# Results

## Emergent Relationship Between Temperature Variability and ECS
And now, for the big reveal! Our **Figure 3** shows that for both our interannual (ψ) and decadal (σb) variability metrics, there is a positive and statistically significant relationship with ECS that ranges from r ≈ 0.59 to 0.62. Interestingly, we see that the relationship holds in both PMIP3-CMIP5 and PMIP4-CMIP6 ensembles, although consistent with prior findings, it is noticeably weaker for the PMIP4-CMIP6 model generation, which is the most recent. The fact that this emergent relationship remains robust over such a long time period which is dominated by a variety of external forcings and extends to a time before pre-industrial CO2 emissions suggests that the emergent relationship may be more robust than some believe, which could make it particularly useful for our purposes of constraining ECS!

![Figure 3](figure_3.png)

## Constraining ECS

Using the emergent constraint approach outlined by Bowman et al. (2018), we calculated the new estimated ranges for ECS in **Figure 4**. The emergent constraint method shows two ECS estimates (depending on two different metrics of temperature variability) centered around 2.5 K (interannual metric) and 2.7 K (decadal metric), with an uncertainty of about ±0.8 K in both cases (uncertainty is defined as the "likely" range, which is the 66% confidence interval). Such measurements are generally consistent with the IPCC's findings of an ECS range between 2.5 and 4.0 K.

![Figure 4](figure_4.png)