Investigating climate tipping points under various emission reduction and carbon capture scenarios with a stochastic climate model

We study the mitigation of climate tipping point transitions using an energy balance model. The evolution of the global mean surface temperature is coupled with the CO 2 concentration through the green-house effect. We model the CO 2 concentration with a stochastic delay differential equation (SDDE), accounting for various carbon emission and capture scenarios. The resulting coupled system of SDDEs exhibits a tipping point phenomena: if CO 2 concentration exceeds a critical threshold (around 478 ppm ), the temperature experiences an abrupt increase of about six degrees Celsius. We show that the CO 2 concentration exhibits a transient growth which may cause a climate tipping point, even if the concentration decays asymptotically. We derive a rigorous upper bound for the CO 2 evolution which quantifies its transient and asymptotic growths, and provides sufficient conditions for evading the climate tipping point. Combining this upper bound with Monte Carlo simulations of the stochastic climate model, we investigate the emission reduction and carbon capture scenarios that would avert the tipping point.

Numerical Development and Evaluation of an Energy Conserving Conceptual Stochastic Climate Model

In this study we aim to present the successful development of an energy conserving conceptual stochastic climate model based on the inviscid 2-layer Quasi-Geostrophic (QG) equations. The stochastic terms have been systematically derived and introduced in such away that the total energy is conserved. In this proof of concept studywe give particular emphasis to the numerical aspects of energy conservation in a highdimensional complex stochastic system andwe analyzewhat kind of assumptions regarding the noise should be considered in order to obtain physical meaningful results. Our results show that the stochastic model conserves energy to an accuracy of about 0.5% of the total energy; this level of accuracy is not affected by the introduction of the noise, but is mainly due to the level of accuracy of the deterministic discretization of the QG model. Furthermore, our results demonstrate that spatially correlated noise is necessary for the conservation of energy and the preservation of important statistical properties, while using spatially uncorrelated noise violates energy conservation and gives unphysical results. A dynamically consistent spatial covariance structure is determined through Empirical Orthogonal Functions (EOFs). We find that only a small number of EOFs is needed to get good results with respect to energy conservation, autocorrelation functions, PDFs and eddy length scale when comparing a deterministic control simulation on a 512 × 512 grid to a stochastic simulation on a 128 × 128 grid. Our stochastic approach has the potential to seamlessly be implemented in comprehensive weather and climate prediction models.

A Theory for the Seasonal Predictability Barrier: Threshold, Timing, and Intensity

A theory is developed in a stochastic climate model for understanding the general features of the seasonal predictability barrier (PB), which is characterized by a band of maximum decline in autocorrelation function phase-locked to a particular season. Our theory determines the forcing threshold, timing, and intensity of the seasonal PB as a function of the damping rate and seasonal forcing. A seasonal PB is found to be an intrinsic feature of a stochastic climate system forced by either seasonal growth rate or seasonal noise forcing. A PB is generated when the seasonal forcing, relative to the damping rate, exceeds a modest threshold. Once generated, all the PBs occur in the same calendar month, forming a seasonal PB. The PB season is determined by the decline of the seasonal forcing as well as the delayed response associated with damping. As such, for a realistic weak damping, the PB season is locked close to the minimum SST variance under the seasonal growth-rate forcing, but after the minimum SST variance under the seasonal noise forcing. The intensity of the PB is determined mainly by the amplitude of the seasonal forcing. The theory is able to explain the general features of the seasonal PB of the observed SST variability over the world. In the tropics, a seasonal PB is generated mainly by a strong seasonal growth rate, whereas in the extratropics a seasonal PB is generated mainly by a strong seasonal noise forcing. Our theory provides a general framework for the understanding of the seasonal PB of climate variability.

ESD Ideas: The stochastic climate model shows that underestimated Holocene trends and variability represent two sides of the same coin

Holocene sea surface temperature trends and variability are underestimated in models compared to paleoclimate data. The idea is presented that the local trends and variability are related, which is elaborated in a conceptual framework of the stochastic climate model. The relation is a consequence of the fluctuation–dissipation theorem, connecting the linear response of a system to its statistical fluctuations. Consequently, the spectrum can be used to estimate the timescale-dependent climate response. The non-normality in the propagation operator introduces enhanced long-term variability related to nonequilibrium and/or Earth system sensitivity. The simple model can guide us to analyze comprehensive models' behavior.

ESD Ideas: The stochastic climate model shows that underestimated Holocene trends and variability represent two sides of the same coin

Holocene sea surface temperature trends and variability are underestimated in models as compared to paleoclimate data. The idea is presented that the trends and variability are related which is elaborated in a conceptual framework of the stochastic climate model. The relation is a consequence of the fluctuation-dissipation theorem, connecting the linear response of a system to its statistical fluctuations. Consequently, the spectrum can be used to estimate the timescale-dependent climate sensitivity. The non-normality in the propagation operator introduces enhanced long-term variability related to non-equilibrium and/or Earth system sensitivity.

Data Assimilation in Slow–Fast Systems Using Homogenized Climate Models

A deterministic multiscale toy model is studied in which a chaotic fast subsystem triggers rare transitions between slow regimes, akin to weather or climate regimes. Using homogenization techniques, a reduced stochastic parameterization model is derived for the slow dynamics. The reliability of this reduced climate model in reproducing the statistics of the slow dynamics of the full deterministic model for finite values of the time-scale separation is numerically established. The statistics, however, are sensitive to uncertainties in the parameters of the stochastic model. It is investigated whether the stochastic climate model can be beneficial as a forecast model in an ensemble data assimilation setting, in particular in the realistic setting when observations are only available for the slow variables. The main result is that reduced stochastic models can indeed improve the analysis skill when used as forecast models instead of the perfect full deterministic model. The stochastic climate model is far superior at detecting transitions between regimes. The observation intervals for which skill improvement can be obtained are related to the characteristic time scales involved. The reason why stochastic climate models are capable of producing superior skill in an ensemble setting is the finite ensemble size; ensembles obtained from the perfect deterministic forecast model lack sufficient spread even for moderate ensemble sizes. Stochastic climate models provide a natural way to provide sufficient ensemble spread to detect transitions between regimes. This is corroborated with numerical simulations. The conclusion is that stochastic parameterizations are attractive for data assimilation despite their sensitivity to uncertainties in the parameters.

Coupled Variability and Predictability in a Stochastic Climate Model of the Tropical Atlantic

The coupled variability and predictability of the tropical Atlantic ocean–atmosphere system were analyzed within the framework of a linear stochastic climate model. Despite the existence of a meridional dipole as the leading mode, tropical Atlantic variability (TAV) is dominated by equatorial features and the subtropical variability is largely uncorrelated between the northern and southern Atlantic. This suggests that atmospheric stochastic forcing plays a dominant role in defining the spatial patterns of TAV, whereas the active air–sea feedbacks mainly enhance variability at interannual and decadal time scales, causing the spectra distinctive from the red spectrum. Under the stochastic forcing, the useful predictive skill for sea surface temperature measured by normalized error variance is limited to 2 months on average, which is 1 month longer than the predictive skill of damped persistence, indicating that the contribution of ocean dynamics and air–sea feedbacks is moderate in the tropical Atlantic. To achieve maximum predictability, processes such as ocean dynamics, thermodynamical and dynamical air–sea feedbacks, and the delicate mode–mode interactions should be correctly resolved in the coupled models. Therefore, predicting TAV poses more challenge than predicting El Niño in the tropical Pacific.

Atlantic Atmosphere–Ocean Interaction: A Stochastic Climate Model–Based Diagnosis

A simple linear stochastic climate model of extratropical wintertime ocean–atmosphere coupling is used to diagnose the daily interactions between the ocean and the atmosphere in a fully coupled general circulation model. Monte Carlo simulations with the simple model show that the influence of the ocean on the atmosphere can be difficult to estimate, being biased low even with multiple decades of daily data. Despite this, fitting the simple model to the surface air temperature and sea surface temperature data from the complex general circulation model reveals an ocean-to-atmosphere influence in the northeastern Atlantic. Furthermore, the simple model is used to demonstrate that the ocean in this region greatly enhances the autocorrelation in overlying lower-tropospheric temperatures at lags from a few days to many months.