Articles | Volume 6, issue 2
https://doi.org/10.5194/ascmo-6-91-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/ascmo-6-91-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
A new energy-balance approach to linear filtering for estimating effective radiative forcing from temperature time series
Department of Mathematics, University of Exeter, Exeter, UK
David B. Stephenson
Department of Mathematics, University of Exeter, Exeter, UK
Peter A. Stott
Department of Mathematics, University of Exeter, Exeter, UK
Met Office Hadley Centre, Exeter, UK
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Cited articles
Adler, A.: Pade: Padé Approximant Coefficients,
available at: https://CRAN.R-project.org/package=Pade (last access: 9 August 2019), R package version
0.1-4, 2015. a
Aldrin, M., Holden, M., Guttorp, P., Skeie, R. B., Myhre, G., and Berntsen,
T. K.: Bayesian estimation of climate sensitivity based on a simple climate
model fitted to observations of hemispheric temperatures and global ocean
heat content, Environmetrics, 23, 253–271, https://doi.org/10.1002/env.2140,
2012. a
Allen, M. R. and Stott, P. A.: Estimating Signal Amplitudes in Optimal
Fingerprinting, Part I: Theory, Clim. Dynam., 21, 477–491,
https://doi.org/10.1007/s00382-003-0313-9, 2003. a
Allen, M. R. and Tett, S. F. B.: Checking for Model Consistency in Optimal
Fingerprinting, Clim. Dynam., 15, 419–434, https://doi.org/10.1007/s003820050291, 1999. a
Álvarez, M., Luengo, D., and Lawrence, N. D.: Latent Force Models, in:
Proceedings of the Twelth International Conference on Artificial Intelligence
and Statistics, edited by: van Dyk, D. and Welling, M., vol. 5 of
Proceedings of Machine Learning Research, pp. 9–16, PMLR, Hilton
Clearwater Beach Resort, Clearwater Beach, Florida USA,
available at: http://proceedings.mlr.press/v5/alvarez09a.html (last access: 10 May 2020), 2009. a
Andrews, T. and Forster, P. M.: Energy budget constraints on historical
radiative forcing, Nat. Clim. Change, 10, 313–316, 2020. a
Andrews, T., Andrews, M. B., Bodas-Salcedo, A., Jones, G. S., Kulhbrodt, T.,
Manners, J., Menary, M. B., Ridley, J., Ringer, M. A., Sellar, A. A., Senior,
C. A., and Tang, Y.: Forcings, Feedbacks and Climate Sensitivity in
HadGEM3-GC3.1 and UKESM1, J. Adv. Model. Earth Syst.,
https://doi.org/10.1029/2019MS001866,
2019 (data available at: https://github.com/timothyandrews/HadGEM3-ERF-Timeseries, last access: 10 December 2019). a, b, c, d, e
Annan, J., Hargreaves, J., Edwards, N., and Marsh, R.: Parameter estimation in
an intermediate complexity earth system model using an ensemble Kalman
filter, Ocean Model., 8, 135–154,
https://doi.org/10.1016/j.ocemod.2003.12.004,
2005. a
Brockwell, P. J. and Davis, R. A.: Introduction to Time Series and Forecasting, 2nd edn.,
Springer, New York, https://doi.org/10.1007/b97391, 2002. a
Chang, M. K., Kwiatkowski, J. W., Nau, R. F., Oliver, R. M., and Pister, K. S.:
Arma Models for Earthquake Ground Motions, Earthquake Engineering &
Struct. Dynam., 10, 651–662, https://doi.org/10.1002/eqe.4290100503,
1982. a
Chung, E.-S. and Soden, B. J.: An Assessment of Methods for Computing Radiative
Forcing in Climate Models, Environ. Res. Lett., 10, 074004,
https://doi.org/10.1088/1748-9326/10/7/074004, 2015. a
Cohen, J. B. and Wang, C.: Estimating global black carbon emissions using a
top-down Kalman Filter approach, J. Geophys. Res.-Atmos., 119, 307–323, https://doi.org/10.1002/2013JD019912,
2014. a
Cowtan, K. and Way, R. G.: Coverage Bias in the HadCRUT4 Temperature Series
and its Impact on Recent Temperature Trends, Q. J. Roy.
Meteor. Soc., 140, 1935–1944, https://doi.org/10.1002/qj.2297,
2014 (data available at: https://www-users.york.ac.uk/~kdc3/papers/coverage2013/had4_krig_annual_v2_0_0.txt, last access: 29 November 2019). a, b
De Groen, P. and De Moor, B.: The fit of a sum of exponentials to noisy
data, J. Comput. Appl. Math., 20, 175–187,
https://doi.org/10.1016/0377-0427(87)90135-X,
1987. a
De Jong, P. and Penzer, J.: The ARMA model in state space form, Stat. Probabil. Lett., 70, 119–125,
https://doi.org/10.1016/j.spl.2004.08.006,
2004. a
Flato, G., Marotzke, J., Abiodun, B.,
Braconnot, P., Chou, S. C., Collins, W., Cox, P., Driouech, F., Emori, S., Eyring, V., Forest, C.,
Gleckler, P., Guilyardi, E., Jakob, C., Kattsov, V., Reason, C., and Rummukainen, M.:
Evaluation of Climate Models, in: Climate Change 2013: The Physical Science Basis,
Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental
Panel on Climate Change, edited by: Stocker, T. F., Qin, D., Plattner, G.-K., Tignor, M., Allen, S. K.,
Boschung, J., Nauels, A., Xia, Y., Bex, V., and Midgley, P. M., Cambridge University Press,
Cambridge, United Kingdom and New York, NY, USA,
2013. a
Forster, P. M., Richardson, T., Maycock, A. C., Smith, C. J., Samset, B. H.,
Myhre, G., Andrews, T., Pincus, R., and Schulz, M.: Recommendations for
Diagnosing Effective Radiative Forcing from Climate Models for CMIP6,
J. Geophys. Res.-Atmos., 121, 12460–12475,
https://doi.org/10.1002/2016JD025320,
2016. a, b
Fredriksen, H. B. and Rypdal, M.: Long-Range Persistence in Global Surface
Temperatures Explained by Linear Multibox Energy Balance Models, J.
Climate, 30, 7157–7168, https://doi.org/10.1175/jcli-d-16-0877.1, 2017. a
Geoffroy, O., Saint-Martin, D., Olivie, D. J. L., Voldoire, A., Bellon, G., and
Tyteca, S.: Transient Climate Response in a Two-Layer Energy-Balance Model.
Part I: Analytical Solution and Parameter Calibration Using CMIP5 AOGCM
Experiments, J. Climate, 26, 1841–1857,
https://doi.org/10.1175/jcli-d-12-00195.1, 2013. a, b
Good, P., Gregory, J. M., and Lowe, J. A.: A Step-Response Simple Climate Model
to Reconstruct and Interpret AOGCM Projections, Geophys. Res. Lett.,
38, L01703, https://doi.org/10.1029/2010GL045208,
2011. a
Gregory, J. M.: Vertical Heat Transports in the Ocean and their Effect on
Time-Dependent Climate Change, Clim. Dynam., 16, 501–515,
https://doi.org/10.1007/s003820000059, 2000. a
Gregory, J. M., Ingram, W. J., Palmer, M. A., Jones, G. S., Stott, P. A.,
Thorpe, R. B., Lowe, J. A., Johns, T. C., and Williams, K. D.: A new method
for diagnosing radiative forcing and climate sensitivity, Geophys.
Res. Lett., 31, L03205, https://doi.org/10.1029/2003GL018747,
2004. a
Hasselmann, K.: Stochastic Climate Models Part I. Theory, Tellus, 28,
473–485, 1976. a
Hasselmann, K.: Multi-Pattern Fingerprint Method for Detection and Attribution
of Climate Change, Clim. Dynam., 13, 601–611,
https://doi.org/10.1007/s003820050185, 1997. a
Haustein, K., Allen, M. R., Forster, P. M., Otto, F. E. L., Mitchell, D. M.,
Matthews, H. D., and Frame, D. J.: A real-time Global Warming Index,
Sci. Rep.-UK, 7, 15417, https://doi.org/10.1038/s41598-017-14828-5, 2017. a
Held, I. M., Winton, M., Takahashi, K., Delworth, T., Zeng, F., and Vallis,
G. K.: Probing the Fast and Slow Components of Global Warming by Returning
Abruptly to Preindustrial Forcing, J. Climate, 23, 2418–2427,
https://doi.org/10.1175/2009JCLI3466.1, 2010. a, b
Johansson, D. J., O’Neill, B. C., Tebaldi, C., and Häggström, O.:
Equilibrium climate sensitivity in light of observations over the warming
hiatus, Nat. Clim. Change, 5, 449–453, 2015. a
Kalman, R. E.: A New Approach to Linear Filtering and Prediction Problems,
J. Basic. Eng.-T. ASME, 82, 35–45, 1960. a
Kaufmann, B.: Fitting a Sum of Exponentials to Numerical Data, ArXiv Physics
e-prints, available at: https://arxiv.org/abs/physics/0305019 (last access: 21 March 2019), 2003. a
Li, S. and Jarvis, A.: Long Run Surface Temperature Dynamics of an A-OGCM:
the HadCM3 4×CO2 Forcing Experiment Revisited, Clim.
Dynam., 33, 817–825, https://doi.org/10.1007/s00382-009-0581-0, 2009. a
Ljungqvist, G. J. E.: Decomposing global warming using Bayesian statistics,
PhD thesis, Chalmers University of Technology, Gothenburg, Sweden, 2015. a
Lourens, E., Reynders, E., Roeck], G. D., Degrande, G., and Lombaert, G.: An
augmented Kalman filter for force identification in structural dynamics,
Mech. Syst. Signal Pr., 27, 446–460,
https://doi.org/10.1016/j.ymssp.2011.09.025,
2012. a
Monahan, J. F.: Fully Bayesian analysis of ARMA time series models, J.
Econometrics, 21, 307–331,
https://doi.org/10.1016/0304-4076(83)90048-9,
1983. a
Morice, C. P., Kennedy, J. J., Rayner, N. A., and Jones, P. D.: Quantifying
Uncertainties in Global and Regional Temperature Change Using an Ensemble of
Observational Estimates: The HadCRUT4 Data Set, J. Geophys.
Res.-Atmos., 117, D08101, https://doi.org/10.1029/2011JD017187,
2012. a
Myhre, G., Shindell, D., Bréon, F.-M.,
Collins, W., Fuglestvedt, J., Huang, J., Koch, D., Lamarque, J.-F., Lee, D., Mendoza, B.,
Nakajima, T., Robock, A., Stephens, G., Takemura, T., and Zhang, H.: Anthropogenic and
Natural Radiative Forc-ing. In: Climate Change 2013: The Physical Science Basis,
Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental
Panel on Climate Change, edited by: Stocker, T. F., Qin, D., Plattner, G.-K., Tignor, M., Allen, S. K.,
Boschung, J., Nauels, A., Xia, Y., Bex, V., and Midgley, P. M., Cambridge University Press,
Cambridge, United Kingdom and New York, NY, USA, 2013. a, b
Otto, F. E., Frame, D. J., Otto, A., and Allen, M. R.: Embracing Uncertainty in
Climate Change Policy, Nat. Clim. Change, 5, 917–920,
https://doi.org/10.1038/nclimate2716, 2015. a
Padilla, L. E., Vallis, G. K., and Rowley, C. W.: Probabilistic Estimates of
Transient Climate Sensitivity Subject to Uncertainty in Forcing and Natural
Variability, J. Climate, 24, 5521–5537,
https://doi.org/10.1175/2011JCLI3989.1, 2011. a, b, c
Richardson, M., Cowtan, K., Hawkins, E., and Stolpe, M. B.: Reconciled climate
response estimates from climate models and the energy budget of Earth, Nat.
Clim. Change, 6, 931–935, 2016. a
Rypdal, K.: Attribution in the presence of a long-memory climate response, Earth Syst. Dynam., 6, 719–730, https://doi.org/10.5194/esd-6-719-2015, 2015. a
Särkkä, S., Álvarez, M. A., and Lawrence, N. D.: Gaussian process
latent force models for learning and stochastic control of physical systems,
IEEE T. Automat. Contr., 64, 2953–2960, 2018. a
signal developers: signal: Signal processing,
available at: http://r-forge.r-project.org/projects/signal/ (last access: 9 August 2019), 2014. a
Smith, C. J.,
Kramer, R. J., Myhre, G., Forster, P. M., Soden, B. J., Andrews, T., Boucher, O., Faluvegi, G.,
Fläschner, D., Hodnebrog, Ø., Kasoar, M., Kharin, V., Kirkevåg, A., Lamarque, J.‐F.,
Mülmenstädt, J., Olivié, D., Richardson, T., Samset, B. H., Shindell, D., Stier, P., Takemura, T.,
Voulgarakis, A., and Watson‐Parris, D.:
Understanding rapid adjustments to diverse forcing agents, Geophys.
Res. Lett., 45, 12023–12031,
https://doi.org/10.1029/2018GL079826, 2018. a
Spolia, S. and Chander, S.: Modelling of Surface Runoff Systems by an ARMA
Model, J. Hydrol., 22, 317–332,
https://doi.org/10.1016/0022-1694(74)90084-5,
1974. a, b
Stern, D. I.: A Three-Layer Atmosphere-Ocean Time Series Model of Global
Climate Change, Rensselaer Working Papers in Economics 0510, Rensselaer
Polytechnic Institute, Department of Economics,
available at: https://www.researchgate.net/publication/24125133_A_Three-Layer_Atmosphere-Ocean_Time_Series_Model_of_Global_Climate_Change (last access: 14 September 2020), 2005. a, b
Tanaka, K., Raddatz, T., O'Neill, B. C., and Reick, C. H.: Insufficient forcing
uncertainty underestimates the risk of high climate sensitivity, Geophys.
Res. Lett., 36, L16709, https://doi.org/10.1029/2009GL039642,
2009. a, b
Tsutsui, J.: Diagnosing Transient Response to CO2 Forcing in Coupled
Atmosphere-Ocean Model Experiments Using a Climate Model Emulator,
Geophys. Res. Lett., 47, e2019GL085844,
https://doi.org/10.1029/2019GL085844, 2020. a
Urban, N. M. and Keller, K.: Probabilistic hindcasts and projections of the
coupled climate, carbon cycle and Atlantic meridional overturning circulation
system: a Bayesian fusion of century-scale observations with a simple model,
Tellus A, 62, 737–750,
https://doi.org/10.1111/j.1600-0870.2010.00471.x, 2010.
a
Urban, N. M., Holden, P. B., Edwards, N. R., Sriver, R. L., and Keller, K.:
Historical and future learning about climate sensitivity, Geophys.
Res. Lett., 41, 2543–2552, https://doi.org/10.1002/2014GL059484,
2014. a
Vial, J., Dufresne, J.-L., and Bony, S.: On the interpretation of inter-model
spread in CMIP5 climate sensitivity estimates, Clim. Dynam., 41,
3339–3362, 2013. a
Wood, S. N.: Fast Stable Restricted Maximum Likelihood and Marginal Likelihood
Estimation of Semiparametric Generalized Linear Models, J. Roy.
Statist. Soc.-Ser. B, 73, 3–36,
https://doi.org/10.1111/j.1467-9868.2010.00749.x,
2011. a
Yu, D. and Chakravorty, S.: An autoregressive (AR) model based stochastic
unknown input realization and filtering technique, in: 2015 American Control
Conference (ACC), pp. 1499–1504, IEEE, 2015. a
Short summary
We have developed a novel and fast statistical method for diagnosing effective radiative forcing (ERF), a measure of the net effect of greenhouse gas emissions on Earth's energy budget. Our method works by inverting a recursive digital filter energy balance representation of global climate models and has been successfully validated using simulated data from UK Met Office climate models. We have estimated time series of historical ERF by applying our method to the global temperature record.
We have developed a novel and fast statistical method for diagnosing effective radiative forcing...