Global mean surface temperature (GMST) fluctuates over decadal to multidecadal time-scales. Patterns of internal variability are partly responsible, but the relationships can be conflated by anthropogenically-forced signals. Here we adopt a physically-based method of separating internal variability from forced responses to examine how trends in large-scale patterns, specifically the Interdecadal Pacific Oscillation (IPO) and Atlantic Multidecadal Variability (AMV), influence GMST. After removing the forced responses, observed variability of GMST is close to the central estimates of Coupled Model Intercomparison Project Phase 5 (CMIP5) simulations, but models tend to underestimate IPO variability at time-scales >10 years, and AMV at time-scales >20 years. Correlations between GMST trends and these patterns are also underrepresented, most strongly at 10- and 35-year time-scales, for IPO and AMV respectively. Strikingly, models that simulate stronger variability of IPO and AMV also exhibit stronger relationships between these patterns and GMST, predominately at the 10- and 35-year time-scales, respectively

Collins, Matthew

England, Matthew

Frankcombe, Leela

Juniper, Marcus

Kajtar, Jules

Osborn, Timothy

Geophysical Research Letters

University of East Anglia digital repository

Global mean surface temperature response to large-scale patterns of variability in observations and CMIP5

Collins M.

Flato G.

Crossref

Global Mean Surface Temperature Response to Large‐Scale Patterns of Variability in Observations and CMIP5

This is the final version. Available from Wiley via the DOI in this record.Global mean surface temperature (GMST) fluctuates over decadal to multidecadal time‐scales. Patterns of internal variability are partly responsible, but the relationships can be conflated by anthropogenically‐forced signals. Here we adopt a physically‐based method of separating internal variability from forced responses to examine how trends in large‐scale patterns, specifically the Interdecadal Pacific Oscillation (IPO) and Atlantic Multidecadal Variability (AMV), influence GMST. After removing the forced responses, observed variability of GMST is close to the central estimates of Coupled Model Intercomparison Project Phase 5 (CMIP5) simulations, but models tend to underestimate IPO variability at time‐scales >10 years, and AMV at time‐scales >20 years. Correlations between GMST trends and these patterns are also underrepresented, most strongly at 10‐ and 35‐year time‐scales, for IPO and AMV respectively. Strikingly, models that simulate stronger variability of IPO and AMV also exhibit stronger relationships between these patterns and GMST, predominately at the 10‐ and 35‐year time‐scales, respectively.Natural Environment Research Council (NERC)Australian Research Counci

Kajtar, J

Collins, M

Frankcombe, LM

England, MH

Osborn, TJ

Juniper, M

Open Research Exeter

  1   Geophysical Research Letters Supporting Information for Global mean surface temperature response to large-scale patterns of variability in observations and CMIP5  Jules B. Kajtar1, Matthew Collins1, Leela. M. Frankcombe2,3, Matthew H. England2,3, Timothy J. Osborn4, Marcus Juniper1  1 College of Engineering, Mathematics, and Physical Sciences, University of Exeter, Exeter, UK. 2 Australian Research Council’s Centre of Excellence for Climate Extremes, Australia. 3 Climate Change Research Centre, University of New South Wales, NSW, Australia. 4 Climatic Research Unit, School of Environmental Sciences, University of East Anglia, Norwich, UK. Corresponding author: Jules B. Kajtar (j.kajtar@exeter.ac.uk)  Contents of this file  Table S1 Text S1 to S3 Figures S1 to S4  Introduction  This document contains the list of CMIP5 models and ensemble members analyzed in this study (Table S1). Additional details regarding the forced response removal method (Text S1), constructing running trend time-series (Text S2), and computing the statistical significance of correlations are also provided. Supporting figures follow the text.     2  Model Ensemble Members Institution ACCESS1-0 r1i1p1 Commonwealth Scientific and Industrial Research Organisation, and Bureau of Meteorology, Australia ACCESS1-3 r1i1p1 bcc-csm1-1 r1i1p1 Beijing Climate Center, China Meteorological Administration bcc-csm1-1-m r1i1p1 CanESM2 r1i1p1, r2i1p1, r3i1p1, r4i1p1, r5i1p1 Canadian Centre for Climate Modelling and Analysis CCSM4 r1i1p1, r2i1p1, r3i1p1, r4i1p1, r5i1p1, r6i1p1 National Center for Atmospheric Research CESM1-BGC r1i1p1 National Science Foundation, Department of Energy, and National Center for Atmospheric Research CESM1-CAM5 r1i1p1, r2i1p1, r3i1p1 CMCC-CESM r1i1p1 Centro Euro-Mediterraneo per I Cambiamenti Climatici CMCC-CM r1i1p1 CMCC-CMS r1i1p1 CNRM-CM5 r1i1p1, r2i1p1, r4i1p1, r6i1p1, r10i1p1 Centre National de Recherches Meteorologiques CSIRO-Mk3-6-0 r1i1p1, r2i1p1, r3i1p1, r4i1p1, r5i1p1, r6i1p1, r7i1p1, r8i1p1, r9i1p1, r10i1p1 Commonwealth Scientific and Industrial Research Organisation EC-EARTH r1i1p1, r2i1p1, r6i1p1, r8i1p1, r9i1p1, r10i1p1 EC-EARTH consortium FIO-ESM r1i1p1, r2i1p1, r3i1p1 The First Institute of Oceanography, SOA, China GFDL-CM3 r1i1p1 Geophysical Fluid Dynamics Laboratory GFDL-ESM2G r1i1p1 GFDL-ESM2M r1i1p1 GISS-E2-H r1i1p1, r1i1p2, r1i1p3, r2i1p3 NASA Goddard Institute for Space Studies GISS-E2-H-CC r1i1p1 GISS-E2-R r1i1p1, r1i1p2, r2i1p1, r2i1p3 GISS-E2-R-CC r1i1p1 HadGEM2-AO r1i1p1 NIMR / Korea Meteorological Administration HadGEM2-CC r1i1p1 Met Office Hadley Centre HadGEM2-ES r1i1p1, r2i1p1, r3i1p1, r4i1p1 inmcm4 r1i1p1 Institute for Numerical Mathematics IPSL-CM5A-LR r1i1p1, r2i1p1, r3i1p1, r4i1p1 Institut Pierre-Simon Laplace IPSL-CM5A-MR r1i1p1 IPSL-CM5B-LR r1i1p1 MIROC-ESM r1i1p1 Japan Agency for Marine-Earth Science and Technology, and Atmosphere and Ocean Research Institute (U. Tokyo), and National Institute for Environmental Studies MIROC-ESM-CHEM r1i1p1 MIROC5 r1i1p1, r2i1p1, r3i1p1, r4i1p1, r5i1p1 MPI-ESM-LR r1i1p1, r2i1p1, r3i1p1 Max Planck Institute for Meteorology (MPI-M) MPI-ESM-MR r1i1p1 MRI-CGCM3 r1i1p1 Meteorological Research Institute MRI-ESM1 r1i1p1 NorESM1-M r1i1p1 Norwegian Climate Centre NorESM1-ME r1i1p1 Table S1. The 38 climate models, and 87 ensemble members, analyzed in this study. Ensemble members were only retained if the historical experiment, and matching RCP8.5 extension, covered the entire analysis period of 1880 to 2017. The 38 ensemble members in bold denote those that had corresponding piControl experiments.   3   Text S1. Forced Response Removal For an individual model realization (or observational dataset) 𝑖, the time-series of a quantity 𝑦 = 𝑦(𝑡) can be decomposed into a forced response component, 𝜙, and an unforced (or internal variability) component, 𝜐, such that                                                                   	𝑦*(𝑡) = 𝜙*(𝑡) + 𝜐*(𝑡).     (1) The term 𝑦(𝑡) can be taken to represent any time-varying quantity (for example, global mean surface temperature, the AMV index, or SST at an individual grid-point). The forced response component, 𝜙*, depends upon both the forcing and the feedbacks in that model. Here the forced response is estimated from an ensemble of model experiments following the single-factor scaling method of Frankcombe et al. (2015). The premise of using a multi-model mean is that, given different initializations, internal variability will not be synchronized across several simulations. If it is assumed that the multi-ensemble and multi-model mean, 𝑀, provides a reasonable approximation to the true forced response, then:                                                                   𝜙*(𝑡) ≅ 𝑀(𝑡)𝛽* + 𝑐*    (2) where 𝛽*  is a scaling factor such that 𝑀(𝑡) is scaled to give a best fit to quantity 𝑦(𝑡) of realization 𝑖. In some sense, 𝛽*  represents a measure of that model realization’s sensitivity to forcing. The ci is a constant, which is zero where the mean of 𝑀 and 𝑦* have been subtracted. The scaling factor 𝛽*  can then be estimated by regressing 𝑀(𝑡) against 𝑦*(𝑡), arriving at an expression for the internal variability:                                                                   𝜐*(𝑡) ≅ 𝑦*(𝑡) − 𝑀(𝑡)𝛽*.   (3)  The approach here only differs from Frankcombe et al. (2015) in that the forced signal 𝑀 is always taken to be the multi-model mean of the CMIP5 historical global mean surface temperature. The term 𝑦* can represent any quantity, be it an SST index, grid-point SST data, or global mean surface temperature, and a corresponding	𝛽*  is computed. Although the rate of global warming might vary substantially in different regions across the globe, and across models, the multi-model mean signature of forcing is scaled in all instances before subtraction in each model realization. Therefore, in regions where the long-term warming is weak, or furthermore, where there is weak correlation with the multi-model mean, then the scaling factor will likewise be small.  To compute the scaling factor 𝛽*, an ordinary least-squares regression is computed between 𝑀 and 𝑦*. Allen & Stott (2003) compare ordinary and total least-squares regressions for computing the scaling factor (see their Figure 2). They show that total least-squares regression should be employed where the sample size of simulated members is small, since there will be residual internal variability (i.e. “expected noise variance”) in the ensemble mean. Their algorithm includes a step of “scaling up” 𝑀 so that the noise variance matches that in 𝑦*. In the present study, the ensemble mean is computed from a large number of model realisations and the residual variability is very low. It is unclear how the noise component should be scaled up, and therefore ordinary rather than total least-squares regression is used.  The single-factor approach, rather than multi-factor (Frankcombe et al. 2015), has been adopted here since not all experiments (e.g. ‘historicalNat’ or ‘historicalGHG’) are available for every model in the CMIP5 archive. Other approaches may have been to compute an ensemble mean for models with multiple realizations (following the "single model ensemble mean" method of Frankcombe et al. 2018), or to retain the multi-model mean, but compute single   4  model-mean scaling factors. The seemingly simplest approach in this regard has been adopted here, which is to treat each realization independently. A comparison of a range of forced response removal processes is presented by Frankcombe et al. (2015, 2018).  In the case of the piControl simulations, where forcings are constant, a simple linear detrending is applied. Some of the models suffer from small residual “drift” (Sen Gupta et al. 2013), and thus here a linear detrending is sufficient.  Text S2. Running trend time-series To construct an N-year running-trend time-series, the linear trend is computed over the first N-year window of an annual time-series. The window is then shifted by one year, the linear trend is again computed. This process is repeated to the end of the annual time-series. Linear trends in each window are computed using an ordinary least-squares fit.  Text S3. Statistical significance of correlations The statistical significance of correlations between running-trend time-series were tested based on a one-tailed Student’s t-distribution with adjusted degrees of freedom. One-tailed tests were chosen in these cases because models and observations are largely in agreement on the sign of the correlation coefficients (positive), over most time-scales. The degrees of freedom in the statistical tests were adjusted to account for non-independence of overlapping periods. The effective degrees of freedom were specified by the number of data-points in the running trend time-series divided by N/2. This choice is analogous to that of Wang et al. (2017), who scale the degrees of freedom by half the filter frequency used in the smoothing of their AMV time-series. The significance test for the model data correlation incorporates the number of available model realizations in the adjusted degrees of freedom.    5   Figure S1. Annual time-series of global mean surface temperature (GMST), the Interdecadal Pacific Oscillation (IPO), and the Atlantic Multidecadal Variability (AMV) indices, in observations and CMIP5 historical simulations. (a-c) Raw annual data, and (d-f) with the forcing response removed. In each case, anomalies with respect to the 1880-1930 baseline period are shown. The shaded blue regions denote the central 68%, 95%, and 100% of the CMIP5 realization ensemble.  (a) GMST, raw annual data1880 1900 1920 1940 1960 1980 2000-1012GMST index (o C) ObservedCMIP5 meanCMIP5 68%, 95%, 100%(d) GMST, forced response removed1880 1900 1920 1940 1960 1980 2000-0.6-0.4-0.200.20.40.6(b) IPO, raw annual data1880 1900 1920 1940 1960 1980 2000-3-2-10123IPO index (oC)(e) IPO, forced response removed1880 1900 1920 1940 1960 1980 2000-3-2-10123(c) AMV, raw annual data1880 1900 1920 1940 1960 1980 2000year-1012AMV index (oC)(f) AMV, forced response removed1880 1900 1920 1940 1960 1980 2000year-1-0.500.51  6   Figure S2. (a,b) Variances of (a) 10-year running trends of the Interdecadal Pacific Oscillation (IPO) index, and (b) 35-year running trends of the Atlantic Multidecadal Variability (AMV) index. The variance in piControl is plotted against the variance in historical (with forcing response removed) for each available ensemble member (Table S1). The one-to-one line is plotted in black, and blue line denotes the inter-model least-squares fit regressed through the origin. Whiskers denote the 99% confidence interval of the computed variance using a chi-squared distribution, with degrees of freedom based on the number of data-points in the running-trend time-series. The red dashed lines denoted the 99% confidence interval for the observed data. (c,d) Correlations of global mean surface temperature with (c) IPO index, and (d) the AMV index, in observations and CMIP5 historical models. The correlations are computed from annual data in 31-year sliding windows, where year on the x-axes denotes the central year of the 31-year window. The shaded blue regions denote the central 68%, 95%, and 100% of the CMIP5 model ensemble. Dashed lines denote the 99% levels for statistically significant correlations based on a two-tailed Student’s t-distribution with 30 degrees of freedom.  (c) Sliding correlation, GMST and IPO1900 1920 1940 1960 1980 2000central year of moving window-1-0.500.51correlation coefficientObservedCMIP5 meanCMIP5 68%, 95%, 100%(d) Sliding correlation, GMST and AMV1900 1920 1940 1960 1980 2000central year of moving window-1-0.500.51correlation coefficientObservedCMIP5 meanCMIP5 68%, 95%, 100%(a) IPO variance, 10-year trends, CMIP5Observed0  0.5 1  1.5piControl variance ( 10-2)0  0.51  1.5historical variance (10-2)(forcing response removed)(b) AMV variance, 35-year trends, CMIP5Observed0  0.5 1  1.5piControl variance ( 10-4)0  0.51  1.5historical variance (10-4)(forcing response removed)  7   Figure S3. Correlations between running trends of global mean surface temperature (GMST) and grid-point sea surface temperature (SST). As in Figure 3, but only for the multi-model means of the CMIP5 (a,c) historical (same panels as Figure 3b,f) and (b,d) piControl simulations.     Figure S4. Standard deviation and correlations in the running trends of global mean surface temperature (GMST), the Interdecadal Pacific Oscillation (IPO), and the Atlantic Multidecadal Variability (AMV) indices, over a range of time-scales. As in Figure 1, but comparing different observational data-sets, including GISTEMP (Hansen et al. 2010; GISTEMP Team 2018) and ERSST (Huang et al. 2017). The thicker red curves for HadCRUT and HadISST are the same as (a) historical, 10-year trends-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1correlation coefficient(b) piControl, 10-year trends(c) historical, 35-year trends(d) piControl, 35-year trends(a) GMST trend variability5 10 15 20 25 30 35 4000.10.20.30.4normalized standarddeviation (oC)HadCRUT (1880-2017)GISTEMP (1880-2017)HadCRUT (1950-2017)GISTEMP (1950-2017)(b) IPO trend variability5 10 15 20 25 30 35 40running trend window length (years)00.511.5normalized standarddeviation (oC)HadISST (1880-2017)ERSST (1880-2017)HadISST (1950-2017)ERSST (1950-2017)(c) AMV trend variability5 10 15 20 25 30 35 4000.10.20.30.4normalized standarddeviation (oC)HadISST (1880-2017)ERSST (1880-2017)HadISST (1950-2017)ERSST (1950-2017)(d) GMST and IPO trend correlations5 10 15 20 25 30 35 40running trend window length (years)-1-0.500.51correlation coefficientHadCRUT&HadISST (1880-2017)GISTEMP&ERSST (1880-2017)HadCRUT&HadISST (1950-2017)GISTEMP&ERSST (1950-2017)(e) GMST and AMV trend correlations5 10 15 20 25 30 35 40running trend window length (years)-1-0.500.51correlation coefficientHadCRUT&HadISST (1880-2017)GISTEMP&ERSST (1880-2017)HadCRUT&HadISST (1950-2017)GISTEMP&ERSST (1950-2017)  8  those shown in Figure 1. For the thinner curves in each panel, the data was first trimmed to the period 1950 to 2017 before computing the standard deviations and correlations.   References Allen MR, Stott PA. Estimating signal amplitudes in optimal fingerprinting, part I: theory. Clim Dyn 21, 477–491 (2003) Frankcombe LM, England MH, Kajtar JB, et al. On the choice of ensemble mean for estimating the forced signal in the presence of internal variability. J Clim 31, 5681–5693 (2018) Frankcombe LM, England MH, Mann ME, Steinman BA. Separating internal variability from the externally forced climate response. J Clim 28, 8184–8202 (2015) GISTEMP Team. GISS Surface Temperature Analysis (GISTEMP). http://www.data.giss.nasa.gov/gistemp/. Dataset accessed 2019-01-15. (2018) Hansen JE, Ruedy R, Sato M, Lo K. Global surface temperature change. Rev Geophys 48, RG4004 (2010) Huang B, Thorne PW, Banzon VF, et al. Extended Reconstructed Sea Surface Temperature version 5 (ERSSTv5): Upgrades, Validations, and Intercomparisons. J Clim 30, 8179–8205 (2017) Sen Gupta A, Jourdain NC, Brown JN, Monselesan DP. Climate drift in the CMIP5 models. J Clim 26, 8597–8615 (2013) Wang J, Yang B, Ljungqvist FC, et al. Internal and external forcing of multidecadal Atlantic climate variability over the past 1,200 years. Nat Geosci 10, 512–517 (2017)  

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Global mean surface temperature response to large‐scale patterns of variability in observations and CMIP5

https://eprints.utas.edu.au/30561/1/133144%20-%20Global%20mean%20surface%20temperature%20response%20to%20large-scale%20patterns%20of%20variability.pdf

Global mean surface temperature response to large-scale patterns of variability in observations and CMIP5

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