Observed allocations of productivity and biomass, and turnover times in tropical forests are not accurately represented in CMIP5 Earth system models

A significant fraction of anthropogenic CO2 emissions is assimilated by tropical forests and stored as biomass, slowing the accumulation of CO2 in the atmosphere. Because different plant tissues have different functional roles and turnover times, predictions of carbon balance of tropical forests depend on how earth system models (ESMs) represent the dynamic allocation of productivity to different tree compartments. This study shows that observed allocation of productivity, biomass, and turnover times of main tree compartments (leaves, wood, and roots) are not accurately represented in Coupled Model Intercomparison Project Phase 5 ESMs. In particular, observations indicate that biomass saturates with increasing productivity. In contrast, most models predict continuous increases in biomass with increases in productivity. This bias may lead to an over-prediction of carbon uptake in response to CO2 or climate-driven changes in productivity. Compartment-specific productivity and biomass are useful benchmarks to assess terrestrial ecosystem model performance. Improvements in the predicted allocation patterns and turnover times by ESMs will reduce uncertainties in climate predictions.


Introduction
Due to anthropogenic activities, atmospheric CO 2 concentrations have increased from ∼280 ppm in 1750 (IPCC 2013) to current levels of ∼400 ppm (Tan and Keeling 2014), with increases projected to continue (IPCC 2013). Concomitant to increases in atmospheric CO 2 concentrations is an increase in air temperatures (IPCC 2013). Tropical forests assimilate a large amount of atmospheric CO 2 , accounting for ∼34% (42 PgC yr −1 ) (Beer et al 2010) of total global terrestrial gross primary production (GPP). Part of this carbon is lost to the atmosphere during metabolism (autotrophic respiration, Ra) and the remaining flux (net primary production, NPP) in tropical forests represent ∼35% (22 PgC yr −1 ) of the total global NPP (Pan et  NPP and biomass are fundamental variables of the global carbon cycle representing net absorption and net storage of carbon respectively. At steady state, forest biomass is the balance between productivity and losses (characterized by turnover times) in tree compartments (Malhi et al 2011): i i i where i = leaves, wood, and roots (i.e., the main tree compartments) and τ i is the turnover time of individual compartments (total biomass is the sum of all  (Taylor et al 2012) and allow for an integrative study of the Earth system. These models predict the allocation of biomass and productivity. Thus, how CMIP5 ESMs reproduce observed allocations and biomass-productivity relationships in tropical ecosystems can be used to test models and provide specific suggestions for model improvements. This work, therefore, has the following objectives: (i) To compare observations and CMIP5 ESM predictions of allocations of productivity and biomass, and turnover times of main tree compartments (leaves, wood, and roots).
(ii) To determine whether CMIP5 ESMs reproduce the observed spatial patterns of NPP and biomass in tropical forests. (flag 0 in quality control files), forest land cover greater than 80% and reliability (assessment) greater than 85%. This forest mask was applied to all model simulations analyzed here, and correspond to CMIP5 cells with ⩾40% of forest cover (figure S1, supplementary data).

CMIP5 models
Monthly fields from historical simulations for the period 1971-2000 from 22 CMIP5 ESMs models (available at http://cmip-pcmdi.llnl.gov/) were used in this study (table S1). Since models from the same institution produce similar results ( CMIP5 ESMs historical simulations are coupled simulations where the increase of atmospheric CO 2 affects both the climate and the carbon cycle components of the models, and can be compared directly with current observations (Taylor et al 2012). In CMIP5 models, total biomass is represented by cVeg and the biomass in the main tree compartments are cLeaf, cWood, and cRoot (coarse + fine roots). Net primary productivity is identified as npp which is disaggregated into nppLeaf, nppWood, and nppRoot. For simplicity, total productivity will be referred to as NPP (MgC ha −1 yr −1 ) and total biomass as cVeg (MgC ha −1 ). The ensemble members available at the time of this study per each CMIP5 model were averaged and monthly data integrated annually (January to December). The annual data per each CMIP5 model were used in our analyses. The ratio of nppLeaf, nppWood, and nppRoot, to NPP and the ratio of cLeaf, cWood, and cRoot to cVeg were compared with observations. Ratios between predicted fluxes and pools (nppLeaf/cLeaf, etc) were compared with observed turnover times calculated in an analogous manner.
The CMIP5 ESM predicted association between NPP and cVeg were presented and discussed with respect to observational studies. We explored quadratic (cVeg = a + b × NPP + c × NPP 2 ) and linear (cVeg = a + b × NPP) models to explain predicted NPP versus cVeg relationships. The MPFIT fitting package (http://purl.com/net/mpfit) (Markwardt 2009) for the interactive data language (IDL, Exelis Inc., McLean, VA) was used for this task. If the linear and quadratic models had statistically similar variance (significance level of 95%), determined by the F-test (Wilks 2006), then the linear model was preferred over the quadratic model because fewer parameters were required (Wilks 2006). If the models had statistically different variance, then the model with lower fitting errors (lower χ 2 Wilks 2006) was preferred. A visual inspection was performed to complement this comparison.
In CMIP5 ESMs, disturbances such as fire and drought can produce dramatic departures from steady state conditions. CMIP5 ESMs with a fire module include CESM1, IPSL, MPI, and GFDL. Under steady state conditions, carbon inputs (GPP) balance outputs (Ra, and soil heterotrophic respiration, Rh), and equation (1) is valid. To ensure that grids cells are not disturbed forests the following condition was considered: 1 − δ ⩽ GPP/(Ra + Rh) ⩽ 1 + δ. The selection of δ must be small to better approximate a steady state condition. For simplicity we selected a common value of δ for all models analyzed.

NPP and biomass data
Mean NPP value for lowland tropical forests was estimated to be 11.86 ± 2.47 MgC ha −1 yr −1 (mean ± SD) (Malhi et al 2011) with a range from 8.4 to 29.8 MgC ha −1 yr −1 (Cleveland et al 2011) (table S2). This mean NPP agrees with another recent tropical estimate (11.08 ± 1.2 MgC ha −1 yr −1 , Cleveland et al 2015). The observationally-based fractional allocation of NPP to leaves, wood, and roots was 34 ± 6%, 39 ± 10%, and 27 ± 11%, respectively (Malhi et al 2011). However, these authors considered only fine roots (in CMIP5 models nppRoot includes coarse and fine roots). Coarse root NPP is difficult to assess but represents a small fraction (4%) of total NPP (Clark et al 2001). Similarly, fine root production is not measured directly and observational assessments have serious limitations (Lukac 2012). Since estimated values of coarse root NPP are in the range of the uncertainties of NPP allocation (Malhi et al 2011) we did not attempt to correct these values. Therefore, the fractional allocation of NPP to nppRoot was directly compared with the observed value. Mean tropical biomass was taken to be 144 ± 54 MgC ha  (table S2). Biomass was divided into leaves, stems, and roots as 4 ± 2%, 78 ± 4%, 18 ± 2%, respectively (Poorter et al 2012, Fernandez-Martinez et al 2014. We combined equation (1), the mean ± SD values of biomass and productivity (taken as representative of tropical forests), and allocation fractions (to leaves, wood, and roots) to calculate turnover times (yr) (using a Monte Carlo simulation with 10 000 iterations) and compare with independent observationally-based values.

Results
Most CMIP5 tropical forest were close to steady state ( figure 1(b)), but departures from this condition exist. Figure 1(c) shows that between 10% and 60% of data per model satisfy 1 − δ ⩽ GPP/(Ra + Rh) ⩽ 1 + δ for δ = 0.025. δ = 0.1 encompassed most of the data. In this study we choose δ = 0.1 as the cut off for steadystate conditions, so that only cells satisfying 0.9 ⩽ GPP/(Ra + Rh) ⩽ 1.1 were used in the following analyses. For the purposes of this study, the selection of δ had little to no effect on our results as observed in all models studied (figure S2).
The models that better reproduced mean NPP (BNU, CESM1, and NorESM1) performed worse for mean biomass (cVeg) (figure 2(b), table S3), simulating the highest values (average of ∼257 MgC ha −1 ) among the CMIP5 models we analyzed. HadGEM2 (157 MgC ha −1 ) and IPSL (183 MgC ha −1 ) predicted biomass values close to observations. The bcc, MIROC, and MPI predictions were the lowest among models. With respect to the allocation of biomass in the main tree compartments, all models predicted a smaller fraction of cVeg allocated to cLeaf than observed, a feature that may be related to the lower NPP allocated to this compartment ( figure 2(a)). Also, all models showed a large fraction of cVeg allocated to cWood consistent with observations, but there were several differences. Relative to observations, the fraction of biomass in wood was high in BNU, CESM1, HadGEM2, and MIROC; this fraction was low in the bcc model. The higher wood allocation relative to observations in productivity and biomass in models using CLM4 could explain higher total biomass (top panel figure 2(b)). Finally, the fraction of biomass in roots varied among models. cRoot was over predicted in bcc and NorESM1 models, and under predicted in BNU, HadGEM2, and MIROC, relative to observations. The fraction of biomass in cRoot simulated by CanESM2 and IPSL were close to observations. Two contrasting patterns in the fractions of biomass in wood and root pools are evident: a set of models with close to zero root biomass and close to 100% wood biomass, and a set of models with ∼20-30% root and 70-80% wood, suggesting that the definition of wood and roots is inconsistent across the CMIP5 models (some labeling coarse roots as wood and some labeling coarse roots as roots). Although CMIP5 ESMs also provide biomass for other minor tree pools, cLeaf, cWood, and cRoot encompass the dominant proportion of total biomass, representing on average 1%, 85% ± 10%, and 12% ± 10% of cVeg.
We found that τ leaf varied between 0.39 and 3.3 yr, and comparable with observed values (1 yr) in tropical forests (Chave et al 2010). τ wood varied between 11 and 54 yr. Using tropical forests plots Galbraith et al (2013) found τ wood between 23 and 129 yr and a median of 50 yr that reflect the high diversity of taxa in tropical forests. In this study we considered τ wood between 11 and 129 yr. Finally, τ root varied between 3 and 23 yr, values that are larger than site estimates (1 to 7 yr) (Jimenez et al 2009). This difference may be explained by the fact that measurements of root turnover are achieved by indirect means resulting in high uncertainties (Lukac 2012). Estimates using 14 C to estimate fine-root turnover in temperate trees has indicated that a spectrum of turnover times exist, with two dominant peaks of ∼1 and ∼10 yr (Riley et al 2009, Gaudinski et al 2010. The range of τ root from 1 to 23 yr was considered in this study. Figure 3 shows these turnover times compared with turnover time obtained from models. For the CMIP5 ESMs that provided sufficient information to calculate these turnover times, the mean leaf lifetime was 3 to 6 months longer than the mean observed value (τ leaf = 1 yr). The predicted turnover time of woody biomass was 10-30 yr shorter than the median of 50 years observed in tropical forests, and roots had mean turnover times about 50% larger than the mean value (9 yr, but see Jimenez et al 2009). NorESM1 models used the same base land model (CLM4) as used in CESM1. However, numerous physical parameterizations were changed in the CLM version used by NorESM1 (Bentsen et al 2013), potentially explaining the differences between these models.
Three patterns of NPP versus cVeg emerged from the CMIP5 models (figure 4, and figure S3): (A) concave up: CESM1, MPI and NorESM1; (B) linear: bcc, BNU, CanESM2, GFDL, IPSL and MIROC; and (C) concave down: HadGEM2. CESM and NorESM1 use the same land model (CLM4) and therefore their NPP-cVeg patterns were very similar. In CLM4, the fractional allocation to wood increases as a function of increasing NPP (Thornton and Zimmermann 2007), which is responsible for the concave-upwards curve. The HadGEM2 models produced the only simulations with a saturating relationship that appears to arise from the TRIFFID vegetation dynamics underlying HadGEM2. In TRIFFID the allocation to woody growth for range expansion of a given PFT (plant functional type) decreases when that PFT occupies a large fraction of a cell, resulting in a density-dependent vegetation turnover time. In addition, HadGEM2 NPP and cVeg maps (figure S4) showed that NPP > ∼15 MgC ha −1 yr −1 and cVeg < ∼190 MgC ha −1 were observed contouring the borders of tropical forests. These forest grid cells included also grasses (figure S5) that are highly productive and have low biomass which may partially explain the decrease of cVeg with an increase in NPP for NPP > ∼15 MgC ha −1 yr −1 (and which is a mechanism different than represented in the observed benchmark relationship, which only considers trees).

Discussion
A full understanding of processes that govern allocation remains elusive. Despite this limitation, models attempt to reproduce allocation using schemes that vary between models and depend on the PFT. CMIP5 models calculate allocation to leaves, wood, and roots using (1) allometric relationships and leaf area index, LAI, (as in AVIM2 in bcc, JULES in HadGEM2, table S1); (2) NPP (CLM4 in CESM1 and NorESM1, JSBACH in MPI. The land model used by BNU is the CoLM that is based on previous versions of CLM4), (3) allometry and resource availability (as CETEM in CanESM and ORCHIDEE in IPSL), (4) environmental conditions at the tree level (as in SEIB-DGVM in MIROC), and (5) tree height (as LM3.0 in GFDL). Our results suggest that the schemes used by CMIP5 models did not accurately represent the observed allocations in leaves, wood, and roots. Additionally, the strategies used to calculate allocation in the CMIP5 models have advantages and disadvantages. For instance, models based on the allometric approach lack the inherent ecosystem adaptation component to predict the effects of environmental variability and climate change (Franklin et al 2012).
Model predicted NPP and biomass values agreed well with the observational range but models seem to be capable of reproducing either the observed mean NPP or the observed mean biomass but not both. This pattern is likely related to the embedded model schemes that calculate NPP and biomass allocations. Models whose allocations are based on NPP better reproduced the observed mean NPP (BNU, CESM1 and NorESM1) and models using allometry better reproduced the observed mean biomass (HadGEM2 and IPSL). The models that report pool-specific allocation consistently overestimate the fraction of productivity allocated to wood, and underestimate the fraction of productivity allocated to leaves, when compared with observations. The allocations to root productivity and leaf biomass appear to be close to observations across most CMIP5 models. CMIP5 models have fractional biomass in leaves at the low end of the mean observational range, and their fractional biomass in roots and wood show a bimodal pattern that suggests an inconsistent definition of coarse roots as either roots or wood between the models. CMIP5 woody parts contain the largest fraction of biomass in agreement with observations but have faster turnover time in that component (10-30 yr faster than the observed median of 50 yr), resulting in predictions of higher productivity or lower biomass. Our analysis was limited due to lack of available model data for the main compartments of NPP and biomass. We suggested that all ESM's participating in future intercomparison projects include and consistently define the main pools (leaves, wood, and root) of productivity and biomass to better understand their predictions.
Models predict a continuous increase in biomass with increased productivity. For instance, CLM4 adopts a continuous increase in the fraction of carbon allocated to wood with increases in NPP (Oleson et al 2010). However observational studies show a different pattern. Keeling and Phillips (2007)   . Relationship between productivity (NPP) and biomass (cVeg) over tropical forests using CMIP5 models. All models but one show continual increasing biomass as a function of NPP, while observations show a saturating response. because highly productive forests have short residence times and their tree species prioritize fast growth that results in low wood density and therefore low biomass (Malhi et al 2015). The fact that ESMs do not reproduce the observed saturation response of biomass at high NPP raises a critical question about model predictions of carbon cycle responses to global change: Do the same saturating conditions hold for the higher productivity environments expected as a result of elevated CO 2 conditions (Norby et al 2005) as for the current spatial patterns? If so, and since the models do not represent the mechanisms behind this saturating response, we expect the models will likely over predict carbon uptake in response to CO 2 or climate-driven changes in productivity. These functionally incorrect responses imply model structural uncertainty associated with vegetation tradeoffs.
Biomass per unit area was found to be larger in Asia, followed by Africa and then Amazonia (Lewis et al 2013, Slik et al 2013, Banin et al 2014. IPSL and CanESM2 appears to capture this regional pattern ( figure S7). However, a close observation revealed that in CanESM2 lower values of biomass in Amazonia were produced by extremely (and unrealistically) low values of biomass over a large fraction of Amazonia ( figure S4). In addition, observational studies show that Northwestern Amazonia is the most productive area in the Amazon ( . CMIP5 models were consistent with observations in predicting higher NPP in Northwestern Amazonia relative to the Amazon basin but inconsistent with observations by simulating higher biomass in this region (figure S4). The models' limited ability to reproduce the decrease of cVeg at high NPP raises concerns about predictions in areas with high productivity. It also raises concerns about carbon stocks projections associated with projected increase in productivity due increase in atmospheric CO 2 (Wieder et al 2015).
Observational data used to benchmark the CMIP5 ESMs are of great value but contain their own uncertainties (Malhi et al 2011, Samanta et al 2011, Mitchard et al 2014, Cleveland et al 2015, Malhi et al 2015. Yet, patterns in productivity and biomass emerge that models were unable to capture and that likely affect model predictions. For instance, to be comparable with observation models need to increase NPP allocation to leaves that in turn may increase LAI and affect climate predictions through changes in albedo, evapotranspiration, and CO 2 surface fluxes (Negrón-Juárez et al 2007, Myneni et al 2007, Bonan 2008. The continuous increase of biomass with increased NPP in all models suggest, for instance, that mortality mechanisms are inaccurate in models. Improved representation of mortality is needed, since tree

Conclusion
The CMIP5 models used in this study did not reproduce the observed allocation of productivity, biomass, and turnover time in the main tree compartments (leaves, wood, and roots) in tropical forests. All models systematically predict an increase in biomass with an increase in NPP in the lower NPP range observed in tropical forests. Observations also suggest a limit for this increase, a pattern not simulated by the models. The models inability to reproduce the observed patterns of allocation of NPP and biomass raises concerns about climate projections, in particular whether the limitations to vegetation accumulation under high productivity conditions also hold for the responses of forest vegetation carbon stocks under future global change. Regional differences of predicted biomass and NPP were observed across models. Model improvements in representing observed allocations of productivity and biomass in the main tree compartments may lead to changes in climate predictions.