Path-dependent reductions in CO2 emission budgets caused by permafrost carbon release

Emission budgets are defined as the cumulative amount of anthropogenic CO2 emission compatible with a global temperature-change target. The simplicity of the concept has made it attractive to policy-makers, yet it relies on a linear approximation of the global carbon–climate system’s response to anthropogenic CO2 emissions. Here we investigate how emission budgets are impacted by the inclusion of CO2 and CH4 emissions caused by permafrost thaw, a non-linear and tipping process of the Earth system. We use the compact Earth system model OSCAR v2.2.1, in which parameterizations of permafrost thaw, soil organic matter decomposition and CO2 and CH4 emission were introduced based on four complex land surface models that specifically represent high-latitude processes. We found that permafrost carbon release makes emission budgets path dependent (that is, budgets also depend on the pathway followed to reach the target). The median remaining budget for the 2 °C target reduces by 8% (1–25%) if the target is avoided and net negative emissions prove feasible, by 13% (2–34%) if they do not prove feasible, by 16% (3–44%) if the target is overshot by 0.5 °C and by 25% (5–63%) if it is overshot by 1 °C. (Uncertainties are the minimum-to-maximum range across the permafrost models and scenarios.) For the 1.5 °C target, reductions in the median remaining budget range from ~10% to more than 100%. We conclude that the world is closer to exceeding the budget for the long-term target of the Paris Climate Agreement than previously thought. Carbon release from permafrost thaw would substantially decrease the amount of carbon emissions required to meet climate targets, according to climate simulations.

latitudes 13,14 will indeed diminish the budget of CO2 humankind can emit while staying below a certain level of global warming. Permafrost carbon release is also an irreversible process over the course of a few centuries 13,14 , and may thus be considered a "tipping" element of the Earth's carbon-climate system centuries 15 , which puts the linear approximation of the emission budget framework 1, 4,5,16,17 to the test.
To quantify the impact of permafrost carbon release on emission budgets, we use an Earth system model of reduced complexity whose processes are parameterized to faithfully emulate more complex models. OSCAR v2.2.1 -a minor update of v2.2 (ref. 18 ) -is run in its default configuration which is comparable to the median of its probabilistic setup. Therefore, all our results are for ~50% chance of meeting the temperature targets. OSCAR is extended here with a new permafrost carbon module that emulates four state-of-the-art land surface models: JSBACH (Methods), ORCHIDEE-MICT (ref. 19 ), and two versions of JULES (ref. 20,21 ). These complex models have been specifically developed to represent high latitude processes, in particular soil thermic and biogeochemistry mechanisms that control carbon sequestration and emission. In this new emulator, permafrost carbon in two high-latitude regions is represented as an initially frozen pool that thaws as global temperature increases. Thawed carbon is not immediately emitted: it is split between several pools, each with its specific timescale of emission. We assume 2.3% of the emission occurs as methane 14 (see discussion and Methods regarding the uncertainty of this value), and this emitted CH4 is fully coupled to the dynamical atmospheric chemistry of OSCAR. More details on the protocol, the emulator and the models are provided in Methods.
We do not assume a priori that reductions in emission budgets can simply be calculated as the cumulative permafrost carbon release in a given scenario. Quite the opposite, we apply three specifically designed approaches to estimating emission budgets. The first one is the "exceedance" approach, in which the budget is a threshold in terms of cumulative anthropogenic CO2 emissions above which the temperature target is exceeded (with a given probability). The second one is the "avoidance" approach, in which the budget is another -typically lower -cumulative emissions threshold below which the target is avoided (also with a given probability). These two approaches were used in the fifth IPCC assessment report 6,22 . However, none of them considers the possibility of overshooting the target first, and returning below it in a second time. To investigate such a case, we adapt the approach by MacDougall et al. 12 to create "overshoot" budgets.

Reductions in exceedance and avoidance budgets
With the exceedance approach, budgets are calculated in any given scenario as the maximum cumulative CO2 emissions before the point in time when global temperature reaches the target level for the first time. This is illustrated in Figure 1   (Uncertainties are the minimum-to-maximum range across permafrost models and scenarios.) Our results are ~2% different from the IPCC estimates based on complex models 6 . This confirms that OSCAR's default configuration gives results consistent with the Earth system models used in previous climate change assessments.
When permafrost carbon processes are included, exceedance budgets are reduced by 30 [10-120] Gt CO2 for 1.5°C and 60  Gt CO2 for 2°C (Figure 2a and Supplementary Table 1). This is only a few percentage points of the total budgets, but it corresponds to a more substantial reduction in the remaining budgets ( Figure 2b). It is also smaller in magnitude than previously estimated with a model of intermediate complexity 12 , which can be explained by the over-sensitivity of the permafrost carbon model used in this earlier study (Table 1). An important (known) caveat of the exceedance approach is that it ignores the system's dynamics after the point in time at which the temperature target is reached 22 . This is especially important for permafrost carbon, since a significant part of the thawed carbon keeps being emitted long after the target is first reached (Supplementary Figure 3), implying the temperature target will actually be surpassed if budgets are based on this approach.
With the avoidance approach, budgets are calculated using a large ensemble of peak-anddecline emission scenarios whose values of peak temperature and maximum cumulative CO2 emissions are used for interpolation (Figure 1, Methods and Supplementary Figure 1). This approach accounts for the complete system's dynamic by ensuring that the temperature target is never exceeded. Its drawback, however, is its intense computing requirement that makes it extremely costly to follow by complex models. Here, we create and use an ensemble of 3,120 scenarios, by combining 520 fossil-fuel CO2 emission scenarios of our own making (Supplementary Figure 4) to the land-use and non-CO2 climate forcers from the six scenarios previously used for exceedance budgets (Methods).
Permafrost carbon reduces avoidance budgets by 60  Gt CO2 for 1.5°C and 100 [20-270] Gt CO2 for 2°C (Figure 2a). This reduction in avoidance budgets is systematically larger than for exceedance budgets: by 20% to 140% across all the emulated permafrost carbon models ( Figure 3). This confirms that the exceedance approach only partially captures the impact of permafrost carbon release on emission budgets. We conjecture that other slow and strongly non-linear processes such as forests dieback 15,24,25 would also be incompletely accounted for with exceedance budgets. Since the exceedance approach was the only one used by complex models in the fifth IPCC assessment report 6,22 , we conclude that future updates of emission budgets based on such models will remain biased without a change in experimental protocol.

Path-dependency and overshooting pathways
Our ensemble of 3,120 scenarios for avoidance budgets covers a large enough spectrum of possible futures that it can be split into two groups (Methods and Supplementary Figure 4). In the subgroup of scenarios which have no net negative emissions (noted "NetNegEm0"), the permafrostinduced reduction in avoidance budgets is 90    Figure 2a). This is systematically more than in the subgroup of scenarios in which net negative emissions are extensively implemented ("NetNegEm+") ( Figure 3). The physical reason for this is that extensive net negative emissions artificially make temperature peak a few years after they are introduced, whereas when net negative emissions are not available the peak of temperature is entirely caused only by natural processes, and permafrost carbon emissions can delay it for decades (Supplementary Figure 5). The fact that the effect of permafrost carbon release depends on the emission pathway is proof that inclusion of such a previously unaccounted for tipping process renders emission budgets path-dependent. In other words, the emission budget compatible with a given target depends on both the timing and magnitude of anthropogenic emissions, and not only on their magnitude.
To investigate further this path-dependency, we look into overshoot budgets using the same ensemble of scenarios as for avoidance budgets (Methods). Net overshoot budgets are calculated as the sum of two gross budgets: a "peak" budget that is exactly the same as an avoidance budget for a given peak temperature above the long-term target, and a "capture" budget that corresponds to the amount of net negative emission required to return below the long-term temperature target (Figure 1 Table 1.) The permafrost-induced reduction is systematically more pronounced in these cases than in non-overshooting scenarios ( Figure 3) because of the additional capture required to counteract the extra emission from thawed permafrost that occur during the overshoot period. It is already known that the rest of the carbon-climate system (i.e. excluding permafrost) exhibits a path-dependent behaviour under overshooting scenarios 29 (see also Supplementary Figure 6), but our results show that permafrost carbon release strongly reinforces this rupture of the linear approximation of the emission budget framework.

Discussion and policy implications
A permafrost-induced path-dependency of emission budgets was already implied by MacDougall et al. 12 , although their quantification of the effect was biased by the high sensitivity of their permafrost carbon release in response to high-latitude warming (Table 1; note that an update of their model showed a lower bias 26 ). Their study also focused on exceedance budgets and a handful of overshooting scenarios that did not correspond to political commitments. The Paris climate agreement indeed aims at avoiding 2°C, which implies avoidance budgets are needed. It also recognizes an overshooting trajectory by setting the long-term target to 1.5°C, which means overshoot budgets are also needed.
A few earlier attempts at quantifying the permafrost-induced reduction in emission budgets were also made 11,13 , albeit without applying any of the budget-calculation approaches we use. They It was not retained in the fifth IPCC assessment report 6 . Additionally, these earlier studies did not find path-dependency, either because only one scenario was investigated 11 or because path-independency was assumed 13 .
The OSCAR v2.2.1 model with its new permafrost carbon emulator estimates future carbon release from thawing permafrost within the range of existing studies (Table 1). A cumulative 60 [11-144] Pg C is projected to be released by 2100 under RCP8.5, slightly lower than the 37-174 Pg C reviewed by Schuur et al. 14 , and close to the 28-113 Pg C obtained with a data-constrained model by Koven et al. 30 . Uncertainties in permafrost-related processes and their response to climate change remain very high, however, and there are elements that suggest our results are conservative. Deep (e.g. Yedoma) and seabed permafrost thaw is not modelled. Should these carbon stocks be mobilized, budgets would be further reduced. Changes in nitrogen cycling caused by permafrost thaw are also ignored. They could lead to emission of N2O (ref. 31 ) but also changes in the ecosystems' net carbon balance 32 .
We also assume a constant fraction of permafrost carbon is emitted as CH4, while the value and future evolution of this fraction are uncertain 14,33,34 . With this constant value, we simulate an emission of 3.7 [0.7-10.5] Tg CH4 per year over the 1980-2012 period, in line with a recent review 35 . This methane contributes a non-negligible fraction of the reduction in emission budgets ( Figure 4). This contribution is also path-dependent, contrary to what was obtained in earlier studies 13,33 by using a fixed global warming potential (GWP). It is, however, a well-known caveat of GWPs (or any other emission metric) that they are linear and constant while the actual Earth system behaves in a complex, dynamical and non-linear fashion 36-39 , and that they cannot be naively used in combination with emission budgets 40 .
Because of all these uncertainty sources, we assume that no probabilistic distribution of the permafrost-induced effect can yet be drawn from our results, and we provide its full range. Reducing this uncertainty, by fostering observation-and model-based research on permafrost and other tipping processes of the Earth system, is key to knowing if and when the world will enter an overshooting climatic regime. Meanwhile, permafrost adds to the uncertain context under which climate policy decisions must be taken 41-43 . Careful policy-making might entail taking the pessimistic end of our estimates.
Nevertheless, we have shown that accounting for tipping elements of the Earth system breaks the apparent linear behaviour of the carbon-climate system, which equates to making emission budgets path-dependent. This renders manipulating budgets more delicate than previously thought, as budget users have to make assumptions regarding the long-term target, but also the shorter-term target (e.g. risk of overshooting) and even the reliance on certain technologies (as we have demonstrated for net negative emissions). Furthermore, we have quantified a substantial permafrost-induced reduction in remaining budgets for low-warming targets. It ranges from ~5% to as much as ~40% for 2°C, and from ~10% to more than 100% for 1.5°C, under present-day non-CO2 forcing and for ~50% chance of meeting the temperature targets. Whether the world has already breached the budget for 1.5°C remains elusive, however. It depends on many factors including the uncertainty on past anthropogenic emissions 44,45 , the amount of forcing by non-CO2 species that will be mitigated in the near future 12,46,47 , and a possible bias in the models' simulated present-day global temperature 7-10 (not accounted for in this study).
Irrespective of these uncertainties, it appears that the attainability of the Paris agreement is more compromised than suggested by an existing literature that largely ignores tipping or irreversible feedbacks of the Earth system.

OSCAR v2.2.1
OSCAR is a compact Earth system model whose modules are calibrated to emulate the behaviour of more complex models 18  The above protocol is further adjusted so that, when atmospheric CH4 concentration deviates from that of the original RCP because of CH4 emission from permafrost thaw, OSCAR also calculates the associated change in radiative forcing from stratospheric H2O and tropospheric O3 (ref. 18,36 ).
In this study, OSCAR is not run in a probabilistic fashion: we use the default configuration of the model to save computing time. This implies that the full uncertainty of the Earth system is not sampled in this study, and only that of the permafrost system is, under a close-to-median configuration of the rest of the model. The default configuration has an equilibrium climate sensitivity for CO2 doubling of ~3.2°C. A comparison of the default and median results for key variables of the model is provided in Supplementary Figure 8, for our six scenarios and in the case without permafrost thaw. The median results are obtained by running an unconstrained Monte Carlo ensemble of 2,000 elements, as in ref. 18 . Supplementary Figure 8 shows that the default and median atmospheric CO2 and global temperature simulated variables remain close, with a normalised root-mean square error (nRMSE) <5%.
Two noticeable biases are identified, however. First, the default configuration gives a lower atmospheric CH4 than the median, which suggests that our results underestimate the additional effect of CH4 emission caused by permafrost thaw. Second, for RCP2.6 (a peak-and-decline scenario) and to a lesser extent for RCP4.5 (a stabilizing scenario), the default configuration warms more than the median, indicating that our capture budgets are likely overestimated (which may partly compensate for the protocol-induced underestimate described in main text).

Permafrost carbon emulator
We couple a permafrost emulator to OSCAR v2.2.1, calibrated on four land surface models: JSBACH (see dedicated section), ORCHIDEE-MICT (ref. 19 ), and JULES (ref. 20 ) following the two different versions "DeepResp" and "SuppressResp" (ref. 21 ). The calibration of the parameters defined hereafter is done using outputs of the complex models for integrations over 1850-2300 of the RCPs 8.5, 4.5 and 2.6. In this emulator, we calibrate and separately run the permafrost system of two aggregated regions of the globe: North America and Eurasia. In these models, we call "permafrost carbon" the carbon that was frozen (and therefore inactive) during preindustrial times. All parameter values are given in Supplementary Table 4. First, we model the regional air surface temperature change (T i ) in each region i with a linear dependency on global temperature change (T): The parameters i are calibrated with a linear fit between T i and T ( Supplementary Figures 9 and 10; first row). Note that this parameter represents a feature of the climate system. It does not actually come from the emulated land surface model, but rather from the climate model it uses as input. In the case of JSBACH, it is the MPI-ESM-LR model's results for CMIP5 (ref. 57 ). In the case of ORCHIDEE and JULES, the detailed protocol of the simulations used is provided by ref. 21 . For JULES, we take the average of all realizations made with IMOGEN, and for ORCHIDEE we take only one realization made with IMOGEN emulating HadCM3.
Second, we calibrate the temperature-dependency of the heterotrophic respiration rate of nonpermafrost carbon (r) following a Gaussian law 58 : Third, we introduce the "theoretical thawed fraction" ( ) that can take values from -pmin to 1, with a preindustrial value of 0. It corresponds to the fraction of thawed permafrost carbon for a given regional temperature change, but neglecting dynamic considerations. It is fitted by an S-shaped function: pmin represents a hypothetical (i.e. never reached) case of fully frozen soils, p is a shape parameter, and p is the sensitivity parameter. The three parameters are calibrated with the same fit ( Supplementary  Figures 9 and 10; third row), with the additional constraint that pmin cannot be greater than the ratio of the model's non-frozen soil carbon over frozen soil carbon in preindustrial times. In the case of JSBACH, because there is no re-freezing in the model, we calibrate this relationship on the scenario with the fastest warming only (i.e. RCP8.5). For ORCHIDEE and JULES, the calibration is made with all scenarios. Therefore, the exact physical meaning of depends on the emulated model. Fourth, we introduce an asymmetric dynamic behaviour in the thawing/freezing process by defining the "actual thawed fraction" (p) which is lagging behind the theoretical thawed fraction : thaw and froz are the speeds of thawing and freezing, respectively. They are calibrated simultaneously with transient simulations ( Supplementary Figures 9 and 10; fourth row), using equations (3), (4) and (5) driven only by the regional temperature change taken from the emulated model, i.e. not using Fifth, a frozen carbon pool (Cfroz) changes with time following the thawing carbon flux (Fthaw) calculated as the product of the frozen pool size during preindustrial times (Cfroz,0) by the speed of change in (i.e. time-derivative of) the actual thawed fraction: Inspired by Koven et al. 30 , the thawing flux is then split between three thawed carbon pools (CtN) following partitioning coefficients ( tN). Note, however, that for some models we reduced the number of thawed carbon pools to avoid over-fitting (see Supplementary Table 4). Each thawed carbon pool is then subjected to heterotrophic respiration with its own turnover time ( tN). The respiration rate is affected by regional temperature change following the same law as in equation (2), except that the sensitivities are modified by a factor t. This gives: To ensure mass balance, we must have: t3 = 1 -t1 -t2. The other six parameters are calibrated simultaneously with transient simulations by fitting the respiration flux simulated by our emulator to the actual complex model's flux ( Supplementary Figures 9 and 10; fifth row). To do so, we use only equation (7), driven by the complex model's thawing carbon fluxes and heterotrophic respiration rates.
Finally, the permafrost carbon emissions (Epf) are deduced as: The overall performance of the emulator is shown in Supplementary Figures 9 and 10

Effect of methane emissions
A fraction of 2.3% (ref. 14 ) of permafrost carbon emission is assumed to be CH4. This value is assumed to remain constant throughout the simulations, since the future response of this fraction to environmental changes (e.g. climate or CO2) is unclear 33 . In OSCAR, the atmospheric evolution of these CH4 molecules is tracked in a separate manner, so that, when the permafrost-induced CH4 is oxidized in the atmosphere, we add the newly formed CO2 to the atmospheric CO2 pool. Therefore, the long-term addition of CO2 to the atmosphere caused directly by permafrost thaw does not depend on the CH4 fraction. The transient warming and ensuing feedbacks in the system, however, are a function of this fraction.
To investigate this effect, two additional series of simulations are performed: one without and one with doubled methane emission (i.e. fractions of 0% and 4.6%, respectively). The methane effect shown in Figure 4 is equal to the difference between the budgets obtained in the main simulations with 2.3% of methane and those obtained in the simulations with 0%. We also find that the difference between the 4.6% and 2.3% simulations is approximately the same as that between 2.3% and 0% (not shown), which suggests the absolute contribution of methane is roughly linear in this domain.

Exceedance budgets protocol
To obtain the exceedance budgets, we run our six scenarios with the permafrost module turned off and with its four alternative configurations. This is a total of 6 × 5 = 30 simulations. By definition, for each of these simulations, the exceedance budget is the maximum cumulative amount of anthropogenic CO2 that is emitted up to the time when the given temperature target is exceeded 22 . So the exceedance budgets are calculated as: for ( ) and where Bexc is the exceedance budget, EFF is the yearly fossil-fuel CO2 emission, ELUC is the yearly CO2 emission from land use change, t0 the year the simulation starts, T the simulated temperature change, and Ttarget the target temperature change.

Fossil-fuel CO2 emission pathways
For the avoidance budgets, we require a set of varied CO2 emission pathways that cover a wide range of possible futures. We create these emission pathways as the sum of one positive emission pathway and one negative: The pathway of positive emission is defined using a parameterized analytical formula of the peak-and-decline form on a semi-infinite interval 59 : where = ( ) exp( ( )). We also define the total cumulative positive emission (Q+) of this pathway: Here, t0 is the starting year of the simulation, t1 the last year of the historical data, tm the time at which mitigation begins, r the historical growth rate of fossil CO2 emissions, and m the mitigation rate. The value of r is taken as the mean of the growth rate over the last ten years of the historical period (r = 0.022623 yr -1 ). The mitigation rate m is deduced from the other parameters: with = (1 exp( ( )). Each positive emission pathway is uniquely defined by the tuple (t1, tm, Q+).
In a similar manner, the negative emission pathways are defined following a logit-normal law on a finite interval: with: where tf is the last year of the simulation, and two shape parameters, tlag the time between mitigation of positive emission starts and negative emissions start, and Q-the cumulative amount of negative emissions. Each negative emission pathway is uniquely defined by the tuple (tlag, , , Q-).
Using the above equations, we create 520 fossil-fuel CO2 emission pathways by combining different values for the positive emission tuple (t1, tm, Q+) and the negative emission one (tlag, , , Q-). A full list of these 520 combinations of parameters is provided in Supplementary Table 5. The obtained emission pathways are also represented in Supplementary Figure 4.

Avoidance budgets protocol
To calculate the avoidance budgets, we run simulations with the 520 fossil-fuel CO2 emission pathways combined with the six scenarios we already have for all other drivers of the model (i.e. non-CO2 forcings and land-use drivers), with the permafrost module turned off and with its four alternative configurations. This leads to a total of 520 × 6 × 5 = 15,600 simulations. We note that our approach of combining two independent sets of scenarios likely lead to an overestimation of the scenario-related uncertainty, since we implicitly combine inconsistent sources of CO2 and non-CO2 emissions 46 . It allows, however, for a systematic analysis of the effect of non-CO2 forcing (using e.g. Supplementary   Table 1).
Then, for each of these simulations (superscript i), we calculate the maximum temperature of the simulation: and its maximum cumulative CO2 emissions: If any of these two maxima occurs at the last time step of the simulation (tf), the simulation is discarded.
With this approach, we are certain that an emission budget of Bmax ensures that global temperature do not go above Tmax, given the non-CO2 and land-use forcings of the ith scenario.
However, we have no control over the individual values of Tmax. Therefore, to deduce the avoidance budgets (Bavo) for an exact temperature target, we interpolate linearly in the ( , ) phase space, within the Tmax value interval of ±0.2°C around Ttarget. We acknowledge this is not exactly the approach followed by ref 46 . However, our approach does respect the philosophy of the "avoidance" budget in ensuring that the temperature target is indeed avoided. Obviously, for a given non-CO2 and land-use scenario, any budget lower than the deduced Bavo also implies avoiding the temperature target.

Net overshoot budgets protocol
Net overshoot budgets (Bnet) are the combination of two budgets: an emission budget to reach peak temperature (Bpeak) and a capture budget consisting of the cumulative amount of negative emission required to go back to the targeted temperature (Bcap < 0): = + . Therefore, net overshoot budgets are defined for a given temperature target and a given level of overshoot (Tover), with peak temperature then being given by: = + .
To calculate Bpeak and Bcap, we use the same ensemble of scenarios as for the avoidance budgets.
In each case, we take only the subset of scenarios whose maximum temperature is ± 0.2°C of the chosen Tpeak and then declines by at least Tover. For each of these scenarios (superscript j), we calculate and exactly as we do for the avoidance budgets in equations (15) and (16). We also calculate : = min ( ) + ( ) ( ) + ( ) 0 for ( ) and using Iverson brackets in the notation. (They take a value of 1 iff the logical test in the brackets is true, and 0 otherwise.) Then, just as with the avoidance budgets, we linearly interpolate Bpeak and Bcap in the ( , ) and ( , ) phase spaces, respectively. The net overshoot budget Bnet is deduced by summation of Bpeak and Bcap. We note again that this protocol, being somewhat similar to the exceedance protocol in its formulation, ignores everything that may occur after the temperature goes back below the targeted value. It therefore provides a lower-bound estimate of future capture requirements.

Extra data processing
To be consistent with IPCC (ref. 6  text. We also discard estimates of Bavo and Bpeak for which the coefficient of determination (R 2 ) of the linear fit is less than 0.50.

Remaining budgets calculation
B) are calculated as = , where B can be Bexc, Bavo or Bnet., and Bhist is the historical cumulative CO2 emission from anthropogenic activities (fossil-fuel burning, industry-and land-related). We take Bhist = 2240 Gt CO2 (ref. 44 ). In Figure 2b, we show the relative reduction in remaining budgets caused by permafrost carbon release, that is: 1, where the subscript "1" is for a case with permafrost carbon processes, and "0" one without. In Figure 3, we show reductions in budgets relative to those in the exceedance case: .

Permafrost in JSBACH
The earlier CMIP5 version of the Max Planck Institute Earth System Model land surface scheme JSBACH (ref. 60,61 ) is extended with a multilayer hydrology scheme 62 , a representation of permafrost physical processes 63 , as well as the improved soil carbon model YASSO (ref. 64 ). For permafrost carbon stocks, we represent carbon cycling in the active layer by the YASSO model, while we prescribe frozen carbon stocks below the active layer from the Northern Circumpolar Soil Carbon Database (NCSCD) version 2 (ref. 65 ). When the active layer thickness changes, we transfer carbon from the prescribed frozen carbon stocks into the active YASSO carbon pools.

Data availability
RCP scenarios are available at: http://www.pik-potsdam.de/~mmalte/rcps/. The data that support the findings of this study are available from the corresponding author upon request.

Code availability
The source code of OSCAR is available at: https://github.com/tgasser/OSCAR. The code used to generate all the results of this study is available from the corresponding author upon request.