### point of no return

Sep. 14th, 2017 05:24 pm**ljgeoff**

I'm studying for my exam on Monday. According to my Prof, one should take a break from the material every 20 or 30 min, to increase comprehension and retention. So I decided to read some papers.

If I'm reading this one right, we have about two years until we hit the point of no return (PNR) on climate change.

From: Brenda C. van Zalinge, Qing Yi Feng, Matthias Aengenheyster, and Henk A. Dijkstra. (2017) On determining the point of no return in climate change.

Given a certain desirable subspace of the climate system state vector (e.g. to avoid dangerous anthropogenic interference) and a suite of control options (e.g. CO2 emission reduction), it is important to know when it is too late to steer the system to “safe” conditions, for example in the year 2100. In other words, when is the point of no return (PNR)? The tolerable windows approach (TWA; Petschel-Held et al., 1999) and viability theory (VT; Aubin, 2009) approaches and the theory in (Heitzig et al., 2016) suffer from the “curse of dimensionality”and cannot be used within CMIP5 climate models.

For example, the optimization problems in VT and TWA lead to dynamic programming schemes which have up to now only been solved for model systems with low-dimensional state vectors. The approach in (Heitzig et al., 2016) requires the computation of regional boundaries in state space, which also becomes tedious in more than two dimensions. Hence,with these approaches it will be impossible to determine a PNR using reasonably detailed models of the climate system.

Pachauri et al. (2014) stated with high confidence that “without additional mitigation efforts beyond those in place today, and even with adaptation, warming by the end of the 21st century will lead to high to very high risk of severe, widespread and irreversible impacts globally”. If no measures are taken to reduce green house gas (GHG) emissions during this century and if there are no new technological developments that can reduce GHGs in the atmosphere, it is likely that the global mean surface temperature (GMST) will be 4 ◦C higher than the pre-industrial GMST at the end of the 21st century (Pachauri et al., 2014). Consequently, it is important that anthropogenic emissions are regulated and significantly reduced before widespread and irreversible impacts occur. It would help motivate mitigation to know when it is “too late”.

In this study we have defined the concept of the point of no return (PNR) in climate change more precisely using stochastic viability theory and a collection of mitigation scenarios. For an energy balance model, as in Sect. 3, the probability density function could be explicitly computed, and hence stochastic viability kernels could be determined. The additional advantage of this model is that a bi-stable regime can easily be constructed to investigate the effects of tipping behaviour on the PNR. We used this model (with the assumption that CO2 could be controlled directly instead of through emissions) to illustrate the concept of PNR based on a tolerance time for which the climate state is non-viable. For the RCP scenarios considered, the PNR is smaller in the bi-stable than in the mono-stable regime of this model. The occurrence of possible transitions to warm states in this model indeedcause the PNR to be “too late” earlier.

The determination of the PNR in the high-dimensional PlaSim climate model, however, shows the key innovation in our approach, i.e. the use of linear response theory (LRT) to estimate the probability density function of the GMST. PlaSim was used to compute another variant of a PNR based only on the requirement that the climate state is viable in the year 2100. Hence, the PNR here is the time at which no allowed mitigation scenario can be chosen to keep GMST below a certain threshold in the year 2100 with a specified probability.

Although our approach provides new insights into the PNR in climate change, we recognize that there is potential for substantial further improvement. First of all, the PlaSim model has a too-high climate sensitivity compared to CMIP5 models. Although in the most realistic case (Sect. 4.3) we somehow compensate for this effect, it would be much better to apply the LRT approach to CMIP5 simulations. Second, in the LRT approach, we assume the GMST distributions to be Gaussian. This is well justified in PlaSim, as can be verified from the PlaSim simulations, but it may not be the case for a typical CMIP5 model. Third, for the more realistic case in Sect. 4.3, we do not capture the uncertainties in the carbon model and hence in the radiative forcing.

A large ensemble such as that available for PlaSim is not available (yet) for any CMIP5 model. However, we have recently applied the same methodology to two CMIP5 model ensembles, i.e. a 34-member ensemble of abrupt CO2 quadrupling and a 35-member ensemble of smooth 1 % CO2 increase per year. The CO2-quadrupling ensemble was used to derive the Green’s function, and then the 1 % CO2 increase ensemble was used as a check on the resulting response.

The probability density function of GMST increase is close to Gaussian for the 1 % CO2 increase ensemble but clearly deviates from a Gaussian distribution for the 4x CO2- forcing ensemble, particularly at later times. Although the ensemble is relatively small and the models within the ensemble are different (but many are related), the results for the LRT-determined GMST response (Aengenheyster, 2017) are surprisingly good. This indicates that the methodology has a high potential to be successfully applied to the results of

CMIP5 model simulations (and in the future, CMIP6). The applicability of LRT to other observables than GMST can in principle be performed, but the results may be less useful (e.g. due to non-Gaussian distributions).

Because PlaSim is highly idealized compared to a typical CMIP5 model, one cannot attribute much importance to the precise PNR values obtained for the PlaSim model as in Fig. 7. However, we think that our approach is general enough to handle many different political and socioeconomic scenarios combined with state-of-the-art climate models when adequate response functions of CMIP5 models have been determined (e.g. using LRT). Hence, it will be possible to make better estimates of the PNR for the real climate system. We therefore hope that these ideas on the PNR in climate change will eventually become part of the decision-making.

If I'm reading this one right, we have about two years until we hit the point of no return (PNR) on climate change.

From: Brenda C. van Zalinge, Qing Yi Feng, Matthias Aengenheyster, and Henk A. Dijkstra. (2017) On determining the point of no return in climate change.

*Earth System Dynamics, 8*, 707–717. https://doi.org/10.5194/esd-8-707-2017*Definitions in the introduction:*Given a certain desirable subspace of the climate system state vector (e.g. to avoid dangerous anthropogenic interference) and a suite of control options (e.g. CO2 emission reduction), it is important to know when it is too late to steer the system to “safe” conditions, for example in the year 2100. In other words, when is the point of no return (PNR)? The tolerable windows approach (TWA; Petschel-Held et al., 1999) and viability theory (VT; Aubin, 2009) approaches and the theory in (Heitzig et al., 2016) suffer from the “curse of dimensionality”and cannot be used within CMIP5 climate models.

For example, the optimization problems in VT and TWA lead to dynamic programming schemes which have up to now only been solved for model systems with low-dimensional state vectors. The approach in (Heitzig et al., 2016) requires the computation of regional boundaries in state space, which also becomes tedious in more than two dimensions. Hence,with these approaches it will be impossible to determine a PNR using reasonably detailed models of the climate system.

*Steaming on to the discussion...*Pachauri et al. (2014) stated with high confidence that “without additional mitigation efforts beyond those in place today, and even with adaptation, warming by the end of the 21st century will lead to high to very high risk of severe, widespread and irreversible impacts globally”. If no measures are taken to reduce green house gas (GHG) emissions during this century and if there are no new technological developments that can reduce GHGs in the atmosphere, it is likely that the global mean surface temperature (GMST) will be 4 ◦C higher than the pre-industrial GMST at the end of the 21st century (Pachauri et al., 2014). Consequently, it is important that anthropogenic emissions are regulated and significantly reduced before widespread and irreversible impacts occur. It would help motivate mitigation to know when it is “too late”.

In this study we have defined the concept of the point of no return (PNR) in climate change more precisely using stochastic viability theory and a collection of mitigation scenarios. For an energy balance model, as in Sect. 3, the probability density function could be explicitly computed, and hence stochastic viability kernels could be determined. The additional advantage of this model is that a bi-stable regime can easily be constructed to investigate the effects of tipping behaviour on the PNR. We used this model (with the assumption that CO2 could be controlled directly instead of through emissions) to illustrate the concept of PNR based on a tolerance time for which the climate state is non-viable. For the RCP scenarios considered, the PNR is smaller in the bi-stable than in the mono-stable regime of this model. The occurrence of possible transitions to warm states in this model indeedcause the PNR to be “too late” earlier.

The determination of the PNR in the high-dimensional PlaSim climate model, however, shows the key innovation in our approach, i.e. the use of linear response theory (LRT) to estimate the probability density function of the GMST. PlaSim was used to compute another variant of a PNR based only on the requirement that the climate state is viable in the year 2100. Hence, the PNR here is the time at which no allowed mitigation scenario can be chosen to keep GMST below a certain threshold in the year 2100 with a specified probability.

**In the PlaSim results, we used a viability region defined as GMSTs lower than 2 ◦C above the pre-industrial value, but with our methodology, the PNR can be easily determined for any threshold defining the viable region. The more academic case in which we assume that GHG levels can be controlled directly provides PNR (for RCP4.5, RCP6.0, and RCP8.5) values around 2050 (Sect. 4.2). However, the more realistic case in which the emissions are controlled (Sect. 4.3) and a carbon model is used reduces the PNR for these three RCP scenarios by about 30 years. The reason is that there is a delay between the decrease in GHG gas emissions and concentrations.***my emphasis... I was reading this and went "wait, wuh?...*Although our approach provides new insights into the PNR in climate change, we recognize that there is potential for substantial further improvement. First of all, the PlaSim model has a too-high climate sensitivity compared to CMIP5 models. Although in the most realistic case (Sect. 4.3) we somehow compensate for this effect, it would be much better to apply the LRT approach to CMIP5 simulations. Second, in the LRT approach, we assume the GMST distributions to be Gaussian. This is well justified in PlaSim, as can be verified from the PlaSim simulations, but it may not be the case for a typical CMIP5 model. Third, for the more realistic case in Sect. 4.3, we do not capture the uncertainties in the carbon model and hence in the radiative forcing.

A large ensemble such as that available for PlaSim is not available (yet) for any CMIP5 model. However, we have recently applied the same methodology to two CMIP5 model ensembles, i.e. a 34-member ensemble of abrupt CO2 quadrupling and a 35-member ensemble of smooth 1 % CO2 increase per year. The CO2-quadrupling ensemble was used to derive the Green’s function, and then the 1 % CO2 increase ensemble was used as a check on the resulting response.

The probability density function of GMST increase is close to Gaussian for the 1 % CO2 increase ensemble but clearly deviates from a Gaussian distribution for the 4x CO2- forcing ensemble, particularly at later times. Although the ensemble is relatively small and the models within the ensemble are different (but many are related), the results for the LRT-determined GMST response (Aengenheyster, 2017) are surprisingly good. This indicates that the methodology has a high potential to be successfully applied to the results of

CMIP5 model simulations (and in the future, CMIP6). The applicability of LRT to other observables than GMST can in principle be performed, but the results may be less useful (e.g. due to non-Gaussian distributions).

Because PlaSim is highly idealized compared to a typical CMIP5 model, one cannot attribute much importance to the precise PNR values obtained for the PlaSim model as in Fig. 7. However, we think that our approach is general enough to handle many different political and socioeconomic scenarios combined with state-of-the-art climate models when adequate response functions of CMIP5 models have been determined (e.g. using LRT). Hence, it will be possible to make better estimates of the PNR for the real climate system. We therefore hope that these ideas on the PNR in climate change will eventually become part of the decision-making.

*so, yeah, if I'm reading this wrong, that would be good to know*