The problem of accurate detection of climate response to slow external forcing in 19-21 centuries is complicated by the presence of internal climate variability, which can also exhibit slow (decadal and multidecadal) large-scale dynamics, and also by the fact that there is only one observed climate realization available. At the same time, state-of-the-art Earth system models (ESMs) exhibit different spatiotemporal content on slow time scales, and their ability to estimate forced and internal climate variability needs further verification, especially given a relatively poor (short) observational statistics with respect to slow time scales.Here we present a method called ensemble linear dynamical mode (E-LDM) decomposition [1] which addresses the problem of forced signal and internal variability detection from small ensembles of ESM simulations. The method is based on the general assumption that the forced response is the same in all ensemble members and the internal variability is uncorrelated, while both of them can be essentially represented by a low-dimensional set of spatial patterns and corresponding forced and internal time series with certain time scales; the patterns, the time series and their time scales are optimized via the Bayesian framework. We compare the E-LDM method with other state-of-the-art methods of forced signal detection on synthetic and ESM-simulated data, and also discuss its applicability to the problem of intercomparison of ESMs and their verification with respect to real data. This research was supported by the state assignment of the Institute of Applied Physics of the Russian Academy of Sciences (Project No. FFUF-2022-0008). 1. Gavrilov, A., Kravtsov, S., Buyanova, M., Mukhin, D., Loskutov, E., & Feigin, A. (2023). Forced response and internal variability in ensembles of climate simulations: identification and analysis using linear dynamical mode decomposition. Climate Dynamics, 1–28. https://doi.org/10.1007/S00382-023-06995-1.

The upward trend of observed global surface air temperature anomalies exhibits a well-known multidecadal undulation, largely muted in the state-of-the-art climate models. We provide a comprehensive spatiotemporal description of these differences in the estimated unforced residuals representing the internal climate variability between a multi-model ensemble of historical simulations and two different reanalysis data sets, using optimal filtering. The signal identification was carried out within a limited set of observed and model simulated Northern Hemisphere's climate indices, but full two-dimensional spatial patterns of this signal, in the global gridded surface air temperature (SAT) and sea-level pressure (SLP) fields were also obtained. We then compared the magnitudes, spatial patterns, and characteristic time scales of the observed and simulated dominant low-frequency variability so defined. The observed variability is characterized by a hemispheric-to-global scale multidecadal signal exhibiting coherent anomalies over the North Atlantic, North Pacific and Southern Oceans. The simulated signals have time scales similar to observed, but different spatial patterns, and are weaker, with substantial sampling variability between different models and between simulations of each individual model. Few outlier models produce multidecadal signals with magnitudes comparable or exceeding those observed yet with vastly different spatial patterns dominated by the North Atlantic SAT variations. In the ensemble average, the simulated SLP pattern is negatively correlated with the observed pattern, which hints at root cause of the observed vs. simulated multidecadal-signal differences, with the former likely reflecting internal ocean dynamics and the latter largely consistent with the ultra-low-frequency atmospheric noise.

Twentieth-century climate variations exhibit, on top of a secular global warming trend, multidecadal variability with globally coherent patterns. Identifying and attributing such patterns requires one to combine modern reanalyses of atmospheric and oceanic observations with estimates of climate response to variable forcings based on ensemble simulations of the twentieth-century climate by the state-of-the-art global coupled models. This contribution is the first installment of the series of papers in which an identical sequence of pattern-recognition methods is applied to a 38-model ensemble of historical simulations within phases 5 and 6 of the Coupled Model Intercomparison Project (CMIP5/6) and to two twentieth-century reanalysis datasets to succinctly describe their global-scale multidecadal variability. The focus here is on characterizing the globally distributed forced response in near-surface air temperature (SAT) and sea level pressure (SLP) using a combination of the signal-to-noise-maximizing pattern (S/NP) filtering and linear-regression-based rescaling. A particular novel aspect of this work lies in isolating the forced-response structures common across the entire model ensemble versus the residual responses of individual models, thus setting the stage for exploring whether the latter responses can serve as a viable explanation of the observed multidecadal climate teleconnections. CMIP5/6 models' common forced response is dominated by two S/NP modes, whose amplitudes differ from model to model. The S/NP-1 describes polar and land-intensified global warming with a slower warming rate prior to mid-60s and a faster warming afterward. The S/NP-2 component is characterized by a pronounced multidecadal variability without much of a centennial-scale trend and exhibits antisymmetric temperature response between the hemispheres. The two mode's SLP signature is associated with the downward trend over the Southern Ocean and Antarctica after mid-60s and is much weaker than the SLP background internal variability elsewhere. The CMIP models that have large contributions from S/NP-1 and small contribution from S/NP-2 to their forced response tend to exhibit large twentieth-century global-mean SAT trend and vice versa. The residual forced responses of individual models unexplained by S/NPs 1 and 2 do exhibit multidecadal variations with the appearance of longrange teleconnections, albeit with a much smaller amplitude than the observed climate's globally connected deviations from the model estimated forced trends. SIGNIFICANCE STATEMENT: Understanding the discrepancies between the observed and simulated multidecadal climate variability constitutes one of the pressing problems in climate science. These discrepancies manifest a coherent global signal which may reflect biases in the simulated response to external forcings or point to the observed internal variability unmatched by the climate models. This study provides a compact characterization of the global-scale forced responses in terms of just a few dominant patterns common across an ensemble of state-of-the-art climate models and the residual forced variability of individual models. The relative amplitudes of these patterns gauge climate sensitivity of individual models, while the residual signals have by far insufficient magnitude to explain the observed multidecadal climate undulations on top of the secular warming trend.

Twentieth-century climate variations exhibit, on top of a secular global warming trend, multidecadal variability with globally coherent patterns. Identifying and attributing such patterns requires one to combine modern reanalyses of atmospheric and oceanic observations with estimates of climate response to variable forcings based on ensemble simulations of the twentieth-century climate by the state-of-the-art global coupled models. This contribution is the first installment of the series of papers in which an identical sequence of pattern-recognition methods is applied to a 38-model ensemble of historical simulations within phases 5 and 6 of the Coupled Model Intercomparison Project (CMIP5/6) and to two twentieth-century reanalysis datasets to succinctly describe their global-scale multidecadal variability. The focus here is on characterizing the globally distributed forced response in near-surface air temperature (SAT) and sea level pressure (SLP) using a combination of the signal-to-noise-maximizing pattern (S/NP) filtering and linear-regression-based rescaling. A particular novel aspect of this work lies in isolating the forced-response structures common across the entire model ensemble versus the residual responses of individual models, thus setting the stage for exploring whether the latter responses can serve as a viable explanation of the observed multidecadal climate teleconnections. CMIP5/6 models’ common forced response is dominated by two S/NP modes, whose amplitudes differ from model to model. The S/NP-1 describes polar and land-intensified global warming with a slower warming rate prior to mid-60s and a faster warming afterward. The S/NP-2 component is characterized by a pronounced multidecadal variability without much of a centennial-scale trend and exhibits antisymmetric temperature response between the hemispheres. The two mode’s SLP signature is associated with the downward trend over the Southern Ocean and Antarctica after mid-60s and is much weaker than the SLP background internal variability elsewhere. The CMIP models that have large contributions from S/NP-1 and small contribution from S/NP-2 to their forced response tend to exhibit large twentieth-century global-mean SAT trend and vice versa. The residual forced responses of individual models unexplained by S/NPs 1 and 2 do exhibit multidecadal variations with the appearance of long-range teleconnections, albeit with a much smaller amplitude than the observed climate’s globally connected deviations from the model estimated forced trends. Understanding the discrepancies between the observed and simulated multidecadal climate variability constitutes one of the pressing problems in climate science. These discrepancies manifest a coherent global signal which may reflect biases in the simulated response to external forcings or point to the observed internal variability unmatched by the climate models. This study provides a compact characterization of the global-scale forced responses in terms of just a few dominant patterns common across an ensemble of state-of-the-art climate models and the residual forced variability of individual models. The relative amplitudes of these patterns gauge climate sensitivity of individual models, while the residual signals have by far insufficient magnitude to explain the observed multidecadal climate undulations on top of the secular warming trend.

A significant fraction of multidecadal fluctuations in the reanalysis-based gridded estimates of the observed climate variability over the past century and a half lie outside of the envelope generated by ensembles of climate-model historical simulations. Several pattern-recognition methods have been previously used to map out a truly global reach of the observed vs. simulated climate-data differences; in our own work we dubbed these global discrepancies the stadium wave to highlight their most striking spatiotemporal characteristic. Here we used a novel combination of such methods in conjunction with a large multi-model ensemble and two popular twentieth-century reanalysis products to: (i) succinctly describe the geographical evolution of the observed stadium wave in the annually sampled near-surface atmospheric temperature and mean sea-level pressure fields in terms of three basic patterns; (ii) show the robustness of this identification with respect to methodological details, including the demonstration of the truly global character of the stadium wave; and (iii) provide essential clues to its dynamical origin. Part I of this study decomposed all input time series into the forced signal and the residual internal variability; multi-model forced-signal estimates were also decomposed into their common-evolution part and the individual-model residuals. Analysis of the latter residuals suggests a contribution to the stadium-wave dynamics from a delayed climate response to variable external forcing despite the observed stadium-wave patterns’ exhibiting the magnitudes and the level of global teleconnectivity unmatched by the forced-signal residuals. Part III of this paper will compare the observed stadium wave with the model simulated internal patterns.

This work continues our earlier studies of the interaction between a monopolar vortex and a sheared zonal flow in the framework of a 1.5-layer quasi-geostrophic model, based on numerical experiments with singular vortices. Earlier examination of flows with shears of fixed sign showed that the interaction depends strongly on the latitudinal distribution of the gradient of background potential vorticity b(y) (y being the latitude). The latitude y0 at which b(y) changes sign turns out to be of particular importance. In the vicinity of y0, under certain conditions, there arises the zonal-strip region, which attracts (repels) prograde (retrograde) vortices. This effect is examined here for the zonal flows in the form of individual jets as well as for the systems of alternating zonal jets; in all these cases, the background-flow velocity shear and the parameter b(y) can change sign depending on y. It is shown that the vortex drifts to the nearest latitude y0 on the prograde side of the zonal flow, and the meridional speed of the trapped vortex almost vanishes, but its zonal speed is directed westward and approaches the Rossby-wave drift velocity.

This work builds on and continues a suite of earlier studies of the interaction between a monopole and a sheared zonal flow in the framework of a 1.5-layer quasi-geostrophic model. In Reznik and Kravtsov [Phys. Fluids 33, 116606 (2021); hereafter RK21], this problem was considered under an f-plane approximation for the case in which the dependence of the zonal velocity U¯(y) on latitude y was linear. Here, the conclusions stemming from that work are generalized for the case of a beta-plane and a variable shear of the background flow. Namely, numerical experiments with singular vortices using the algorithm of Kravtsov and Reznik [“Numerical solutions of the singular vortex problem,” Phys. Fluids 31, 066602 (2019); hereafter KR19] confirm the existence of the trapping latitude ytr, which attracts (repels) prograde (retrograde) vortices and clarifies the underlying mechanisms. Unlike in the case of a linear shear on an f-plane, the latitude ytr here does not necessarily coincide with the latitude at which the effective beta-parameter β¯=β−∂yyU¯+Rd−2U¯ vanishes (here, β denotes the derivative of the Coriolis parameter with respect to latitude and Rd is the Rossby radius of deformation). Another important difference is that in the presence of nonzero β≠0, a trapped prograde vortex exhibits a near-zonal westward drift with the zonal velocity close to the phase speed of long Rossby waves −βRd2 and the meridional velocity at least two orders of magnitude smaller than that. On the other hand, the meridional velocity of a retrograde vortex appears to be unrestricted; such a vortex can rapidly move in any direction, including the direction across the zonal current.

This study introduces a novel method for comparing vertical thermodynamic profiles, focusing on the atmospheric boundary layer, across a wide range of meteorological conditions. This method is developed using observed temperature and dewpoint temperature data from 31 153 soundings taken at 0000 UTC and 32 308 soundings taken at 1200 UTC between May 2019 and March 2020. Temperature and dewpoint temperature vertical profiles are first interpolated onto a height above ground level (AGL) coordinate, after which the temperature of the dry adiabat defined by the surface-based parcel’s temperature is subtracted from each quantity at all altitudes. This allows for common sounding features, such as turbulent mixed layers and inversions, to be similarly depicted regardless of temperature and dewpoint temperature differences resulting from altitude, latitude, or seasonality. The soundings that result from applying this method to the observed sounding collection described above are then clustered to identify distinct boundary layer structures in the data. Specifically, separately at 0000 and 1200 UTC, a k -means clustering analysis is conducted in the phase space of the leading two empirical orthogonal functions of the sounding data. As compared to clustering based on the original vertical profiles, which results in clusters that are dominated by seasonal and latitudinal differences, clusters derived from transformed data are less latitudinally and seasonally stratified and better represent boundary layer features such as turbulent mixed layers and pseudoadiabatic profiles. The sounding-comparison method thus provides an objective means of categorizing vertical thermodynamic profiles with wide-ranging applications, as demonstrated by using the method to verify short-range Global Forecast System model forecasts.

Estimating climate response to observed and projected increases in atmospheric greenhouse gases usually requires averaging among multiple independent simulations of computationally expensive global climate models to filter out the internal climate variability. Studies have shown that advanced pattern recognition methods allow one to obtain accurate estimates of the forced climate signal from just a handful of such climate realizations. The accuracy of these methods for a fixed ensemble size, however, decreases with an increasing magnitude of the low-frequency, decadal and longer internal climate variability. Here we generalize a previously developed Bayesian methodology of Linear Dynamical Mode (LDM) decomposition for spatially extended time series to enable joint identification and analysis of forced signal and internal variability in ensembles of climate simulations, a methodology dubbed here an ensemble LDM, or ELDM. The new ELDM method is shown to outperform its pattern-recognition competitors by more accurately isolating the forced signal in small ensembles of both toy- and state-of-the-art climate-model simulations. It is able to do so by explicitly recognizing a non-random structure of the internal variability, identified by the ELDM algorithm alongside the optimal forced-signal estimate, which allows one to study possible dynamical connections between the two types of variability. The optimal ELDM filtering provides a unique opportunity for objective intercomparison of decadal and longer climate variability across different global climate models-a task that proved difficult due to uncertainties associated with the noisy character and limited length of historical climate simulations combined with parameter uncertainties of alternative signal-detection methods.

Natural and social systems exhibit complex behavior reflecting their rich dynamics, whose governing laws are not fully known. This study develops a unified data-driven approach to estimate predictability of such systems when several independent realizations of the system's evolution are available. If the underlying dynamics are quasi-linear, the signal associated with the variable external factors, or forcings, can be estimated as the ensemble mean; this estimation can be optimized by filtering out the part of the variability with a low ensemble-mean-signal-to-residual-noise ratio. The dynamics of the residual internal variability is then encapsulated in an optimal, in a Bayesian sense, linear stochastic model able to predict the observed behavior. This model's self-forecast covariance matrices define a basis of patterns (directions) associated with the maximum forecast skill. Projecting the observed evolution onto these patterns produces the corresponding component time series. These ideas are illustrated by applying the proposed analysis technique to (1) ensemble data of regional sea-surface temperature evolution in the tropical Pacific generated by a state-of-the-art climate model and (2) consumer-spending records across multiple regions of the Russian Federation. These examples map out a range of possible solutions-from a solution characterized by a low-dimensional forced signal and a rich spectrum of predictable internal modes (1)-to the one in which the forced signal is extremely complex, but the number of predictable internal modes is limited (2). In each case, the proposed decompositions offer clues into the underlying dynamical processes, underscoring the usefulness of the proposed framework.

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.

This paper utilizes statistical and statistical-dynamical methodologies to select, from the full observational record, a minimal subset of dates that would provide representative sampling of local precipitation distributions across the contiguous United States (CONUS). The CONUS region is characterized by a great diversity of precipitation-producing systems, mechanisms, and large-scale meteorological patterns (LSMPs), which can provide favorable environment for local precipitation extremes. This diversity is unlikely to be adequately captured in methodologies that rely on grossly reducing the dimensionality of the data-by representing it in terms of a few patterns evolving in time-and thus requires data thinning techniques based on high-dimensional dynamical or statistical data modeling. We have built a novel high-dimensional empirical model of temperature and precipitation capable of producing statistically accurate surrogate realizations of the observed 1979-99 (training period) evolution of these fields. This model also provides skillful hindcasts of precipitation over the 2000-20 (validation) period. We devised a subsampling strategy based on the relative entropy of the empirical model's precipitation (ensemble) forecasts over CONUS and demonstrated that it generates a set of dates that captures a majority of high-impact precipitation events, while substantially reducing a heavy-precipitation bias inherent in an alternative methodology based on the direct identification of large precipitation events in the Global Ensemble Forecast System (GEFS), version 12 reforecasts. The impacts of data thinning on the accuracy of precipitation statistical postprocessing, as well as on the calibration and validation of the Hydrologic Ensemble Forecast Service (HEFS) reforecasts are yet to be established. Significance StatementHigh-impact weather events are usually associated with extreme precipitation, which is notoriously difficult to predict even using highly resolved state-of-the-art numerical weather prediction models based on first physical principles. The same is true for statistical models that use past data to anticipate the future behavior likely to stem from an observed initial state. Here we use both types of models to identify the occurrences of the states, over the historical climate record, which are likely to lead to extreme precipitation events. We show that the overall statistics of precipitation over the contiguous United States is encapsulated in a greatly reduced set of such states, which could substantially alleviate the computational burden associated with testing of hydrological forecast models used for decision support.

Abstract. This paper contains a description of recent changes to the formulation and numerical implementation of the Quasi-Geostrophic Coupled Model (Q-GCM), which constitute a major update of the previous version of the model (Hogg et al., 2014). The Q-GCM model has been designed to provide an efficient numerical tool to study the dynamics of multi-scale mid-latitude air–sea interactions and their climatic impacts. The present additions/alterations were motivated by an inquiry into the dynamics of mesoscale ocean–atmosphere coupling and, in particular, by an apparent lack of Q-GCM atmosphere’s sensitivity to mesoscale sea-surface temperature (SST) anomalies, even at high (mesoscale) atmospheric resolutions, contrary to ample theoretical and observational evidence otherwise. Major modifications aimed at alleviating this problem include an improved radiative-convective scheme resulting in a more realistic model mean state and associated model parameters, a new formulation of entrainment in the atmosphere, which prompts more efficient communication between the atmospheric mixed layer and free troposphere, as well as an addition of temperature-dependent wind component in the atmospheric mixed layer and the resulting mesoscale feedbacks. The most drastic change is, however, the inclusion of moist dynamics in the model, which may be key to midlatitude ocean–atmosphere coupling. Accordingly, this version of the model is to be referred to as the MQ-GCM model. Overall, the MQ-GCM model is shown to exhibit a rich spectrum of behaviours reminiscent of many of the observed properties of the Earth’s climate system. It remains to be seen whether the added processes are able to affect in fundamental ways the simulated dynamics of the mid-latitude ocean–atmosphere system’s coupled decadal variability.

Dynamical systems like the one described by the three-variable Lorenz-63 model may serve as metaphors for complex natural systems such as climate systems. When these systems are perturbed by external forcing factors, they tend to relax back to their equilibrium conditions after the forcing has shut off. Here we investigate the behavior of such transients in the Lorenz-63 model by studying its trajectories initialized far away from the asymptotic attractor. Counterintuitively, these transient trajectories exhibit complex routes and, in particular, the sensitivity to initial conditions is akin to that of the asymptotic behavior on the attractor. Thus, similar extreme events may lead to widely different variations before the perturbed system returns back to its statistical equilibrium.

Purpose. This paper briefly reviews the theory of singular vortices (SV) on a beta-plane. Methods and Results : The primary focus of the paper is on a long-term evolution of an individual SV: the governing equations and integrals of motion are given, the algorithm of numerical implementation of these equations for investigation of such an evolution is described, and the results of some numerical experiments are presented. It is shown that the vortex evolution consists of two stages. At an initial (quasi-linear) stage, the near-field radiation of Rossby waves by the vortex produces, near the vortex, a non-stationary secondary dipole – the beta-gyres – which forces the vortex to move (a cyclone drifts northwestward, an anticyclone – southwestward). At the next (nonlinear) stage, the far-field radiation of Rossby waves and self-interactions within the regular component of the motion become of importance. A singular cyclone (anticyclone) migrates slowly into the anticyclonic (cyclonic) beta-gyre; the SV and the beta-gyre form a compact vortex pair which continues to move northwestward (southwestward). As this process takes place, the cyclonic (anticyclonic) beta-gyre gradually drifts away from and ceases to affect the SV, while the SV starts to interact with the Rossby waves it radiated previously, which results in oscillations of its translation speed. The duration of the quasi-linear stage rapidly increases with an increasing amplitude of the SV; for vortices of small or moderate amplitude, this stage ends rapidly and gives way to the nonlinear stage. The first phenomenological description of the nonlinear stage of a singular monopole’s evolution appeared in our recent work on the dynamics of the SV on a beta-plane. Conclusions : The theory of singular vortices on a beta-plane developed here significantly broadens our understanding of the evolution and dynamics of localized geophysical vortices which play an important role in the large-scale circulation of the ocean and atmosphere.

An analysis of the climate system is usually complicated by its very high dimensionality and its nonlinearity which impedes spatial and time scale separation. An even more difficult problem is to obtain separate estimates of the climate system’s response to external forcing (e.g. anthropogenic emissions of greenhouse gases and aerosols) and the contribution of the climate system’s internal variability into recent climate trends. Identification of spatiotemporal climatic patterns representing forced signals and internal variability in global climate models (GCMs) would make it possible to characterize these patterns in the observed data and to analyze dynamical relationships between these two types of climate variability. In contrast with real climate observations, many GCMs are able to provide ensembles of many climate realizations under the same external forcing, with relatively independent initial conditions (e.g. LENS [1], MPI-GE [2], CMIP ensembles of 20th century climate). In this report, a recently developed method of empirical spatio-temporal data decomposition into linear dynamical modes (LDMs) [3] based on Bayesian approach, is modified to address the problem of self-consistent separation of the climate system internal variability modes and the forced response signals in such ensembles. The LDM method provides the time series of principal components and corresponding spatial patterns; in application to an ensemble of realizations, it determines both time series of the internal variability modes of current realization and the time series of forced response (defined as signal shared by all realizations). The advantage of LDMs is the ability to take into account the time scales of the system evolution better than some other linear techniques, e.g. traditional empirical orthogonal function decomposition. Furthermore, the modified ensemble LDM (E-LDM) method is designed to determine the optimal number of principal components and to distinguish their time scales for both internal variability modes and forced response signals. The technique and results of applying LDM method to different GCM ensemble realizations will be presented and discussed. This research was supported by the Russian Science Foundation (Grant No. 18-12-00231). [1] Kay, J. E., Deser, C., Phillips, A., Mai, A., Hannay, C., Strand, G., Arblaster, J., Bates, S., Danabasoglu, G., Edwards, J., Holland, M. Kushner, P., Lamarque, J.-F., Lawrence, D., Lindsay, K., Middleton, A., Munoz, E., Neale, R., Oleson, K., Polvani, L., and M. Vertenstein (2015), The Community Earth System Model (CESM) Large Ensemble Project: A Community Resource for Studying Climate Change in the Presence of Internal Climate Variability, Bulletin of the American Meteorological Society, doi: 10.1175/BAMS-D-13-00255.1, 96, 1333-1349 [2] Maher, N., Milinski, S., Suarez-Gutierrez, L., Botzet, M., Dobrynin, M., Kornblueh, L., Kröger, J., Takano, Y., Ghosh, R., Hedemann, C., Li, C., Li, H., Manzini, E., Notz, N., Putrasahan, D., Boysen, L., Claussen, M., Ilyina, T., Olonscheck, D., Raddatz, T., Stevens, B. and Marotzke, J. (2019). The Max Planck Institute Grand Ensemble: Enabling the Exploration of Climate System Variability. Journal of Advances in Modeling Earth Systems, 11, 1-21. https://doi.org/10.1029/2019MS001639 [3] Gavrilov, A., Kravtsov, S., Mukhin, D. (2020). Analysis of 20th century surface air temperature using linear dynamical modes. Chaos: An Interdisciplinary Journal of Nonlinear Science, 30(12), 123110. https://doi.org/10.1063/5.0028246

Proxy temperature data records featuring local time series, regional averages from areas all around the globe, as well as global averages, are analyzed using the Slow Feature Analysis (SFA) method. As explained in the paper, SFA is much more effective than the traditional Fourier analysis in identifying slow-varying (low-frequency) signals in data sets of a limited length. We find the existence of a striking gap from ~1000 to about ~20,000 years, which separates intrinsic climatic oscillations with periods ranging from ~60 years to ~1000 years, from the longer time-scale periodicities (20,000 year+) involving external forcing associated with Milankovitch cycles. The absence of natural oscillations with periods within the gap is consistent with cumulative evidence based on past data analyses, as well as with earlier theoretical and modeling studies.

Building on the work of Kravtsov and Reznik [J. Fluid Mech. 909, A23 (2021); hereafter KR21], we studied the interactions of a localized monopole with a rectilinear, constant-shear flow in a 1½-layer, f-plane, quasi-geostrophic model. The non-invariance of this model with respect to Galilean transformations plays a crucial role in the dynamics of such interactions. Of particular importance here are two configurations in which the center of the vortex is located on the line of zero zonal current and remains motionless in the background of a nonstationary flow field generated via interactions of the vortex with the zonal flow. In configuration I (II), the vortex is prograde (retrograde), that is, its vorticity is of the same (opposite) sign with the vorticity of the background flow. Configuration I is stable, whereas configuration II eventually breaks down: a retrograde vortex drifts off of the zero-current line, rapidly accelerates and radiates intense Rossby waves, which results in a gradual weakening of the vortex. Naturally, the same scenario plays out if a retrograde vortex is initially off of the zero-current line. On the other hand, a prograde vortex initially located at some distance from the zero-current line drifts toward this line, albeit at a rate that decreases with time, so the solution always tends to configuration I. Therefore, the line of zero zonal current “attracts” prograde vortices and “repels” retrograde vortices. The present numerical experiments with singular vortices, using the scheme developed in KR21, confirm the above scenarios and clarify their dynamics.

This paper addresses the dynamics of internal hemispheric-scale multidecadal climate variability by postulating an energy-balance (EBM) model comprising two deep-ocean oscillators in the Atlantic and Pacific basins, coupled through their surface mixed layers via atmospheric teleconnections. This system is linear and driven by the atmospheric noise. Two sets of the EBM model parameters are developed by fitting the EBM-based mixed-layer temperature covariance structure to best mimic basin-average North Atlantic/Pacific sea surface temperature (SST) covariability in either observations or control simulations of comprehensive climate models within the CMIP5 project. The differences between the dynamics underlying the observed and CMIP5-simulated multidecadal climate variability and predictability are encapsulated in the algebraic structure of the two EBM model versions so obtained: EBMCMIP5 and EBMOBS. The multidecadal variability in EBMCMIP5 is overall weaker and amounts to a smaller fraction of the total SST variability than in EBMOBS, pointing to a lower potential decadal predictability of virtual CMIP5 climates relative to that of the actual climate. The EBMCMIP5 decadal hemispheric teleconnections (and, by inference, those in CMIP5 models) are largely controlled by the variability of the Pacific, in which the ocean, due to its large thermal and dynamical memory, acts as a passive integrator of atmospheric noise. By contrast, EBMOBS features a stronger two-way coupling between the Atlantic and Pacific multidecadal oscillators, thereby suggesting the existence of a hemispheric-scale and, perhaps, global multidecadal mode associated with internal ocean dynamics. The inferred differences between the observed and CMIP5 simulated climate variability stem from a stronger communication between the deep ocean and surface processes implicit in the observational data.

A Bayesian Linear Dynamical Mode (LDM) decomposition method is applied to isolate robust modes of climate variability in the observed surface air temperature (SAT) field. This decomposition finds the optimal number of internal modes characterized by their own time scales, which enter the cost function through a specific choice of prior probabilities. The forced climate response, with time dependence estimated from state-of-the-art climate-model simulations, is also incorporated in the present LDM decomposition and shown to increase its optimality from a Bayesian standpoint. On top of the forced signal, the decomposition identifies five distinct LDMs of internal climate variability. The first three modes exhibit multidecadal scales, while the remaining two modes are attributable to interannual-to-decadal variability associated with El Niño–Southern oscillation; all of these modes contribute to the secular climate signal—the so-called global stadium wave—missing in the climate-model simulations. One of the multidecadal LDMs is associated with Atlantic multidecadal oscillation. The two remaining slow modes have secular time scales and patterns exhibiting regional-to-global similarities to the forced-signal pattern. These patterns have a global scale and contribute significantly to SAT variability over the Southern and Pacific Oceans. In combination with low-frequency modulation of the fast LDMs, they explain the vast majority of the variability associated with interdecadal Pacific oscillation. The global teleconnectivity of the secular climate modes and their possible crucial role in shaping the forced climate response are the two key dynamical questions brought about by the present analysis.