eLeMentos para una
A. Modelo de Supervisión
4. Instituciones: funciones generales y perímetro regulatorio a) Comisión de Solvencia
The seasonal version of the “global” method used in the main body of the paper is estimated
586
using the least squares fit on this regression:
587 λglobal, f ,s= ~T0 s· ~R0f,s k~T0 sk2 (A10)
where ~Ts and ~Rf,sare globally and seasonally averaged time series of control simulation surface
588
temperature and TOA flux f respectively, sampled every fourth seasonal value so that all elements
589
of the time series are from season s. The four seasonal feedbacks are used to recreate estimates of
590
the global averaged time series ~Rf,abrupt4x, which in turn is used, as above, to estimate abrupt4x
591
feedbacks. Once more, different averaging of the control time series and groupings of regression
592
equations can be used to make the annual, monthly, and all months versions of this method featured
593
in Tables S3 and S4.
594
The normalized spatial pattern of TOA flux change can be found by first estimating the “local
595
contribution” (Boer and Yu 2003a,b; Crook et al. 2011; Zelinka et al. 2012; Andrews et al. 2015),
596
using Equation 1, but replacing the time series vector ~R0f,s with the spatial time series matrix
597
R0f,sfrom above, and replacing the single feedback λglobal, f ,swith the spatial vector of feedbacks,
598 ~λ global, f. 599 2) THE LOCAL METHOD 600
The “local” method assumes the statistical model
601
Spatial feedbacks are estimated using least squares: 602 ~λ local, f = λlocal, f ,1 λlocal, f ,2 .. . λlocal, f ,ngrid = ~ T10·~R0f,1 k~T0 1k2 ~ T20·~R0f,2 k~T20k2 .. . ~T0 ngrid·~R0f,ngrid k~T0 ngridk2 (A12)
where ~Ti0 and ~R0f,i are the ith rows of T0 and R0f respectively. We can then generate estimates of
603
R0f,abrupt4x as above. We apply these estimates to Equations A6 and A7 to estimate forced global
604
feedbacks and spatial patterns of TOA flux change.
605
h. Local regression
606
We use LOESS (LOcally Estimated Scatterplot Smoothing; Cleveland and Devlin 1988) to take
607
local regression of scatterplots of N vs T0. LOESS uses a weighted regression of a certain number
608
of nearest neighbors, in our case 30. Full details can be found in the code for this paper listed
609
above and in the LocallyWeightedRegression.jl Julia package (https://github.com/juliohm/
610
LocallyWeightedRegression.jl).
611
References
612
Andrews, T., J. M. Gregory, and M. J. Webb, 2015: The Dependence of Radiative Forcing and
613
Feedback on Evolving Patterns of Surface Temperature Change in Climate Models. Journal of
614
Climate, 28 (4), 1630–1648.
615
Andrews, T., and M. J. Webb, 2017: The Dependence of Global Cloud and Lapse Rate Feedbacks
616
on the Spatial Structure of Tropical Pacific Warming. Journal of Climate, 31 (2), 641–654.
Andrews, T., and Coauthors, 2018: Accounting for Changing Temperature Patterns Increases
618
Historical Estimates of Climate Sensitivity. Geophysical Research Letters, 45 (16), 8490–
619
8499, doi:10.1029/2018GL078887, URL https://agupubs.onlinelibrary.wiley.com/doi/abs/10.
620
1029/2018GL078887.
621
Armour, K. C., 2017: Energy budget constraints on climate sensitivity in light of inconstant cli-
622
mate feedbacks. Nature Climate Change, 7 (5), 331.
623
Armour, K. C., C. M. Bitz, and G. H. Roe, 2012: Time-Varying Climate Sensitivity from Regional
624
Feedbacks. Journal of Climate, 26 (13), 4518–4534.
625
Arrhenius, P. S., 1896: XXXI. On the influence of carbonic acid in the air upon the temperature
626
of the ground. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of
627
Science, 41 (251), 237–276, doi:10.1080/14786449608620846.
628
Bloch-Johnson, J., R. T. Pierrehumbert, and D. S. Abbot, 2015: Feedback temperature dependence
629
determines the risk of high warming. Geophysical Research Letters, 42 (12), 2015GL064 240.
630
Boer, G., and B. Yu, 2003a: Climate sensitivity and response. Climate Dynamics, 20 (4), 415–429.
631
Boer, G. J., and B. Yu, 2003b: Climate sensitivity and climate state. Climate Dynamics, 21 (2),
632
167–176.
633
Brown, P. T., W. Li, J. H. Jiang, and H. Su, 2015: Unforced Surface Air Temperature Variability
634
and Its Contrasting Relationship with the Anomalous TOA Energy Flux at Local and Global
635
Spatial Scales. Journal of Climate, 29 (3), 925–940.
636
Ceppi, P., and J. M. Gregory, 2017: Relationship of tropospheric stability to climate sensitivity and
637
Earth’s observed radiation budget. Proceedings of the National Academy of Sciences, 114 (50),
638
13 126–13 131.
Ceppi, P., and J. M. Gregory, 2019: A refined model for the Earths global energy balance. Climate
640
Dynamics, 53 (7), 4781–4797, doi:10.1007/s00382-019-04825-x, URL https://doi.org/10.1007/
641
s00382-019-04825-x.
642
Charney, J. G., and Coauthors, 1979: Carbon Dioxide and Climate: A Scientific Assessment. doi:
643
10.17226/12181.
644
Choi, Y.-S., H. Cho, C.-H. Ho, R. S. Lindzen, S. K. Park, and X. Yu, 2014: Influence of
645
non-feedback variations of radiation on the determination of climate feedback. Theoretical
646
and Applied Climatology, 115 (1), 355–364, doi:10.1007/s00704-013-0998-6, URL https:
647
//doi.org/10.1007/s00704-013-0998-6.
648
Cleveland, W. S., and S. J. Devlin, 1988: Locally Weighted Regression: An Approach to Re-
649
gression Analysis by Local Fitting. Journal of the American Statistical Association, 83 (403),
650
596–610, doi:10.2307/2289282, URL https://www.jstor.org/stable/2289282.
651
Colman, R., and L. Hanson, 2017: On the relative strength of radiative feedbacks under climate
652
variability and change. Climate Dynamics, 49 (5-6), 2115–2129.
653
Cox, P. M., C. Huntingford, and M. S. Williamson, 2018: Emergent constraint on equilibrium
654
climate sensitivity from global temperature variability. Nature, 553 (7688), 319–322, doi:10.
655
1038/nature25450, URL https://www.nature.com/articles/nature25450.
656
Crook, J. A., P. M. Forster, and N. Stuber, 2011: Spatial Patterns of Modeled Climate Feedback and
657
Contributions to Temperature Response and Polar Amplification. Journal of Climate, 24 (14),
658
3575–3592.
659
Dessler, A. E., 2010: A Determination of the Cloud Feedback from Climate Variations over the
660
Past Decade. Science, 330 (6010), 1523–1527.
Dessler, A. E., 2012: Observations of Climate Feedbacks over 2000-10 and Comparisons to Cli-
662
mate Models. Journal of Climate, 26 (1), 333–342.
663
Dessler, A. E., T. Mauritsen, and B. Stevens, 2018: The influence of internal variability on Earth’s
664
energy balance framework and implications for estimating climate sensitivity. Atmospheric
665
Chemistry and Physics, 18 (7), 5147–5155, doi:https://doi.org/10.5194/acp-18-5147-2018,
666
URL https://www.atmos-chem-phys.net/18/5147/2018/.
667
Dong, Y., C. Proistosescu, K. C. Armour, D. S. Battisti, Y. Dong, C. Proistosescu, K. C.
668
Armour, and D. S. Battisti, 2019: Attributing Historical and Future Evolution of Radia-
669
tive Feedbacks to Regional Warming Patterns using a Green’s Function Approach: The Pre-
670
eminence of the Western Pacific. Journal of Climate, doi:10.1175/JCLI-D-18-0843.1, URL
671
https://journals.ametsoc.org/doi/abs/10.1175/JCLI-D-18-0843.1.
672
Feldl, N., and G. H. Roe, 2013a: Four perspectives on climate feedbacks. Geophysical Research
673
Letters, 40 (15), 4007–4011.
674
Feldl, N., and G. H. Roe, 2013b: The Nonlinear and Nonlocal Nature of Climate Feedbacks.
675
Journal of Climate, 26 (21), 8289–8304, doi:10.1175/JCLI-D-12-00631.1.
676
Forster, P. M. F., and J. M. Gregory, 2006: The Climate Sensitivity and Its Components Diagnosed
677
from Earth Radiation Budget Data. Journal of Climate, 19 (1), 39–52.
678
Fueglistaler, S., 2019: Observational Evidence for Two Modes of Coupling Between Sea Surface
679
Temperatures, Tropospheric Temperature Profile, and Shortwave Cloud Radiative Effect in the
680
Tropics. Geophysical Research Letters, 46 (16), 9890–9898, doi:10.1029/2019GL083990, URL
681
https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2019GL083990.
Gregory, J., and M. Webb, 2008: Tropospheric Adjustment Induces a Cloud Component in CO2
683
Forcing. Journal of Climate, 21 (1), 58–71, doi:10.1175/2007JCLI1834.1.
684
Gregory, J. M., and T. Andrews, 2016: Variation in climate sensitivity and feedback
685
parameters during the historical period. Geophysical Research Letters, 43 (8), 3911–
686
3920, doi:10.1002/2016GL068406, URL https://agupubs.onlinelibrary.wiley.com/doi/abs/10.
687
1002/2016GL068406.
688
Gregory, J. M., R. J. Stouffer, S. C. B. Raper, P. A. Stott, and N. A. Rayner, 2002: An Obser-
689
vationally Based Estimate of the Climate Sensitivity. Journal of Climate, 15 (22), 3117–3121,
690
doi:10.1175/1520-0442(2002)015h3117:AOBEOTi2.0.CO;2.
691
Jim´enez-de-la Cuesta, D., and T. Mauritsen, 2019: Emergent constraints on Earths transient
692
and equilibrium response to doubled CO 2 from post-1970s global warming. Nature Geo-
693
science, 12 (11), 902–905, doi:10.1038/s41561-019-0463-y, URL https://www.nature.com/
694
articles/s41561-019-0463-y.
695
Jonko, A. K., K. M. Shell, B. M. Sanderson, and G. Danabasoglu, 2012: Climate Feedbacks in
696
CCSM3 under Changing CO2 Forcing. Part II: Variation of Climate Feedbacks and Sensitivity
697
with Forcing. Journal of Climate, 26 (9), 2784–2795, doi:10.1175/JCLI-D-12-00479.1.
698
Klein, S. A., A. Hall, J. R. Norris, and R. Pincus, 2017: Low-Cloud Feedbacks from Cloud-
699
Controlling Factors: A Review. Surveys in Geophysics, 38 (6), 1307–1329.
700
Klein, S. A., and D. L. Hartmann, 1993: The Seasonal Cycle of Low Stratiform Clouds. Journal
701
of Climate, 6 (8), 1587–1606.
702
Klein, S. A., B. J. Soden, and N.-C. Lau, 1999: Remote Sea Surface Temperature Variations during
703
ENSO: Evidence for a Tropical Atmospheric Bridge. Journal of Climate, 12 (4), 917–932, doi:
10.1175/1520-0442(1999)012h0917:RSSTVDi2.0.CO;2, URL https://journals.ametsoc.org/
705
doi/full/10.1175/1520-0442%281999%29012%3C0917%3ARSSTVD%3E2.0.CO%3B2.
706
Koll, D. D. B., and T. W. Cronin, 2018: Earth’s outgoing longwave radiation linear due to H2o
707
greenhouse effect. Proceedings of the National Academy of Sciences, 115 (41), 10 293–10 298,
708
doi:10.1073/pnas.1809868115, URL https://www.pnas.org/content/115/41/10293.
709
Leconte, J., F. Forget, B. Charnay, R. Wordsworth, and A. Pottier, 2013: Increased insolation
710
threshold for runaway greenhouse processes on Earth-like planets. Nature, 504 (7479), 268–
711
271, doi:10.1038/nature12827.
712
Lewis, N., and J. Curry, 2018: The Impact of Recent Forcing and Ocean Heat Uptake Data
713
on Estimates of Climate Sensitivity. Journal of Climate, 31 (15), 6051–6071, doi:10.1175/
714
JCLI-D-17-0667.1.
715
Lewis, N., and J. A. Curry, 2015: The implications for climate sensitivity of AR5 forcing and heat
716
uptake estimates. Climate Dynamics, 45 (3-4), 1009–1023.
717
Li, W., and C. E. Forest, 2014: Estimating the Sensitivity of the Atmospheric Teleconnec-
718
tion Patterns to SST Anomalies Using a Linear Statistical Method. Journal of Climate,
719
27 (24), 9065–9081, doi:10.1175/JCLI-D-14-00231.1, URL https://journals.ametsoc.org/doi/
720
full/10.1175/JCLI-D-14-00231.1.
721
Li, W., C. E. Forest, and J. Barsugli, 2012: Comparing two methods to estimate the sensitivity of
722
regional climate simulations to tropical SST anomalies. Journal of Geophysical Research: At-
723
mospheres, 117 (D20), doi:10.1029/2011JD017186, URL https://agupubs.onlinelibrary.wiley.
724
com/doi/abs/10.1029/2011JD017186.
Libardoni, A. G., C. E. Forest, A. P. Sokolov, and E. Monier, 2019: Underestimating Internal Vari-
726
ability Leads to Narrow Estimates of Climate System Properties. Geophysical Research Letters,
727
46 (16), 10 000–10 007, doi:10.1029/2019GL082442, URL https://agupubs.onlinelibrary.wiley.
728
com/doi/abs/10.1029/2019GL082442.
729
Lindzen, R. S., M.-D. Chou, and A. Y. Hou, 2001: Does the Earth Have an Adaptive In-
730
frared Iris? Bulletin of the American Meteorological Society, 82 (3), 417–432, doi:10.1175/
731
1520-0477(2001)082h0417:DTEHAAi2.3.CO;2, URL https://journals.ametsoc.org/doi/abs/10.
732
1175/1520-0477%282001%29082%3C0417%3ADTEHAA%3E2.3.CO%3B2.
733
Liu, F., J. Lu, O. Garuba, L. R. Leung, Y. Luo, and X. Wan, 2018: Sensitivity of Surface
734
Temperature to Oceanic Forcing via q-Flux Greens Function Experiments. Part I: Linear Re-
735
sponse Function. Journal of Climate, 31 (9), 3625–3641, doi:10.1175/JCLI-D-17-0462.1, URL
736
https://journals.ametsoc.org/doi/10.1175/JCLI-D-17-0462.1.
737
Liu, Z., N. Wen, and Y. Liu, 2008: On the Assessment of Nonlocal Climate Feedback. Part I:
738
The Generalized Equilibrium Feedback Assessment. Journal of Climate, 21 (1), 134–148, doi:
739
10.1175/2007JCLI1826.1, URL http://journals.ametsoc.org/doi/abs/10.1175/2007JCLI1826.1.
740
Lutsko, N. J., and M. Popp, 2019: Probing the Sources of Uncertainty in Transient
741
Warming on Different Timescales. Geophysical Research Letters, 46 (20), 11 367–11 377,
742
doi:10.1029/2019GL084018, URL https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/
743
2019GL084018.
744
Lutsko, N. J., and K. Takahashi, 2018: What Can the Internal Variability of CMIP5 Models Tell
745
Us about Their Climate Sensitivity? Journal of Climate, 31 (13), 5051–5069, doi:10.1175/
746
JCLI-D-17-0736.1.
Mauritsen, T., and B. Stevens, 2015: Missing iris effect as a possible cause of muted hydrological
748
change and high climate sensitivity in models. Nature Geoscience, 8 (5), 346–351, doi:10.1038/
749
ngeo2414, URL https://www.nature.com/articles/ngeo2414.
750
Meraner, K., T. Mauritsen, and A. Voigt, 2013: Robust increase in equilibrium climate sensitivity
751
under global warming. Geophysical Research Letters, 40 (22), 5944–5948.
752
Murphy, D. M., S. Solomon, R. W. Portmann, K. H. Rosenlof, P. M. Forster, and T. Wong, 2009:
753
An observationally based energy balance for the Earth since 1950. Journal of Geophysical Re-
754
search: Atmospheres, 114 (D17).
755
Murphy, J. M., 1995: Transient Response of the Hadley Centre Coupled Ocean-Atmosphere
756
Model to Increasing Carbon Dioxide. Part 1: Control Climate and Flux Adjustment. Journal
757
of Climate, 8 (1), 36–56.
758
Otto, A., and Coauthors, 2013: Energy budget constraints on climate response. Nature Geoscience,
759
6 (6), 415.
760
Po-Chedley, S., K. C. Armour, C. M. Bitz, M. D. Zelinka, B. D. Santer, and Q. Fu, 2018: Sources
761
of intermodel spread in the lapse rate and water vapor feedbacks. Journal of Climate.
762
Proistosescu, C., A. Donohoe, K. C. Armour, G. H. Roe, M. F. Stuecker, and C. M. Bitz, 2018: Ra-
763
diative Feedbacks From Stochastic Variability in Surface Temperature and Radiative Imbalance.
764
Geophysical Research Letters, 45 (10), 5082–5094, doi:10.1029/2018GL077678.
765
Proistosescu, C., and P. J. Huybers, 2017: Slow climate mode reconciles historical and model-
766
based estimates of climate sensitivity. Science Advances, 3 (7), e1602 821, doi:10.1126/sciadv.
767
1602821.
Roe, G. H., and M. B. Baker, 2007: Why Is Climate Sensitivity So Unpredictable? Science,
769
318 (5850), 629–632, doi:10.1126/science.1144735.
770
Rose, B. E. J., K. C. Armour, D. S. Battisti, N. Feldl, and D. D. B. Koll, 2014: The dependence of
771
transient climate sensitivity and radiative feedbacks on the spatial pattern of ocean heat uptake.
772
Geophysical Research Letters, 41 (3), 1071–1078.
773
Rose, B. E. J., and L. Rayborn, 2016: The Effects of Ocean Heat Uptake on Transient Climate
774
Sensitivity. Current Climate Change Reports, 2 (4), 190–201.
775
Rugenstein, M., and Coauthors, 2019: LongRunMIP - motivation and design for a large col-
776
lection of millennial-length AO-GCM simulations. Bulletin of the American Meteorological
777
Society, doi:10.1175/BAMS-D-19-0068.1, URL https://journals.ametsoc.org/doi/abs/10.1175/
778
BAMS-D-19-0068.1.
779
Rugenstein, M. A. A., K. Caldeira, and R. Knutti, 2016: Dependence of global radiative feedbacks
780
on evolving patterns of surface heat fluxes. Geophysical Research Letters, 43 (18), 9877–9885,
781
doi:10.1002/2016GL070907.
782
Seager, R., M. Cane, N. Henderson, D.-E. Lee, R. Abernathey, and H. Zhang, 2019: Strengthening
783
tropical Pacific zonal sea surface temperature gradient consistent with rising greenhouse gases.
784
Nature Climate Change, 9 (7), 517–522, doi:10.1038/s41558-019-0505-x, URL https://www.
785
nature.com/articles/s41558-019-0505-x.
786
Senior, C. A., and J. F. B. Mitchell, 2000: The time-dependence of climate sensitivity. Geophysical
787
Research Letters, 27 (17), 2685–2688.
788
Soden, B. J., A. J. Broccoli, and R. S. Hemler, 2004: On the Use of Cloud Forcing to Estimate
789
Cloud Feedback. Journal of Climate, 17 (19), 3661–3665.
Spencer, R. W., and W. D. Braswell, 2008: Potential Biases in Feedback Diagnosis from Observa-
791
tional Data: A Simple Model Demonstration. Journal of Climate, 21 (21), 5624–5628, doi:10.
792
1175/2008JCLI2253.1, URL https://journals.ametsoc.org/doi/full/10.1175/2008JCLI2253.1.
793
Spencer, R. W., and W. D. Braswell, 2011: On the Misdiagnosis of Surface Temperature Feed-
794
backs from Variations in Earth’s Radiant Energy Balance. Remote Sensing, 3 (8), 1603–1613,
795
doi:10.3390/rs3081603, URL https://www.mdpi.com/2072-4292/3/8/1603.
796
Trenberth, K. E., Y. Zhang, J. T. Fasullo, and S. Taguchi, 2015: Climate variability and relation-
797
ships between top-of-atmosphere radiation and temperatures on Earth. Journal of Geophysical
798
Research: Atmospheres, 120 (9), 3642–3659, doi:10.1002/2014JD022887.
799
Watterson, I. G., 2000: Interpretation of Simulated Global Warming Using a Simple Model. Jour-
800
nal of Climate, 13 (1), 202–215.
801
Wetherald, R. T., and S. Manabe, 1988: Cloud Feedback Processes in a General Circulation
802
Model. Journal of the Atmospheric Sciences, 45 (8), 1397–1416, doi:10.1175/1520-0469(1988)
803
045h1397:CFPIAGi2.0.CO;2.
804
Winton, M., K. Takahashi, and I. M. Held, 2010: Importance of Ocean Heat Uptake Efficacy to
805
Transient Climate Change. Journal of Climate, 23 (9), 2333–2344, doi:10.1175/2009JCLI3139.
806
1.
807
Wood, R., and C. S. Bretherton, 2006: On the Relationship between Stratiform Low Cloud Cover
808
and Lower-Tropospheric Stability. Journal of Climate, 19 (24), 6425–6432.
809
Zelinka, M. D., S. A. Klein, and D. L. Hartmann, 2012: Computing and Partitioning Cloud Feed-
810
backs Using Cloud Property Histograms. Part I: Cloud Radiative Kernels. Journal of Climate,
811
25 (11), 3715–3735.
Zhou, C., M. D. Zelinka, and S. A. Klein, 2016: Impact of decadal cloud variations on the Earth’s
813
energy budget. Nature Geoscience, 9 (12), 871–874, doi:10.1038/ngeo2828, URL https://www.
814
nature.com/articles/ngeo2828.
815
Zhou, C., M. D. Zelinka, and S. A. Klein, 2017: Analyzing the dependence of global cloud feed-
816
back on the spatial pattern of sea surface temperature change with a Green’s function approach.
817
Journal of Advances in Modeling Earth Systems, 9 (5), 2174–2189.
LIST OF TABLES
819
Table 1. Feedback errors. Root mean square errors of estimates of abrupt4x feedbacks
820
(λ4x,early, λ4x,late) and their change with time (∆λ4x), for net TOA fluxes and 821
each component flux (in Wm−2K−1) and for the seasonal versions of the three
822
methods presented in Section 2 (see Appendix for details). For annual and
823
monthly values, see Table S2, and for fluxes north of 30◦S, see Table S5. . . 43
824
Table 2. Spatial errors. The model-mean area-weighted root mean square error of esti-
825
mates of the warming-normalized change in TOA fluxes during the early and
826
late periods of the abrupt4x simulations, and the change in pattern between
827
these period (see Appendix for details). All values have units of Wm−2K−1.
828
For annual and monthly versions in addition to seasonal, see Table S2, for in-
829
dividual models see Table S4, and for fluxes north of 30◦S, see Table S6. . . 44
TABLE1. Feedback errors. Root mean square errors of estimates of abrupt4x feedbacks (λ4x,early, λ4x,late) and
their change with time (∆λ4x), for net TOA fluxes and each component flux (in Wm−2K−1) and for the seasonal
versions of the three methods presented in Section 2 (see Appendix for details). For annual and monthly values, see Table S2, and for fluxes north of 30◦S, see Table S5.
831
832
833
834
net LW clear SW clear LW cloud SW cloud
MR global local MR global local MR global local MR global local MR global local
early 0.69 0.74 2.54 0.08 0.12 0.63 0.18 0.48 1.21 0.13 0.23 0.02 0.45 0.55 1.19
late 0.29 0.26 1.87 0.15 0.21 0.47 0.13 0.52 1.09 0.31 0.35 0.17 0.2 0.6 0.65
TABLE2. Spatial errors. The model-mean area-weighted root mean square error of estimates of the warming- normalized change in TOA fluxes during the early and late periods of the abrupt4x simulations, and the change in pattern between these period (see Appendix for details). All values have units of Wm−2K−1. For annual and monthly versions in addition to seasonal, see Table S2, for individual models see Table S4, and for fluxes north of 30◦S, see Table S6. 835 836 837 838 839
net LW clear SW clear LW cloud SW cloud
MR global local MR global local MR global local MR global local MR global local
early 1.02 3.41 2.77 0.33 2.29 1.02 0.7 5.23 2.15 0.82 1.09 0.71 1.05 5.15 2.25
late 0.8 3.08 1.86 0.34 2.27 0.75 0.52 5.13 1.67 1.28 1.21 1.03 1.09 5.1 1.85
LIST OF FIGURES
840
Fig. 1. A schematic representation of the conceptual model used in Section 2, consisting of an over-
841
turning cell with a convecting (1) and a subsiding (2) region. Warming of the surface tem-
842
perature T1has nonlocal effects: it increases the horizontal heat transport H, and it changes 843
properties of the atmosphere aloft in region 2 that affect its net top-of-atmosphere radiative
844
flux, N2, for instance by warming its free troposphere, increasing its lower tropospheric sta- 845
bility, and therefore increasing its low cloud cover. The dependence of N2on T1(holding T2 846
fixed) is an example of a nonlocal radiative feedback. . . 47
847
Fig. 2. Two experiments are performed with the conceptual model in Equation 1: an unforced “con-
848
trol” simulation (panels a,b) and a forced “abrupt4x” simulation (panels c,d). Values of N vs.
849
T0from each experiment are given by the black dots in panels a and c, representing annual
850
averages for the control simulation and exponentially increasing averages for the abrupt4x
851
simulation. The global method assumes that the slope of the regression in panel a (blue line)
852
gives the slope of the black dots in the lower left panel, underestimating the increase in this
853
slope over time (blue lines and markers, panels c,d). The local method regresses Ni0against
854
Ti0to estimate λi for both regions (dotted lines, panel b), which leads to an overestimate of 855
the combined feedback associated with region 1 (λ1= λ1,1+ λ2,1, dotted red line in panel 856
b), and therefore an overestimate of the feedback early on (orange lines and markers, panels
857
c,d). The MR method, given sufficient years to regress over, correctly estimates all spatial
858
feedbacks (dashed lines, panel b), accurately predicting the feedbacks and its change with
859
time (green lines and markers, panels c,d). . . 48
860
Fig. 3. Plots of N vs. T0for control simulations of six coupled atmosphere-ocean general circulation
861
models (see Table S1 for details). We use the simulations to estimate spatial feedbacks using
862
the global, local, and MR methods. We regrid simulations to 15◦ × 15◦ grids, giving 288
863
regions. . . 49
864
Fig. 4. N vs. T0for abrupt4x simulations of the same six GCMs from Figure 3 (black dots). Col-
865
ored dots show estimates of Nabrupt4x(t) made using the spatial feedbacks inferred from each 866
model’s control simulation and its spatial pattern of warming (~Tabrupt4x0 (t)) using the three
867
methods described in the text; year one is not included in any method. Larger dots repre-
868
sent averages taken over exponentially increasing periods, except gray dots, which show all
869
years. Solid lines show local regressions using LOESS. Global estimates for GISSE2R does
870
not appear because it is nearly identical with MR estimates. . . 50
871
Fig. 5. True and estimated abrupt4x feedbacks as a function of time calculated using slopes of
872
the local regression from Figure 4 (solid lines). Vertical dotted lines show the division
873
between the early (2-20 years) and late (21-end) periods. Dots show true and estimated
874
values of λ4x,earlyand λ4x,late. Feedbacks get more positive over time for all models. The MR 875
and global methods initially overestimate feedbacks. The MR estimate increases with time
876
as well, while the global method predicts a roughly constant feedback. The local method
877
greatly overestimates the true feedback for all models except GISSE2R. Figures S2-5 give
878
the same plot for component fluxes. . . 51
879
Fig. 6. True vs. estimated feedbacks for the early (panels a, b, and c) and late (panels d, e, and f)
880
periods and the change between them (panels g, h, and i). Black dots give values for the net
881
feedback, while colored markers give values of the component feedbacks, which sum to the
882
net feedback. The MR and global methods overestimate the early feedback due to SW cloud
883
(red) feedbacks. The MR estimate of the late period has a small error across all components
884
(panel d), while the global estimate has a smaller net error due to offsetting errors between
885
LW and SW cloud feedbacks (panel e). As in Figure 5, the MR method is able to capture
some of the change in feedback, while the global method does not. The local method greatly
887
overestimates the net feedback, primarily due to cloud feedbacks. Numerical values of the
888
feedbacks are given in Table S7 and S8. . . 52
889
Fig. 7. Multi-model mean spatial pattern of net TOA flux change associated with the early (top
890
row) and late (middle row) periods and the change between them (bottom row), calculated
891
by taking the finite difference across each period. Changes are normalized by the total
892
warming in each period, giving units of Wm−2K−1. The MR method is close to the true
893
pattern except for overestimates south of 30◦S and during the early period in the North
894
Atlantic. This holds for individual flux components as well (Figures S9-S17). The global
895
and local methods both have substantial errors over most of the globe. Figures S6-S8 show
896
errors (estimates - true values) for the multi-model mean and individual models. . . 53
897
Fig. 8. Net cloud feedbacks associated with warming in regions circled in green estimated for
898
CAM5 by Zhou et al. (2017) using fixed-SST experiments (panels a, b, and c) or as a multi-
899
model and multi-season mean using the MR method (panels d, e, and f). For perturbations
900
outside of tropical convecting regions (panels a, c, d, and f), the effects are mostly local and
901
positive, while perturbations in tropical convecting regions have significant negative nonlo-
902
cal effects in many regions of the Earth (panels b, e). Note that fixed-SST experiments allow
903
some land warming in response to these perturbations (panel b), while the MR method is
904
agnostic about whether the surface is land or ocean, and so does not include resulting land
905
warming (panel e). . . 54
906
Fig. 9. Multi-model and multi-season mean spatial feedbacks estimated by the MR method. Panel