Statistical analysis of global surface air temperature and sea level using cointegration methods

Global sea levels are rising which is widely understood as a consequence of thermal expansion and melting of glaciers and land-based ice caps. Due to physically-based models being unable to simulate observed sea level trends, semi-empirical models have been applied as an alternative for projecting of future sea levels. There is in this, however, potential pitfalls due to the trending nature of the time series. We apply a statistical method called cointegration analysis to observed global sea level and surface air temperature, capable of handling such peculiarities. We find a relationship between sea level and temperature and find that temperature causally depends on the sea level, which can be understood as a consequence of the large heat capacity of the ocean. We further find that the warming episode in the 1940s is exceptional in the sense that sea level and warming deviates from the expected relationship. This suggests that this warming episode is mainly due to internal dynamics of the ocean rather than external radiative forcing. On the other hand, the present warming follows the expected relationship, suggesting that it is mainly due to radiative forcing. In a second step, we use the total radiative forcing as an explanatory variable, but unexpectedly find that the sea level does not depend on the forcing. We hypothesize that this is due to a long adjustment time scale of the ocean and show that the number of years of data needed to build statistical models that have the relationship expected from physics exceeds what is currently available by a factor of almost ten.

Do emissions and income have a common trend? A country-specific, time-series, global analysis, 1970-2008

This paper uses Vector Autoregressions that allow for nonstationarity and cointegration to investigate the dynamic relation between income and emissions in the period 1970-2008, for all world countries. We consider three emissions compounds, namely CO2, SO2 and a composite global warming index (GWP100). These emissions include energy-related activities with a share varying from 60% (GWP100) to almost 90% (SO2). For all chemical compounds, it is found that for over two thirds of cases income and emissions are driven by unrelated random walks with drift, at 5% significance level. For one quarter of the cases the variables are found to be driven by a common random walk with drift. Finally, for the remaining 4.5% of cases the variables are trend-stationary. Tests of Granger-causality show evidence of both directions of causality. For the case of unrelated stochastic trends, one finds a predominance of emissions causing income (in growth rates), which accords with a production-function rather than with a consumption-function interpretation of the emissions-income relation. The evidence challenges the main implications of the Environmental Kuznets Curve hypothesis, namely that the dominant direction of causality should be from income to emissions, and that for increasing levels of income, emissions should tend to decrease.Environmental Kuznets Curve; Emissions; Income; Cointegration; Common trends JEL Classification: Q53, Q54

Could detection and attribution of climate change trends be spurious regression?

Since the 1970s, scientists have developed statistical methods intended to formalize detection of changes in global climate and to attribute such changes to relevant causal factors, natural and anthropogenic. Detection and attribution (D&A) of climate change trends is commonly performed using a variant of Hasselmann’s “optimal fingerprinting” method, which involves a linear regression of historical climate observations on corresponding output from numerical climate models. However, it has long been known in the field of time series analysis that regressions of “non-stationary” or “trending” variables are, in general, statistically inconsistent and often spurious. When non-stationarity is caused by “integrated” processes, as is likely the case for climate variables, consistency of least-squares estimators depends on “cointegration” of regressors. This study has shown, using an idealized linear-response-model framework, that if standard assumptions hold then the optimal fingerprinting estimator is consistent, and hence robust against spurious regression. In the case of global mean surface temperature (GMST), parameterizing abstract linear response models in terms of energy balance provides this result with physical interpretability. Hypothesis tests conducted using observations of historical GMST and simulation output from 13 CMIP6 general circulation models produced no evidence that standard assumptions required for consistency were violated. It is therefore concluded that, at least in the case of GMST, detection and attribution of climate change trends is very likely not spurious regression. Furthermore, detection of significant cointegration between observations and model output indicates that the least-squares estimator is “superconsistent”, with better convergence properties than might previously have been assumed. Finally, a new method has been developed for quantifying D&A uncertainty, exploiting the notion of cointegration to eliminate the need for pre-industrial control simulations

Beyond equilibrium climate sensitivity

ISSN:1752-0908ISSN:1752-089

Chapter 10 - Detection and attribution of climate change: From global to regional

This chapter assesses the causes of observed changes assessed in Chapters 2 to 5 and uses understanding of physical processes, climate models and statistical approaches. The chapter adopts the terminology for detection and attribution proposed by the IPCC good practice guidance paper on detection and attribution (Hegerl et al., 2010) and for uncertainty Mastrandrea et al. (2011). Detection and attribution of impacts of climate changes are assessed by Working Group II, where Chapter 18 assesses the extent to which atmospheric and oceanic changes influence ecosystems, infrastructure, human health and activities in economic sectors

Quantification of the Past and Future Anthropogenic Effect on Climate Change Using the Empirical Model of Global Climate, an Energy Balance Multiple Linear Regression Model

The current episode of global warming is one of, if not the, biggest challenge to modern society as the world moves into the 21st century. Rising global temperatures due to anthropogenic emissions of greenhouse gases are causing sea level rise, extreme heat waves, droughts and floods, and other major social and economic disruptions. To prepare for and potentially reverse this warming trend, the causes of climate change must not only be understood, but thoroughly quantified so that we can attempt to make reasonable predictions of the future rise in global temperature and its associated consequences. The project described in this dissertation seeks to use a simple model of global climate, utilizing an energy balance and multiple linear regression approach, to provide a quantification of historical temperature trends and use that knowledge to provide probabilistic projections of future temperature. By considering many different greenhouse gas and aerosol emissions scenarios along with multiple possibilities for the role of the ocean in the climate system and the extent of climate feedbacks, I have determined that there is a 50% probability of keeping global warming beneath 2 °C if society can keep future emissions on the pathway suggested by the RCP 4.5 scenario, which includes moderately ambitious emissions reductions policies, and a 67% probability of keeping global warming beneath 1.5 °C if society can keep emissions in line with the very ambitious RCP 2.6 scenario. These probabilities are higher, e.g. more optimistic, than similar probabilities for the same scenarios given by the most recent IPCC assessment report. Similarly, we find larger carbon budgets than those from GCM analyses for any warming limitation target and confidence level, e.g. the EM-GC predicts a total carbon budget of 710 GtC for limiting global warming to 1.5 °C with 95% confidence. The results from our simple climate model suggest that the difference in future temperatures is related to an overestimation of recent warming by the IPCC global climate models. We postulate that this difference is partially due to an overestimation of cloud feedback processes in the global climate models. Importantly, though, I also reaffirm the consensus that anthropogenic emissions are driving current warming trends, and discuss both the effects of shifting the energy sector toward increase methane emissions and the timeline we have for emitting the remainder of our carbon budget – less than a decade if we wish to prevent global warming from exceeding the 1.5 °C threshold with 95% certainty

Climate change 2013: the physical science basis

This report argues that it is extremely likely that human influence has been the dominant cause of the observed warming since the mid-20th century. This is an an unedited version of the Intergovernmental Panel on Climate Change\u27s Working Group I contribution to the Fifth Assessment Report following the release of its Summary for Policymakers on 27 September 2013.  The full Report is posted in the version distributed to governments on 7 June 2013 and accepted by Working Group I and the Panel on 27 September 2013. It includes the Technical Summary, 14 chapters and an Atlas of Global and Regional Climate Projections. Following copy-editing, layout, final checks for errors and adjustments for changes in the Summary for Policymakers, the full Report will be published online in January 2014 and in book form by Cambridge University Press a few months later