Editing IPCC:AR6/WGI/Chapter-3 (section)

== 3.2 Methods ==

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New methods for model evaluation that are used in this chapter are described in [[IPCC:Wg1:Chapter:Chapter-1#1.5.4|Section 1.5.4]] . These include new techniques for process-based evaluation of climate and Earth system models against observations that have rapidly advanced since the publication of AR5 ( [[#Eyring--2019|Eyring et al., 2019]] ) as well as newly developed CMIP evaluation tools that allow a more rapid and comprehensive evaluation of the models with observations ( [[#Eyring--2016a|Eyring et al., 2016a]] , b).

In this chapter, we use the Earth System Model Evaluation Tool (ESMValTool, [[#Eyring--2020|Eyring et al., 2020]] ; [[#Lauer--2020|Lauer et al., 2020]] ; [[#Righi--2020|Righi et al., 2020]] ) and the NCAR Climate Variability Diagnostic Package (CVDP, [[#Phillips--2014|Phillips et al., 2014]] ) that is included in the ESMValTool to produce most of the figures. This ensures traceability of the results and provides an additional level of quality control. The ESMValTool code to produce the figures in this chapter was released as open source software at the time of the publication of this Report (see details in the Chapter Data Table, Table SM.3.1). Figures in this chapter are produced either using one ensemble member from each model, or using all available ensemble members and weighting each simulation by 1/( ''NM'' <sub>i</sub> ), where ''N'' is the number of models and ''M'' <sub>i</sub> is the ensemble size of the ''i'' th model, prior to calculating means and percentiles. Both approaches ensure that each model used is given equal weight in the figures, and details on which approach is used are provided in the figure captions.

An introduction to recent developments in detection and attribution methods in the context of this Report is provided in the Cross-Working Group Box on Attribution in Chapter 1. Here we discuss new methods and improvements applicable to the attribution of changes in large-scale indicators of climate change which are used in this chapter.

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==== 3.2.1 Methods Based on Regression ====

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Regression-based methods, also known as fingerprinting methods, have been widely used for detection of climate change and attribution of the change to different external drivers. Initially, these methods were applied to detect changes in global surface temperature, and were then extended to other climate variables at different time and spatial scales (e.g., [[#Hegerl--1996|Hegerl et al., 1996]] ; [[#Hasselmann--1997|Hasselmann, 1997]] ; [[#Allen--1999|Allen and Tett, 1999]] ; [[#Gillett--2003b|Gillett et al., 2003b]] ; [[#Zhang--2007|Zhang et al., 2007]] ; [[#Min--2008a|Min et al., 2008a]] , 2011). These approaches are based on multivariate linear regression and assume that the observed change consists of a linear combination of externally forced signals plus internal variability, which generally holds for large-scale variables ( [[#Hegerl--2011|Hegerl and Zwiers, 2011]] ). The regressors are the expected space–time response patterns to different climate forcings (fingerprints), and the residuals represent internal variability. Fingerprints are usually estimated from climate model simulations following spatial and temporal averaging. A regression coefficient which is significantly greater than zero implies that a detectable change is identified in the observations. When the confidence interval of the regression coefficient includes unity and is inconsistent with zero, the magnitude of the model simulated fingerprints is assessed to be consistent with the observations, implying that the observed changes can be attributed in part to a particular forcing. Variants of linear regression have been used to address uncertainty in the fingerprints due to internal variability ( [[#Allen--2003|Allen and Stott, 2003]] ) as well as structural model uncertainty ( [[#Huntingford--2006|Huntingford et al., 2006]] ).

In order to improve the signal-to-noise ratio, observations and model-simulated responses are usually normalized by an estimate of internal variability derived from climate model simulations. This procedure requires an estimate of the inverse covariance matrix of the internal variability, and some approaches have been proposed for more reliable estimation of this ( [[#Ribes--2009|Ribes et al., 2009]] ). A signal can be spuriously detected due to too-small noise, and hence simulated internal variability needs to be evaluated with care. Model-simulated variability is typically checked through comparing modelled variance from unforced simulations with the observed residual variance using a standard residual consistency test ( [[#Allen--1999|Allen and Tett, 1999]] ), or an improved one ( [[#Ribes--2013|Ribes and Terray, 2013]] ). [[#Imbers--2014|Imbers et al. (2014)]] tested the sensitivity of detection and attribution results to different representations of internal variability associated with short-memory and long-memory processes. Their results supported the robustness of previous detection and attribution statements for the global mean temperature change but they also recommended the use of a wider variety of robustness tests.

Some recent studies focused on the improved estimation of the scaling factor (regression coefficient) and its confidence interval. [[#Hannart--2014|Hannart et al. (2014)]] described an inference procedure for scaling factors which avoids making the assumption that model error and internal variability have the same covariance structure. An integrated approach to optimal fingerprinting was further suggested in which all uncertainty sources (i.e., observational error, model error, and internal variability) are treated in one statistical model without a preliminary dimension reduction step ( [[#Hannart--2016|Hannart, 2016]] ). [[#Katzfuss--2017|Katzfuss et al. (2017)]] introduced a similar integrated approach based on a Bayesian model averaging. On the other hand, [[#DelSole--2019|DelSole et al. (2019)]] suggested a bootstrap method to better estimate the confidence intervals of scaling factors even in a weak-signal regime. It is notable that some studies do not optimize fingerprints, as uncertainty in the covariance introduces a further layer of complexity, but results in only a limited improvement in detection ( [[#Polson--2017|Polson and Hegerl, 2017]] ).

Another fingerprinting approach uses pattern similarity between observations and fingerprints, in which the leading empirical orthogonal function obtained from the time-evolving multi-model forced simulation is usually defined as a fingerprint (e.g., [[#Santer--2013|Santer et al., 2013]] ; [[#Marvel--2019|Marvel et al., 2019]] ; [[#Bonfils--2020|Bonfils et al., 2020]] ). Observations and model simulations are then projected onto the fingerprint to measure the degree of spatial pattern similarity with the expected physical response to a given forcing. This projection provides the signal time series, which is in turn tested against internal variability, as estimated from long control simulations. As a way to extend this pattern-based approach to a high-dimensional detection variable at daily time scales, Sippel et al. (2019, 2020) proposed using the relationship pattern with a global climate change metric as a fingerprint. To solve the high-dimensional regression problem which makes regression coefficients not well constrained, they incorporated a statistical learning technique based on a regularized linear regression, which optimizes a global warming signal by giving lower weight to regions with large internal variability.

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==== 3.2.2 Other Probabilistic Approaches ====

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Considering the difficulty in accounting for climate modelling uncertainties in the regression-based approaches, [[#Ribes--2017|Ribes et al. (2017)]] introduced a new statistical inference framework based on an additivity assumption and likelihood maximization, which estimates climate model uncertainty based on an ensemble of opportunity and tests whether observations are inconsistent with internal variability and consistent with the expected response from climate models. The method was further developed by [[#Ribes--2021|Ribes et al. (2021)]] , who applied it to narrow the uncertainty range in the estimated human-induced warming. [[#Hannart--2018|Hannart and Naveau (2018)]] , on the other hand, extended the application of standard causal theory ( [[#Pearl--2009|Pearl, 2009]] ) to the context of detection and attribution by converting a time series into an event, and calculating the probability of causation, an approach which maximizes the causal evidence associated with the forcing. On the other hand, [[#Schurer--2018|Schurer et al. (2018)]] employed a Bayesian framework to explicitly consider climate modelling uncertainty in the optimal regression method. Application of these approaches to attribution of large-scale temperature changes supports a dominant anthropogenic contribution to the observed global warming.

Climate change signals can vary with time and discriminant analysis has been used to obtain more accurate estimates of time-varying signals, and has been applied to different variables such as seasonal temperatures ( [[#Jia--2012|Jia and DelSole, 2012]] ) and the South Asian monsoon ( [[#Srivastava--2014|Srivastava and DelSole, 2014]] ). The same approach was applied to separate aerosol forcing responses from other forcings (X. [[#Yan--2016|]] [[#Yan--2016|]] [[#Yan--2016|Yan et al., 2016]] ) and results using climate model output indicated that detectability of the aerosol response is maximized by using a combination of temperature and precipitation data. [[#Paeth--2017|Paeth et al. (2017)]] introduced a detection and attribution method applicable for multiple variables based on a discriminant analysis and a Bayesian classification method. Finally, a systematic approach has been proposed to translating quantitative analysis into a description of confidence in the detection and attribution of a climate response to anthropogenic drivers ( [[#Stone--2016|Stone and Hansen, 2016]] ).

Overall, these new fingerprinting and other probabilistic methods for detection and attribution as well as efforts to better incorporate the associated uncertainties have addressed a number of shortcomings in previously applied detection and attribution techniques. They further strengthen the confidence in attribution of observed large-scale changes to a combination of external forcings as assessed in the following sections.

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