An open question in climate research has long been fodder for climate change denialists and a puzzling debate for scientists: why do models’ consistently predict increases in global mean surface temperature (MST) since 1998 while reality indicates a global warming hiatus during that same time (red region in figure below)? The debate has raged on, both between the two groups and within scientific communities to provide an answer.

Consider the question largely solved, due to a new paper out today in *Nature *by two authors at the Max Planck Institute and the University of Leeds! They find that the difference between observed and modeled climate trends can be explained by random internal variability in the climate system. This means that the models haven’t been overestimating the impact of various forcings (which denialists suggest!), but rather the climate system has a large degree of random variability over short 15 year-or-so timescales that will limit model accuracy when looking at that short of a range. So we need to look at longer timescales, which consistently show global warming!

Differences between experimentally observed and modeled MST trends could arrive from three factors (for a description of climate forcing, see my previous post or a review here):

1) **Improper modeling of forcings**: This would mean the models incorrectly under- or overestimate the impact of outside influences on the climate system – maybe the models incorrectly represent the amount of radiative energy hitting Earth from the Sun over a given time period.

2) **Improper modeling of response to forcing**: Here, the model would not accurately reflect how the climate system changes due to forcings; for example, incorrectly modeling how air circulation in the atmosphere changes with more radiation.

3) **Internal variability**: Finally, there’s some intrinsic randomness in the climate system that can’t be explained even if we knew the exact inner workings of all the forcings and their effects on the climate system. This actually happens in any chaotic system – the humbling realization that we can never predict anything exactly because we can’t understand every variable with absolutely perfect knowledge.

No one had picked apart the relative contributions of each of these factors before! The authors looked at trends from 1900-2012, to not just focus on the last fifteen years and to see if internal variability could be the sole explanatory factor over such a short time. They used the HadCRUT4 data set for experimental observations (well-known) and the CMIP5 modeling data (also well-known and reliable), which includes 114 different simulations that provide an ensemble mean and a frequency distribution of temperatures for every year to compare with experiment. Below are the two plotted together to predict 15-year GMST trends (circles are experimental data and colored regions are modeled data):

Remember, at each year, there is a histogram of modeled data. As shown on the right, darker colors represent more frequencies, so a higher percentage of the 114 simulations for each year predicted temperatures in those regions. Also, note the y-axis is a trend, in C/decade.At a glance, there appears to be no systematic preference for behavior in the modeled data compared to experimental data. For example, experiment reports much higher temperatures in 1930, at the edge of any modeled data, whereas by 1940 the situation is reversed. This is the first clue that internal randomness of the system might be at play, but can we assess this quantitatively?

Yes, we can! The authors used a multiple regression analysis to look at how each of the factors – forcings, response to forcings, and randomness – contribute individually to model data. Each forcing and forcing response is an independent variable in the model, with temperature trend as the dependent variable, and a mathematical equation is constructed to fit modeled data for each of the 114 simulations. Residuals from fitting this equation to data provide a measure of internal variability in the system -randomness that cannot be predicted beforehand that leads to a mismatch between equation and data.

Now, before we see the results, what should we expect if the models are accounting for forcings and responses correctly? We should see that the regression predicts climate data with a fairly small spread. And if internal variability is the key factor, we should see a large, consistent spread in residuals over all times. So what do we see? Below are graphs of the regression prediction and residuals. The mean has been subtracted out, so an exact match between a given regression and the 114-ensemble mean would be zero on the graph.

The results show exactly what we thought if the models are capturing all the forcings correctly! The residuals (bottom graph) has much greater spread between -0.2 to 0.2 C/decade across all years, whereas the regression results have a minimal spread except around 1960.The spread around 1960 does indicate the regression is not doing a great job predicting climate in that region – some forcings are missing in the mathematical model so that the equation leads to predictions all over the map. But the authors can account for this. They attribute this variation to the Mount Agung eruption in 1963, and admit that models need to do a better job of accounting for volcanic forcing that play a big role in shifting climate dynamics (often providing a cooling effect by launching particulates into the atmosphere that reflect/scatter light).

Overall, however, the radiative forcing and responses to forcings included in the CMIP5 model do not appear to be systematically and incorrectly modeling actual climate interactions. To hit this point home, here’s a comparison of regression results to experimental data:

The red line here is the mean across all 114 regression simulations, and the black line is the experimental data with error bars representing the 95% confidence interval (a common statistical representation to suggest the window of certainty in data). The ensemble mean from modeled data stays within the error bars through the century, only wandering outside during the 1963 volcanic eruption, again indicating a great match in trends between modeled and experimental data.So, beyond the complicated regression methods used, the take-home is that current climate models are likely doing a great job in accurately representing the forcings and climate responses to them. Huge variability exists in such a large, dynamic and chaotic system like Earth’s climate, which will lead to significant randomness on timescales. These past fifteen years can likely be explained due to this randomness, and do not justify claims that climate research is not matching experimental trends. Over longer timescales, models and experiments both see global warming, a trend that we must attend to and ameliorate with policy and action.

**References**

1)

Marotzke J, & Forster PM (2015). Forcing, feedback and internal variability in global temperature trends. Nature, 517 (7536), 565-70 PMID: 25631444