Forced signal and predictability in a prototype climate model: Implications for fingerprinting based detection in the presence of multidecadal natural variability

Advanced numerical models used for climate prediction are known to exhibit biases in their simulated climate response to variable concentrations of the atmospheric greenhouse gases and aerosols that force a non-uniform, in space and time, secular global warming. We argue here that these biases can be particularly pronounced due to misrepresentation, in these models, of the multidecadal internal climate variability characterized by large-scale, hemispheric-to-global patterns. This point is illustrated through the development and analysis of a prototype climate model comprised of two damped linear oscillators, which mimic interannual and multidecadal internal climate dynamics and are set into motion via a combination of stochastic driving, representing weather noise, and deterministic external forcing inducing a secular climate change. The model time series are paired with pre-specified patterns in the physical space and form, conceptually, a spatially extended time series of the zonal-mean near-surface temperature, which is further contaminated by a spatiotemporal noise simulating the rest of climate variability. The choices of patterns and model parameters were informed by observations and climate-model simulations of the 20th century near-surface air temperature. Our main finding is that the intensity and spatial patterns of the internal multidecadal variability associated with the slow-oscillator model component greatly affect (i) the ability of modern pattern-recognition/fingerprinting methods to isolate the forced response of the climate system in the 20th century ensemble simulations and (ii) climate-system predictability, especially decadal predictability, as well as the estimates of this predictability using climate models in which the internal multidecadal variability is underestimated or otherwise misrepresented.

Applying interval stability concept to empirical model of middle Pleistocene transition

Interval stability is a novel method for the study of complex dynamical systems, allowing for the estimation of their stability to strong perturbations. This method describes how large perturbation should be to disrupt the stable dynamical regime of the system (attractor). In our work, interval stability is used for the first time to study the properties of a real natural system: to analyze the stability of the earth's climate system during the last 2.6×10⁶ years. The main abrupt shift in global climate during this period is the middle Pleistocene transition (MPT), which occurred about 1×10⁶ years ago as a change of the periodicity of glacial cycles from 41 to 100 kyr. On the basis of the empirical nonlinear stochastic model proposed in our recent work, we demonstrate that the global climate stability to any perturbations decreases throughout the Pleistocene period (including the MPT), enhancing its response to fast (with a millennial scale or less) internal disturbances.

Data-driven stochastic model for cross-interacting processes with different time scales

In this work, we propose a new data-driven method for modeling cross-interacting processes with different time scales represented by time series with different sampling steps. It is a generalization of a nonlinear stochastic model of an evolution operator based on neural networks and designed for the case of time series with a constant sampling step. The proposed model has a more complex structure. First, it describes each process by its own stochastic evolution operator with its own time step. Second, it takes into account possible nonlinear connections within each pair of processes in both directions. These connections are parameterized asymmetrically, depending on which process is faster and which process is slower. They make this model essentially different from the set of independent stochastic models constructed individually for each time scale. All evolution operators and connections are trained and optimized using the Bayesian framework, forming a multi-scale stochastic model. We demonstrate the performance of the model on two examples. The first example is a pair of coupled oscillators, with the couplings in both directions which can be turned on and off. Here, we show that inclusion of the connections into the model allows us to correctly reproduce observable effects related to coupling. The second example is a spatially distributed data generated by a global climate model running in the middle 19th century external conditions. In this case, the multi-scale model allows us to reproduce the coupling between the processes which exists in the observed data but is not captured by the model constructed individually for each process.