Global temperature projections from a statistical energy balance model using multiple sources of historical data

This paper estimates a two-component energy balance model as a linear state space system (EBM-SS model) using historical data. It is a joint model for the temperature in the mixed layer, the temperature in the deep ocean layer, and radiative forcing. The EBM-SS model allows for the modeling of non-stationarity in forcing and the incorporation of multiple data sources for the unobserved processes. We estimate the EBM-SS model using historical datasets at the global level for the period 1955 to 2020 by maximum likelihood. We show in the empirical estimation and in simulations that using multiple data sources for the unobserved processes reduces parameter estimation uncertainty. When fitting the EBM-SS model to six observational global mean surface temperature (GMST) anomaly series, the GMST projections under Representative Concentration Pathway scenarios are comparable to those from Coupled Model Intercomparison Project models. The results show that a simple statistical climate model estimated on the historical period can produce GMST projections compatible with output from large-scale Earth System Models.

[1]  H. Addleman,et al.  NOAA National Centers for Environmental Information Fisheries Acoustics Archive Network Deep Dive , 2021 .

[2]  Geordie Z. Zhang,et al.  Regionally aggregated, stitched and de‐drifted CMIP‐climate data, processed with netCDF‐SCM v2.0.0 , 2021, Geoscience Data Journal.

[3]  J. Kennedy,et al.  An Updated Assessment of Near‐Surface Temperature Change From 1850: The HadCRUT5 Data Set , 2020, Journal of Geophysical Research: Atmospheres.

[4]  K. Trenberth,et al.  Improved Estimates of Changes in Upper Ocean Salinity and the Hydrological Cycle , 2020, Journal of Climate.

[5]  Jennifer L. Castle,et al.  Climate Econometrics: An Overview , 2020 .

[6]  P. Cox,et al.  Emergent constraints on transient climate response (TCR) and equilibrium climate sensitivity (ECS) from historical warming in CMIP5 and CMIP6 models , 2020 .

[7]  P. Stott,et al.  Optimal Estimation of Stochastic Energy Balance Model Parameters , 2020, Journal of Climate.

[8]  S. Sherwood,et al.  Emergent constraints on equilibrium climate sensitivity in CMIP5: do they hold for CMIP6? , 2020, Earth System Dynamics.

[9]  Z. Hausfather,et al.  The Berkeley Earth Land/Ocean Temperature Record , 2020, Earth System Science Data.

[10]  S. Seneviratne,et al.  Heat stored in the Earth system: where does the energy go? , 2020, Earth System Science Data.

[11]  R. Colman,et al.  Understanding the links between climate feedbacks, variability and change using a two-layer energy balance model , 2020, Climate Dynamics.

[12]  E. Mun,et al.  A comparison of Bayesian to maximum likelihood estimation for latent growth models in the presence of a binary outcome , 2020, International journal of behavioral development.

[13]  T. Mauritsen,et al.  Emergent constraints on Earth’s transient and equilibrium response to doubled CO2 from post-1970s global warming , 2019, Nature Geoscience.

[14]  Nathan Lenssen,et al.  Improvements in the GISTEMP Uncertainty Model , 2019, Journal of Geophysical Research: Atmospheres.

[15]  R. Colman,et al.  Climate variability from annual to multi-decadal timescales in a two-layer stochastic energy balance model: analytic solutions and implications for general circulation models , 2019, Tellus A: Dynamic Meteorology and Oceanography.

[16]  T. Cronin,et al.  Earth’s outgoing longwave radiation linear due to H2O greenhouse effect , 2018, Proceedings of the National Academy of Sciences.

[17]  John M. Reilly,et al.  Modeling Uncertainty in Integrated Assessment of Climate Change: A Multimodel Comparison , 2018, Journal of the Association of Environmental and Resource Economists.

[18]  N. Urban,et al.  Towards Bayesian hierarchical inference of equilibrium climate sensitivity from a combination of CMIP5 climate models and observational data , 2018, Climatic Change.

[19]  Christopher J. Smith,et al.  FAIR v1.3: a simple emissions-based impulse response and carbon cycle model , 2018, Geoscientific Model Development.

[20]  Robert F. Cahalan,et al.  Energy Balance Climate Models , 2017 .

[21]  J. Helske,et al.  KFAS: Exponential Family State Space Models in R , 2016, 1612.01907.

[22]  M. Flechsig,et al.  Integrating parameter uncertainty of a process-based model in assessments of climate change effects on forest productivity , 2016, Climatic Change.

[23]  E. Hawkins,et al.  Connecting Climate Model Projections of Global Temperature Change with the Real World , 2016 .

[24]  Jean-Pascal van Ypersele de Strihou.  Climate Change 2014 - Synthesis Report , 2015 .

[25]  K. Cowtan,et al.  Coverage bias in the HadCRUT4 temperature series and its impact on recent temperature trends , 2014 .

[26]  D. Saint‐Martin,et al.  Transient Climate Response in a Two-Layer Energy-Balance Model. Part I: Analytical Solution and Parameter Calibration Using CMIP5 AOGCM Experiments , 2013 .

[27]  J. Stock,et al.  Does temperature contain a stochastic trend: linking statistical results to physical mechanisms , 2013, Climatic Change.

[28]  Eric Winsberg.  Values and Uncertainties in the Predictions of Global Climate Models , 2012, Kennedy Institute of Ethics journal.

[29]  S. Levitus,et al.  World ocean heat content and thermosteric sea level change (0–2000 m), 1955–2010 , 2012 .

[30]  K. Calvin,et al.  The RCP greenhouse gas concentrations and their extensions from 1765 to 2300 , 2011 .

[31]  J. Hansen,et al.  Earth's energy imbalance and implications , 2011, 1105.1140.

[32]  T. Wigley,et al.  Emulating coupled atmosphere-ocean and carbon cycle models with a simpler model, MAGICC6 - Part 1: Model description and calibration , 2011 .

[33]  Tom M. L. Wigley,et al.  Emulating atmosphere-ocean and carbon cycle models with a simpler model, MAGICC6 – Part 2: Applications , 2011 .

[34]  T. Delworth,et al.  Probing the Fast and Slow Components of Global Warming by Returning Abruptly to Preindustrial Forcing , 2010 .

[35]  S. Schwartz.  Heat capacity, time constant, and sensitivity of Earth's climate system , 2007 .

[36]  Melvin J. Hinich,et al.  Time Series Analysis by State Space Methods , 2001 .

[37]  J. Gregory.  Vertical heat transports in the ocean and their effect on time-dependent climate change , 2000 .

[38]  Jerome Chappellaz,et al.  The Ice Record of Greenhouse Gases , 1993, Science.

[39]  Robert Sausen,et al.  On the cold start problem in transient simulations with coupled atmosphere-ocean models , 1992 .

[40]  D. C. Cox,et al.  Methods for Uncertainty Analysis: A Comparative Survey , 1981 .

[41]  G. Paltridge,et al.  Thermodynamic dissipation and the global climate system , 1981 .

[42]  W. Fuller,et al.  Distribution of the Estimators for Autoregressive Time Series with a Unit Root , 1979 .

[43]  G. Box,et al.  On a measure of lack of fit in time series models , 1978 .

[44]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[45]  C. Granger,et al.  Spurious regressions in econometrics , 1974 .

[46]  M. Budyko.  The effect of solar radiation variations on the climate of the Earth , 1969 .

[47]  William D. Sellers,et al.  A Global Climatic Model Based on the Energy Balance of the Earth-Atmosphere System. , 1969 .

[48]  P. Graefe.  Linear stochastic systems , 1966 .

[49]  Chang Sik Kim,et al.  Evaluating trends in time series of distributions: A spatial fingerprint of human effects on climate , 2020 .

[50]  Felix Pretis,et al.  Econometric modelling of climate systems: The equivalence of energy balance models and cointegrated vector autoregressions , 2020 .

[51]  Jennifer L. Castle,et al.  Modelling our Changing World , 2019 .

[52]  J. Thepaut,et al.  A reassessment of temperature variations and trends from global reanalyses and monthly surface climatological datasets , 2017 .

[53]  C. Kobayashi,et al.  The JRA-55 Reanalysis: General Specifications and Basic Characteristics , 2015 .

[54]  D. Shindell,et al.  Anthropogenic and Natural Radiative Forcing , 2014 .

[55]  M. Budyko.  The Effects of Changing the Solar Constant on the Climate of a General Circulation Model , 2008 .

[56]  J. Overpeck,et al.  Climate Change 2007: The Physical Science Basis , 2007 .

[57]  G. Casella,et al.  Generalized Accept-Reject sampling schemes , 2004 .

[58]  P. Imkeller.  Energy balance models — viewed from stochastic dynamics , 2001 .

[59]  Y. Ye,et al.  Interior Algorithms for Linear, Quadratic, and Linearly Constrained Convex Programming , 1997 .

[60]  Peter C. Young,et al.  Recursive forecasting, smoothing and seasonal adjustment of non‐stationary environmental data , 1991 .

[61]  Anil K. Bera,et al.  Efficient tests for normality, homoscedasticity and serial independence of regression residuals: Monte Carlo Evidence , 1981 .

[62]  Anil K. Bera,et al.  Efficient tests for normality, homoscedasticity and serial independence of regression residuals , 1980 .

[63]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..