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Impulse-response-function (IRF) models are designed for applications requiring a large number of climate change simulations, such as multi-scenario climate impact studies or cost-benefit integrated-assessment studies. The models apply linear response theory to reproduce the characteristics of the climate response to external forcing computed with s...
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In the context of climate change, emissions of different species (e.g.,
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different radiative efficiencies and lifetimes. Since comparisons via
detailed climate models are computationally expensive and complex,
emission metrics were developed to allow a simple and straightforward...
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... Response theory [9, 10,11] is perfectly suited to both objectives 1.) and 2.), 71 as it is predicting the (appropriate) expectation value of the variable of interest, also referred to as the 72 "forced response" or the climatic (ensemble) mean of the variable [12,13,14,15,16,17]. Response theory 73 is increasingly favoured in climate science [18,19,20,21,22,23,24,25,26,27,7,28,29]; and we have 74 applied it to develop our own ESM-or climate emulator (Methods) in order to facilitate our analysis. 75 2 Main 76 The existential threat by climate change is associated with the so-called "business as usual" (BAU) 77 greenhouse gas (GHG) emission-or socio-economic development scenario, one when no effort is made 78 to cut carbon emissions, commonly termed as "abatement", in conflict with economic dynamics, i.e. no 79 policy intervention is applied. ...
There is a palpable shift in mainstream attitude towards geoengineering, seen now as a potential part of a climate policy mix. Still, no-one wants to get on a slippery slope, compounding the risks, and, therefore, we should ask ourselves what is the minimal geoengineering that we can get away with. Such questions lead mathematically to inverse problems. Solving them is feasible only with lightweight models of the climate system, various types of which are nowadays often referred to as emulators – some more accurate than others. Here we develop an emulator using nonlinear response theory and apply it to two paradigmatic inverse problems relevant to climate policy. First, we investigate the attainability of the coveted Paris15 temperature targets. Second, through a simple multi-stable model, we determine what it takes to save the Greenland ice sheet (GrIS) as we know it. Our results suggest, first, that solar radiation management (SRM) geoengineering, most commonly envisaged as sulfate aerosol injection, will likely have to be part of our climate policy mix, because realistic CO2 abatement effort to come alone cannot restrict global temperatures below 1.5 ◦C change or below even higher levels of change. Minimal sulfate use for a threshold target is achieved by immediate and abrupt deployment. Second, we demonstrate also the importance of precisely knowing not only the stable but also the unstable so-called Melancholia states of climate tipping elements, such as the GrIS, as miscalculations can lead to acting too late – whether it is CO2 abatement on the short term or SRM geoengineering deployed in the far future.
... Joos and Bruno, 1996). Because with accumulation of CO 2 in upper layers of the ocean the ability for further uptake of CO 2 decreases (Hooß et al., 2001), we use a logarithmic representation for the 810 perturbation to try to explicitly describe the nonlinearity between CO 2 concentration and the carbon flux into the ocean. As Using the pre-transformation techniques described above, in the following we recover the generalized sensitivity χ (O) β and evaluate the quality of the results. ...
The response of the global climate-carbon cycle system to anthropogenic perturbations happens differently at different time scales. The unraveling of the memory structure underlying this time-scale dependence is a major challenge in climate research. Recently the widely applied α-β-γ framework proposed by Friedlingstein et al. (2003) to quantify climate-carbon cycle feedbacks has been generalized to account also for such internal memory. By means of this generalized framework, we investigate the time-scale dependence of the airborne fraction for a set of Earth System Models that participated in CMIP5 (Coupled Model Intercomparison Project Phase 5); the analysis is based on published simulation data from C4MIP-type experiments with these models. Independently of the considered scenario, the proposed generalization describes at global scale the reaction of the climate-carbon system to sufficiently weak perturbations. One prediction from this theory is how the time-scale resolved airborne fraction depends on the underlying feedbacks between climate and carbon cycle. These feedbacks are expressed as time-scale resolved functions depending solely on analogues of the α, β, and γ sensitivities, introduced in the generalized framework as linear response functions. In this way a feedback-dependent quantity (airborne fraction) is predicted from feedback-independent quantities (the sensitivities). This is the key relation underlying our study. As a preparatory step, we demonstrate the predictive power of the generalized framework exemplarily for simulations with the MPI Earth System Model. The whole approach turns out to be valid for perturbations up to about 100 ppm CO2 rise above pre-industrial level; beyond this value the response gets nonlinear. By means of the generalized framework we then derive the time-scale dependence of the airborne fraction from the underlying climate-carbon cycle feedbacks for an ensemble of CMIP5 models. Our analysis reveals that for all studied CMIP5 models (1) the total climate-carbon cycle feedback is negative at all investigated time scales; (2) the airborne fraction generally decreases for increasing time scales; and (3) the land biogeochemical feedback dominates the model spread in the airborne fraction at all these time scales. Qualitatively similar results were previously found by employing the original α-β-γ framework to particular perturbation scenarios, but our study demonstrates that, although obtained from particular scenario simulations, they are characteristics of the coupled climate-carbon cycle system as such, valid at all considered time scales. These more general conclusions are obtained by accounting for the internal memory of the system as encoded in the generalized sensitivities, which in contrast to the original α, β, and γ are scenario-independent.
... The substitute (or emulator) can be used to explore responses over long time scales or to run many sensitivity studies, which are computationally inaccessible with more comprehensive and therefore more expensive models. The spatio-temporal response of a complex model, its Green's function, can be captured in an idealized model simulation where the forcing is changed in a step-or pulse-like manner (e.g., Bastiaansen et al., 2021;Hooss et al., 2001;Joos & Bruno, 1996;Joos et al., 2013;Maier-Reimer & Hasselmann, 1987;Metzler et al., 2018;Strassmann & Joos, 2018;Thompson & Randerson, 1999). Idealized response simulations allow for a better understanding of underlying processes as they reveal the characteristic timescales and spatial patterns of the system's adjustment to an external perturbation, for example, a change in weathering. ...
The causes of CO2 variations over the past million years remain poorly understood. Imbalances between the input of elements from rock weathering and their removal from the atmosphere‐ocean‐biosphere system to the lithosphere likely contributed to reconstructed changes. We employ the Bern3D model to investigate carbon‐climate responses to step‐changes in the weathering input of phosphorus, alkalinity, carbon, and carbon isotope ratio (δ¹³C) in simulations extending up to 600,000 years. CO2 and climate approach a new equilibrium within a few ten thousand years, whereas equilibrium is established after several hundred thousand years for δ¹³C. These timescales represent a challenge for the initialization of sediment‐enabled models and unintended drifts may be larger than forced signals in simulations of the last glacial–interglacial cycle. Changes in dissolved CO2 change isotopic fractionation during marine photosynthesis. This causes distinct spatio‐temporal perturbations in δ¹³C and affects the burial flux of ¹³C. We force a cost‐efficient emulator, based on the Bern3D results, with contrasting literature‐based weathering histories over the last 800 thousand years. Glacial–interglacial amplitudes of up to 30 ppm in CO2, 0.05‰ in δ¹³C, and ∼15 mmol m⁻³ in deep ocean CO32− ${\text{CO}}_{3}^{2-}$ are emulated for changes in carbonate rock weathering. Plausible input from the decomposition of organic matter on shelves causes variations of up to 10 ppm in CO2, 0.09‰ in δ¹³C, and 5 mmol m⁻³ in CO32− ${\text{CO}}_{3}^{2-}$, highlighting the non‐negligible effect of weathering‐burial imbalances.
... To validate the performance of our MAC curves emulating IAM responses (i.e., emIAM), we couple emIAM with the ACC2 model. ACC2 dates back impulse response functions of the global carbon cycle and climate system (Hasselmann et al., 1997;Hooss et al., 2001;Bruckner et al., 2003). The representations of natural Earth system processes in the first three modules of ACC2 are at the global-annual-mean level as in other simple climate models (Joos et al., 2013;Nicholls et al., 2020). ...
We developed an emulator for Integrated Assessment Models (emIAM) based on a marginal abatement cost (MAC) curve approach. Using the output of IAMs in the ENGAGE Scenario Explorer and the GET model, we derived a large set of MAC curves: ten IAMs; global and eleven regions; three gases CO2, CH4, and N2O; eight portfolios of available mitigation technologies; and two emission sources. We tested the performance of emIAM by coupling it with a simple climate model ACC2. We found that the optimizing climate-economy model emIAM-ACC2 adequately reproduced a majority of original IAM emission outcomes under similar conditions, allowing systematic explorations of IAMs with small computational resources. emIAM can expand the capability of simple climate models as a tool to calculate cost-effective pathways linked directly to a temperature target.
... atmosphere-ocean interactions) incorporated in the CGCM. Later on, the resulting model has been further elaborated into a nonlinear impulse response model of the coupled carbon cycle climate system that yields spatially explicit simulations with enhanced inclusion of ocean carbon chemistry and the terrestrial biosphere (Hooss et al 2001). ...
Klaus Hasselmann has earned the 2021 Nobel Prize in physics for his breakthroughs in analysing the climate system as a complex physical system. Since decades, as a leading climate scientist he is aware of the need for creative cooperation between climate scientists and researchers from other fields, especially economics. To facilitate such cooperation, he has designed a productive research program for economic analysis in view of climate change. Without blurring the differences between economics and physics, the Hasselmann program stresses the complexities of today’s economy. This includes the importance of heterogeneous actors and different time scales, of making major uncertainties explicit and bringing researchers and practitioners in close interaction. The program has triggered decades of collaborative research, especially in the network of the Global Climate Forum, that he has founded for this purpose. Research inspired by Hasselmann’s innovative ideas has led to a farewell to outdated economic approaches: single-equilibrium models, a single constant discount rate, framing the climate challenge as a kind of prisoner’s dilemma and framing it as a problem of scarcity requiring sacrifices from the majority of today’s population. Instead of presenting the climate problem as the ultimate apocalyptic narrative, he sees it as a challenge to be mastered. To meet this challenge requires careful research in order to identify underutilisation of human, technical and social capacities that offer the keys to a climate friendly world economy. Climate neutrality may then be achieved by activating these capacities through investment-oriented climate strategies, designed and implemented by different actors both in industrialised and developing countries. The difficulties to bring global greenhouse gas emissions down to net zero are enormous; the Hasselmann program holds promise of significant advances in this endeavour.
... To calculate the temperature responses to emission pathways, we used a simple climate model Aggregated Carbon Cycle, Atmospheric Chemistry, and Climate model (ACC2) [25,36] developed on the basis of earlier work [37,38]. The model comprises four modules: carbon cycle, atmospheric chemistry, climate, and economy modules. ...
Now that many countries have set goals for reaching net zero emissions by the middle of the century, it is important to clarify the role of each country in achieving the 1.5 °C target of the Paris Agreement. Here, we evaluated China’s role by calculating the global temperature impacts caused by China’s emission pathways available in global emissions scenarios toward the 1.5 °C target. Our results show that China’s contribution to global warming in 2050 (since 2005) is 0.17 °C on average, with a range of 0.1 °C to 0.22 °C. The peak contributions of China vary from 0.1 °C to 0.23 °C, with the years reached distributing between 2036 and 2065. The large difference in peak temperatures arises from the differences in emission pathways of carbon dioxide (CO2), methane (CH4), and sulfur dioxide (SO2). We further analyzed the effect of the different mix of CO2 and CH4 mitigation trajectories in China’s pathways on the global mean temperature. We found that China’s near-term CH4 mitigation reduces the peak temperature in the middle of the century, whereas it plays a less important role in determining the end-of-the-century temperature. Early CH4 mitigation action in China is an effective way to shave the peak temperature, further contributing to reducing the temperature overshoot along the way toward the 1.5 °C target. This underscores the necessity for early CO2 mitigation to ultimately achieve the long-term temperature goal.
... The impulse response analysis (IRF) is intended to quantify the responses of each variable to climate change (Hooss et al. 2001;Joos et al. 1999). This method simulates the dynamic changes of EVI by giving EVI an impulse of climate force in the amount of standard deviation (ε t ) to observe the EVI response process in the simultaneous and future periods (based on equation (1)). ...
Climate change affects vegetation growth around the world. It has been recognized that the effect of climate change on vegetation growth exhibits hysteresis. However, the duration and intensity of time-lag effect of climate factors on vegetation growth is still difficult to quantify. We analyzed the impacts of climate on vegetation growth in 32 major cities of China from 2010 to 2016. Vegetation growth conditions were characterized using enhanced vegetation index (EVI) datasets from Moderate Resolution Imaging Spectrometer (MODIS). The climate data were extracted from the Daily Value Data Set of China Surface Climate Data (V3.0), including precipitation (PRE; mm), air temperature (TEM; o C), sunshine duration (SSD; h), humidity (RHU; %), and evapotranspiration (EVP; mm). We used the vector autoregressive model (VAR) to analyze the lagged effects of climate factors on EVI, predict vegetation responses to future global changes, and validate its accuracy. Results showed that RHU had the longest (6.13 ± 1.96 months) and strongest (median 0.34 EVI per unit RHU in the first lag period) time-lag effect on EVI, while EVP had the shortest (3.45 ± 1.09 months) and weakest (median − 0.02 EVI per unit EVP in the first lag period) time-lag effect on EVI. The time-lag effects of PRE and SSD on EVI were stronger in the south than in the north. Meanwhile, the EVI predicted by the VAR model was highly consistent with the observed EVI (root mean squared error, RMSE < 0.08), and the prediction accuracy generally improved by 23.43% compared with the EVI predicted by the multiple linear regression model (MLR). Our study highlights the necessity of considering time-lag effects when exploring vegetation-climate interaction. The methods developed in this study can be used to reveal the lagged effects of climatic factors on vegetation growth and improve prediction of EVI dynamics under climate change.
... 5000 members randomly drawn from the constrained ensemble for use here. Millar et al. (2017), Haustein et al. (2017), , and Leach et al. (2020) Hectorv2.5.0 10,000 member ensemble sampled from Markov chain Monte Carlo chains constrained with global surface temperature and ocean heat content Vega-Westhoff et al. (2019) MAGICCv7.5.1 7,000,000 member Monte Carlo Markov Chain, 600 member subsample selected to match proxy assessed ranges Meinshausen et al. (2009Meinshausen et al. ( , 2011Meinshausen et al. ( , 2020 MCE v1.2 600 members sampled with a Metropolis-Hastings algorithm through Bayesian updating to reflect an ensemble of complex climate models constrained with the proxy assessed ranges Tsutsui (2017Tsutsui ( , 2020) (see also Joos et al. (1996) and Hooss et al. (2001)) OSCARv3.1 10,000 Monte Carlo members, weighted using their agreement with a set of assessed ranges (supplementary Text S1) Gasser et al. ( , (2018Gasser et al. ( , 2020 SCM4OPT v2.1 For each emission scenario, 2,000 sample members are used to reflect uncertainties resulting from carbon cycle, aerosol forcings and temperature change, while constrained by the historical mean surface temperature of HadCRUT.4.6.0.0 (Morice et al., 2012) Su et al. (2017, 2020 Note. Detailed descriptions of each model are available in supplementary Text S1. ...
Over the last decades, climate science has evolved rapidly across multiple expert domains. Our best tools to capture state‐of‐the‐art knowledge in an internally self‐consistent modeling framework are the increasingly complex fully coupled Earth System Models (ESMs). However, computational limitations and the structural rigidity of ESMs mean that the full range of uncertainties across multiple domains are difficult to capture with ESMs alone. The tools of choice are instead more computationally efficient reduced complexity models (RCMs), which are structurally flexible and can span the response dynamics across a range of domain‐specific models and ESM experiments. Here we present Phase 2 of the Reduced Complexity Model Intercomparison Project (RCMIP Phase 2), the first comprehensive intercomparison of RCMs that are probabilistically calibrated with key benchmark ranges from specialized research communities. Unsurprisingly, but crucially, we find that models which have been constrained to reflect the key benchmarks better reflect the key benchmarks. Under the low‐emissions SSP1‐1.9 scenario, across the RCMs, median peak warming projections range from 1.3 to 1.7°C (relative to 1850–1900, using an observationally based historical warming estimate of 0.8°C between 1850–1900 and 1995–2014). Further developing methodologies to constrain these projection uncertainties seems paramount given the international community's goal to contain warming to below 1.5°C above preindustrial in the long‐term. Our findings suggest that users of RCMs should carefully evaluate their RCM, specifically its skill against key benchmarks and consider the need to include projections benchmarks either from ESM results or other assessments to reduce divergence in future projections.
... The IRM for the airborne fraction defines five components, one of which has infinity time constant, paired with an amplitude corresponding to an asymptotic long-term fraction. In the current configuration, the remaining four time constants are fixed at 236.5, 59.52, 12.17, and 1.271 years, adjusted to a specific three-dimensional ocean carbon cycle model in Hooss et al. (2001). The corresponding amplitudes assume perturbations at reference values of 0.24, 0.21, 0.25, and 0.1, respectively, 100 with a reference long-term airborne fraction of 0.20. ...
Climate model emulators have a crucial role in assessing warming levels of many emission scenarios from probabilistic climate projections, based on new insights into Earth system response to CO2 and other forcing factors. This article describes one such tool, MCE, from model formulation to application examples associated with a recent model intercomparison study. The MCE is based on impulse response functions and parameterized physics of effective radiative forcing and carbon uptake over ocean and land. Perturbed model parameters for probabilistic projections are generated from statistical models and constrained with a Metropolis-Hastings independence sampler. A part of the model parameters associated with CO2-induced warming have a covariance structure, as diagnosed from complex climate models of the Coupled Model Intercomparison Project (CMIP). Although perturbed ensembles can cover the diversity of CMIP models effectively, they need to be constrained toward substantially lower climate sensitivity for the resulting historical warming to agree with the observed trends over recent decades. The model's simplicity and resulting successful calibration imply that a method with less complicated structures and fewer control parameters offers advantages when building reasonable perturbed ensembles in a transparent way. Experimental results for future scenarios show distinct differences between CMIP- and observation-consistent ensembles, suggesting that perturbed ensembles for scenario assessment need to be properly constrained with new insights into forced response over historical periods.
... The current model was developed from earlier simple climate models (68,69) and produces an equivalent output with the one used in (23). The performance of the model (except for the economic module) was evaluated with those of other simple climate models under a set of common scenarios (70). ...
Greenhouse gas (GHG) metrics, that is, conversion factors to evaluate the emissions of non-CO 2 GHGs on a common scale with CO 2 , serve crucial functions in the implementation of the Paris Agreement. While different metrics have been proposed, their economic cost-effectiveness has not been investigated under a range of pathways, including those substantially overshooting the temperature targets. Here, we show that cost-effective metrics for methane that minimize the overall mitigation costs are time-dependent, primarily determined by the pathway, and strongly influenced by temperature overshoot. Parties to the Paris Agreement have already adopted the conventional GWP100 (100-year global warming potential), which is shown to be a good approximation of cost-effective metrics for the coming decades. In the longer term, however, we suggest that parties consider adapting the choice of common metrics to the future pathway as it unfolds, as part of the recurring global stocktake, if global cost-effectiveness is a key consideration.
