Uncertainty, noise and the art of model-data comparison

In the real world, there are other sources of uncertainty which add to the ‘noise’ part of this discussion. First of all there is the uncertainty that any particular climate metric is actually representing what it claims to be. This can be due to sparse sampling or it can relate to the procedure by which the raw data is put together. It can either be random or systematic and there are a couple of good examples of this in the various surface or near-surface temperature records.

Sampling biases are easy to see in the difference between the GISTEMP surface temperature data product (which extrapolates over the Arctic region) and the HADCRUT3v product which assumes that Arctic temperature anomalies don’t extend past the land. These are both defendable choices, but when calculating global mean anomalies in a situation where the Arctic is warming up rapidly, there is an obvious offset between the two records (and indeed GISTEMP has been trending higher). However, the long term trends are very similar.

A more systematic bias is seen in the differences between the RSS and UAH versions of the MSU-LT (lower troposphere) satellite temperature record. Both groups are nominally trying to estimate the same thing from the same data, but because of assumptions and methods used in tying together the different satellites involved, there can be large differences in trends. Given that we only have two examples of this metric, the true systematic uncertainty is clearly larger than the simply the difference between them.

What we are really after is how to evaluate our understanding of what’s driving climate change as encapsulated in models of the climate system. Those models though can be as simple as an extrapolated trend, or as complex as a state-of-the-art GCM. Whatever the source of an estimate of what ‘should’ be happening, there are three issues that need to be addressed:

  • Firstly, are the drivers changing as we expected? It’s all very well to predict that a pedestrian will likely be knocked over if they step into the path of a truck, but the prediction can only be validated if they actually step off the curb! In the climate case, we need to know how well we estimated forcings (greenhouse gases, volcanic effects, aerosols, solar etc.) in the projections.
  • Secondly, what is the uncertainty in that prediction given a particular forcing? For instance, how often is our poor pedestrian saved because the truck manages to swerve out of the way? For temperature changes this is equivalent to the uncertainty in the long-term projected trends. This uncertainty depends on climate sensitivity, the length of time and the size of the unforced variability.
  • Thirdly, we need to compare like with like and be careful about what questions are really being asked. This has become easier with the archive of model simulations for the 20th Century (but more about this in a future post).

It’s worthwhile expanding on the third point since it is often the one that trips people up. In model projections, it is now standard practice to do a number of different simulations that have different initial conditions in order to span the range of possible weather states. Any individual simulation will have the same forced climate change, but will have a different realisation of the unforced noise. By averaging over the runs, the noise (which is uncorrelated from one run to another) averages out, and what is left is an estimate of the forced signal and its uncertainty. This is somewhat analogous to the averaging of all the short trends in the figure above, and as there, you can often get a very good estimate of the forced change (or long term mean).

Problems can occur though if the estimate of the forced change is compared directly to the real trend in order to see if they are consistent. You need to remember that the real world consists of both a (potentially) forced trend but also a random weather component. This was an issue with the recent Douglass et al paper, where they claimed the observations were outside the mean model tropospheric trend and its uncertainty. They confused the uncertainty in how well we can estimate the forced signal (the mean of the all the models) with the distribution of trends+noise.

Page 2 of 3 | Previous page | Next page