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Climate change is typically modeled using sophisticated mathematical models (climate models) of physical processes that range in temporal and spatial scales. Multi-model ensemble means of climate models show better correlation with the observations than any of the models separately. Currently, an open research question is how climate models can be combined to create an ensemble mean in an optimal way. We present a novel stochastic approach based on Markov chains to estimate model weights in order to obtain ensemble means. The method was compared to existing alternatives by measuring its performance on training and validation data, as well as model-as-truth experiments. The Markov chain method showed improved performance over those methods when measured by the root mean squared error in validation and comparable performance in model-as-truth experiments. The results of this comparative analysis should serve to motivate further studies in applications of Markov chain and other nonlinear methods that address the issues of finding optimal model weight for constructing ensemble means.

In this study, probabilistic future changes in sea surface temperature (SST) over East Asian marginal seas between historical (1971–2000) and late twenty-first century (2061–2100) periods are calculated by using both unweighted and weighted averaging methods. Unlike most previous studies, the present study considers uncertainty caused by internal variability and model error, which could reduce the credible intervals. Here, marginal seas are divided into three regions of Yellow Sea, South Sea, and East/Japan Sea, and the projections are computed separately for January–February–March (JFM), April–May–June, July–August–September (JAS), and October–November–December seasons. Our results show that the SSTs for the three regions are projected to increase by about 1–3 K and 2–6 K under the representative concentration pathway (RCP) 4.5 and the RCP8.5 scenarios, respectively, in terms of the 90% credible intervals. The future SST change over the Yellow and the East/Japan seas is larger than that over the South Sea, which is similar to recent observed trends. SSTs are expected to increase more in JAS than in JFM for all three regions. Before making the projections, the method is tested in a suite of one-at-a-time cross-validation experiments. The method well-calibrated results as measured by the 90% posterior credible intervals.

Climate change is expected to increase temperatures globally, and consequently more frequent, longer, and hotter heat waves are likely to occur. Ambiguity in defining heat waves appropriately makes it difficult to compare changes in heat wave events over time. This study provides a quantitative definition of a heat wave and makes probabilistic heat wave projections for the Korean Peninsula under two global warming scenarios. Changes to heat waves under global warming are investigated using the representative concentration pathway 4.5 (RCP4.5) and 8.5 (RCP8.5) experiments from 30 coupled models participating in phase five of the Coupled Model Inter-comparison Project. Probabilistic climate projections from multi-model ensembles have been constructed using both simple and weighted averaging. Results from both methods are similar and show that heat waves will be more intense, frequent, and longer lasting. These trends are more apparent under the RCP8.5 scenario as compared to the RCP4.5 scenario. Under the RCP8.5 scenario, typical heat waves are projected to become stronger than any heat wave experienced in the recent measurement record. Furthermore, under this scenario, it cannot be ruled out that Korea will experience heat wave conditions spanning almost an entire summer before the end of the 21st century.

Model simulations of El Niño-Southern Oscillation (ENSO) are usually evaluated by comparing them to observations using a multitude of metrics. However, this approach cannot provide an objective summary metric of model performance. Here, we propose that such an objective model evaluation should involve comparing the full joint probability density functions (pdf's) of ENSO. For simplicity, ENSO state is defined here as sea surface temperature anomalies over the Niño 3 region and equatorial Pacific thermocline depth anomalies. We argue that all ENSO metrics are a function of the joint pdf, the latter fully specifying the underlying stochastic process. Unfortunately, there is a lack of methods to recover the joint ENSO pdf from climate models or observations. Here, we develop a data-driven stochastic model for ENSO that allows for an analytic solution of the non-Markov non-Gaussian cyclostationary ENSO pdf. We show that the model can explain relevant ENSO features found in the observations and can serve as an ENSO simulator. We demonstrate that the model can reasonably approximate ENSO in most GCMs and is useful at exploring the internal ENSO variability. The general approach is not limited to ENSO and could be applied to other cyclostationary processes.

A major conundrum in climate science is how to account for dependence between climate models. This complicates interpretation of probabilistic projections derived from such models. Here we show that this problem can be addressed using a novel method to test multiple non-exclusive hypotheses, and to make predictions under such hypotheses. We apply the method to probabilistically estimate the level of global warming needed for a September ice-free Arctic, using an ensemble of historical and representative concentration pathway 8.5 emissions scenario climate model runs. We show that not accounting for model dependence can lead to biased projections. Incorporating more constraints on models may minimize the impact of neglecting model non-exclusivity. Most likely, September Arctic sea ice will effectively disappear at between approximately 2 and 2.5 K of global warming. Yet, limiting the warming to 1.5 K under the Paris agreement may not be sufficient to prevent the ice-free Arctic., Climate models depend on each other which makes meaningful comparisons difficult. Here, the authors apply a novel Bayesian method to test non-exclusive hypotheses to a set of climate models and show that the Arctic is likely to be ice-free at 2 to 2.5 °C of warming, with a sizeable risk even at lower rates.

This study presents future changes in extreme precipitation as projected within the New South Wales and Australian Capital Territory Regional Climate Modelling (NARCliM) project’s regional climate ensemble for south-east Australia. Model performance, independence and projected future changes were considered when designing the ensemble. We applied a quantile mapping bias correction to the climate model outputs based on theoretical distribution functions, and the implications of this for the projected precipitation extremes is investigated. Precipitation extremes are quantified using several indices from the Expert Team on Climate Change Detection and Indices set of indices. The bias correction was successful in removing most of the magnitude bias in extreme precipitation but does not correct biases in the length of maximum wet and dry spells. The bias correction also had a relatively small effect on the projected future changes. Across a range of metrics, robust increases in the magnitude of precipitation extreme indices are found. While these increases are often in-line with a continuation of the trends present over the last century, they are not found to be statistically significant within the ensemble as a whole. The length of the maximum consecutive wet spell is projected to remain at present-day levels, while the length of the maximum dry spell is projected to increase into the future. The combination of longer dry spells and increases in extreme precipitation magnitude indicate an important change in the character of the precipitation time series. This could have considerable hydrological implications since changes in the sequencing of events can be just as important as changes in event magnitude for hydrological impacts.

Recent studies using Regional Climate Models to make probabilistic projections break important new ground. However, they typically lack cross-validation, pull the projections towards agreeing models (which can agree due to shared biases), and ignore model skill at reproducing internal variability when weighing the models. Here we conduct the first, to our knowledge, application of Bayesian Model Averaging (BMA) to make probabilistic projections using Regional Climate Models (RCMs). We weigh the RCMs from the NARCliM project based on their skill at representing temperature over twelve south-east Australian regions in terms of trend, bias and internal variability. The weights do not depend on model agreement with other models. Using the weighted ensemble, we provide probabilistic seasonal temperature projections. We cross-validate the method, and demonstrate that weighted projections are well-calibrated and more precise than the unweighted ones. We find considerable differences between the weighted and the unweighted projections in some cases.

Air pollution has significant impacts on human health. Temperature inversions, especially near surface temperature inversions, can amplify air pollution by preventing convective movements and trapping pollutants close to the ground, thus decreasing air quality and increasing health issues. This effect of temperature inversions implies that trends in their frequency, strength and duration can have important implications for air quality. In this study, we evaluate the ability of three reanalysis-driven high-resolution regional climate model (RCM) simulations to represent near surface inversions at 9 sounding sites in southeast Australia. Then we use outputs of 12 historical and future RCM simulations (each with three time periods: 1990?2009, 2020?2039, and 2060?2079) from the NSW/ACT (New South Wales/Australian Capital Territory) Regional Climate Modelling (NARCliM) project to investigate changes in near surface temperature inversions. The results show that there is a substantial increase in the strength of near surface temperature inversions over southeast Australia which suggests that future inversions may intensify poor air quality events. Near surface inversions and their future changes have clear seasonal and diurnal variations. The largest differences between simulations are associated with the driving GCMs, suggesting that the large-scale circulation plays a dominant role in near surface inversion strengths. Fil: Ji, Fei. New South Wales. Office of Environment and Heritage; Australia Fil: Evans, Jason Peter. University of New South Wales; Australia Fil: Di Luca, Alejandro. University of New South Wales; Australia Fil: Jiang, Ningbo. New South Wales. Office of Environment and Heritage; Australia Fil: Olson, Roman. Yonsei University; Corea del Sur Fil: Fita Borrell, Lluís. Centre National de la Recherche Scientifique; Francia. Universite Pierre et Marie Curie; Francia. Laboratoire de Meteorologie Dynamique; Francia. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Centro de Investigaciones del Mar y la Atmósfera. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Centro de Investigaciones del Mar y la Atmósfera; Argentina Fil: Argüeso, Daniel. Universidad de Las Islas Baleares. Departamento de Fisica; España Fil: Chang, Lisa T. C.. New South Wales. Office of Environment and Heritage; Australia Fil: Scorgie, Yvonne. New South Wales. Office of Environment and Heritage; Australia Fil: Riley, Matt. New South Wales. Office of Environment and Heritage; Australia

The ability of regional climate models (RCMs) to accurately simulate current and future climate is increasingly important for impact assessment. This is the first evaluation of all reanalysis-driven RCMs within the CORDEX Australasia framework [four configurations of the Weather Forecasting and Research (WRF) model, and single configurations of COSMO-CLM (CCLM) and the Conformal-Cubic Atmospheric Model (CCAM)] to simulate the historical climate of Australia (1981–2010) at 50 km resolution. Simulations of near-surface maximum and minimum temperature and precipitation were compared with gridded observations at annual, seasonal, and daily time scales. The spatial extent, sign, and statistical significance of biases varied markedly between the RCMs. However, all RCMs showed widespread, statistically significant cold biases in maximum temperature which were the largest during winter. This bias exceeded − 5 K for some WRF configurations, and was the lowest for CCLM at ± 2 K. Most WRF configurations and CCAM simulated minimum temperatures more accurately than maximum temperatures, with biases in the range of ± 1.5 K. RCMs overestimated precipitation, especially over Australia’s populous eastern seaboard. Strong negative correlations between mean monthly biases in precipitation and maximum temperature suggest that the maximum temperature cold bias is linked to precipitation overestimation. This analysis shows that the CORDEX Australasia ensemble is a valuable dataset for future impact studies, but improving the representation of land surface processes, and subsequently of surface temperatures, will improve RCM performance. The varying RCM capabilities identified here serve as a foundation for the development of future regional climate projections and impact assessments for Australia.

We present a novel quasi-Bayesian method to weight multiple dynamical models by their skill at capturing both potentially non-linear trends and first-order autocorrelated variability of the underlying process, and to make weighted probabilistic projections. We validate the method using a suite of one-at-a-time cross-validation experiments involving Atlantic meridional overturning circulation (AMOC), its temperature-based index, as well as Korean summer mean maximum temperature. In these experiments the method tends to exhibit superior skill over a trend-only Bayesian model averaging weighting method in terms of weight assignment and probabilistic forecasts. Specifically, mean credible interval width, and mean absolute error of the projections tend to improve. We apply the method to a problem of projecting summer mean maximum temperature change over Korea by the end of the 21st century using a multi-model ensemble. Compared to the trend-only method, the new method appreciably sharpens the probability distribution function (pdf) and increases future most likely, median, and mean warming in Korea. The method is flexible, with a potential to improve forecasts in geosciences and other fields.

[1] Many studies have attempted to estimate the equilibrium climate sensitivity (CS) to the doubling of CO2concentrations. One common methodology is to compare versions of Earth models of intermediate complexity (EMICs) to spatially and/or temporally averaged historical observations. Despite the persistent efforts, CS remains uncertain. It is, thus far, unclear what is driving this uncertainty. Moreover, the effects of the internal climate variability on the CS estimates obtained using this method have not received thorough attention in the literature. Using a statistical approximator (“emulator”) of an EMIC, we show in an observation system simulation study that unresolved internal climate variability appears to be a key driver of CS uncertainty (as measured by the 68% credible interval). We first simulate many realizations of pseudo‒observations from an emulator at a “true” prescribed CS, and then reestimate the CS using the pseudo‒observations and an inverse parameter estimation method. We demonstrate that a single realization of the internal variability can result in a sizable discrepancy between the best CS estimate and the truth. Specifically, the average discrepancy is 0.84°C, with the feasible range up to several °C. The results open the possibility that recent climate sensitivity estimates from global observations and EMICs are systematically considerably lower or higher than the truth, since they are typically based on the same realization of climate variability. This possibility should be investigated in future work. We also find that estimation uncertainties increase at higher climate sensitivities, suggesting that a high CS might be difficult to detect.

We present a novel Bayesian statistical approach to computing model weights in climate change We present a novel Bayesian statistical approach to computing model weights in climate change projection ensembles. The weight of each climate model is obtained by weighting the current day observed data under the posterior distribution admitted under competing climate models. We use a linear model to describe the model output and observations. The approach accounts for uncertainty in model bias, trend and internal variability, as well as including error in the observations used. Our framework is general, requires very little problem specific input, and works well with default priors. We carry out cross-validation checks that confirm that the method produces the correct coverage.

Anthropogenic sea-level rise (SLR) causes considerable risks. Designing a sound SLR risk-management strategy requires careful consideration of decision-relevant uncertainties such as the reasonable upper bound of future SLR. The recent Intergovernmental Panel on Climate Change’s (IPCC) Fourth Assessment reported a likely upper SLR bound in the year 2100 near 0.6 m (meter). More recent studies considering semi-empirical modeling approaches and kinematic constraints on glacial melting suggest a reasonable 2100 SLR upper bound of approximately 2 m. These recent studies have broken important new ground, but they largely neglect uncertainties surrounding thermal expansion (thermosteric SLR) and/or observational constraints on ocean heat uptake. Here we quantify the effects of key parametric uncertainties and observational constraints on thermosteric SLR projections using an Earth system model with a dynamic three-dimensional ocean, which provides a mechanistic representation of deep ocean processes and heat uptake. Considering these effects nearly doubles the contribution of thermosteric SLR compared to previous estimates and increases the reasonable upper bound of 2100 SLR projections by 0.25 m. As an illustrative example of the effect of overconfidence, we show how neglecting thermosteric uncertainty in projections of the SLR upper bound can considerably bias risk analysis and hence the design of adaptation strategies. For conditions close to the Port of Los Angeles, the 0.25 m increase in the reasonable upper bound can result in a flooding-risk increase by roughly three orders of magnitude. Results provide evidence that relatively minor underestimation of the upper bound of projected SLR can lead to major downward biases of future flooding risks.

Concerns about the risks of unmitigated greenhouse gas emissions are growing. At the same time, confidence that international policy agreements will succeed in considerably lowering anthropogenic greenhouse gas emissions is declining. Perhaps as a result, various geoengineering solutions are gaining attention and credibility as a way to manage climate change. Serious consideration is currently being given to proposals to cool the planet through solar-radiation management. Here we analyze how the unique and nontrivial risks of geoengineering strategies pose fundamental questions at the interface between science and ethics. To illustrate the importance of integrated ethical and scientific analysis, we define key open questions and outline a coupled scientific-ethical research agenda to analyze solar-radiation management geoengineering proposals. We identify nine key fields of coupled research including whether solar-radiation management can be tested, how quickly learning could occur, normative decisions em...

Characterizing the risks of anthropogenic climate change poses considerable statistical challenges. A key problem is how to combine the information contained in large-scale observational data sets with simulations of Earth system models in a statistically sound and computationally tractable manner. Here, we describe a statistical approach for improving projections of the North Atlantic meridional overturning circulation (AMOC). The AMOC is part of the global ocean conveyor belt circulation and transfers heat between low and high latitudes in the Atlantic basin. The AMOC might collapse in a “tipping point” response to anthropogenic climate forcings. Assessing the risk of an AMOC collapse is of considerable interest because it may result in major impacts on natural and human systems. AMOC projections rely on simulations from complex climate models. One key source of uncertainty in AMOC projections is uncertainty about background ocean vertical diffusivity (Kv), an important model parameter. Kv cannot be directly observed but can be inferred by combining climate model output with observations on the oceans (so-called tracers). Here, we combine information from multiple tracers, each observed on a spatial grid. Our two-stage approach emulates the computationally expensive climate model using a flexible hierarchical model to connect the tracers. We then infer Kv using our emulator and the observations via a Bayesian approach, accounting for observation error and model discrepancy. We utilize kernel mixing and matrix identities in our Gaussian process model to considerably reduce the computational burdens imposed by the large data sets. We find that our approach is flexible, reduces identifiability issues, and enables inference about Kv based on large data sets. We use the resulting inference about Kv to improve probabilistic projections of the AMOC. Copyright © 2012 John Wiley & Sons, Ltd.

How will the climate system respond to anthropogenic forcings? One approach to this question relies on climate model projections. Current climate projections are considerably uncertain. Characterizing and, if possible, reducing this uncertainty is an area of ongoing research. We consider the problem of making projections of the North Atlantic meridional overturning circulation (AMOC). Uncertainties about climate model parameters play a key role in uncertainties in AMOC projections. When the observational data and the climate model output are high-dimensional spatial data sets, the data are typically aggregated due to computational constraints. The effects of aggregation are unclear because statistically rigorous approaches for model parameter inference have been infeasible for high-resolution data. Here we develop a flexible and computationally efficient approach using principal components and basis expansions to study the effect of spatial data aggregation on parametric and projection uncertainties. Our Bayesian reduced-dimensional calibration approach allows us to study the effect of complicated error structures and data-model discrepancies on our ability to learn about climate model parameters from high-dimensional data. Considering high-dimensional spatial observations reduces the effect of deep uncertainty associated with prior specifications for the data-model discrepancy. Also, using the unaggregated data results in sharper projections based on our climate model. Our computationally efficient approach may be widely applicable to a variety of high-dimensional computer model calibration problems., Comment: Published in at http://dx.doi.org/10.1214/14-AOAS733 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

[1] Current climate model projections are uncertain. This uncertainty is partly driven by the uncertainty in key model parameters such as climate sensitivity (CS), vertical ocean diffusivity (Kv), and strength of anthropogenic sulfate aerosol forcing. These parameters are commonly estimated using ensembles of model runs constrained by observations. Here we obtain a probability density function (pdf) of these parameters using the University of Victoria Earth System Climate Model (UVic ESCM) - an intermediate complexity model with a dynamic three-dimensional ocean. Specifically, we run an ensemble of UVic ESCM runs varying parameters that affect CS, ocean vertical diffusion, and the effects of anthropogenic sulfate aerosols. We use a statistical emulator that interpolates the UVic ESCM output to parameter settings where the model was not evaluated. We adopt a Bayesian approach to constrain the model output with instrumental surface temperature and ocean heat observations. Our approach accounts for the uncertainties in the properties of model-data residuals. We use a Markov chain Monte Carlo method to obtain a posterior pdf of these parameters. The mode of the climate sensitivity estimate is 2.8°C, with the corresponding 95% credible interval ranging from 1.8 to 4.9°C. These results are generally consistent with previous studies. The CS pdf is sensitive to the assumptions about the priors, to the effects of anthropogenic sulfate aerosols, and to the background vertical ocean diffusivity. Our method can be used with more complex climate models.