It is available online and titled “Observational Estimate of Climate Sensitivity from Changes in the Rate of Ocean Heat Uptake and Comparison to CMIP5 Models”. Apparently Nic Lewis’s paper beat mine to online release by a day, and though my estimated confidence interval for equilibrium sensitivity is significantly wider, the median sensitivity in my paper also tends to be on the lower end relative to the IPCC AR4 likely value. It is pay-walled, but please contact me if you need a copy and do not have University access. Anyhow, a zip that includes all my code and data is available here. From the abstract:

Climate sensitivity is estimated based on 0-2000m ocean heat content (OHC) and surface temperature observations from the second half of the 20th century and first decade of the 21st century, using a simple energy balance model and the change in the rate of ocean heat uptake to determine the radiative restoration strength over this time period. The relationship between this 30-50 year radiative restoration strength and longer term effective sensitivity is investigated using an ensemble of 32 model configurations from the Coupled Model Intercomparison Project phase 5 (CMIP5), suggesting a strong correlation between the two. The mean radiative restoration strength over this period for the CMIP5 members examined is 1.16 Wm-2K-1, compared to 2.05 Wm-2K-1 from the observations. This suggests that temperature in these CMIP5 models may be too sensitive to perturbations in radiative forcing, although this depends on the actual magnitude of the anthropogenic aerosol forcing in the modern period. The potential change in the radiative restoration strength over longer timescales is also considered, resulting in a likely (67%) range of 1.5 K to 2.9 K for equilibrium climate sensitivity, and a 90% confidence interval of 1.2 K to 5.1 K.

To explain further on what I consider to be three of the more important conclusions of the paper:

First, there seems to be a relationship between the estimates of effective sensitivity from the last 30-50 years and the longer-term multi-century effective sensitivity (which is arguably more important than equilibrium sensitivity) as they are calculated in models. To me, this gives hope that as the length of satellite record increases, we might start to narrow down a more accurate value for sensitivity that is relevant to the timescales of greatest interest.

Second, most of the CMIP5 models seem (albeit not without caveats) to show too high of sensitivity over this period. From figure 3 of the paper:

This is showing the radiative restoration strength in the CMIP5 models examined (each X is a different run from that model), which is generally inversely related to sensitivity. The solid gray line represents the likely value from observations, and the dashed lines represent +/- one standard deviation. As can be seen, the vast majority of these runs fall below the observational likely value for radiative restoration strength, suggesting these CMIP5 models likely have too high a sensitivity relative to the observations. Interestingly, inmcm4 and MRI-CGCM3 are both well above the line, and while they are among the CMIP5 models with the lowest sensitivity, they are not nearly as insensitive as the 50-yr radiative restoration strength would make them appear (which would be ~ 1.2 K for ECS if we performed a naïve calculation). Obviously, the relationship between this radiative restoration strength and ECS can be complicated, as discussed previously at this blog and within the paper.

Finally, there is the estimate of ECS, for which I have tried to consider some effect of the potential change in Effective Sensitivity to ECS based on the CMIP3 relationships, although again I would argue that effective sensitivity is generally of more interest (but it is not the standard benchmark at this point). Nonetheless, from figure 5 of the paper:

The gray indicates the pdf of “ECS” if we keep the radiative restoration strength fixed after the 50-year observational period, whereas the black line indicates the pdf for ECS if we take the uncertainty in the T_eff/T_eq into account based on this relationship in CMIP3 models. The latter is reported in the upper right box and in the abstract. The orange and purple lines represent the “likely” values for sensitivity when switching in the JAMSTEC or CSIRO OHC data rather using that from NOAA.

Clearly, the median estimate for ECS of 1.98K seems to match some other observationally-based estimates with a lower sensitivity, and the “likely” (67%) range of 1.5K to 2.9K is on the lower end as well. Unfortunately, due to the large uncertainties in 0-2000m OHC data earlier in the record, this method continues to yield large uncertainties at the extremes, which due to the inverse relationship between sensitivity and the radiative restoration tends to increase the higher end of the range much more than the lower end. Hence the 90% interval of 1.2K to 5.1K is not a particularly strong constraint.