We chose the historical simulations of 21 CMIP6 GCMs (see Table ) that provide the three meteorological forcing variables needed to run LPJ-GUESS, i.e., the near-surface air temperature (tas), the total precipitation flux (pr), and the incoming shortwave radiation (rsds), and examine the r1i1p1f1 realization that covers the time period 1850–2100. Four GCMs (ACCESS-CM2, ACCESS-ESM1-5, BCC-CSM2-MR, and NESM3) provide incoming shortwave radiation starting in 1950 only. For these GCMs, we recycled the climate forcing of the first 25 years of the available forcing (i.e., 1950–1974) for the first 100 years (i.e., 1850–1949). All GCMs provide daily data but differ in their spatial resolution. We therefore regridded all GCMs to a common 0.5∘ grid using first-order conservative remapping to match the resolution of the reanalysis and the native grid of LPJ-GUESS and focus on the historical time period (1901–2019).

We chose the CRUJRA reanalysis product as the reference dataset to compare with the unconstrained CMIP6 results, as well as to derive bias corrections and ensemble weights. In addition, we use LPJ-GUESS runs forced with the CRUJRA reanalysis as reference datasets for carbon variables. CRUJRA is derived from the Climatic Research Unit gridded Time Series (CRU TS) v4.03 monthly data and from the Japanese 55-year Reanalysis data (JRA-55) . Temperature, downward solar radiation flux, specific humidity, and precipitation in JRA-55 are aligned to temperature, cloud fraction, vapor pressure, and precipitation in CRU TS (v4.03), respectively. The CRUJRA dataset spans the years 1901–2018 on a 6 h time step, which we aggregated to a daily temporal resolution at a 0.5∘ spatial resolution.

The CRUJRA reanalysis is not “observations” and, as with all reanalyses, is subject to uncertainty itself. To test the sensitivity to the choice of reference dataset, we compared the CRUJRA to the ERA5 reanalysis dataset.

ERA5 is the fifth-generation reanalysis from the European Centre for Medium-Range Weather Forecasts (ECMWF; ). It uses a linearized quadratic 4D-Var assimilation scheme that takes the timing of the observations and model evolution within the assimilation window into account. Compared to the predecessor ERA-Interim reanalysis, it has a higher spatiotemporal resolution and assimilates more observations. The reanalysis is produced at an hourly time step and covers the time period 1979–2020. Its horizontal resolution is 0.1∘. As for the CRUJRA reanalysis, we aggregated the data to a daily time step and regridded the dataset to a 0.5∘ spatial resolution using first-order conservative regridding.

In addition to the climate forcing, both atmospheric CO2 concentration and nitrogen deposition are transient. We force LPJ-GUESS with the atmospheric CO2 forcing following historical data until the year 2014. For the remaining years, values for the shared socio-economic pathway SSP245 are used (both from ). We further prescribe historical nitrogen deposition until 2009. After 2009, LPJ-GUESS is forced with the nitrogen deposition following the representative concentration pathway RCP4.5 (based on ).

Our first step was to decide whether to use the full CMIP6 ensemble (“full ensemble”) or to select a subset of GCMs based on a selection criterion (“skilled”, “independent”, “bounding”; see Fig.  step 1 and Fig.  in the Appendix). Since precipitation is the single largest driver of variability in the Australian carbon cycle , we selected the GCMs solely based on the performance of projected precipitation. We next describe each of the selection criteria in more detail (see Fig.  step 1).

Once a selection of GCMs is made, the biases of a given GCM can be corrected (see Fig.  step 2). We explored six approaches using CRUJRA as our reference dataset. We corrected the three climate forcing variables, i.e., temperature, precipitation, and incoming shortwave radiation, and derived the correction based on the calibration time period 1989–2010 given this is common to both reanalysis products used here. We applied each method per pixel so that the different grid points were corrected independently of each other and tested the correction on both daily and monthly timescales, and we note that none of the correction methods used here are designed to correct temporal properties of the climate forcing. We show the corrections based on daily timescales in the main figures and use the corrections based on monthly timescales to assess the sensitivity to the correction timescale in the Supplement. To understand the sensitivity to the correction technique, we only corrected the five bounding models (see Sect. ) because they defined the total CMIP6 ensemble spread. In the subsections below, we describe the methods in more detail. In the following, O and S represent the observed and simulated variables at the same grid point for the calibration time period. P is the simulated variable for the projection period to adjust with bias correction methods, and C is the resulting bias-corrected variable. The projection period was split into 10 separate 25-year slices. The bias correction was then derived and applied to each calendar month on a daily time step within each time slice separately. Let Pt and Ct be the values of the variables at time t.

We ran LPJ-GUESS with a reference dataset (CRUJRA reanalysis), the full raw CMIP6 ensemble (which includes the skilled, independent, and bounding models) and additionally with the bounding models (see Sect. ) after they were bias-corrected according to the methods described in Sects. –.

LPJ-GUESS (; Lund–Potsdam–Jena General Ecosystem Simulator) is a widely used dynamic global vegetation model for climate–carbon studies . LPJ-GUESS simulates the exchange of water, carbon, and nitrogen through the soil–plant–atmosphere continuum by accounting for resource competition for light and space between plants. We adopted the global configuration of the model that uses 12 plant functional types (PFTs), simulating differences in growth form (grasses, broadleaved trees, or deciduous trees), photosynthetic pathway (C3 or C4), phenology (evergreen, summer green, or rain green), tree allometry, life history strategy, fire sensitivity, and bioclimatic limits for establishment and survival (see , for details). LPJ-GUESS is a second-generation DGVM part of the TRENDY ensemble (compare ) and explicitly represents demographic processes, such as stand age and size structure development, mortality, and competition, among locally co-occurring PFT populations, as well as disturbance-induced heterogeneity across the landscape of a grid cell.

We use LPJ-GUESS version 4.0.1 in “cohort mode”, where woody plants of the same size and age co-occur in a “patch” and, as such, are represented by a single average individual. Each PFT is represented by multiple average individuals, and one PFT cohort is defined as the average of several individuals. We run LPJ-GUESS with the plant and soil nitrogen dynamics switched on. Fire is simulated annually (stochastically) based on temperature, fuel availability, and the moisture content of upper soil layer as a proxy for litter moisture content .

After running LPJ-GUESS with either the raw or corrected climate data (step 3), the final step was to calculate an ensemble average of the resulting carbon fluxes. We focused on the total carbon storage (CTotal) and foliar projective cover (FPC) over Australia at annual time steps and the gross primary productivity (GPP) at seasonal time steps. We explored three different approaches based on the full ensemble or the selected models (see Sect. )

Our methods examine many of the approaches previously used to select from and/or constrain the CMIP6 ensemble in carbon cycle modeling. In this study, we seek to examine how applying these corrections methods affects the simulation of the Australian carbon cycle by LPJ-GUESS as a case study. In the following, we use the abbreviations defined in Table .

We tested six different methods for bias-correcting the CMIP model forcing driving LPJ-GUESS. Four methods incorporate univariate approaches (each climate variable is corrected independently), while the remaining two employ multivariate approaches (inter-variable relationships are accounted for). The methods tested range in complexity. The widely used scaling method applied in this study can correct the mean values of the variables; however, it cannot adjust variability and extreme values correctly (see, for example, ). The mean and variance approach therefore builds on the scaling method by correcting both mean and variance. We also considered two alternative approaches that attempt to correct the bias based on their distribution, i.e., quantile mapping and CDF-t. The basic quantile mapping method not only corrects the mean bias but also adjusts the distribution and may therefore be more suitable when both the average and extremes are studied. Based on quantile mapping, the CDF-t method additionally incorporates projected changes in mean and variability simulated by the GCM. In contrast to the univariate approaches discussed, multivariate correction methods allow us to adjust inter-variable dependencies. One of the main differences between the dOTC and R2D2 methods applied here is that dOTC is designed to transfer some of the multidimensional properties from the GCM to the bias-corrected data (such as the change in time; see ). The R2D2 approach instead assumes that inter-variable and intersite rank correlations are stable in time.

We found that all bias correction methods reduce the average bias of CTotal to that of the reference run for the five individual models. When deriving an arithmetic ensemble average of the raw and bias-corrected results, the values for the ensemble averages are relatively similar. Correcting the climate forcing significantly reduces the spread amongst the ensemble members compared to the raw model forcing. We further explored regional differences for Australia in the CTotal bias compared to our reference run and found that all bias correction methods reduce the magnitude of the bias. The spatial patterns in bias were consistent across the bias correction methods, implying that the relative spatial distribution of CTotal remains similar. We note that all maps display high values for both bias and CV in CTotal across the Tropic of Capricorn (23∘26′10.7′′ S). This is an artifact resulting from assumed model bioclimatic limits. In LPJ-GUESS, vegetation growth of C4 grasses and tropical trees is restricted by a lower temperature boundary such that these vegetation types cannot establish or survive when the 20-year-average minimum temperature falls below 15.5 ∘C. Therefore, C4 grasses and tropical trees only grow north of the Tropic of Capricorn, while south of it only temperate trees and C3 grasses are simulated. The strong variation across GCMs in simulated temperature thus leads to very different simulated vegetation cover (and thus high CV) in LPJ-GUESS.

In contrast to the average CTotal results, bias-correcting the forcing CMIP models does not necessarily lead to better results for other variables simulated by LPJ-GUESS. The different bias correction approaches did not necessarily lead to improved simulations of the change in CTotal compared to the target dataset. The arithmetic average across all five bounding models is relatively close to that of the reference run, and the upper boundary of the model spread was reduced when bias correction methods were applied. However, the lower boundary was almost the same or slightly worse than before (EC-Earth3-Veg). The different biases and magnitudes in CTotal reflect that the underlying vegetation composition may vary depending on the CMIP6 ensemble member used to run LPJ-GUESS and the bias correction method.

The foliar projective cover gives an indication of the fidelity of vegetation cover. In LPJ-GUESS, FPC results from simulated vegetation competition, which in turn is influenced by the climate input forcing. For example, water-limited regions such as arid Australia will have limited tree growth and increased grass growth. Further, competitive processes amongst tree species and C3 and C4 grasses that are driven by temperature (either dynamically or prescribed) can drive vegetation competition and therefore FPC. We found that temperate trees and C4 grasses in particular can vary strongly in dominance and relative cover depending on the GCM used as the input forcing and the bias correction applied. Only the two multivariate approaches adjust the distribution so that it is more comparable to the reference dataset and the other ensemble members. This implies that both the model selection and the bias correction method can lead to small but potentially important differences in composition of vegetation distributions across the landscape. Models that show large differences in the vegetation distribution are also sensitive to the bias correction for seasonal GPP. For the two models with the strongest divergence in C4 grass distribution, all bias correction methods improve the seasonal productivity compared to the target dataset. However, correcting the climate forcing also led to a lower skill in predicting seasonal GPP for one model (LGNorESM2-MM). We also found the foliar projective cover, especially that of C4 grasses, showed a strong sensitivity to the bias correction method chosen for some models (e.g., MPI-ESM1-2-HR). However, the spatial patterns in average bias of CTotal remain relatively consistent across all bias correction methods tested and show some similarity to that of the raw model forcing (LGEC-Earth3-Veg, LGKIOST-ESM, and LGNorESM2-MM). This outcome may emerge as we corrected each grid cell independently. When correct their climate variables taking into account spatial properties, both methods tested here improved the results for small regional scales. Given the heterogeneity of climate and large area of the Australian continent, we did not attempt to correct the spatial scales given limitations in computation time, but this would be worth exploring in future work.

In summary, within a framework of testing bias correction methods on the five models spanning the CMIP6 model spread, we found that the bias correction methods successfully reduced the bias to the reference dataset for averages over time and space (CTotal). Overall, the two multivariate approaches achieved a stronger reduction in bias for both individual GCMs and the ensemble average while also presenting a lower uncertainty across the ensemble. A clear advantage of applying multivariate approaches is that they account for inter-variable dependencies and can therefore preserve the consistency between the climate variables used to drive LPJ-GUESS. However, the variation across the different correction methods is small, and value ranges for multivariate approaches are comparable to the univariate quantile mapping approaches. Given the increased computation cost associated with multivariate approaches and the limited benefit demonstrated in this study, multivariate bias correction methods may therefore not necessarily be the best approach in future impact studies. Further, all correction methods show limited impact for other temporal properties (such as the change over time; e.g., ). For example, found that bias correction does not necessarily lead to a more realistic climate change signal. In a different study focusing on precipitation, demonstrated that long-term changes in simulated precipitation can artificially deteriorate following quantile mapping. Further, find that quantile mapping approaches can inflate relative trends in precipitation extremes projected by GCMs. The lack of skill in correcting temporal properties was also demonstrated for multivariate bias correction approaches . Using single models or even a subset of the ensemble may therefore not inform trends and processes on short timescales for studies exploring the future carbon cycle. Conversely, explicitly bias-correcting trends based on historical data, when the spatiotemporal nature may not yet have clearly emerged, could equally be problematic for unbiased estimation of climate system properties like equilibrium climate sensitivity. Despite the demonstrated limited impact of bias correction on temporal and spatial scales, correcting the driving forcing is still preferable to using raw climate forcing. DGVMs largely rely on bioclimatic limits that define where specific types of vegetation can grow. Relying on a biased climate forcing dataset might therefore result in a misrepresentation of the vegetation. Indeed, we found strong differences in the foliar projective cover of different vegetation groups. This mismatch in vegetation composition that can result from threshold-defined boundaries is likely to lead to diverging carbon and water cycle responses to the climate, which might be even more pronounced in areas with higher vegetation carbon mass than Australia. Future studies could further explore options to improve temporal features in climate variables. , for example, include time as an additional variable for their multivariate bias correction, which may be a promising avenue for future research.

Climate change impact studies need to be aware of the limitations of bias correction methods. As we have shown, bias correction cannot solve fundamental deficiencies in GCMs . A possible flaw in applying univariate bias correction methods to a set of climate variables needed to force a dynamic vegetation model is a resulting inconsistency within the climate forcing. While all bias correction methods improve the averages of CTotal compared to the target dataset, importantly, based on our findings it is not clear that one method systematically outperforms any other. This may be because the carbon cycle in Australia is mostly driven by precipitation, and for vegetation limited by both temperature and precipitation, multivariate approaches may outperform univariate approaches more distinctly . While the ensemble average is mostly insensitive to the choice of raw or corrected data, the spread between the outlier models is significantly reduced by any of the correction methods (especially the quantile mapping approaches and the multivariate dOTC method). Other temporal properties, such as the change over time, are not necessarily improved or can even deteriorate compared to the raw climate forcing, such as the trend, interannual variability or extreme events. Researchers should be especially cautious when they rely on a small sub-sample or even single models for their impact study, given different GCMs can react differently to the same bias correction method (e.g., for LGINM-CM4-8, the magnitude in bias is reduced, while for LGNorESM2-MM the sign in bias can change depending on correction method applied).

We also tested the commonly used arithmetic ensemble average, a weighted averaging approach following , and a random forest regression approach. We found that the weighted average and the random forest approach outperform the arithmetic ensemble average for average CTotal, and seasonal GPP with results very similar to the reference dataset. The random forest approach produces a small error magnitude when spatial dimensions are explored (see Fig. ) while for the arithmetic and weighted ensemble average, systematic biases persist. While the FPC of tropical trees and C3 grasses seems to be broadly captured by all averaging methods, C4 grasses shows a strong bias where only the random forest approach achieves a median value within the IQR of the LGCRUJRA run. As shown in previous studies (e.g., ) there is benefit to avoiding the use of the arithmetic ensemble-averaging method for impact studies. An additional caveat of the arithmetic ensemble average is the sensitivity to the model selection. The ensemble average somewhat depends on the models it is derived from. Counterintuitively, choosing the models that show high skill in simulating precipitation led to the worst results in most cases (a result similar to ).

All methods explored in this study rely on the general assumption that the reanalyses used to describe the historical time period are accurate and that the methods employed apply equally to the past and the future. It seems reasonable to argue that methods that fail to constrain models in the historical period are unlikely to work well for future periods. Unfortunately, the converse point that methods that work well in the historical period will necessarily work well in the future is not always true. Shifts in atmospheric circulation, emergence of novel climates, or the triggering of ecosystem tipping points might alter land–atmosphere feedbacks that lead to changes in the climate such that methods that are reliable in the historical period cease to be reliable in the future.

A possible caveat in our study setup is the design of the ensemble subsets. We selected all models based on the simulated precipitation based on the assumption that precipitation is the most important driver of Australia's carbon cycle. However, temperature and perhaps the extremes of temperature may also be an important constraint for vegetation distribution (especially in LPJ-GUESS where vegetation grows within predefined bioclimatic limits that are based on temperature like the boundary between C3 and C4 grasses). However, when we repeated the analysis using the raw temperature and incoming shortwave radiation forcing and bias-corrected precipitation data, the results were almost identical compared to the runs where all climate variables were corrected, confirming that precipitation drives the carbon cycle response within this framework. Further, for simulating vegetation the skill of the variables may be important on multiple timescales. We attempt to account for this in the model selection methods by applying the respective metrics on monthly and annual timescales. In addition, the response of the simulated terrestrial carbon cycle to the climate forcing is intimately linked to the sensitivity to the atmospheric CO2 concentration. This study chose a model setup with both transient atmospheric CO2 concentration and nitrogen deposition, and therefore it does not fully isolate the impact of the climate forcing. However, given all LPJ-GUESS simulations have the same configuration apart from the climate forcing, i.e., the prescribed atmospheric CO2 concentration and nitrogen deposition are identical, we argue that our experiment setup is suitable for this study. Lastly, five models for all selection methods may seem like a small subset. However, earlier studies (e.g., ) found that the multi-model ensemble mean tends to converge towards a similar value after including five models. We therefore conclude that five models was a sufficient number in our testing framework.

We further chose a relatively short calibration time period (1989–2010) to allow sensitivity tests with multiple reanalysis datasets. While these 22 years may not cover decadal variability, we assume it is sufficient to account for interannual variability such as the El Niño–Southern Oscillation, the Indian Ocean Dipole, and Southern Annular Mode, which have been shown to be important influences on the Australian carbon cycle (e.g., ).

Other areas of uncertainty may include the sensitivity of the methods to the reference dataset. Several studies have discussed that both bias correction methods (e.g., ) and weighted ensemble-averaging methods (e.g., ) depend on the observation dataset they are calibrated on. demonstrate that precipitation in particular is sensitive to the choice of reference dataset. We therefore repeated the bias correction and chose ERA5 as a second dataset. We found high correlation coefficients between LPJ-GUESS runs that are based on GCMs corrected to CRUJRA and LPJ-GUESS runs that were based on GCMs corrected to ERA5 for CTotal (0.96–0.98; not shown here). We conclude that our results were robust to the choice of reference dataset. Another concern frequently discussed is impact of the mismatch in spatial resolution (high-resolution reanalysis product vs. low-resolution GCM output). A solution to reduce the mismatch in spatial resolution might be to use dynamically downscaled datasets such as CORDEX. However, find the impact of the horizontal resolution on the bias correction results to be small in comparison to the impact of the bias correction method. Given dynamically downscaled products were only available for older CMIP generations (CORDEX is based on CMIP5, while NarCLIM is based on CMIP3) or contained only a small subset of GCMs (ISIMIP), and we expected the uncertainty associated with the spatial mismatch to be small, we chose the state-of-the-art CMIP6 GCM output.

Further, in this study, we chose just one realization from each GCM, and therefore the results presented in this study do not fully reflect the uncertainty in simulations of the terrestrial carbon cycle linked to the entire spectrum of possible GCM forcings. Adding more realizations would significantly increase the computational costs, and we do not expect that our results would differ significantly. looked at the effects of additional ensemble members in their assessment of future rainfall change and found limited sensitivity. Nevertheless, to fully understand the impact of uncertainty in simulated climate within individual GCMs, future work could consider using the CESM large ensemble. In addition, showed significant uncertainty in the simulated terrestrial carbon cycle linked to the choice of DGVM, but in this study we chose a single DGVM to study the impact of climate uncertainty. However, to capture the full uncertainty and to achieve a stronger constraint on the simulated terrestrial carbon cycle, future work could explore the response in other members of the TRENDY ensemble and create an ensemble composed of both different DGVMs and different GCM climate forcings.

Lastly, we chose to correct daily climate data for the main analysis. However, correcting monthly data may be statistically more robust, especially for highly variable climate variables with a large number of null values such as daily precipitation. Indeed, our analysis of the corrected input variables surprisingly showed an increase in bias in simulated precipitation for two GCMs after correction (see Fig. ) that is likely linked to a mismatch in simulated days without rain in the target dataset and the GCM simulation. We additionally tested the importance of timescales; i.e., we bias-corrected the GCMs on both daily and monthly timescales before forcing LPJ-GUESS with them. CTotal simulated by LPJ-GUESS driven by daily and monthly corrected GCM output was strongly correlated (0.92–0.99; not shown here). Given only a few grid cells displayed an unreasonably high bias in precipitation (not shown) and the fact that vegetation growth is also driven by temperature and incoming shortwave radiation in LPJ-GUESS, we assume that the impact on the simulated carbon on monthly to multidecadal timescales is small.

Based on our findings, we conclude that decisions in regard to model selection, bias correction of GCM output, and ensemble-averaging methods, may alter future projections of ecosystem studies, especially the uncertainty estimates. Selecting a subset of models to reduce computation time is common, but sensitive to the criterion chosen for both arithmetic average and uncertainty estimate. While choosing GCMs based on how well they represent the historical climate may seem intuitive, we find that the arithmetic average based on a subset representing only independent models or models that define the full ensemble spread reduces the bias compared to our reference run. Conversely, a subset of only skilled models reduces the ensemble uncertainty. However, this reduction in uncertainty may stem from the wrong biophysical reasons, and a sub-selection of skilled models might not truly represent all plausible GCM outputs.

We further demonstrate that correcting GCM output can significantly alter Australia's carbon cycle projections. Bias corrections, however, only reduce the biases in relatively steady vegetation variables, such as the longer-term carbon states. Averaged over the continent, we find that LPJ-GUESS forced with individually corrected GCM output can be sensitive to the bias correction method, but the arithmetic ensemble averages were found to be insensitive. Some bias correction methods did reduce the ensemble uncertainty more than others (e.g., scaling vs. dOTC). On smaller scales, i.e., exploring regional differences or on PFT level, the choice of bias correction method can have a big influence on species distribution and magnitude in fluxes. Correcting biases may also lead to different outcomes relying on thresholds of absolute values when applied to individual GCMs, such as for climate threshold studies exploring tipping points.

Importantly, bias correction methods do not correct temporal (such as IAV or trend) and spatial properties unless the methods are specifically designed and set up to do so. We found that using corrected GCM output can even increase the distance in change compared to our reference dataset. Future studies of ecosystem and carbon cycle impacts based on GCM climate forcing should therefore carefully choose a subset of models that is representative of the ensemble uncertainty and not rely on using a single GCM.

To conclude, when Pandora opened the lid on her box she released the evils of the world, and these could never be put back into the box. We fear that we have also made the challenge of constraining the future regional-scale carbon budgets more difficult. We have, for example, raised more questions than answers, identified limitations of existing approaches, and ultimately provided a challenge to the community to find more robust strategies to reduce the uncertainty in the projection of regional carbon stores. We acknowledge we have not provided easy answers, but we hope that by highlighting the challenges, strategies may be developed that can robustly constrain regional estimates of carbon storage.