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The Paleocene-Eocene Thermal Maximum (PETM; 56 Ma) is one of our best geological analogs for understanding climate dynamics in a "greenhouse" world. However, proxy data representing the event are only available from select marine and terrestrial sedimentary sequences that are unevenly distributed across Earth's surface, limiting our view of the spatial patterns of climate change. Here, we use paleoclimate data assimilation (DA) to combine climate model and proxy information and create a spatially complete reconstruction of the PETM and the climate state that precedes it ("PETM-DA"). Our data-constrained results support strong polar amplification, which in the absence of an extensive cryosphere, is related to temperature feedbacks and loss of seasonal snow on land. The response of the hydrological cycle to PETM warming consists of a narrowing of the Intertropical Convergence Zone, off-equatorial drying, and an intensification of seasonal monsoons and winter storm tracks. Many of these features are also seen in simulations of future climate change under increasing anthropogenic emissions. Since the PETM-DA yields a spatially complete estimate of surface air temperature, it yields a rigorous estimate of global mean temperature change (5.6 ∘C; 5.4 ∘C to 5.9 ∘C, 95% CI) that can be used to calculate equilibrium climate sensitivity (ECS). We find that PETM ECS was 6.5 ∘C (5.7 ∘C to 7.4 ∘C, 95% CI), which is much higher than the present-day range. This supports the view that climate sensitivity increases substantially when greenhouse gas concentrations are high.

Climate records exhibit scaling behavior with large exponents, resulting in larger fluctuations at longer timescales. It is unclear whether climate models are capable of simulating these fluctuations, which draws into question their ability to simulate such variability in the coming decades and centuries. Using the latest simulations and data syntheses, we find agreement for spectra derived from observations and models on timescales ranging from interannual to multimillennial. Our results confirm the existence of a scaling break between orbital and annual peaks, occurring around millennial periodicities. That both simple and comprehensive ocean-atmosphere models can reproduce these features suggests that long-range persistence is a consequence of the oceanic integration of both gradual and abrupt climate forcings. This result implies that Holocene low-frequency variability is partly a consequence of the climate system's integrated memory of orbital forcing. We conclude that climate models appear to contain the essential physics to correctly simulate the spectral continuum of global-mean temperature; however, regional discrepancies remain unresolved. A critical element of successfully simulating suborbital climate variability involves, we hypothesize, initial conditions of the deep ocean state that are consistent with observations of the recent past.

Climate changes across the past 24,000 years provide key insights into Earth system responses to external forcing. Climate model simulations.sup.1,2 and proxy data.sup.3-8 have independently allowed for study of this crucial interval; however, they have at times yielded disparate conclusions. Here, we leverage both types of information using paleoclimate data assimilation.sup.9,10 to produce the first proxy-constrained, full-field reanalysis of surface temperature change spanning the Last Glacial Maximum to present at 200-year resolution. We demonstrate that temperature variability across the past 24 thousand years was linked to two primary climatic mechanisms: radiative forcing from ice sheets and greenhouse gases; and a superposition of changes in the ocean overturning circulation and seasonal insolation. In contrast with previous proxy-based reconstructions.sup.6,7 our results show that global mean temperature has slightly but steadily warmed, by ~0.5 °C, since the early Holocene (around 9 thousand years ago). When compared with recent temperature changes.sup.11, our reanalysis indicates that both the rate and magnitude of modern warming are unusual relative to the changes of the past 24 thousand years. Paleoclimate datasets are integrated with a climate model to reconstruct global surface temperature since the Last Glacial Maximum, showing sustained warming until the mid-Holocene., Author(s): Matthew B. Osman [sup.1] , Jessica E. Tierney [sup.1] , Jiang Zhu [sup.2] , Robert Tardif [sup.3] , Gregory J. Hakim [sup.3] , Jonathan King [sup.1] , Christopher J. [...]

The Last Glacial Maximum (LGM), one of the best studied palaeoclimatic intervals, offers an excellent opportunity to investigate how the climate system responds to changes in greenhouse gases and the cryosphere. Previous work has sought to constrain the magnitude and pattern of glacial cooling from palaeothermometers.sup.1,2, but the uneven distribution of the proxies, as well as their uncertainties, has challenged the construction of a full-field view of the LGM climate state. Here we combine a large collection of geochemical proxies for sea surface temperature with an isotope-enabled climate model ensemble to produce a field reconstruction of LGM temperatures using data assimilation. The reconstruction is validated with withheld proxies as well as independent ice core and speleothem [delta].sup.18O measurements. Our assimilated product provides a constraint on global mean LGM cooling of -6.1 degrees Celsius (95 per cent confidence interval: -6.5 to -5.7 degrees Celsius). Given assumptions concerning the radiative forcing of greenhouse gases, ice sheets and mineral dust aerosols, this cooling translates to an equilibrium climate sensitivity of 3.4 degrees Celsius (2.4-4.5 degrees Celsius), a value that is higher than previous LGM-based estimates but consistent with the traditional consensus range of 2-4.5 degrees Celsius.sup.3,4. A compilation of proxy data are used with an isotope-enabled climate model ensemble to constrain cooling during the Last Glacial Maximum, producing estimates of equilibrium climate sensitivity that agree well with the current consensus range., Author(s): Jessica E. Tierney [sup.1] , Jiang Zhu [sup.2] [sup.3] , Jonathan King [sup.1] , Steven B. Malevich [sup.1] , Gregory J. Hakim [sup.4] , Christopher J. Poulsen [sup.3] Author [...]

Glaciers in the Amundsen Sea Embayment of West Antarctica are rapidly retreating and contributing to sea level rise. Ice loss is occurring primarily via exposure to warm ocean water, which varies in response to local wind variability. There is evidence that retreat was initiated in the mid-20th century, but the perturbation that may have triggered retreat remains unknown. A leading hypothesis is that large pressure and wind anomalies in the 1940s drove exceptionally strong oceanic ice-shelf melting. However, the characteristics, drivers, and rarity of the atmospheric event remain poorly constrained. We investigate the 1940s atmospheric event using paleoclimate reconstructions and climate model simulations. The reconstructions show that large westerly wind anomalies occurred from ∼1938 –1942, a combined response to the very large El Niño event from 1940–1942 and other variability beginning years earlier. Climate model simulations provide evidence that events of similar magnitude and duration may occur tens to hundreds of times per 10 kyr of internal climate variability (∼0.2 to 2.5 occurrences per century). Our results suggest that the 1940s westerly event is unlikely to have been exceptional enough to be the sole explanation for the initiation of Amundsen Sea glacier retreat. Additional factors are likely needed to explain the onset of retreat in West Antarctica, such as naturally arising variability in ocean conditions prior to the 1940s or anthropogenically driven trends since the 1940s. [ABSTRACT FROM AUTHOR]

Climate field reconstruction (CFR) refers to the estimation of spatiotemporal climate fields (such as surface temperature) from a collection of pointwise paleoclimate proxy datasets. The climate fields can provide rich information on climate dynamics and provide an out-of-sample validation of climate models. However, most CFR workflows are complex and timeconsuming, as they involve: (i) preprocessing of the proxy records, climate model simulations, and instrumental observations, (ii) application of one or more statistical methods, and (iii) analysis and visualization of the reconstruction results. Historically, this process has lacked transparency and accessibility, limiting reproducibility and experimentation by non-specialists. This article presents an open-source and object-oriented Python package called cfr that aims to make CFR workflows easy to understand and conduct, saving climatologists from technical details and facilitating efficient and reproducible research. It provides user-friendly utilities for common CFR tasks such as proxy and climate data analysis and visualization, proxy system modeling, and modularized workflows for multiple reconstruction methods, enabling methodological intercomparisons within the same framework. The package is supported with an extensive documentation of the application interface (API) and a growing number of tutorial notebooks illustrating its usage. As an example, we present two cfr -driven reconstruction experiments using the PAGES 2k temperature database: applying the last millennium reanalysis (LMR) paleoclimate data assimilation (PDA) framework and the Graphical Expectation-Maximization (GraphEM) algorithm, respectively. [ABSTRACT FROM AUTHOR]

Climate field reconstruction (CFR) refers to the estimation of spatiotemporal climate fields (such as surface temperature) from a collection of pointwise paleoclimate proxy datasets. The climate fields can provide rich information on climate dynamics and provide an out-of-sample validation of climate models. However, most CFR workflows are complex and timeconsuming, as they involve: (i) preprocessing of the proxy records, climate model simulations, and instrumental observations, (ii) application of one or more statistical methods, and (iii) analysis and visualization of the reconstruction results. Historically, this process has lacked transparency and accessibility, limiting reproducibility and experimentation by non-specialists. This article presents an open-source and object-oriented Python package called cfr that aims to make CFR workflows easy to understand and conduct, saving climatologists from technical details and facilitating efficient and reproducible research. It provides user-friendly utilities for common CFR tasks such as proxy and climate data analysis and visualization, proxy system modeling, and modularized workflows for multiple reconstruction methods, enabling methodological intercomparisons within the same framework. The package is supported with an extensive documentation of the application interface (API) and a growing number of tutorial notebooks illustrating its usage. As an example, we present two cfr-driven reconstruction experiments using the PAGES 2k temperature database: applying the last millennium reanalysis (LMR) paleoclimate data assimilation (PDA) framework and the Graphical Expectation-Maximization (GraphEM) algorithm, respectively. [ABSTRACT FROM AUTHOR]

We evaluate Linear Inverse Models (LIMs) trained on last millennium model data to predict Arctic sea‐ice concentration, thickness, and other atmospheric and oceanic variables on monthly timescales. We find that more than 500 years of training data and 100 years of validation data are needed to reliably estimate LIM forecast skill. The best LIM has skill up to 8 months lead time and outperforms an autoregressive model of order one (AR1) forecast at all locations, with particularly large outperformance near the ice edge. However, for out‐of‐sample validation tests using data from various different model simulations and reanalysis products, they underperform an AR1 model due to differences in the location of the sea‐ice edge from the training data. We present a metric for predicting LIM forecast skill, based on the spatial correlation of the variance in the training and validation data sets. Plain Language Summary: Rapid changes in sea‐ice concentration in recent decades have produced new navigational challenges and hazards in the region, elevating the importance of seasonal sea‐ice forecasts. Arctic sea ice has been shown to contain inherent predictability on seasonal timescales, yet current predictions generally show poor skill. Here, we employ a statistical technique referred to as Linear Inverse Modeling, which uses linearized dynamical modes estimated from a training data set to predict sea‐ice conditions on monthly timescales. We find a Linear Inverse Model is able to outperform a baseline statistical model throughout the Arctic when initialized on the data derived from the same model. Key Points: A Linear Inverse Model is evaluated using last millennium model simulations for Arctic climate predictionThe Linear Inverse Model successfully predicts Arctic conditions when the same model simulation is used for training and validationLinear Inverse Model forecast skill is proportional to the spatial correlation of variance in the validation and training data [ABSTRACT FROM AUTHOR]

Glaciers in the Amundsen Sea Embayment of West Antarctica are rapidly retreating and contributing to sea level rise. Ice loss is occurring primarily via exposure to warm ocean water, which varies in response to local wind variability. There is evidence that retreat was initiated in the mid-20111 century, but the perturbation that may have triggered retreat remains unknown. A leading hypothesis is that large pressure and wind anomalies in the 1940s drove exceptionally strong oceanic ice-shelf melting. However, the characteristics, drivers, and rarity of the atmospheric event remain poorly constrained. We investigate the 1940s atmospheric event using paleoclimate reconstructions and climate model simulations. The reconstructions show that large westerly wind anomalies occurred from ~1938-1942, a combined response to the very large El Niño event from 1940-1942 and other variability beginning years earlier. Climate model simulations provide evidence that events of similar magnitude and duration are unusual but may have occurred tens to hundreds of times throughout the Holocene. Our results suggest that the 1940s westerly event is unlikely to have been exceptional enough to be the sole explanation for the initiation of Amundsen Sea glacier retreat. Naturally arising variability in ocean conditions prior to the 1940s, or anthropogenically driven trends since the 1940s, may be needed to explain the onset of retreat in West Antarctica. [ABSTRACT FROM AUTHOR]

Balance dynamics are proposed in a probabilistic framework, assuming that the state variables and the master, or control, variables are random variables described by continuous probability density functions. Balance inversion, defined as recovering the state variables from the control variables, is achieved through Bayes' theorem. Balance dynamics are defined by the propagation of the joint probability of the state and control variables through the Liouville equation. Assuming Gaussian statistics, balance inversion reduces to linear regression of the state variables onto the control variables, and assuming linear dynamics, balance dynamics reduces to a Kalman filter subject to perfect observations given by the control variables. Example solutions are given for an elliptical vortex in shallow water having unity Rossby and Froude numbers, which produce an outward-propagating pulse of inertia-gravity wave activity. Applying balance inversion to the potential vorticity reveals that, because potential vorticity and divergence share welldefined patterns of covariability, the inertia-gravity wave field is recovered in addition to the vortical field. Solutions for a probabilistic balance dynamics model applied to the elliptical vortex reveal smaller errors ('imbalance') for height control compared to potential vorticity control. Important attributes of the probabilistic balance theory include quantification of the concept of balance manifold 'fuzziness,' and clear state-independent definitions of balance and imbalance in terms of the range of the probabilistic inversion operators. Moreover, the theory provides a generalization of the notion of balance that may prove useful for problems involving moist physics, chemistry, and tropical circulations.

The impact of transient mountain waves on a large-scale flow is examined through idealized numerical simulations of the passage of a time-evolving synoptic-scale jet over an isolated 3D mountain. Both the global momentum budget and the spatial flow response are examined to illustrate the impact of transient mountain waves on the large-scale flow. Additionally, aspects of the spatial response are quantified by potential vorticity inversion. Nearly linear cases exhibit a weak loss of domain-averaged absolute momentum despite the absence of wave breaking. This transient effect occurs because, over the time period of the large-scale flow, the momentum flux through the top boundary does not balance the surface pressure drag. Moreover, an adiabatic spatial redistribution of momentum is observed in these cases, which results in an increase (decrease) of zonally averaged zonal momentum south (north) of the mountain. For highly nonlinear cases, the zonally averaged momentum field shows a region of flow deceleration downstream of the mountain, flanked by broader regions of weak flow acceleration. Cancellation between the accelerating and decelerating regions results in weak fluctuations in the volume-averaged zonal momentum, suggesting that the mountain-induced circulations are primarily redistributing momentum. Potential vorticity anomalies develop in a region of wave breaking near the mountain, and induce local regions of flow acceleration and deceleration that alter the large-scale flow. A 'perfect' conventional gravity wave-drag parameterization is implemented on a coarser domain not having a mountain, forced by the momentum flux distribution from the fully nonlinear simulation. This parameterization scheme produces a much weaker spatial response in the momentum field and it fails to produce enough flow deceleration near the 20 m [s.sup.-1] jet. These results suggest that the potential vorticity sources attributable to the gravity wave-drag parameterization have a controlling effect on the longtime downstream influence of the mountain.