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

Abstract

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.

Forced response and internal variability in ensembles of climate simulations: Identification and analysis using Linear Dynamical Mode decomposition

“…Although its contribution to the total variance is small, the fact that it is detected in four independent sub-ensembles ensures its statistical significance. This mode resembles most the internal mode 1 of the SAT reanalysis study in Gavrilov et al (2020); it also exhibits some signatures of the those in Kravtsov et al (2022), where different forced-signal estimation methods have a similarly good overall performance in the absence of a pronounced low-frequency internal variability.…”

“…First, we tested the new method in the context of a didactic lowdimensional example, similar to an earlier study by Kravtsov et al (2022) We documented a superior performance of the ELDM method in isolating the forced signal in small ensembles of synthetic climate realizations described above relative to several other advanced pattern-recognition-based methods of forced-signal detection (Wills et al, 2018(Wills et al, , 2020, especially in the cases with a pronounced low-frequency internal variability and substantial lowfrequency dynamical forced response. We argue that this improvement is due to the ELDM method's self-consistent identification of both the forced signal and internal variability.…”

“…The model ( 16), ( 17) is analogous to the one studied in Kravtsov et al (2022), but has a lower effective dimension by only including one mode for either the slow or fast component of the system's internal variability (instead of two modes for each in Kravtsov et al, 2022); this choice was made here to facilitate the discussion of the LDM method's performance in isolating these modes. Note that the time series s(t) enters the model formulation in two ways.…”

“…Section 3 is devoted to the applications of the ELDM method. First, a didactic low-dimensional problem -a simpler version of the one considered in Kravtsov et al (2022) -is designed to illustrate the ELDM method's capabilities in isolating the forced and internal variability in a small ensemble of synthetic climate simulations, and to compare this method's performance with that of alternative methodologies. This example also elucidates a potentially important role of the so-called dynamical forced response (associated with the low-frequency internal climate modes' adjustment to a non-uniform in time external forcing) in limiting the accuracy of the forced signal detection by these methods.…”

“…However, should this not be the case, the method would tend to obtain a biased pattern of the forced response that 'avoids' the signature of the internal variability spatially overlapping with the true forced response, or at least would spread the signature of such a mode over multiple S/NP patterns. Kravtsov et al (2022) illustrated these limitations using an ensemble of simulations produced by a low-dimensional ad hoc climate model.…”