scholarly journals A Bayesian framework for emergent constraints: case studies of climate sensitivity with PMIP

2020 ◽  
Author(s):  
Martin Renoult ◽  
James Annan ◽  
Julia Hargreaves ◽  
Navjit Sagoo ◽  
Clare Flynn ◽  
...  
Keyword(s):  
Climate Sensitivity ◽  
Bayesian Method ◽  
Ordinary Least Squares ◽  
Bayesian Framework ◽  
Future Climate Change ◽  
Filter Method ◽  
Data Sets ◽  
Uncertainty Estimates ◽  
Emergent Constraints ◽  
Model Ensembles

<p>In this study we introduce a Bayesian framework, which is flexible and explicit about the prior assumptions, for using model ensembles and observations together to constrain future climate change. The emergent constraint approach has seen broad application in recent years, including studies constraining the equilibrium climate sensitivity (ECS) using the Last Glacial Maximum (LGM) and the mid-Pliocene Warm Period (mPWP). Most of these studies were based on Ordinary Least Squares (OLS) fits between a variable of the climate state, such as tropical temperature, and climate sensitivity. Using our Bayesian method, and considering the LGM and mPWP separately, we obtain values of ECS of 2.7 K (1.1 - 4.8, 5 - 95 percentiles) using the PMIP2, PMIP3 and PMIP4 data sets for the LGM, and 2.4 K (0.4 - 5.0) with the PlioMIP1 and PlioMIP2 data sets for the mPWP. Restricting the ensembles to include only the most recent version of each model, we obtain 2.7 K (1.1 - 4.3) using the LGM and  2.4 K (0.4 - 5.1) using the mPWP. An advantage of the Bayesian framework is that it is possible to combine the two periods assuming they are independent, whereby we obtain a slightly tighter constraint of 2.6 K (1.1 - 3.9). We have explored the sensitivity to our assumptions in the method, including considering structural uncertainty, and in the choice of models, and this leads to 95% probability of climate sensitivity mostly below 5 and never exceeding 6 K. The approach is compared with other approaches based on OLS, a Kalman filter method and an alternative Bayesian method. An interesting implication of this work is that OLS-based emergent constraints on ECS generate tighter uncertainty estimates, in particular at the lower end, suggesting a higher bound by construction in case of weaker correlation. Although some fundamental challenges related to the use of emergent constraints remain, this paper provides a step towards a better foundation of their potential use in future probabilistic estimation of climate sensitivity.</p>

scholarly journals A Bayesian framework for emergent constraints: case studies of climate sensitivity with PMIP

2020 ◽  
Author(s):  
Martin Renoult ◽  
James Douglas Annan ◽  
Julia Catherine Hargreaves ◽  
Navjit Sagoo ◽  
Clare Flynn ◽  
...  
Keyword(s):  
Climate Sensitivity ◽  
Bayesian Method ◽  
Ordinary Least Squares ◽  
Bayesian Framework ◽  
Future Climate Change ◽  
Filter Method ◽  
Data Sets ◽  
Uncertainty Estimates ◽  
Emergent Constraints ◽  
Model Ensembles

Abstract. In this paper we introduce a Bayesian framework, which is flexible and explicit about the prior assumptions, for using model ensembles and observations together to constrain future climate change. The emergent constraint approach has seen broad application in recent years, including studies constraining the equilibrium climate sensitivity (ECS) using the Last Glacial Maximum (LGM) and the mid-Pliocene Warm Period (mPWP). Most of these studies were based on Ordinary Least Squares (OLS) fits between a variable of the climate state, such as tropical temperature, and climate sensitivity. Using our Bayesian method, and considering the LGM and mPWP separately, we obtain values of ECS of 2.7 K (1.1–4.8, 5–95 percentiles) using the PMIP2, PMIP3 and PMIP4 data sets for the LGM, and 2.4 K (0.4–5.0) with the PlioMIP1 and PlioMIP2 data sets for the mPWP. Restricting the ensembles to include only the most recent version of each model, we obtain 2.7 K (1.1–4.3) using the LGM and 2.4 K (0.4–5.1) using the mPWP. An advantage of the Bayesian framework is that it is possible to combine the two periods assuming they are independent, whereby we obtain a slightly tighter constraint of 2.6 K (1.1–3.9). We have explored the sensitivity to our assumptions in the method, including considering structural uncertainty, and in the choice of models, and this leads to 95 % probability of climate sensitivity mostly below 5 and never exceeding 6 K. The approach is compared with other approaches based on OLS, a Kalman filter method and an alternative Bayesian method. An interesting implication of this work is that OLS-based emergent constraints on ECS generate tighter uncertainty estimates, in particular at the lower end, suggesting a higher bound by construction in case of weaker correlation. Although some fundamental challenges related to the use of emergent constraints remain, this paper provides a step towards a better foundation of their potential use in future probabilistic estimation of climate sensitivity.

scholarly journals A Bayesian framework for emergent constraints: case studies of climate sensitivity with PMIP

2020 ◽  
Vol 16 (5) ◽  
pp. 1715-1735 ◽  
Author(s):  
Martin Renoult ◽  
James Douglas Annan ◽  
Julia Catherine Hargreaves ◽  
Navjit Sagoo ◽  
Clare Flynn ◽  
...  
Keyword(s):  
Climate Sensitivity ◽  
Bayesian Method ◽  
Regression Line ◽  
Ordinary Least Squares ◽  
Bayesian Framework ◽  
Future Climate Change ◽  
Filter Method ◽  
Structural Uncertainty ◽  
Uncertainty Estimates ◽  
Emergent Constraints

Abstract. In this paper we introduce a Bayesian framework, which is explicit about prior assumptions, for using model ensembles and observations together to constrain future climate change. The emergent constraint approach has seen broad application in recent years, including studies constraining the equilibrium climate sensitivity (ECS) using the Last Glacial Maximum (LGM) and the mid-Pliocene Warm Period (mPWP). Most of these studies were based on ordinary least squares (OLS) fits between a variable of the climate state, such as tropical temperature, and climate sensitivity. Using our Bayesian method, and considering the LGM and mPWP separately, we obtain values of ECS of 2.7 K (0.6–5.2, 5th–95th percentiles) using the PMIP2, PMIP3, and PMIP4 datasets for the LGM and 2.3 K (0.5–4.4) with the PlioMIP1 and PlioMIP2 datasets for the mPWP. Restricting the ensembles to include only the most recent version of each model, we obtain 2.7 K (0.7–5.2) using the LGM and 2.3 K (0.4–4.5) using the mPWP. An advantage of the Bayesian framework is that it is possible to combine the two periods assuming they are independent, whereby we obtain a tighter constraint of 2.5 K (0.8–4.0) using the restricted ensemble. We have explored the sensitivity to our assumptions in the method, including considering structural uncertainty, and in the choice of models, and this leads to 95 % probability of climate sensitivity mostly below 5 K and only exceeding 6 K in a single and most uncertain case assuming a large structural uncertainty. The approach is compared with other approaches based on OLS, a Kalman filter method, and an alternative Bayesian method. An interesting implication of this work is that OLS-based emergent constraints on ECS generate tighter uncertainty estimates, in particular at the lower end, an artefact due to a flatter regression line in the case of lack of correlation. Although some fundamental challenges related to the use of emergent constraints remain, this paper provides a step towards a better foundation for their potential use in future probabilistic estimations of climate sensitivity.

scholarly journals On the Emergent Constraints of Climate Sensitivity

2018 ◽  
Vol 31 (2) ◽  
pp. 863-875 ◽  
Author(s):  
Xin Qu ◽  
Alex Hall ◽  
Anthony M. DeAngelis ◽  
Mark D. Zelinka ◽  
Stephen A. Klein ◽  
...  
Keyword(s):  
Climate Sensitivity ◽  
Climate Models ◽  
Selection Process ◽  
Temperature Response ◽  
Cloud Feedback ◽  
Emergent Constraints ◽  
Low Cloud ◽  
Model Ensembles ◽  
Statistical Connection ◽  
Emergent Constraint

Differences among climate models in equilibrium climate sensitivity (ECS; the equilibrium surface temperature response to a doubling of atmospheric CO2) remain a significant barrier to the accurate assessment of societally important impacts of climate change. Relationships between ECS and observable metrics of the current climate in model ensembles, so-called emergent constraints, have been used to constrain ECS. Here a statistical method (including a backward selection process) is employed to achieve a better statistical understanding of the connections between four recently proposed emergent constraint metrics and individual feedbacks influencing ECS. The relationship between each metric and ECS is largely attributable to a statistical connection with shortwave low cloud feedback, the leading cause of intermodel ECS spread. This result bolsters confidence in some of the metrics, which had assumed such a connection in the first place. Additional analysis is conducted with a few thousand artificial metrics that are randomly generated but are well correlated with ECS. The relationships between the contrived metrics and ECS can also be linked statistically to shortwave cloud feedback. Thus, any proposed or forthcoming ECS constraint based on the current generation of climate models should be viewed as a potential constraint on shortwave cloud feedback, and physical links with that feedback should be investigated to verify that the constraint is real. In addition, any proposed ECS constraint should not be taken at face value since other factors influencing ECS besides shortwave cloud feedback could be systematically biased in the models.

scholarly journals Methods for estimating uncertainty in factor analytic solutions

2014 ◽  
Vol 7 (3) ◽  
pp. 781-797 ◽  
Author(s):  
P. Paatero ◽  
S. Eberly ◽  
S. G. Brown ◽  
G. A. Norris
Keyword(s):  
Environmental Protection Agency ◽  
Synthetic Data ◽  
Analytic Solutions ◽  
Data Sets ◽  
Random Errors ◽  
Data Set ◽  
Factor Analytic ◽  
Uncertainty Estimates ◽  
Multilinear Engine ◽  
Analytic Models

Abstract. The EPA PMF (Environmental Protection Agency positive matrix factorization) version 5.0 and the underlying multilinear engine-executable ME-2 contain three methods for estimating uncertainty in factor analytic models: classical bootstrap (BS), displacement of factor elements (DISP), and bootstrap enhanced by displacement of factor elements (BS-DISP). The goal of these methods is to capture the uncertainty of PMF analyses due to random errors and rotational ambiguity. It is shown that the three methods complement each other: depending on characteristics of the data set, one method may provide better results than the other two. Results are presented using synthetic data sets, including interpretation of diagnostics, and recommendations are given for parameters to report when documenting uncertainty estimates from EPA PMF or ME-2 applications.

scholarly journals Bayesian estimation of Earth's climate sensitivity and transient climate response from observational warming and heat content datasets

2021 ◽  
Vol 12 (2) ◽  
pp. 709-723
Author(s):  
Philip Goodwin ◽  
B. B. Cael
Keyword(s):  
Climate Sensitivity ◽  
Future Climate ◽  
Climate Feedback ◽  
Future Climate Change ◽  
Climate Projections ◽  
Climate Response ◽  
Ocean Heat Uptake ◽  
Transient Climate Response ◽  
Posterior Probability Distribution ◽  
The Impact

Abstract. Future climate change projections, impacts, and mitigation targets are directly affected by how sensitive Earth's global mean surface temperature is to anthropogenic forcing, expressed via the climate sensitivity (S) and transient climate response (TCR). However, the S and TCR are poorly constrained, in part because historic observations and future climate projections consider the climate system under different response timescales with potentially different climate feedback strengths. Here, we evaluate S and TCR by using historic observations of surface warming, available since the mid-19th century, and ocean heat uptake, available since the mid-20th century, to constrain a model with independent climate feedback components acting over multiple response timescales. Adopting a Bayesian approach, our prior uses a constrained distribution for the instantaneous Planck feedback combined with wide-ranging uniform distributions of the strengths of the fast feedbacks (acting over several days) and multi-decadal feedbacks. We extract posterior distributions by applying likelihood functions derived from different combinations of observational datasets. The resulting TCR distributions when using two preferred combinations of historic datasets both find a TCR of 1.5 (1.3 to 1.8 at 5–95 % range) ∘C. We find the posterior probability distribution for S for our preferred dataset combination evolves from S of 2.0 (1.6 to 2.5) ∘C on a 20-year response timescale to S of 2.3 (1.4 to 6.4) ∘C on a 140-year response timescale, due to the impact of multi-decadal feedbacks. Our results demonstrate how multi-decadal feedbacks allow a significantly higher upper bound on S than historic observations are otherwise consistent with.

scholarly journals Emergent constraints on equilibrium climate sensitivity in CMIP5: do they hold for CMIP6?

2020 ◽  
Vol 11 (4) ◽  
pp. 1233-1258
Author(s):  
Manuel Schlund ◽  
Axel Lauer ◽  
Pierre Gentine ◽  
Steven C. Sherwood ◽  
Veronika Eyring
Keyword(s):  
Climate Sensitivity ◽  
Statistical Significance ◽  
Coupled Model ◽  
Surface Air Temperature ◽  
Co2 Concentration ◽  
Intergovernmental Panel ◽  
Equilibrium Climate Sensitivity ◽  
Emergent Constraints ◽  
Statistical Relationships ◽  
Emergent Constraint

Abstract. An important metric for temperature projections is the equilibrium climate sensitivity (ECS), which is defined as the global mean surface air temperature change caused by a doubling of the atmospheric CO2 concentration. The range for ECS assessed by the Intergovernmental Panel on Climate Change (IPCC) Fifth Assessment Report is between 1.5 and 4.5 K and has not decreased over the last decades. Among other methods, emergent constraints are potentially promising approaches to reduce the range of ECS by combining observations and output from Earth System Models (ESMs). In this study, we systematically analyze 11 published emergent constraints on ECS that have mostly been derived from models participating in the Coupled Model Intercomparison Project Phase 5 (CMIP5) project. These emergent constraints are – except for one that is based on temperature variability – all directly or indirectly based on cloud processes, which are the major source of spread in ECS among current models. The focus of the study is on testing if these emergent constraints hold for ESMs participating in the new Phase 6 (CMIP6). Since none of the emergent constraints considered here have been derived using the CMIP6 ensemble, CMIP6 can be used for cross-checking of the emergent constraints on a new model ensemble. The application of the emergent constraints to CMIP6 data shows a decrease in skill and statistical significance of the emergent relationship for nearly all constraints, with this decrease being large in many cases. Consequently, the size of the constrained ECS ranges (66 % confidence intervals) widens by 51 % on average in CMIP6 compared to CMIP5. This is likely because of changes in the representation of cloud processes from CMIP5 to CMIP6, but may in some cases also be due to spurious statistical relationships or a too small number of models in the ensemble that the emergent constraint was originally derived from. The emergently- constrained best estimates of ECS also increased from CMIP5 to CMIP6 by 12 % on average. This can be at least partly explained by the increased number of high-ECS (above 4.5 K) models in CMIP6 without a corresponding change in the constraint predictors, suggesting the emergence of new feedback processes rather than changes in strength of those previously dominant. Our results support previous studies concluding that emergent constraints should be based on an independently verifiable physical mechanism, and that process-based emergent constraints on ECS should rather be thought of as constraints for the process or feedback they are actually targeting.

The GravIS Portal: User-friendly Global Mass Variations from GRACE and GRACE-FO

2021 ◽  
Author(s):  
Christoph Dahle ◽  
Eva Boergens ◽  
Henryk Dobslaw ◽  
Andreas Groh ◽  
Ingo Sasgen ◽  
...  
Keyword(s):  
Time Series ◽  
Information Service ◽  
Research Centre ◽  
Data Sets ◽  
Ocean Bottom ◽  
Climatic Regions ◽  
Uncertainty Estimates ◽  
Terrestrial Water ◽  
User Friendly ◽  
Global Mean

<p>The German Research Centre for Geosciences (GFZ) maintains the “Gravity Information Service” (GravIS, gravis.gfz-potsdam.de) portal in collaboration with the Alfred-Wegener-Institute (AWI) and Technische Universität Dresden. Main objective of this portal is the dissemination of data describing mass variations in the Earth system based on observations of the satellite gravimetry missions GRACE and GRACE-FO.</p><p>The provided data sets encompass products of terrestrial water storage (TWS) variations over the continents, ocean bottom pressure (OBP) variations from which global mean barystatic sea-level rise can be estimated, and mass changes of the ice sheets in Greenland and Antarctica. All data sets are provided as time series of regular grids for each area, as well as in the form of regional basin averages. Regarding the latter, for the continental TWS data the user can choose between classical river basins and a novel segmentation based on climatic regions. For the oceans, the segmentation into different regions is derived similarly but based on modelled OBP data. All time series are accompanied by realistic uncertainty estimates.</p><p>All data sets can be interactively displayed at the portal and are freely available for download. This contribution aims to show the features and possibilities of the GravIS portal to researchers without a dedicated geodetic background, working in the fields of hydrology, oceanography, and cryosphere.</p>

Modelling Migration with Poisson Regression

2010 ◽  
pp. 261-279 ◽  
Author(s):  
Robin Flowerdew
Keyword(s):  
Poisson Regression ◽  
Goodness Of Fit ◽  
Negative Binomial ◽  
Census Data ◽  
Ordinary Least Squares ◽  
Negative Integer ◽  
Data Sets ◽  
Explanatory Variables ◽  
Recent Developments ◽  
Generalised Linear Modelling

Most statistical analysis is based on the assumption that error is normally distributed, but many data sets are based on discrete data (the number of migrants from one place to another must be a whole number). Recent developments in statistics have often involved generalising methods so that they can be properly applied to non-normal data. For example, Nelder and Wedderburn (1972) developed the theory of generalised linear modelling, where the dependent or response variable can take a variety of different probability distributions linked in one of several possible ways to a linear predictor, based on a combination of independent or explanatory variables. Several common statistical techniques are special cases of the generalised linear models, including the usual form of regression analysis, Ordinary Least Squares regression, and binomial logit modelling. Another important special case is Poisson regression, which has a Poisson-distributed dependent variable, linked logarithmically to a linear combination of independent variables. Poisson regression may be an appropriate method when the dependent variable is constrained to be a non-negative integer, usually a count of the number of events in certain categories. It assumes that each event is independent of the others, though the probability of an event may be linked to available explanatory variables. This chapter illustrates how Poisson regression can be carried out using the Stata package, proceeding to discuss various problems and issues which may arise in the use of the method. The number of migrants from area i to area j must be a non-negative integer and is likely to vary according to zone population, distance and economic variables. The availability of high-quality migration data through the WICID facility permits detailed analysis at levels from the region to the output areas. A vast range of possible explanatory variables can also be derived from the 2001 Census data. Model results are discussed in terms of the significant explanatory variables, the overall goodness of fit and the big residuals. Comparisons are drawn with other analytic techniques such as OLS regression. The relationship to Wilson’s entropy maximising methods is described, and variants on the method are explained. These include negative binomial regression and zero-censored and zero-truncated models.

scholarly journals Mass Appraisal Modeling of Real Estate in Urban Centers by Geographically and Temporally Weighted Regression: A Case Study of Beijing’s Core Area

Land ◽  
2020 ◽  
Vol 9 (5) ◽  
pp. 143 ◽  
Author(s):  
Daikun Wang ◽  
Victor Jing Li ◽  
Huayi Yu
Keyword(s):  
Real Estate ◽  
Large Data ◽  
Ordinary Least Squares ◽  
Core Area ◽  
Weighted Regression ◽  
Data Sets ◽  
Residential Areas ◽  
Urban Centers ◽  
Policy Makers ◽  
Evaluation Approach

The traditional linear regression model of mass appraisal is increasingly unable to satisfy the standard of mass appraisal with large data volumes, complex housing characteristics and high accuracy requirements. Therefore, it is essential to utilize the inherent spatial-temporal characteristics of properties to build a more effective and accurate model. In this research, we take Beijing’s core area, a typical urban center, as the study area of modeling for the first time. Thousands of real transaction data sets with a time span of 2014, 2016 and 2018 are conducted at the community level (community annual average price). Three different models, including multiple regression analysis (MRA) with ordinary least squares (OLS), geographically weighted regression (GWR) and geographically and temporally weighted regression (GTWR), are adopted for comparative analysis. The result indicates that the GTWR model, with an adjusted R2 of 0.8192, performs better in the mass appraisal modeling of real estate. The comparison of different models provides a useful benchmark for policy makers regarding the mass appraisal process of urban centers. The finding also highlights the spatial characteristics of price-related parameters in high-density residential areas, providing an efficient evaluation approach for planning, land management, taxation, insurance, finance and other related fields.

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