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How Ominous is the Premonition of Future Global Warming?

Debashis Chatterjee, Sourabh Bhattacharya

Abstract

Global warming, the phenomenon of increasing global average temperature in the recent decades, is receiving wide attention due to its very significant adverse effects on climate. Whether global warming will continue even in the future, is a question that is most important to investigate. In this regard, the so-called general circulation models (GCMs) have attempted to project the future climate, and nearly all of them exhibit alarming rates of global temperature rise in the future. Although global warming in the current time frame is undeniable, it is important to assess the validity of the future predictions of the GCMs. In this article, we attempt such a study using our recently-developed Bayesian multiple testing paradigm for model selection in inverse regression problems. The model we assume for the global temperature time series is based on Gaussian process emulation of the black box scenario, realistically treating the dynamic evolution of the time series as unknown. We apply our ideas to datasets available from the Intergovernmental Panel on Climate Change (IPCC) website. The best GCM models selected by our method under different assumptions on future climate change scenarios do not convincingly support the present global warming pattern when only the future predictions are considered known. Using our Gaussian process idea, we also forecast the future temperature time series given the current one. Interestingly, our results do not support drastic future global warming predicted by almost all the GCM models.

How Ominous is the Premonition of Future Global Warming?

Abstract

Global warming, the phenomenon of increasing global average temperature in the recent decades, is receiving wide attention due to its very significant adverse effects on climate. Whether global warming will continue even in the future, is a question that is most important to investigate. In this regard, the so-called general circulation models (GCMs) have attempted to project the future climate, and nearly all of them exhibit alarming rates of global temperature rise in the future. Although global warming in the current time frame is undeniable, it is important to assess the validity of the future predictions of the GCMs. In this article, we attempt such a study using our recently-developed Bayesian multiple testing paradigm for model selection in inverse regression problems. The model we assume for the global temperature time series is based on Gaussian process emulation of the black box scenario, realistically treating the dynamic evolution of the time series as unknown. We apply our ideas to datasets available from the Intergovernmental Panel on Climate Change (IPCC) website. The best GCM models selected by our method under different assumptions on future climate change scenarios do not convincingly support the present global warming pattern when only the future predictions are considered known. Using our Gaussian process idea, we also forecast the future temperature time series given the current one. Interestingly, our results do not support drastic future global warming predicted by almost all the GCM models.

Paper Structure

This paper contains 31 sections, 49 equations, 8 figures, 4 tables.

Table of Contents

  1. Introduction
  2. An overview of our methodological contributions
  3. Compositional GP emulator for nonparametric climate dynamics
  4. Hierarchical structure induced by our GP approach
  5. Joint distribution of $\{x_t:t=1,\ldots,T\}$
  6. The key concept
  7. Auxiliary variables for emulating the look-up table
  8. Distribution of $x_t$ given $\mathbf D^*_n$
  9. Summary of the look-up table procedure
  10. Joint distribution of $\{x_1,\ldots,x_{T},\mathbf D^*_n\}$
  11. Non-Markovian dependence structure of $\{x_1,\ldots,x_{T}\}$
  12. Prior distributions for $\hbox{\boldmath $\theta$}_f$ and $\sigma^2_\epsilon$
  13. Posterior distributions of current and future time series in our dynamic GP approach
  14. Posterior of current given the future
  15. Posterior of future given the current
  16. ...and 16 more sections

Figures (8)

  • Figure 1.1: Visualization of the HadCRUT4 data (thick, black line) and the GCM based time series. The temperature is in $\degree$C.
  • Figure 8.1: cFDR and cFNR for GCM selection in the climate scenarios A1B and A2 using Bayesian multiple testing.
  • Figure 8.2: cFDR and cFNR for GCM selection in the climate scenarios B1 and Commitment using Bayesian multiple testing.
  • Figure 8.3: The posteriors corresponding to the HadCRUT4 data or the current global temperature (CGT) conditional on GCM-based average time series are shown as colour plots with progressively higher densities depicted by progressively intense colours. Also shown are the HadCRUT4 data (CGT), GCM based time series (MBGT) and the average of GCM based time series (AMBGT). The temperature is in $\degree$C and in the log-scale.
  • Figure 8.4: The posteriors corresponding to the HadCRUT4 data or the current global temperature (CGT) conditional on individual best GCM time series are shown as colour plots with progressively higher densities depicted by progressively intense colours. Also shown are the HadCRUT4 data (CGT), GCM based time series (MBGT) and the average of GCM based time series (AMBGT). The temperature is in $\degree$C and in the log-scale.
  • ...and 3 more figures