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A tipping point is defined by the IPCC as a critical threshold beyond which a system reorganizes, often abruptly and/or irreversibly. Tipping points can be crossed solely by internal variation in the system or by approaching a bifurcation point where the current state loses stability and forces the system to move to another stable state. It is currently debated whether or not Dansgaard-Oeschger (DO) events, abrupt warmings occurring during the last glacial period, are noise-induced or caused by the system reaching a bifurcation point. It can be shown that before a bifurcation point is reached there are observable changes in the statistical properties of the state variable. These are known as early warning signals and include increased fluctuation and correlation time. To express this behaviour we propose a new model based on the well-known first order autoregressive process (AR), with modifications to the correlation parameter such that it depends linearly on time. In order to estimate the time evolution of the correlation parameter we adopt a hierarchical Bayesian modeling framework, from which Bayesian analysis can be performed using the methodology of integrated nested Laplace approximations. We then apply the model to segments of the oxygen isotope ratios from the Northern Greenland Ice Core Project record corresponding to 17 DO events. Early warning signals were detected and found statistically significant for a number of DO events, suggesting that such events could indeed be caused by approaching a bifurcation point. The methodology developed to perform the given early warning analyses can be applied more generally, and is publicly available as the R-package INLA.ews. [ABSTRACT FROM AUTHOR]

Melting of the Greenland ice sheet (GrIS) in response to anthropogenic global warming poses a severe threat in terms of global sea-level rise (SLR)1. Modelling and palaeoclimate evidence suggest that rapidly increasing temperatures in the Arctic can trigger positive feedback mechanisms for the GrIS, leading to self-sustained melting2–4, and the GrIS has been shown to permit several stable states5. Critical transitions are expected when the global mean temperature (GMT) crosses specific thresholds, with substantial hysteresis between the stable states6. Here we use two independent ice-sheet models to investigate the impact of different overshoot scenarios with varying peak and convergence temperatures for a broad range of warming and subsequent cooling rates. Our results show that the maximum GMT and the time span of overshooting given GMT targets are critical in determining GrIS stability. We find a threshold GMT between 1.7 °C and 2.3 °C above preindustrial levels for an abrupt ice-sheet loss. GrIS loss can be substantially mitigated, even for maximum GMTs of 6 °C or more above preindustrial levels, if the GMT is subsequently reduced to less than 1.5 °C above preindustrial levels within a few centuries. However, our results also show that even temporarily overshooting the temperature threshold, without a transition to a new ice-sheet state, still leads to a peak in SLR of up to several metres.Simulations using two state-of-the-art ice-sheet models show that abrupt melting of the Greenland ice sheet following overshooting of the global mean temperature critical threshold can be mitigated by subsequent cooling to below 1.5 °C. [ABSTRACT FROM AUTHOR]

Paleoclimate proxy records have non-negligible uncertainties that arise from both the proxy measurement and the dating processes. Knowledge of the dating uncertainties is important for a rigorous propagation to further analyses, for example, for identification and dating of stadial–interstadial transitions in Greenland ice core records during glacial intervals, for comparing the variability in different proxy archives, and for model-data comparisons in general. In this study we develop a statistical framework to quantify and propagate dating uncertainties in layer counted proxy archives using the example of the Greenland Ice Core Chronology 2005 (GICC05). We express the number of layers per depth interval as the sum of a structured component that represents both underlying physical processes and biases in layer counting, described by a regression model, and a noise component that represents the fluctuations of the underlying physical processes, as well as unbiased counting errors. The joint dating uncertainties for all depths can then be described by a multivariate Gaussian process from which the chronology (such as the GICC05) can be sampled. We show how the effect of a potential counting bias can be incorporated in our framework. Furthermore we present refined estimates of the occurrence times of Dansgaard–Oeschger events evidenced in Greenland ice cores together with a complete uncertainty quantification of these timings. [ABSTRACT FROM AUTHOR]

Paleoclimate proxy records have non-negligible uncertainties that arise from both the proxy measurement and the dating processes. Knowledge of the dating uncertainties is important for a rigorous propagation to further analyses; for example for identification and dating of stadial-interstadial transitions in Greenland ice core records during glacial intervals, for comparing the variability in different proxy archives, and for model-data comparisons in general. In this study we develop a statistical framework to quantify and propagate dating uncertainties in layer-counted proxy archives using the example of the Greenland Ice Core Chronology 2005 (GICC05). We express the number of layers per depth interval as the sum of a structured component that represents both underlying physical processes and biases in layer counting, described by a regression model, and a noise component that represents the fluctuations of the underlying physical processes, as well as unbiased counting errors. The age-depth relationship of the joint dating uncertainties can then be described by a multivariate Gaussian process from which realizations of the chronology can be sampled. We show how the effect of an unknown counting bias can be incorporated in our framework and present refined estimates of the occurrence times of Dansgaard-Oeschger events evidenced in Greenland ice cores together with a complete uncertainty quantification of these timings. [ABSTRACT FROM AUTHOR]

The Greenland Ice Sheet (GrIS) is a potentially unstable component of the Earth system and may exhibit a critical transition under ongoing global warming. Mass reductions of the GrIS have substantial impacts on global sea level and the speed of the Atlantic Meridional Overturning Circulation, due to the additional freshwater caused by increased meltwater runoff into the northern Atlantic. The stability of the GrIS depends crucially on the positive melt-elevation feedback (MEF), by which melt rates increase as the overall ice sheet height decreases under rising temperatures. Melting rates across Greenland have accelerated nonlinearly in recent decades, and models predict a critical temperature threshold beyond which the current ice sheet state is not maintainable. Here, we investigate long-term melt rate and ice sheet height reconstructions from the central-western GrIS in combination with model simulations to quantify the stability of this part of the GrIS. We reveal significant earlywarning signals (EWS) indicating that the central-western GrIS is close to a critical transition. By relating the statistical EWS to underlying physical processes, our results suggest that the MEF plays a dominant role in the observed, ongoing destabilization of the central-western GrIS. Our results suggest substantial further GrIS mass loss in the near future and call for urgent, observation-constrained stability assessments of other parts of the GrIS. [ABSTRACT FROM AUTHOR]

Experiments and models suggest that climate affects mosquito‐borne disease transmission. However, disease transmission involves complex nonlinear interactions between climate and population dynamics, which makes detecting climate drivers at the population level challenging. By analysing incidence data, estimated susceptible population size, and climate data with methods based on nonlinear time series analysis (collectively referred to as empirical dynamic modelling), we identified drivers and their interactive effects on dengue dynamics in San Juan, Puerto Rico. Climatic forcing arose only when susceptible availability was high: temperature and rainfall had net positive and negative effects respectively. By capturing mechanistic, nonlinear and context‐dependent effects of population susceptibility, temperature and rainfall on dengue transmission empirically, our model improves forecast skill over recent, state‐of‐the‐art models for dengue incidence. Together, these results provide empirical evidence that the interdependence of host population susceptibility and climate drives dengue dynamics in a nonlinear and complex, yet predictable way. [ABSTRACT FROM AUTHOR]

Background: To suppress the COVID-19 outbreak, the Norwegian government closed all schools on March 13, 2020. The kindergartens reopened on April 20, and the schools on April 27 and May 11 of 2020. The effect of these measures is largely unknown since the role of children in the spread of the SARS-CoV-2 virus is still unclear. There are only a few studies of school closures as a separate intervention to other social distancing measures, and little research exists on the effect of school opening during a pandemic. Objective: This study aimed to model the effect of opening kindergartens and the schools in Norway in terms of a change in the reproduction number (R). A secondary objective was to assess if we can use the estimated R after school openings to infer the rates of transmission between children in schools. Methods: We used an individual-based model (IBM) to assess the reopening of kindergartens and schools in two Norwegian cities, Oslo, the Norwegian capital, with a population of approximately 680 000, and Tromsø, which is the largest city in Northern Norway, with a population of approximately 75 000. The model uses demographic information and detailed data about the schools in both cities. We carried out an ensemble study to obtain robust results in spite of the considerable uncertainty that remains about the transmission of SARS-CoV-2. Results: We found that reopening of Norwegian kindergartens and schools are associated with a change in R of 0.10 (95%CI 0.04–0.16) and 0.14 (95%CI 0.01–0.25) in the two cities under investigation if the in-school transmission rates for the SARS-CoV-2 virus are equal to what has previously been estimated for influenza pandemics. Conclusion: We found only a limited effect of reopening schools on the reproduction number, and we expect the same to hold true in other countries where nonpharmaceutical interventions have suppressed the pandemic. Consequently, current R-estimates are insufficiently accurate for determining the transmission rates in schools. For countries that have closed schools, planned interventions, such as the opening of selected schools, can be useful to infer general knowledge about children-to-children transmission of SARS-CoV-2. [ABSTRACT FROM AUTHOR]

One of the most intriguing facets of the climate system is that it exhibits variability across all temporal and spatial scales; pronounced examples are temperature and precipitation. The structure of this variability, however, is not arbitrary. Over certain spatial and temporal ranges, it can be described by scaling relationships in the form of power laws in probability density distributions and autocorrelation functions. These scaling relationships can be quantified by scaling exponents which measure how the variability changes across scales and how the intensity changes with frequency of occurrence. Scaling determines the relative magnitudes and persistence of natural climate fluctuations. Here, we review various scaling mechanisms and their relevance for the climate system.We show observational evidence of scaling and discuss the application of scaling properties and methods in trend detection, climate sensitivity analyses, and climate prediction. [ABSTRACT FROM AUTHOR]

Reliable quantification of the global mean surface temperature (GMST) response to radiative forcing is essential for assessing the risk of dangerous anthropogenic climate change. We present the statistical foundations for an observation-based approach using a stochastic linear response model that is consistent with the long-range temporal dependence observed in global temperature variability. We have incorporated the model in a latent Gaussian modeling framework, which allows for the use of integrated nested Laplace approximations (INLAs) to perform full Bayesian analysis. As examples of applications, we estimate the GMST response to forcing from historical data and compute temperature trajectories under the Representative Concentration Pathways (RCPs) for future greenhouse gas forcing. For historic runs in the Model Intercomparison Project Phase 5 (CMIP5) ensemble, we estimate response functions and demonstrate that one can infer the transient climate response (TCR) from the instrumental temperature record. We illustrate the effect of long-range dependence by comparing the results with those obtained from one-box and two-box energy balance models. The software developed to perform the given analyses is publicly available as the R package INLA.climate. [ABSTRACT FROM AUTHOR]

Reliable quantification of the global mean surface temperature (GMST) response to radiative forcing is essential for assessing the risk of dangerous anthropogenic climate change. We present the statistical foundations for an observation-based approach, using a stochastic linear-response model that is consistent with the long-range temporal dependence observed in global temperature variability. We have incorporated the model in a latent Gaussian modeling framework, which allows for the use of integrated nested Laplace approximations (INLAs) to perform full Bayesian analysis. As examples of applications, we estimate the GMST response to forcing from historical data and compute temperature trajectories under the Representative Concentration Pathways (RCPs) for future greenhouse gas forcing. For historic runs in the Model Intercomparison Project Phase 5 (CMIP5) ensemble, we estimate response functions and demonstrate that one can infer the transient climate response (TCR) from the instrumental temperature record. We illustrate the effect of long-range dependence by comparing the results with those obtained from a 1-box energy balance model. The software developed to perform the given analyses is publicly available as the R-package INLA.climate. [ABSTRACT FROM AUTHOR]

The skill of the state-of-the-art climate field reconstruction technique BARCAST (Bayesian Algorithm for Reconstructing Climate Anomalies in Space and Time) to reconstruct temperature with pronounced long-range memory (LRM) characteristics is tested. A novel technique for generating fields of target data has been developed and is used to provide ensembles of LRM stochastic processes with a prescribed spatial covariance structure. Based on different parameter setups, hypothesis testing in the spectral domain is used to investigate if the field and spatial mean reconstructions are consistent with either the fractional Gaussian noise (fGn) process null hypothesis used for generating the target data, or the autoregressive model of order 1 (AR(1)) process null hypothesis which is the assumed temporal evolution model for the reconstruction technique. The study reveals that the resulting field and spatial mean reconstructions are consistent with the fGn process hypothesis for some of the tested parameter configurations, while others are in better agreement with the AR(1) model. There are local differences in reconstruction skill and reconstructed scaling characteristics between individual grid cells, and the agreement with the fGn model is generally better for the spatial mean reconstruction than at individual locations. Our results demonstrate that the use of target data with a different spatiotemporal covariance structure than the BARCAST model assumption can lead to a potentially biased climate field reconstruction (CFR) and associated confidence intervals. [ABSTRACT FROM AUTHOR]

The temporal fluctuations in global mean surface temperature are an example of a geophysical quantity that can be described using the notions of long-range persistence and scale invariance/scaling, but this description has suffered from lack of a generally accepted physical explanation. Processes with these statistical signatures can arise from nonlinear effects, for instance, through cascade-like energy transfer in turbulent fluids, but they can also be produced by linear models with scale-invariant impulse-response functions. This paper demonstrates that, on time scales from months to centuries, the scale-invariant impulse-response function of global surface temperature can be explained by simple linear multibox energy balance models. This explanation describes both the scale invariance of the internal variability and the lack of a characteristic time scale of the response to external forcings. With parameters estimated from observational data, the climate response is approximately scaling in these models, even if the response function is not chosen to be scaling a priori. It is also demonstrated that the differences in scaling exponents for temperatures over land and for sea surface temperatures can be reproduced by a version of the multibox energy balance model with two distinct surface boxes. [ABSTRACT FROM AUTHOR]

Lovejoy and Varotsos (2016) (L&V) analyse the temperature response to solar, volcanic, and solar plus volcanic forcing in the Zebiak-Cane (ZC) model, and to solar and solar plus volcanic forcing in the Goddard Institute for Space Studies (GISS) E2-R model. By using a simple wavelet filtering technique they conclude that the responses in the ZC model combine subadditively on timescales from 50 to 1000 years. Nonlinear response on shorter timescales is claimed by analysis of intermittencies in the forcing and the temperature signal for both models. The analysis of additivity in the ZC model suffers from a confusing presentation of results based on an invalid approximation, and from ignoring the effect of internal variability. We present tests without this approximation which are not able to detect nonlinearity in the response, even without accounting for internal variability. We also demonstrate that internal variability will appear as subadditivity if it is not accounted for. L&V's analysis of intermittencies is based on a mathematical result stating that the intermittencies of forcing and response are the same if the response is linear. We argue that there are at least three different factors that may invalidate the application of this result for these data. It is valid only for a power-law response function; it assumes power-law scaling of structure functions of forcing as well as temperature signal; and the internal variability, which is strong at least on the short timescales, will exert an influence on temperature intermittence which is independent of the forcing. We demonstrate by a synthetic example that the differences in intermittencies observed by L&V easily can be accounted for by these effects under the assumption of a linear response. Our conclusion is that the analysis performed by L&V does not present valid evidence for a detectable nonlinear response in the global temperature in these climate models. [ABSTRACT FROM AUTHOR]

This paper studies regional climate variability for the time period 1900-2013 using parsimonious stochastic models. Instrumental data records on 5° × 5°, 2° × 2°, and equal-area grids are examined. A long-range dependent (LRD) stochastic process is used as a simplified description of the multitude of response times in the climate system. Fitting a linear trend to the global mean surface temperature (GMST) implies a warming of 0.08 decade−1, which is highly significant under an LRD null hypothesis ( p < 10−4). The regional trends are distributed around the global mean trend, while the fluctuation levels increases when going from global to regional scale. The temperature fluctuations of the tropical oceans are observed to be strongly influenced by El Niño-Southern Oscillation (ENSO) and, therefore, more consistent with autoregressive processes of order 1 [AR(1)]. A likelihood-ratio test is used to systematically determine the best null model [AR(1) or LRD]. About 80% of the regional warming trends are found to be significant (with a 5% significance level). [ABSTRACT FROM AUTHOR]

The climate system approaches a tipping point if the prevailing climate state loses stability, making a transition to a different state possible. A result from the theory of randomly driven dynamical systems is that the reduced stability in the vicinity of a tipping point is accompanied by increasing fluctuation levels and longer correlation times (critical slowing down) and can in principle serve as early-warning signals of an upcoming tipping point. This study demonstrates that the high-frequency band of the δ18O variations in the North Greenland Ice Core Project displays fluctuation levels that increase as one approaches the onset of an interstadial (warm) period. Similar results are found for the locally estimated Hurst exponent for the high-frequency fluctuations, signaling longer correlation times. The observed slowing down is found to be even stronger in the Younger Dryas, suggesting that both the Younger Dryas-Preboreal transition and the onsets of the Greenland interstadials are preceded by decreasing stability of the climate state. It is also verified that the temperature fluctuations during the stadial periods can be approximately modeled as a scale-invariant persistent noise, which can be approximated as an aggregation of processes that respond to perturbations on certain characteristic time scales. The results are consistent with the hypothesis that both the onsets of the Greenland interstadials and the Younger Dryas-Preboreal transition are caused by tipping points in dynamical processes with characteristic time scales on the order of decades and that the variability of other processes on longer time scales masks the early-warning signatures in the δ18O signal. [ABSTRACT FROM AUTHOR]

In order to have a scaling description of the climate system that is not inherently non-stationary, the rapid shifts between stadials and interstadials during the last glaciation (the Dansgaard-Oeschger events) cannot be included in the scaling law. The same is true for the shifts between the glacial and interglacial states in the Quaternary climate. When these events are omitted from a scaling analysis the climate noise is consistent with a 1/f law on timescales from months to 105 years. If the shift events are included, the effect is a break in the scaling with an apparent 1/fβ law, with β > 1, for the low frequencies. No evidence of multifractal intermittency has been found in any of the temperature records investigated, and the events are not a natural consequence of multifractal scaling. [ABSTRACT FROM AUTHOR]

In order to have a scaling description of the climate system that is not inherently non-stationary, the rapid shifts between stadials and interstadials during the last glaciation (the Dansgaard-Oeschger events) cannot be included in the scaling law. The same is true for the shifts between the glacial and interglacial states in the Quaternary climate. When these events are omitted from a scaling analysis the climate noise is consistent with a 1/f law on timescales from months to 105 years. If the shift events are included, the effect is a break in the scaling with an apparent 1/fβ law, with β > 1, for the low frequencies. No evidence of multifractal intermittency has been found in any of the temperature records investigated, and the events are not a natural consequence of multifractal scaling. [ABSTRACT FROM AUTHOR]

A two-dimensional stochastic-diffusive energy balance model (EBM) formulated on a sphere by G. R. North et al. is explored and generalized. Instantaneous and frequency-dependent spatial autocorrelation functions and local temporal power spectral densities are computed for local sites and for spatially averaged surface temperature signals up to the global scale. On time scales up to the relaxation time scale given by the effective heat capacities of the ocean mixed layer and land surface, respectively, scaling features are obtained that are reminiscent of what can be derived from the observed temperature field. On longer time scales, however, the EBM predicts a transition to a white-noise scaling, which is not reflected in the observed records. A fractional generalization, which can be considered as a spatial generalization of the zero-dimensional, long-memory EBM of M. Rypdal and K. Rypdal, is proposed and explored. It is demonstrated that this generalized model describes qualitatively the main correlation characteristics of the temperature field reported in the literature and those derived herein from 500-yr-long control simulations of the NorESM Earth system model. A further generalization of the model, to include long-term persistence in the stochastic forcing, is also discussed. [ABSTRACT FROM AUTHOR]

A linearized energy-balance model for global temperature is formulated, featuring a scale-invariant long-range memory (LRM) response and stochastic forcing representing the influence on the ocean heat reservoir from atmospheric weather systems. The model is parameterized by an effective response strength, the stochastic forcing strength, and the memory exponent. The instrumental global surface temperature record and the deterministic component of the forcing are used to estimate these parameters by means of the maximum-likelihood method. The residual obtained by subtracting the deterministic solution from the observed record is analyzed as a noise process and shown to be consistent with a long-memory time series model and inconsistent with a short-memory model. By decomposing the forcing record in contributions from solar, volcanic, and anthropogenic activity one can estimate the contribution of each to twentieth-century global warming. The LRM model is applied with a reconstruction of the forcing for the last millennium to predict the large-scale features of Northern Hemisphere temperature reconstructions, and the analysis of the residual also clearly favors the LRM model on millennium time scale. The decomposition of the forcing shows that volcanic aerosols give a considerably greater contribution to the cooling during the Little Ice Age than the reduction in solar irradiance associated with the Maunder Minimum in solar activity. The LRM model implies a transient climate response in agreement with IPCC projections, but the stronger response on longer time scales suggests replacing the notion of equilibrium climate sensitivity by a time scale-dependent sensitivity. [ABSTRACT FROM AUTHOR]

For dengue fever and other seasonal epidemics we show how the stability of the preceding inter-outbreak period can predict subsequent total outbreak magnitude, and that a feasible stability metric can be computed from incidence data alone. As an observable of a dynamical system, incidence data contains information about the underlying mechanisms: climatic drivers, changing serotype pools, the ecology of the vector populations, and evolving viral strains. We present mathematical arguments to suggest a connection between stability measured in incidence data during the inter-outbreak period and the size of the effective susceptible population. The method is illustrated with an analysis of dengue incidence in San Juan, Puerto Rico, where forecasts can be made as early as three to four months ahead of an outbreak. These results have immediate significance for public health planning, and can be used in combination with existing forecasting methods and more comprehensive dengue models. Directly measuring the size of the susceptible population is usually unfeasible before dengue outbreaks. Here, the authors show that the stability of low-incidence periods provides a proxy measure, which can be estimated from incidence data, and show its utility for forecasting outbreaks. [ABSTRACT FROM AUTHOR]

A correction to this article has been published and is linked from the HTML and PDF versions of this paper. The error has not been fixed in the paper. [ABSTRACT FROM AUTHOR]

Earth's global surface temperature shows variability on an extended range of temporal scales and satisfies an emergent scaling symmetry. Recent studies indicate that scale invariance is not only a feature of the observed temperature fluctuations, but an inherent property of the temperature response to radiative forcing, and a principle that links the fast and slow climate responses. It provides a bridge between the decadal- and centennial-scale fluctuations in the instrumental temperature record, and the millennial-scale equilibration following perturbations in the radiative balance. In particular, the emergent scale invariance makes it possible to infer equilibrium climate sensitivity (ECS) from the observed relation between radiative forcing and global temperature in the instrumental era. This is verified in ensembles of Earth system models (ESMs), where the inferred values of ECS correlate strongly to estimates from idealized model runs. For the range of forcing data explored in this paper, the method gives best estimates of ECS between 1.8 and 3.7 K, but statistical uncertainties in the best estimates themselves will provide a wider likely range of the ECS. [ABSTRACT FROM AUTHOR]

Kawasaki Disease (KD) is the most common cause of pediatric acquired heart disease, but its etiology remains unknown. We examined 1164 cases of KD treated at a regional children’s hospital in San Diego over a period of 15 years and uncovered novel structure to disease incidence. KD cases showed a well-defined seasonal variability, but also clustered temporally at much shorter time scales (days to weeks), and spatiotemporally on time scales of up to 10 days and spatial scales of 10-100 km. Temporal clusters of KD cases were associated with strongly significant regional-scale air temperature anomalies and consistent larger-scale atmospheric circulation patterns. Gene expression analysis further revealed a natural partitioning of KD patients into distinct groups based on their gene expression pattern, and that the different groups were associated with certain clinical characteristics that also exhibit temporal autocorrelation. Our data suggest that one or more environmental triggers exist, and that episodic exposures are modulated at least in part by regional weather conditions. We propose that characterization of the environmental factors that trigger KD in genetically susceptible children should focus on aerosols inhaled by patients who share common disease characteristics. [ABSTRACT FROM AUTHOR]