Editing IPCC:AR6/WGI/Chapter-10 (section)

==== 10.4.1.2 Other Spatiotemporal Statistical Methods for Isolating Regional Climate Responses to External Forcing ====

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The primary objective of any attribution method is to optimally separate the influences of external forcing and internal variability on a global or regional climate record. In a multi-model ensemble context, the estimation of the externally-forced climate response has been typically performed by ensemble averaging of linear trends or regional domain spatial average, thus not taking into account the available and complete space and time co-variance information. Since AR5, methods using spatiotemporal information have been further developed and used to improve the separation between external and internal drivers in multiple or single historical climate realizations performed by a given global model.

The typical ensemble size of CMIP historical climate simulations for a given model traditionally range between one and ten members, with three often being the default choice. At the regional scale, a simple ensemble average with such sample sizes does not provide robust estimates of the response patterns to external forcing ( [[#Maher--2019|Maher et al., 2019]] ; [[#Deser--2020|Deser et al., 2020]] ). Since AR5, pattern filtering methods such as signal-to-noise maximizing empirical orthogonal functions ( [[#Ting--2009|Ting et al., 2009]] ) have been shown to improve the identification of forced response patterns when few model members are available ( [[#Wills--2020|Wills et al., 2020]] ). Using SMILEs as a test bed, it has been shown that pattern filtering strongly reduces the number of ensemble members needed to estimate the forced response pattern compared to simple ensemble averaging. Pattern filtering allows the identification of low signal-to-noise signals such as the El Niño-like response to volcanic eruptions ( [[#Khodri--2017|Khodri et al., 2017]] ; [[#Wills--2020|Wills et al., 2020]] ).

Methods to extract the response to external forcing in an observed or simulated single realization include dynamical adjustment ( [[#Smoliak--2015|Smoliak et al., 2015]] ; [[#Deser--2016|Deser et al., 2016]] ; [[#Sippel--2019|Sippel et al., 2019]] ) and time scale separation methods ( [[#DelSole--2011|DelSole et al., 2011]] ; [[#Wills--2018|Wills et al., 2018]] , 2020). Dynamical adjustment seeks to isolate changes in surface air temperature or precipitation that are due purely to atmospheric circulation changes. The residual can then be analysed and attributed to internal changes in both land or ocean surface conditions and the thermodynamical response to external forcing. [[#Smoliak--2015|Smoliak et al. (2015)]] performed their dynamical adjustment using partial least squares regression of temperature to remove variations arising from sea level pressure changes. [[#Deser--2016|Deser et al. (2016)]] used constructed atmospheric circulation analogues and resampling to estimate the dynamical contribution to changes in temperature. [[#Sippel--2019|Sippel et al. (2019)]] used machine learning techniques known as regularized linear regression to provide estimates of circulation-induced components of precipitation and temperature variability from global to local scales. It is noteworthy that the dynamical adjustment method by itself cannot account for the component of the forced response associated with circulation changes that project onto atmospheric internal variability. However, this component can be estimated within a model framework by averaging the dynamical contribution across multiple members of a SMILE ( [[#Deser--2016|Deser et al., 2016]] ).

Dynamical adjustment methods have been used by, for instance, [[#Deser--2016|Deser et al. (2016)]] , [[#Saffioti--2016|Saffioti et al. (2016)]] , [[#O’Reilly--2017|O’Reilly et al. (2017)]] , [[#Gong--2019|Gong et al. (2019)]] , and R. [[#Guo--2019|]] [[#Guo--2019|Guo et al. (2019)]] . [[#Deser--2016|Deser et al. (2016)]] focused on the causes of observed and simulated multi-decadal trends in North American temperature. They demonstrated that the main advantage of this technique is to narrow the spread of temperature trends found by the model ensemble and to bring the dynamically-adjusted observational trend much closer to the forced response estimated by the model ensemble mean. Similar results were obtained by [[#Saffioti--2016|Saffioti et al. (2016)]] regarding recent observed winter temperature and precipitation trends over Europe. Similarly, [[#O’Reilly--2017|O’Reilly et al. (2017)]] applied dynamical adjustment techniques to more carefully determine the influence of the Atlantic Multi-decadal Variability (AMV; Annex IV.2.7) on continental climates. Over Europe, summer temperature anomalies induced thermodynamically by the warm phase of the AMV are further reinforced by circulation anomalies; meanwhile, precipitation signals are largely controlled by dynamical responses to the AMV. Based on a partial least-squares approach, [[#Gong--2019|Gong et al. (2019)]] showed that recent winter temperature 30-year trends over northern East Asia are strongly influenced by internal variability linked to decadal changes of the Arctic Oscillation. Using dynamical adjustment purely on precipitation observations, R. [[#Guo--2019|]] [[#Guo--2019|Guo et al. (2019)]] showed that human influence has led to increased winter precipitation across north-eastern North America, as well as a small region of north-western North America, and to an increase in precipitation across much of north-western and north central Eurasia. The latter results confirm previous findings obtained by standard optimal fingerprinting methods ( [[#Wan--2015|Wan et al., 2015]] ).

Time scale separation methods such as the low-frequency component analysis and ensemble empirical mode decomposition methods take advantage of the longer time scale associated with anthropogenic external forcing compared to that of most internal modes of variability. The low-frequency component analysis method tries to find low-frequency variability patterns by searching for linear combinations of a moderate number of empirical orthogonal functions that maximize the ratio of low-frequency to total variance. It has first been used to separate internal modes of interannual and decadal variability from slowly varying and externally-forced variability in the Pacific and Atlantic oceans ( [[#Wills--2018|Wills et al., 2018]] , 2019). The methodology has also been applied to patterns of observed surface air temperature to isolate the slow components of observed changes that are consistent with the expected response to anthropogenic greenhouse gas and aerosol forcing ( [[#Wills--2020|Wills et al., 2020]] ).

The ensemble empirical mode decomposition method ( [[#Wu--2009|Wu and Huang, 2009]] ; [[#Wilcox--2013|Wilcox et al., 2013]] ; [[#Ji--2014|Ji et al., 2014]] ; [[#Qian--2014|Qian and Zhou, 2014]] ) decomposes data, such as time series of historical temperature and precipitation, into independent oscillatory modes of decreasing frequency. The last step of the method leaves behind a smooth and low-frequency residual time series. Typically, the non-linear anthropogenic trend (e.g., of 20th-century temperature) can be reconstructed by summing the long-term mean, the residual, and eventually the lowest-frequency mode to account for a multi-decadal forced signal, for instance associated with anthropogenic aerosol forcing. The ensemble empirical mode decomposition method is an example of a data-driven, non-parametric approach that can be used to directly provide an estimate of the forced response without the need for model data ( [[#Qian--2016|Qian, 2016]] ).

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