melting temperature of water, the factor 86 400 is the number of seconds per day, the factor 1000 converts from mm to m and the factor 3.22 is a dimensionless empirical parameter. s snow is the snow reservoir on 10 the surface, measured in m 3 liquid water equivalents per m 2 , p ∆ t is the time step of the model and f snow, atm is the input flow of snow from the atmosphere. The balance of the snow reservoir s snow is written as: where the last term describes lateral movement of the snow pack. The parameter p τ ice 15 represents the turnover of ice shields and it is set by "best guess" to 1 % per year.
To convert the snow reservoir s snow from water equivalents to thickness of snow cover ∆ snow in meters, s snow is multiplied by the fraction of density of water and density of snow (Domine et al., 2011): In case a lichen or bryophyte is covered by a snow layer that exceeds the critical thickness p ∆ snow , a different method than Eq. (B31) is used to compute the surface 3780 Introduction where p k snow is the thermal conductivity of snow (Domine et al., 2011), ∆ snow is the thickness of the snow layer, T air is air temperature, k soil is the thermal conductivity of the soil, p ∆ z is the damping depth of the soil for a diurnal cycle and s T soil is soil tem-5 perature. Note that Eq. (B35) does not have any effects on the metabolism of lichens or bryophytes, since they are assumed to be inactive under snow. Equation (B35) is only implemented in the model to compute approximate values for the surface temperature under snow. In a snow-covered canopy, the surface temperature is assumed to be equal to air temperature, for simplicity. On the snow-covered ground, the surface 10 temperature is assumed to be controlled only by heat conduction from atmosphere to surface and from surface to soil. Equation (B35) results from assuming a steady state of the surface.

B5 Carbon exchange flows
The model simulates the following flows of carbon related to lichens and bryophytes: 15 1. Inflow of CO 2 from the atmosphere into the pore space of the thallus (see Sect. B5.1).

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The relations of these flows to the balances of the carbon reservoirs of a lichen or bryophyte are described in Sect. B5.7.

B5.1 Inflow of CO 2 into the thallus
The inflow of CO 2 from the atmosphere into the pore space of the thallus, f CO 2 , in , is 5 proportional to the gradient between the partial pressures of CO 2 in the atmosphere and in the pore space. It is written as: where D CO 2 is the diffusivity of the thallus for CO 2 , CO 2, atm is the atmospheric CO 2 concentration, CO 2, thallus is the CO 2 concentration in the pore space of the thallus and 10 the factor 1.0E6 is used to convert the gradient from ppm to a fraction between 0 and 1. The variable Φ area converts f CO 2 , in from a flow per m 2 lichen or bryophyte into a flow per m 2 ground. Note that f CO 2 , in can also be negative, which means that the CO 2 concentration inside the thallus is higher than in the atmosphere and consequently CO 2 flows out of the thallus.

B5.2 GPP
The uptake of CO 2 from the pore space (Gross Primary Productivity, GPP) is computed according to Farquhar and von Caemmerer (1982) as a minimum of a light-limited rate and a CO 2 -limited rate. The light-limited rate is an increasing function of the absorption of light by a lichen or bryophyte. The organism, however, cannot absorb light to an ar-20 bitrary extent. Hence, the light-limited rate is constrained to a maximum rate J max . The CO 2 -limited rate is an increasing function of the CO 2 concentration in the chloroplasts of a lichen or bryophyte. It saturates, however, at very high values of CO 2 concentration. The maximum rate at saturation is V C, max . The maximum carboxylation rate V C, max of a lichen or bryophyte is calculated as: where x V C, max is the molar carboxylation rate of Rubisco (see Sect. B1.6) and Ξ Rub is the specific Rubisco content of a lichen or bryophyte. The exponential describes the influence of surface temperature T surf on V C, max (Medlyn et al., 2002). V C, max is assumed 5 to peak around an optimum surface temperature x T opt, PS (see Sect. B1.9) and the shape of the temperature response curve is determined by the parameter p Ω (June et al., 2004). The Rubisco content Ξ Rub is a function of the reference respiration rate at 10 • C, x R ref . This relationship represents a tradeoff and results from a physiological constraint, 10 namely maintenance costs of enzymes (see Sect. 2.2). The exact shape of this relation could not be determined, since we could not find enough studies where both Ξ Rub and x R ref are measured. Thus, we assume a simple linear function: where the tradeoff-parameter w Rub, R , which represents the slope of the line, is de-  Table B9. To compute Ξ Rub we also use Eq. (B2) with N = 0.5, although the range of possible values of Ξ Rub (see Table B6 where V C, max is the maximum carboxylation rate and φ JV is the ratio of J max to V C, max . 5 φ JV depends on the surface temperature of a lichen or bryophyte and is written as: where T surf is surface temperature and c T melt, H 2 O is the melting temperature of water. The two parameters w JV , 1 and w JV , 2 are derived by the data shown in Fig. B13. φ JV is limited to non-negative values since a negative J max would make no sense from a 10 physiological viewpoint. The fact that V C, max and J max are positively correlated implies a tradeoff between these two variables. This tradeoff results from physiological constraints (see Sect. 2.2) in form of metabolic costs of V C, max and J max . Since both the maximum of the lightdependent rate and the maximum of the CO 2 -dependent rate are associated with costs 15 for the organism, but GPP is computed as a minimum of the two rates it would be inefficient if V C, max and J max were independent from each other.
The actual rate of electron transport J is calculated as the minimum of the maximum rate of the photosystems J max and the supply by shortwave radiation: where f rad SW↓ is the flow of shortwave radiation, φ rad S is a conversion factor that includes albedo and LAI (see Sect. B2.1), p PAR is a factor that converts shortwave radiation into photosynthetically active radiation and p quant converts quanta of light into electrons. w CCM, e is a factor that represents the investment of electrons in a Carbon Concentration Mechanism if present (see Sect. B5.3 below). Φ area reduces the electron flow to the area covered by a lichen or bryophyte and s B is the biomass of the organism. Besides V C, max and J max , the Michaelis-Menten constants of the carboxylation and oxygenation reactions of Rubisco, K C and K O , affect the shape of the light-dependent rate and the CO 2 -dependent rate of GPP. They are calculated as: and where O 2, cell is the concentration of O 2 in the chloroplast of a lichen or bryophyte, x V C, max and x V O, max are the maximum velocities and K C and K O are the Michaelis-Menten constants of the carboxylation and oxygenation reactions, respectively.

5
The O 2 concentration in the chloroplast O 2, cell is calculated as a function of the O 2 concentration in the pore space of the thallus, which is assumed to be equal to the atmospheric one: where O 2, atm is the atmospheric O 2 concentration and p S O 2 is the solubility of O 2 (von 10 Caemmerer, 2000, p. 9). The factor 1000 is used to write O 2, cell in mol per m 3 .
Accordingly, the CO 2 concentration in the chloroplast CO 2, cell is calculated as a function of the CO 2 concentration in the pore space of the thallus, which depends on the exchange flows of carbon between the organism and the atmosphere: CO 2, cell = 1000.0 p S CO 2 CO 2, thallus (B46) 15 where CO 2, thallus is the pore space CO 2 concentration and p S CO 2 is the solubility of CO 2 (von Caemmerer, 2000, p. 9). The factor 1000 is used to write CO 2, cell in mol per m 3 . Knowing CO 2, cell , O 2, cell , J, K C , K O , x V C, max and x V O, max , the light-limited rate and the CO 2 -limited rate of photosynthesis can be calculated. They are written according to Farquhar and von Caemmerer (1982) as: where CO 2, cell is the concentration of CO 2 in the chloroplast, Γ * is the CO 2 compensation point, K C and K O are the Michaelis-Menten constants of the carboxylation and oxygenation reactions, respectively, and O 2, cell is the O 2 concentration in the chloroplast.

5
Φ act is the metabolic activity of a lichen or bryophyte (see Sect. B3.4). It accounts for the effect of poikilohydry on photosynthesis and it represents an extension to the original equations of Farquhar and von Caemmerer (1982). x V C, max is the maximum specific carboxylation rate and s B is the biomass of a lichen or bryophyte. The GPP of a lichen or bryophyte is then calculated as the minimum of f GPP, L and 10 f GPP, W :

B5.3 Carbon Concentration Mechanism
Some lichens and bryophytes possess a Carbon Concentration Mechanism (CCM, see Sects. 2.2 and B1.11). If a CCM is active, a fraction of the electrons generated by 15 the photosystems is invested in increasing the CO 2 concentration in the chloroplasts instead of being used in the Calvin cycle. This increased CO 2 concentration in the chloroplasts can be calculated as a function of pore space CO 2 concentration: CO 2, cell = min w CCM, 1 CO 2, thallus , w CCM, 2 CO 2, thallus + w CCM,3 (B50) 20 where CO 2, cell and CO 2, thallus are the CO 2 concentrations in the chloroplast and the pore space, respectively. w CCM, 1 , w CCM, 2 and w CCM, 3 are parameters derived from the data of Reinhold et al. (1989) which is shown in Fig. B14 The CCM represents a tradeoff for a lichen or bryophyte: The increased CO 2 concentration in the chloroplasts which depends on w CCM, 1 , w CCM, 2 and w CCM, 3 directly leads to higher productivity, but the maintenance of the high concentration requires energy which is taken from the electron transport chain in the thylakoid membranes. These costs are represented by the parameter w CCM, e (see Eq. B41). The relation between pore space CO 2 and CO 2 in the chloroplasts as well as the costs of establishing this relation constitute the physiological constraints of the CCM.

B5.4 Respiration & growth
Respiration consists of two parts: Maintenance respiration and growth respiration. The specific maintenance respiration rate R spec is modelled by a Q 10 relationship (Kruse 10 et al., 2011). It is illustrated in Fig. B8 in Sect. B1.8 and it is written as: where x R ref is the reference respiration rate at 10 • C, x Q 10 is the Q 10 value of respiration, T surf is the surface temperature of the organism, p T ref, R is the reference temperature and c T melt, H 2 O is the melting temperature of water. 15 The maintenance respiration of a lichen or bryophyte, f R main , is then calculated as a function of R spec and the biomass of the organism: where s C is the sugar reserve of a lichen or bryophyte, c M C is the molar mass of carbon, p ∆ t is the time step of the model, R spec is the specific maintenance respiration rate, s B 20 is the biomass of the organism and Φ act is its metabolic activity. The minimum in Eq. (B52) is used because a lichen or bryophyte cannot respire more carbon per time step than is stored in the sugar reservoir. The respired CO 2 is released into the pore space. The growth of a lichen or bryophyte is computed as the minimum of the available amount of sugar per time step and a potential flow, which is a function of the sugar reservoir: where s C is the sugar reserve of a lichen or bryophyte, c M C is the molar mass of carbon, 5 p ∆ t is the time step of the model and f R main is maintenance respiration. x alloc is the fraction of the sugar reservoir allocated to growth per day, 86 400 is the number of seconds per day, Φ act is metabolic activity, and p η growth is the efficiency of the transformation of sugars to biomass. The respiration associated with growth, f R growth is then written as a function of growth 10 efficiency p η growth and growth f growth :

B5.5 Steady State of internal CO 2
Two carbon exchange flows depend on the internal CO 2 concentration of the thallus CO 2, thallus , namely the inflow of CO 2 from the atmosphere into the pore space, f CO 2 , in 15 (Eq. B36), and the uptake of CO 2 from the pore space by GPP, f GPP (Eq. B49). The model, however, does not simulate explicitly the pore space of the thallus. Hence, it is not possible to determine the absolute amount of CO 2 in the thallus. Instead, a steadystate approach is used to calculate CO 2, thallus . It is assumed that the exchange flow of CO 2 between pore space and atmosphere, f CO 2 ,in , balances the net CO 2 exchange 20 flow between pore space and the cells of the organism. This net exchange flow is equal to the sum of uptake from the pore space f GPP and release of CO 2 into the pore space, consisting of maintenance respiration f R main and growth respiration f R growth (Eqs. B52 and B54). The equation for the steady state of pore space CO 2 is thus written as: Equation (B55) is then solved for CO 2, thallus to determine the values for f CO 2 , in and f GPP .

B5.6 Biomass loss
The turnover rate of the biomass of lichens or bryophytes, τ B , is calculated similarly to the Rubisco content (see Sect. B5.2) as a function of the reference respiration rate at 10 • C, x R ref . The relation between τ B and x R ref represents a tradeoff and results from a physiological constraint, namely metabolic stability of enzymes (see Sect. 2.2). The 10 exact shape of this relation could not be determined, since we could not find enough studies where both τ B and x R ref are measured. Thus, we assume a simple linear function: where the tradeoff-parameter w loss, R , which represents the slope of the line, is deter-  Table B9. To compute τ B we also use Eq. (B2) with N = 0.5 (see Fig. B15). The range of possible values of τ B is set to 0.03-1.5 (see Sect. B1).

20
The flow of biomass loss f loss , is then calculated as a function of τ B and the biomass of the organism: where τ B is the turnover rate, s B is the biomass of a lichen or bryophyte and c M C is the molar mass of carbon. The factor of 3.1536E7 is used to convert τ B from yr −1 to s −1 . Note that f loss also includes leaching of carbohydrates and small-scale regular herbivory.

5
Two carbon reservoirs of lichens and bryophytes are simulated in the model: Biomass and sugar reserves. The balance of the sugar reservoir s C is written as: where f GPP is GPP, f R main is maintenance respiration, f R growth is growth respiration, f growth is growth c M C is the molar mass of carbon and p ∆ t is the time step of the model. 10 The balance of the biomass reservoir s B is written as: where f growth is growth, f loss is biomass loss, c M C is the molar mass of carbon and p ∆ t is the time step of the model. 15 The water exchange between a lichen or bryophyte and its environment is represented by three flows: water uptake via rainfall or snowmelt, evaporation from the surface of the thallus and runoff. Water uptake f water,up is calculated as: where f rain, atm is rainfall, f snowmelt is snowmelt, φ prec is the fraction of precipitation that reaches the thallus surface and Φ area reduces water uptake to the area covered by a lichen or bryophyte. Evaporation f evap is calculated as a minimum of demand by potential evaporation and supply by the water reservoir of a lichen or bryophyte:

B6 Water exchange flows
where s Θ is the water content of a lichen or bryophyte, p ∆ t is the time step of the model and E pot is potential evaporation (see Eq. B30). Runoff f runoff is generated when net water uptake exceeds the water storage capacity of the thallus: where s Θ is the water content of a lichen or bryophyte, f water, up is water uptake, f evap is evaporation, p ∆ t is the time step of the model and Θ max is the water storage capacity of the thallus (see Eq. B17). The water balance is then written as: where s Θ is the water content of a lichen or bryophyte, f water, up is water uptake, f evap is evaporation, f runoff is runoff and p ∆ t is the time step of the model.

B7 Exchange flows of energy
Additionally to exchange flows of carbon and water, the model computes the exchange Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | f Q atm, L , is calculated from evaporation as: where f evap is evaporation, c ∆H vap, H 2 O is the enthalpy of vaporisation and c ρ H 2 O is the density of liquid water. The flow of sensible heat, f Q atm, S , is written as: where T surf is surface temperature, T air is air temperature, c C air is the heat capacity of air, r H is the aerodynamic resistance to heat transfer and Φ area is the fraction of available area covered by a lichen or bryophyte. E pot is potential evaporation, f evap is actual evaporation, c ∆H vap, H 2 O is the enthalpy of vaporisation and c ρ H 2 O is the density of liquid water. Note that f Q atm, S consists of two parts. The first part depends on the gradient 10 between surface temperature of the organism and air temperature. The second part is the difference between the potential flow of latent heat and the actual one (see Eq. B64). This means, that the ratio of latent heat to sensible heat decreases if the supply of water is not sufficient to support potential evaporation. The energy balance of the thallus surface, which can be either on the ground or in 15 the canopy, is then calculated as: where f H is net radiation (see Eq. B25), f Q atm, L , is the flow of latent heat and f Q atm, S is the flow of sensible heat.

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Interactive Discussion
Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Wullschleger, S. D.: Biochemical limitations to carbon assimilation in C3 plants -a retrospective analysis of the A/C i -curves from 109 species. J. Exp. Bot., 44, 907-920, doi:10.1093/jxb/44.5.907, 1993 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Table 2. Influence of uncertain model parameters on simulated net carbon uptake. "Average" and "Maximum" correspond to two different weighting methods for the results (see Sect. 2.3). The "+" sign denotes an increase in the value of a parameter and "−" signs denotes a decrease. The rightmost column shows the type of increase or decrease.  Table B10. Overview of model parameters associated with lichen or bryophyte tradeoffs. Parameters marked by the D symbol are included in a sensitivity analysis (see Table 2) because their values are not known very accurately. Note that in some cases several parameters are changed simultaneously to test model sensitivity towards a certain property, e.g. both w D CO 2 , max and w D CO 2 , min for CO 2 diffusivity. Only one of the CCM parameters is included in the sensitivity analysis: changing w CCM, e would be redundant since decreasing the costs of the CCM is analogous to increasing its positive effect. w CCM, 2 and w CCM, 3 are only relevant at a transient state of very high pore space CO 2 levels.  2. Effect of the Leaf Area Index (LAI) on area for growth and climate forcing. Available area on ground is a linearly decreasing function of LAI. The same function is used to partition precipitation between canopy and soil. The vertical distribution of light is calculated according to Beer's law as a function of LAI. 10,2013 Estimating global carbon uptake by lichens and bryophytes P. Porada et al.  Fig. 3. Schematic of the carbon and water relations of a lichen or bryophyte simulated by the model. Dotted arrows illustrate effects of climate forcing, living environment and state variables on physiological processes of a lichen or bryophyte. These processes are associated with exchange flows (solid arrows) of carbon (black), water (blue) and energy (red). 10,2013 Estimating global carbon uptake by lichens and bryophytes P. Porada et al.  Example: in a hot desert, strategy 1 survives, because a small specific area reduces water loss by evaporation and a high Rubisco content is adequate to high light intensities. Strategy 2, however, dies out since too much water evaporates due to a large specific area. In a moist forest, strategy 1 dies out because a high Rubisco content is associated with high respiration costs which cannot be covered by low light conditions under a canopy. Strategy 2 can survive since it does not have high respiration costs. Note that these examples are not generally applicable. High specific area, for instance, could also be useful in a desert to collect dew. Introduction  10,2013 Estimating global carbon uptake by lichens and bryophytes P. Porada et al.   10,2013 Estimating global carbon uptake by lichens and bryophytes P. Porada et al.  Fig. 7. Comparison of net carbon uptake estimated by the model to observational data. Each symbol corresponds to a different field study site. Model estimates based on "average" as well as "maximum" weighting are shown (see Sect. 2.3). The vertical bars represent the range between the most and least productive grid cell in a certain biome, while the dots show the mean productivity of all grid cells in this biome. To be consistent with the measurements from the field studies, only the simulated carbon uptake in the canopy was considered for the biome "Tropical Forest", while for the other biomes only carbon uptake on the ground was considered.

BGD
The model results are derived from a 2000-yr run with 3000 initial strategies. 10,2013 Estimating global carbon uptake by lichens and bryophytes P. Porada et al.  show optimum temperature and CCM fraction of lichens and bryophytes living in the canopy, which adds to Fig. 6, where the corresponding estimates for the ground are shown. In (c) the fraction of available area covered by lichens and bryophytes is shown, which is highest in regions where available area on ground is limited due to agriculture. In (d) carbon uptake by lichens and bryophytes is shown for a 400-run with 300 initial strategies. This run is used for the sensitivity analysis. The estimate is based on the "average" weighting method. Areas where no strategy has been able to survive are shaded in grey. Introduction 3833 BGD 10,2013 Estimating global carbon uptake by lichens and bryophytes P. Porada et al. Nash III (1996) Sundberg et al. (1999) Lange and Green (2005) Palmqvist and Sundberg (2000) Sundberg et al. (1997) Lange (

3841
BGD 10,2013 Estimating global carbon uptake by lichens and bryophytes P. Porada et al.  . B10. Diffusivity for CO 2 , D CO 2 , as a function of water saturation Φ Θ . The black data points are derived from the studies listed in the right column.