Statistical models and the global temperature record
May 2013 - Below is the executive summary of a paper written by Professor Julia Slingo, the Met Office's Chief Scientist, on statistical models and the global temperature record. You can read the full paper by clicking on the link to the pdf at the bottom of this story.
This briefing paper has been produced to provide background information relating to analyses undertaken in response to a series of Parliamentary Questions on the use of statistical models to assess the global temperature record, and to address misleading ideas currently appearing in various online discussions.
The global mean warming observed since the late 19th century is far outside the range of observational uncertainty in global temperature datasets, and there is therefore no doubt that the world has warmed. A wide range of observed climate indicators continue to show changes that are consistent with a globally warming world, and our understanding of how the climate system responds to rising greenhouse gas levels.
The analysis of the nature and causes of climate change is based on comprehensive observations of the climate system in combination with theoretical understanding of its physics and general circulation models, themselves based on the fundamental laws of physics. Sophisticated statistics are used to demonstrate the significance of recent changes in the climate system.
Statistical models seek to assess the statistical properties of a specific set of data, in this case the global mean surface temperature timeseries. The models mentioned in the recent Parliamentary Questions are mathematical constructs that are not rooted in the fundamental laws of physics. In comparison with global scientifically based climate models, they are too crude to capture the complexity and non-linearity of the holistic climate system, its internal variability and its physical response to external forcing agents. It should be noted that the Met Office does not rely solely on statistical models in its detection and attribution of climate change.
The Parliamentary Questions requested a statement of the relative likelihood of one statistical model rather than another, emulating the statistical properties of the instrumental record of global average temperature. The models concerned were a linear trend model with first-order autoregressive noise and a driftless third-order autoregressive integrated model. The Met Office has performed this analysis as requested, noting however that the results depend on the starting date of the timeseries, and which of the three global surface temperature datasets is used.
The results show that the linear trend model with first-order autoregressive noise is less likely to emulate the global surface temperature timeseries than the driftless third-order autoregressive integrated model. The relative likelihood values range from 0.001 to 0.32 for the time periods and datasets studied, where a value of 1 equates to equal likelihoods. This provides some evidence against the use of a linear trend model with first-order autoregressive noise for the purpose of emulating the statistical properties of instrumental records of global average temperatures, as would be expected from physical understanding of the climate system.
This is not, however, evidence for the efficacy of the driftless autoregressive integrated model. Similar comparisons between the driftless (trendless) model and two autoregressive integrated models that allow for drift (trend) give likelihood values ranging from 0.45 to 2.58 for the HadCRUT4 dataset. The comparison is therefore inconclusive in terms of selecting the notionally best model. Furthermore, these comparisons do not provide evidence against the existence of a trend in the data.
These results have no bearing on our understanding of the climate system or of its response to human influences such as greenhouse gas emissions and so the Met Office does not base its assessment of climate change over the instrumental record on the use of these statistical models.
Nor do the results provide any reason to disregard observational evidence of global warming. In an analysis such as that undertaken here, if the tested models are poorly specified then even the most likely of the tested set of models will be a poor representation of the behaviour of the real climate. In such cases the relative likelihood of the models considered here is of little scientific value.