Assessing the impact of future anthropogenic carbon emissions is currently impeded by uncertainties in our knowledge of equilibrium climate sensitivity to atmospheric carbon dioxide doubling. ...Previous studies suggest 3 kelvin (K) as the best estimate, 2 to 4.5 K as the 66% probability range, and nonzero probabilities for much higher values, the latter implying a small chance of high-impact climate changes that would be difficult to avoid. Here, combining extensive sea and land surface temperature reconstructions from the Last Glacial Maximum with climate model simulations, we estimate a lower median (2.3 K) and reduced uncertainty (1.7 to 2.6 K as the 66% probability range, which can be widened using alternate assumptions or data subsets). Assuming that paleoclimatic constraints apply to the future, as predicted by our model, these results imply a lower probability of imminent extreme climatic change than previously thought.
Abstract Pharmacodynamic (PD) models are mathematical models of cellular reaction networks that include drug mechanisms of action. These models are useful for studying predictive therapeutic outcomes ...of novel drug therapies in silico. However, PD models are known to possess significant uncertainty with respect to constituent parameter data, leading to uncertainty in the model predictions. Furthermore, experimental data to calibrate these models is often limited or unavailable for novel pathways. In this study, we present a Bayesian optimal experimental design approach for improving PD model prediction accuracy. We then apply our method using simulated experimental data to account for uncertainty in hypothetical laboratory measurements. This leads to a probabilistic prediction of drug performance and a quantitative measure of which prospective laboratory experiment will optimally reduce prediction uncertainty in the PD model. The methods proposed here provide a way forward for uncertainty quantification and guided experimental design for models of novel biological pathways.
Stochastic reduced models are an important tool in climate systems whose many spatial and temporal scales cannot be fully discretized or underlying physics may not be fully accounted for. One form of ...reduced model, the linear inverse model (LIM), has been widely used for regional climate predictability studies—typically focusing more on tropical or midlatitude studies. However, most LIM fitting techniques rely on point estimation techniques deriving from fluctuation–dissipation theory. In this methodological study we explore the use of Bayesian inference techniques for LIM parameter estimation of sea surface temperature (SST), to quantify the skillful decadal predictability of Bayesian LIM models at high latitudes. We show that Bayesian methods, when compared to traditional point estimation methods for LIM-type models, provide better calibrated probabilistic skill, while simultaneously providing better point estimates due to the regularization effect of the prior distribution in high-dimensional problems. We compare the effect of several priors, as well as maximum likelihood estimates, on 1) estimating parameter values on a perfect model experiment and 2) producing calibrated 1-yr SST anomaly forecast distributions using a preindustrial control run of the Community Earth System Model (CESM). Finally, we employ a host of probabilistic skill metrics to determine the extent to which an LIM can forecast SST anomalies at high latitudes. We find that the choice of prior distribution has an appreciable impact on estimation outcomes, and priors that emphasize physically relevant properties enhance the model’s ability to capture variability of SST anomalies.
The Gaussian process regression model is a popular type of "emulator" used as a fast surrogate for computationally expensive simulators (deterministic computer models). For simulators with ...multivariate output, common practice is to specify a separable covariance structure for the Gaussian process. Though computationally convenient, this can be too restrictive, leading to poor performance of the emulator, particularly when the different simulator outputs represent different physical quantities. Also, treating the simulator outputs as independent can lead to inappropriate representations of joint uncertainty. We develop nonseparable covariance structures for Gaussian process emulators, based on the linear model of coregionalization and convolution methods. Using two case studies, we compare the performance of these covariance structures both with standard separable covariance structures and with emulators that assume independence between the outputs. In each case study, we find that only emulators with nonseparable covariances structures have sufficient flexibility both to give good predictions and to represent joint uncertainty about the simulator outputs appropriately. This article has supplementary material online.
Since near‐term predictions of present‐day climate are controlled by both initial condition predictability and boundary condition predictability, initialized prediction experiments aim to augment the ...external‐forcing‐related predictability realized in uninitialized projections with initial‐condition‐related predictability by appropriate observation‐based initialization. However, and notwithstanding the considerable effort expended in finding such “good” initial states, a striking feature of current, state‐of‐the‐art, initialized decadal hindcasts is their tendency to quickly drift away from the initialized state, with attendant loss of skill. We derive a dynamical model for such drift, and after validating it we show that including a recalibrated version of the model in a postprocessing framework is able to significantly augment the skill of initialized predictions beyond that achieved by a use of current techniques of postprocessing alone. We also show that the new methodology provides further crucial insights into issues related to initialized predictions.
Key Points
A model for the behavior of initialized decadal predictions is presented and then used to develop a technique for postprocessing predictions
The technique is shown to improve hindcast skill in scenarios with widely different bias and interannual variability characteristics
The technique throws light on issues such as expected versus realized time scale for loss of memory of IC and regional quirks in initialization
ABSTRACT
Projections of ice-sheet mass balance require regional ocean warming projections derived from atmosphere-ocean general circulation models (AOGCMs). However, the coarse resolution of AOGCMs: ...(1) may lead to systematic or AOGCM-specific biases and (2) makes it difficult to identify relevant water masses. Here, we employ a large-scale metric of Antarctic Shelf Bottom Water (ASBW) to investigate circum-Antarctic temperature biases and warming projections in 19 different Coupled Model Intercomparison Project Phase 5 (CMIP5) AOGCMs forced with two different ‘representative concentration pathways’ (RCPs). For high-emissions RCP 8.5, the ensemble mean 21st century ASBW warming is 0.66, 0.74 and 0.58°C for the Amundsen, Ross and Weddell Seas (AS, RS and WS), respectively. RCP 2.6 ensemble mean projections are substantially lower: 0.21, 0.26, and 0.19°C. All distributions of regional ASBW warming are positively skewed; for RCP 8.5, four AOGCMs project warming of greater than 1.8°C in the RS. Across the ensemble, there is a strong, RCP-independent, correlation between WS and RS warming. AS warming is more closely linked to warming in the Southern Ocean. We discuss possible physical mechanisms underlying the spatial patterns of warming and highlight implications of these results on strategies for forcing ice-sheet mass balance projections.
•Uncertainty of carbon fluxes at regional and global scales has rarely been quantified.•We use a model-data fusion approach to assess uncertainty in parameters and fluxes.•Parameter values vary ...substantially both within and across plant functional types.•Our approach can provide uncertainty bounds to regional carbon flux estimates.•Parameter uncertainty can lead to a large uncertainty in regional carbon fluxes.
Models have been widely used to estimate carbon fluxes at regional scales, and the uncertainty of modeled fluxes, however, has rarely been quantified and remains a challenge. A quantitative uncertainty assessment of regional flux estimates is essential for better understanding of terrestrial carbon dynamics and informing carbon and climate decision-making. We use a simple ecosystem model, eddy covariance (EC) flux observations, and a model-data fusion approach to assess the uncertainty of regional carbon flux estimates for the Upper Midwest region of northern Wisconsin and Michigan, USA. We combine net ecosystem exchange (NEE) observations and an adaptive Markov chain Monte Carlo (MCMC) approach to quantify the parameter uncertainty of the Diagnostic Carbon Flux Model (DCFM). Our MCMC approach eliminates the need for an initial equilibration or “burn-in” phase of the random walk, and also improves the performance of the algorithm for parameter optimization. For each plant functional type (PFT), we use NEE observations from multiple EC sites to estimate parameters, and the resulting parameter estimates are more representative of the PFT than estimates based on observations from a single site. A probability density function (PDF) is generated for each parameter, and the spread of the PDF provides an estimate of parameter uncertainty. We then apply the model with parameter PDFs to estimate NEE for each grid cell across our study region, and propagate the parameter uncertainty through simulations to produce probabilistic flux estimates. Over the period from 2001 to 2007, the mean annual NEE of the region was estimated to be −30.0TgCyr−1, and the associated uncertainty as measured by standard deviation was±7.6TgCyr−1. Uncertainty in parameters can lead to a large uncertainty to estimates of regional carbon fluxes, and our model-data approach can provide uncertainty bounds to regional carbon fluxes. Future research is needed to apply our approach to more complex ecosystem models, assess the usefulness, validity, and alternatives of the PFT and vegetation type concepts, and to fully quantify the uncertainty of regional carbon fluxes by incorporating other sources of uncertainty.
Despite decades of research, large multi-model uncertainty remains about the Earth’s equilibrium climate sensitivity to carbon dioxide forcing as inferred from state-of-the-art Earth system models ...(ESMs). Statistical treatments of multi-model uncertainties are often limited to simple ESM averaging approaches. Sometimes models are weighted by how well they reproduce historical climate observations. Here, we propose a novel approach to multi-model combination and uncertainty quantification. Rather than averaging a discrete set of models, our approach samples from a continuous distribution over a reduced space of simple model parameters. We fit the free parameters of a reduced-order climate model to the output of each member of the multi-model ensemble. The reduced-order parameter estimates are then combined using a hierarchical Bayesian statistical model. The result is a multi-model distribution of reduced-model parameters, including climate sensitivity. In effect, the multi-model uncertainty problem within an ensemble of ESMs is converted to a parametric uncertainty problem within a reduced model. The multi-model distribution can then be updated with observational data, combining two independent lines of evidence. We apply this approach to 24 model simulations of global surface temperature and net top-of-atmosphere radiation response to abrupt quadrupling of carbon dioxide, and four historical temperature data sets. Our reduced order model is a 2-layer energy balance model. We present probability distributions of climate sensitivity based on (1) the multi-model ensemble alone and (2) the multi-model ensemble and observations.
Anomaly-diffusing energy balance models (AD-EBMs) are routinely employed to analyze and emulate the warming response of both observed and simulated Earth systems. We demonstrate a deficiency in ...common multi-layer as well as continuous-diffusion AD-EBM variants: They are unable to, simultaneously, properly represent surface warming and the vertical distribution of heat uptake. We show that this inability is due to the diffusion approximation. On the other hand, it is well understood that transport of water from the surface mixed layer into the ocean interior is achieved, in large part, by the process of ventilation—a process associated with outcropping isopycnals. We, therefore, start from a configuration of outcropping isopycnals and demonstrate how an AD-EBM can be modified to include the effect of ventilation on ocean uptake of anomalous radiative forcing. The resulting EBM is able to successfully represent both surface warming and the vertical distribution of heat uptake, and indeed, a simple four-layer model suffices. The simplicity of the models notwithstanding, the analysis presented and the necessity of the modification highlight the role played by processes related to the down-welling branch of global ocean circulation in shaping the vertical distribution of ocean heat uptake.
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.
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